text:
5

# Three randomly selected households are surveyed_ The numbers of people in the households are 2 7, and 12. Assume that samples of size n = 2 are randomly selected wi...

## Question

###### Three randomly selected households are surveyed_ The numbers of people in the households are 2 7, and 12. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 7 , and 12. Construct probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of sizes n = 2 are randomly selected_ Does the mean of the sample proportions equal the proportion of even numbers in the population? Do the sampl proport

Three randomly selected households are surveyed_ The numbers of people in the households are 2 7, and 12. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 7 , and 12. Construct probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of sizes n = 2 are randomly selected_ Does the mean of the sample proportions equal the proportion of even numbers in the population? Do the sampl proportions target the value of the population proportion? Does the sample proportion make good estimator of the population proportion? Listed below are the nine possible samples_ 2,2 2,7 2,12 7,2 7,7 7,12 12,2 12,7 12,12 Construct the probability distribution table _ Sample Probability Proportlon (Type an integer or fraction )

#### Similar Solved Questions

##### Problem 2. (24 points) Use induction to prove that for any n 2 1, if a > b 2 1 and Euclid(a,b) takes n iterations then a > fn+2 and b > fn+l where fn is the nth term of Fibonacci sequence:hint: Consult with the slides and posted video for the lecture 20.Problem (15 points) Prove the following corollaries where fn is the nth term of Fibonacci sequence. (A Corollary is proposition that follows from proved theorem:) a) Corollary 1: For all n > 1 if a > b 2 1 and b < fn+l then Eucl
Problem 2. (24 points) Use induction to prove that for any n 2 1, if a > b 2 1 and Euclid(a,b) takes n iterations then a > fn+2 and b > fn+l where fn is the nth term of Fibonacci sequence: hint: Consult with the slides and posted video for the lecture 20. Problem (15 points) Prove the follo...
##### Question 61ptsThe average resident of Metro City produces 580 pounds of solid waste each year;and the standard deviation is approximately 70 pounds: Use Chebyshev's theorem to find the weight range that contains at least 75%0 of all residents' annual garbage weights.Between 300and 860 poundsBetween 440 and 720 poundsBetween 370and 790 poundsBetween 510and 650 pounds
Question 6 1pts The average resident of Metro City produces 580 pounds of solid waste each year;and the standard deviation is approximately 70 pounds: Use Chebyshev's theorem to find the weight range that contains at least 75%0 of all residents' annual garbage weights. Between 300and 860 p...
##### Find the displacement (in mi) on the time interval [0,2] and [2,3]. NOTE: displacement is net distance from starting pointFind the distance traveled over the interval (0.31 NOTE; distance Ine total dsuance without regard direction.Page 30/ 6
Find the displacement (in mi) on the time interval [0,2] and [2,3]. NOTE: displacement is net distance from starting point Find the distance traveled over the interval (0.31 NOTE; distance Ine total dsuance without regard direction. Page 30/ 6...
##### 3. Let Xiand zbe iid observations from the pdf f(r 0) = 010 e" â‚¬ (0, 0); 0 â‚¬ (0, x). Let Yi = log(X;) and Yz = log(-X2). Show that Yi/Yzis an ancillary statistic. 1) Apply the technique of ranclom variable transformation and distribution marginalization. Apply the property of location-scale lamily.
3. Let Xiand zbe iid observations from the pdf f(r 0) = 010 e" â‚¬ (0, 0); 0 â‚¬ (0, x). Let Yi = log(X;) and Yz = log(-X2). Show that Yi/Yzis an ancillary statistic. 1) Apply the technique of ranclom variable transformation and distribution marginalization. Apply the property of locat...
##### 5. Solve the following Bernoulli equation; dy y = 2ce y2 dx with the initial condition 9(0) 2, using an appropriate substitution_
5. Solve the following Bernoulli equation; dy y = 2ce y2 dx with the initial condition 9(0) 2, using an appropriate substitution_...
##### Pis 66 66 9L 86 FRRAEE lelelels 80 80 08 80 85Complete the frequency distribution for the data.Height [60,65)Frequency[65,70)[70,75)[75,80)[80,85)[85,90)
pis 66 66 9L 86 FRRAEE lelelels 80 80 08 80 85 Complete the frequency distribution for the data. Height [60,65) Frequency [65,70) [70,75) [75,80) [80,85) [85,90)...
##### This Question;0'29 (29 conpteto)Frdalrurd =FheactnJecolnlalstach Veuc & * Qite E WMr dame ericlimannioucieiQm lono Aricn Innumiloeit wintK6o=)0seed 5r CDTocI coce helod eu nroersany Mnthn Answur boxes) #stn Yuur chore tnnt! eor-mlu unanul ~hec|aicunmyounatiho emalvulutJla WltnallnOecorinunurd dcoinol aual Ond i nd @64o 'rncy} =Jitinkc VneHortul 'or I = Wre' value hCACoctcnAlnWung , =Tnn Amnilesmiaiiug Vale IbmiotJmdct Ywl dong ncr orai0L 01,DarannnmKalee4 Minegno' &a
This Question; 0'29 (29 conpteto) Frdalrurd = Fheactn Jecolnlals tach Veuc & * Qite E WMr dame ericlim anniouciei Qm lono Aricn Innumiloeit wint K6o=)0 seed 5r CDTocI coce helod eu nroersany Mnthn Answur boxes) #stn Yuur chore tnnt! eor-mlu unanul ~hec| aicunmyounatiho emalvulut Jla Wltnall...
##### Question 15 Not yet answeredMarked out of 1.00Flag questionLet X be a discrete random variable with cumulative distrbution function given byX <10.40 1 < X< 3 F(x) = 0.60 3 < X <5 0.80 5 < X < 7 X> 7then P(x<3) =0.60none0.400.800.20
Question 15 Not yet answered Marked out of 1.00 Flag question Let X be a discrete random variable with cumulative distrbution function given by X <1 0.40 1 < X< 3 F(x) = 0.60 3 < X <5 0.80 5 < X < 7 X> 7 then P(x<3) = 0.60 none 0.40 0.80 0.20...
##### Oblems 56356_1{_alo4i Eva uate #ke kltowng_Kbgel ; 8 <_x (Cans ) : 3 si' t3x)+c) 1-9*727 _ 2 dx Jran? 82e* -24x+C
oblems 5 6356_1{_alo 4i Eva uate #ke kltowng_Kbgel ; 8 <_x (Cans ) : 3 si' t3x)+c) 1-9*7 27 _ 2 dx Jr an? 82e* -24x+C...
##### Nonci^ Toa6RFJG| AIJ| K
Nonci^ Toa 6 R FJG| AIJ| K...
##### Yout liave r dollars in Four bank aCcount, which Ol receive A AHAL interest rate of 2%7 COmpounded continously: Write down differential equatiou that describes this situation_
Yout liave r dollars in Four bank aCcount, which Ol receive A AHAL interest rate of 2%7 COmpounded continously: Write down differential equatiou that describes this situation_...
##### An arrow is shot at a stationary bird witha starting velocity of (20 m/s) with anangle of 65 degrees with respect tothe horizontall. 1a. What is the top height of the arrow right before ithits its target? 1b. What is the vertical component ofthe arrowâ€™s velocity, right as it reachesthe top of its motion and hits itstarget? 1c. What is the horizontal distance traveled bythe arrow, right as it reaches the top of itsmotion hitting its target?
An arrow is shot at a stationary bird with a starting velocity of (20 m/s) with an angle of 65 degrees with respect to the horizontall. 1a. What is the top height of the arrow right before it hits its target? 1b. What is the vertical component of the arrowâ€™s velocity, right as it reaches t...
##### The object from the previous question is now placed in oil, which has a density 1/2 that of water. What happens? The block sinks to the bottomThe block floats lower.The block floats as before:The block floats higher CURA
The object from the previous question is now placed in oil, which has a density 1/2 that of water. What happens? The block sinks to the bottom The block floats lower. The block floats as before: The block floats higher CURA...


text:
1
500 gm of dry soil was subjected to a sieve analysis. The weight of soil retained on each sieve is as follows as:-
I.S sieve size weight of soilg I.S sieve size weight of soilg
4.75 mm 10 425 $\mu$ 85
2.00 mm 165 212 $\mu$ 40
1.00 mm 100 1.50 $\mu$ 30
75 $\mu$ 50

Plot the grain size distribution curve and determine the following:-

1. Percentage of gravel, coarse and medium sand, fine sand and slit clay fraction in the soil as per IS: 1498 - 1970.
2. Effective size
3. Uniformly coefficient
4. Coefficient of curve
sieve analysis • 568  views
1
0

The diameter of soil grain and the corresponding percent fines than are calculated as below:-

I.S sieve size Diameter of grain mm Weight retained(g) Cumulative weight retained (g) % retained % finer than
4.75 4.75 10 10 2.0 98.0
2.00 2.00 165 175 35.0 65.0
1.00 1.00 100 275 55.0 45.0
425 0.425 85 360 72.0 28.0
212 0.212 60 420 84 18
150 0.150 20 440 88 15
75 0.075 40 480 96 4

The grain size distribution curve is plotted between the diameter of soil as shown in fig.

A) Is grain size classification scale is fitted on the abscissa,

1. Percentage of gravel = 100 - 98 = 2% > 4.75 mm
2. Percentage of coarse sand = 98 - 65 = 33% (4.75 mm - 2.0 mm)
3. Percentage of medium sand = 65 - 28 = 37% (2.00 mm - 0.425 mm)
4. Percentage of fine sand = 28 - 4 = 24% (0.425 mm - 0.075 mm)
5. Percentage of fine sand = 4% (<0.075 mm)

B) Effective size $D_{10} = 0.13 mm$

C) Uniformly coefficient = $C_U = \frac{D_{60}}{D_{10}} = 13.8$

D) Coefficient of curvature = $C_C = \frac{(D_{30})^2}{D_{10}*D_{60}} = 1.1$

E) The sand soil is classed as well- graded sand (SW) since $C_U$ > 6 and $C_c$ is between 1 & 3.

0

format: plain


text:
# Can I trigger input/controls via code?

I have the 3rd person controller in my game, which moves with the WASD keys. But since I am developing for a mobile release, I want touch controls.

I have already the touch control-script in a new script-file, but attached to the same 3rd person controller-prefab.

When I swipe right for instance, I want Unity to trigger the D-key etc.

How can I do that?

...
if (Mathf.Abs(delta.x) > Mathf.Abs(delta.y))
{
if (delta.x > 0)
//trigger D?
else if (delta.x < 0)
//trigger A?
}
...

First make a function that triggers the real action:

void moveLeft() { .. }

Then determine when to call it based on the platform:

Desktop: if(A key down) { moveLeft(); }
Mobile: if(swiping left) { moveLeft(); }

Another solution is to do the opposite:

Create some kind of interface/class that reads input:

// (this is a general solution not specific to Unity)
interface ICharacterController
{
bool shouldMoveLeft();
bool shouldJump();
}

Then, in your character class, have a method like setController(ICharacterController c). In your character's logic code, call the aforementioned methods to determine what action to take.

Finally, implement the given interface and assign it separate for desktop and mobile.

Looking quickly at the Unity docs, it seems like using sendMessage() might be a good alternative to keeping references, if you want to reduce dependencies between your classes.

• So you guess using sendMessage then? Because the movement-method and the touch-method are in two different scripts – IMX Dec 16 '13 at 13:24
• @Anko Thanks for the formatting. I've been doing the LD48 all weekend and I'm pretty tired ~_~ – tacospice Dec 16 '13 at 15:45
• @IMX I haven't touched Unity in quite a while, this is just a general solution, but sendMessage() might do the trick. I'd keep a reference somewhere to the object being controlled (or to the input). I'll add some more to the answer. – tacospice Dec 16 '13 at 15:47

Your best choice, whilst keeping code simple, is to use Platform Specific Compilation. This will allow you to have one component that houses player input for multiple platforms.

For example:

public class PlayerController : MonoBehaviour {
void Update () {

#if UNITY_STANDALONE
if (Input.GetKey(KeyCode.A))
moveLeft();
// Etc.
#endif

#if UNITY_IPHONE
// Touch logic for iPhone here
#endif

#if UNITY_ANDROID
// Touch logic for Android here
#endif
}
}

The compiler will then cherry pick which block to use based on your build target and will discard any non applicable clauses.


text:
# Bachelier model in terms of normal distribution to simulate price

Bachelier Model is $$dS_t = rdt + 𝜎dW_t$$ and can also write to $$S_t = S_0 + 𝜎W_t$$ How can write $$W_t$$ in terms of normal distribution?

Basically I want to simulated the underlying asset in the Bachelier Model. Thank you.

import numpy as np
from matplotlib import pyplot as plt

def terminal_value(S0, sigma, M):
S = np.zeros(M)
S[0] = S0
for i in range(1, M):
S[i] = S[i-1] + sigma * np.random.standard_normal() * np.sqrt(1/M)
return S

for i in range(10):
series = terminal_value(100, 10, 100)
plt.plot(series)

It works now and produces the following:

• Thank you for your answer, but I am not asking about coding. I am not sure whether the formula that I used to produce St is correct or not. I want to ask about how to write St's formula in terms of normal distribution. Oct 8 '20 at 0:51
• Your code is correct. $\sigma W_t$ is normally distributed, with mean 0 and variance $\sigma^2 t$ Oct 8 '20 at 0:56
• Ok. Thank you so much! Oct 8 '20 at 1:00
• @user50317: What StackG is implying is that, if you want to simulate the continuous trajectory of $W$ from time $t$ to time $t+\triangle t$, then a good discrete approximation is N(0, $\triangle t$). Oct 8 '20 at 1:02
• @markleeds it is more than just a good approximation, as in this case this Euler-Maruyama update is a sample from the exact distribution, and so has no bias. Oct 8 '20 at 6:08


text:
# How to make a human that doesn't need to breathe

I want to make a creature very similar to a human but with one major difference: they breathe like any human in their everyday life, but if they are suffocating, drowning, or there isn't O2 in the air they can survive for several hours (or maybe more) without air, obviously with reduced physical activity and metabolism (if it's necessary, the creature can be unconscious).

My question is: how they would be able to survive without oxygen. Basically I'm asking how to make a facultative anaerobic animal...

I know that humans are able to make lactic acid fermentation in their muscles when they are doing a lot of exercise and they can't breathe enough oxygen to feed all the cells. But that mechanism, called Cori cycle has a very limited use, the cells aren't able to get rid of all the lactic acid produced by the fermentation, and when the acid reaches a high concentration in the muscle it causes acute pain until you stop exercising. Also, it's very inefficient way of producing energy.

I need a mechanism that can be used by extended periods of time without collapsing due high levels of something (like acid in the above example).

The answer doesn't need to exactly provide a new mechanism to get energy without air, if you know how to improve the actual, you are free to post it here.

P.S: I found that Narwhal have some capabilities to reduce their air consumption while they are under water. In the english wikipedia there aren't described but they have:

• Reduce flow of blood to non-vital organs.
• Increased amount of myoglobin in their muscles (to store oxygen).
• Increased amount of slow twitch muscle fiber ("red" muscle) that contain high amount of myoglobin and mitochondria for large periods of constant use instead of fast twitch muscle fiber ("white" muscle) for small periods of strong use.
• Dolphins are similar in size to humans and are able to sustain prolonged strenuous activity between breaths while submerged in water. Research their adaptations. Nov 21 '17 at 1:23
• some form of oxygen storage is the only reasonable solution, the brain needs oxygen and there is no way around it. It would mean spending hours or day rebuilding the storage between uses however. a protein complex that stores huge amounts of oxygen would fit the bill. If course such a molecule would be a masterpiece of protein engineering far beyond anything we could even hope to achieve right now.
– John
Nov 21 '17 at 4:22
• move consciousness of human to machine ..maybe.. Nov 21 '17 at 4:57
• how about creating these oxygen by themselves? Like some sort of photosynthesis that used chemical energy instead of sunlight Nov 21 '17 at 4:59

## 4 Answers

Nitrate Reduction Cycle. Bacteria used to breath nitrates when they haven’t developed the necessary complex IV for oxygen reduction. So they used nitrates. The primary drive away from non-water respiratory metabolism was primarily the high cost and low availability of the hetereoatom substrates, not because of the lower efficiency.

If the mitochondria within your people somehow gained a bacterial complex VI gene from horizontal gene transfer......

Then, we can conceive that your people accumulates the nitrates when there is enough oxygen (probably by respiratory oxidization of urea), accumulating a very high concentration within a buffer within their vital organs(probably because their need for frequent diving, or having to live extensively underwater, as an example), using it when the membrane potential of their mitochondria is lowered below a certain threshold, converting the nitrates into ammonia and releasing a lot of energy(up to 8 hours normal metabolism without oxygen, if not for consuming slightly more sugars per unit of energy), (the complex normally for reducing oxygen can use nitrates when oxygen is not available), effectively granting your people a built-in rechargeable bioelectrochemical battery.

You can add in a cooldown for the skill as well, since the nitrate synthesis process is exoenergetic, it will require time and about as much metabolism as it is used to charge up the "battery", therefore once the 8 hours have expired, just a few breaths won’t be sufficient for another long term diving immediately.

• Please add this link to your post. It explains exactly your idea. Look at the efficiency of normal and nitrate respiration: $\text{C}_6\text{H}_12\text{O}_6 + 6 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O} (\Delta\text{Gº'} = -2.870 \text{ kJ/mol of glucose})$ and $5\text{C}_6\text{H}_12\text{O}_6 + 24 \text{NO}_3^{-} \rightarrow 30 \text{CO}_2 + 12 \text{N}_2 + 42 \text{H}_2\text{O} (\Delta\text{Gº'} = -2.670 \text{ kJ/mol of glucose})$. I love it! Jul 23 '18 at 16:20

Simple answer: increase the amount of myoglobin in these people's tissues. Myoglobin stores oxygen and is what allows whales to hold their breath for more than an hour even while exerting themselves. May not work for "several hours", but perhaps an hour or slightly more.

In addtion to the increased myoglobin, have the creature able to drop it's metabolic rate without harm. A number of animals can do that including some hummingbirds so they don't starve to death while sleeping.

This more useful if the creature goes unconsious as the brain uses huge amount of energy and thus oxygen. Think of that rare occurance where a human recovers from an extended period of asphyxia because they fell into icy water and hypothermia was induced at the same time.

In Hal Clement’s The Nitrogen Fix, intelligent beings that don’t live in an oxygen atmosphere are described using nitrogen chemistry. He explains he has to eat a balance of oxidizing and reducing forms to produce energy from his food.

In Ocean on Top by the same author, the human doesn't understand why they don’t breathe, and speculates (incorrectly) that some special food is supplying oxygen.


text:
# Thread: Differential Equation - Newton's Law Of Cooling?

1. ## Differential Equation - Newton's Law Of Cooling?

I have a homework problem I'm not sure about.

At 6:00 pm a 50 degree drink is pulled from the refrigerator into a room that is 72 degrees. Three minutes later, at 6:03, the drink is now 53 degrees. How long, in minutes, will it be until the drink is 70 degrees?

2. Originally Posted by xvaliant
I have a homework problem I'm not sure about.

At 6:00 pm a 50 degree drink is pulled from the refrigerator into a room that is 72 degrees. Three minutes later, at 6:03, the drink is now 53 degrees. How long, in minutes, will it be until the drink is 70 degrees?
$\frac{dT}{dt} = k(72 - T)$

$T(0) = 50$

$T(3) = 53$

solve the differential equation using the given conditions.

3. ok, I integrated both sides an got ln(72-T)=kt. I'm confused as how to find the constant, k.

4. Originally Posted by xvaliant
ok, I integrated both sides an got ln(72-T)=kt. I'm confused as how to find the constant, k.
where is your constant of integration?

5. (72-T)=C(1) e^kt

6. Originally Posted by xvaliant
(72-T)=C(1) e^kt
use $T(0) = 50$ to find $C_1$

use $T(3) = 53$ to find $k$

7. Got it. Thanks!


text:
# Effective Kotlin Item 52: Consider associating elements to a map

This is a chapter from the book Effective Kotlin. You can find it on LeanPub or Amazon.

It is not uncommon to have a bigg set of elements in which we need to find elements by a key many times. This might be:

• A class that stores configurations\ that are loaded from one or more files.
• An in-memory repository (such repositories are often used for tests).

This data might represent a list of users, ids, configurations, etc. It is generally fetched as a list, and it is tempting to represent it in memory in the same way:

class ConfigurationsRepository( private val configurations: List<Configuration> ) { fun getByName(name: String) = configurations .firstOrNull { it.name == name } } class NetworkUserRepo( private val userService: UserService ) : UserRepo { private var users: List<User>? = null suspend fun loadUsers() { users = userService.getUsers() } override fun getUser(id: UserId): User? = users ?.firstOrNull { it.id == id } } class InMemoryUserRepo : UserRepo { private val users: MutableList<User> = mutableListOf() override fun getUser(id: UserId): User? = users .firstOrNull { it.id == id } fun addUser(user: User) { user.add(user) } }

### Using Maps

However, this is rarely the best way to store these elements. Notice how the data we load is used: we most often access an element by an identifier or name (which is typically connected to how we design our data so as to have unique keys in databases). Finding an element in a list has linear complexity (O(n), where n is the size of the list, or more concretely, it takes on average n/2 comparisons to find an element in a list). This is especially problematic for big lists because finding each element requires comparing it with many other elements. A better solution is to use a Map instead of a List. Kotlin by default uses a hashmap (LinkedHashMap), and, as is described in Item 43: Respect the contract of hashCode, performance when finding an element using a hashmap is much better. On JVM, finding an element takes only one comparison because the size of the used hashmap is adjusted to the size of the map itself (given that the hashCode function is implemented properly).

For example, this is the InMemoryRepo from before, but its implementation is using a map instead of a list:

class InMemoryUserRepo : UserRepo { private val users: MutableMap<UserId, User> = mutableMapOf() override fun getUser(id: UserId): User? = users[id] fun addUser(user: User) { user.put(user.id, user) } }

Most other operations, like modifying or iterating over data (likely using collection processing methods like filter, map, flatMap, sorted, sum, etc.) have more or less the same performance for the standard map and list, but finding an element by key is much faster.

### Associating elements with keys

The crucial question is how do we transform from a list to a map and vice versa? For this, we use the associate* functions, the most common of which is associateBy, which builds a map by associating each element with the key specified by the key selector function. This key selector function (typically a lambda expression next to associateBy) might point to the property we use to identify the element.

import kotlin.* data class User(val id: Int, val name: String) fun main() { val users = listOf(User(1, "Michal"), User(2, "Marek")) val byId: Map<Int, User> = users.associateBy { it.id } println(byId) // {1=User(id=1, name=Michal), // 2=User(id=2, name=Marek)} val byName: Map<String, User> = users .associateBy { it.name } println(byName) // {Michal=User(id=1, name=Michal), // Marek=User(id=2, name=Marek)} }

Notice that keys in a map must be unique, or duplicates must be removed. This is why we should only associate elements using a unique identifier (to group by something that is not unique, use the groupBy function).

import kotlin.* data class User(val id: Int, val name: String) fun main() { val users = listOf(User(1, "Michal"), User(2, "Michal")) val byName = users.associateBy { it.name } println(byName) // {Michal=User(id=2, name=Michal)} val group: Map<String, List<User>> = users.groupBy { it.name } println(group) // {Michal=[User(id=1, name=Michal), // User(id=2, name=Michal)]} }

To transform from a map to a list, you can use the values property of Map:

import kotlin.* data class User(val id: Int, val name: String) fun main() { val users = listOf(User(1, "Michal"), User(2, "Michal")) val byId = users.associateBy { it.id } println(byId.values) // [User(id=1, name=Michal), User(id=2, name=Michal)] }

Here are some sample usages of this technique:

class ConfigurationsRepository( configurations: List<Configuration> ) { private val configurations: Map<String, Configuration> = configurations.associateBy { it.name } fun getByName(name: String) = configurations[name] } class NetworkUserRepo( private val userService: UserService ) : UserRepo { private var users: Map<UserId, User>? = null suspend fun loadUsers() { users = userService.getUsers() .associateBy { it.id } } override fun getUser(id: UserId): User? = users?.get(id) }

This technique is important, but it is not suitable for all cases. It is most useful when we need to access elements frequently, therefore it is especially important on the backend, where collections might be accessed many times per second. It is not so important on the frontend (by that, I also mean Android or iOS), where a user will access most repositories at most a few times. We also need to remember that mapping from a list to a map also takes time, so it might also impact performance if we do it often.


text:
# Calculating energy released in nuclear fission

Consider the neutron induced fission $\text{U-235} + n \to \dots \to \text{La-139} + \text{Mo-95} + 2n$, where $\dots$ denotes intermediate decay steps.

I want to calculate the released energy from this fission. One way would be to calculate the difference of the binding-energies ($B$):

$$\Delta E = B(139,57) + B(95,42) - B(235,92) \approx 202,3 \, \mathrm{MeV}$$

(Btw. I didn't use the binding energies from a semi-empirical binding energy formula but calculated them directly via mass defect).

Another way is:

$$\Delta E = (m(\text{U-235}) + m_{\text{Neutron}} - m(\text{Mo-95}) - m(\text{La-139}) - 2m_{\text{Neutron}} )c^2 \approx 211,3 \, \mathrm{MeV}$$

Which one gives the correct result? Why?

You notice that $57+42 \neq 92$, if that was the case, it would be equal, but I don't clearly see where the difference physically comes from and what to add or subtract (and why) from to the first or from the second term to get the other result. How to make this clear?

A slightly other point of view: What different questions do both calculations answer?

Below I show how the discrepancy $(202.3 \, \mathrm{MeV})$ and $(211.3 \, \mathrm{MeV})$ between your two methods has arisen.

$B(139,57) = \rm {57p +82n+57e} -m(139,57)$
$B(95,42) = \rm {42p +53n+42e} -m(95,42)$
$B(235,92) = \rm {92p +143n+92e} -m(235,92)$

$B(139,57) + B(95,42) - B(235,92) = m(235,92) - m(139,57)\rm -n +7e +[7p-7n]$

$\rm 7p-7n = 7(938.272-939.565)= - 9.051$

Note that your original equation was unbalanced if you used the masses of the atoms because there is a difference of seven electrons between the left hand side $(\rm U235 + n)$ and the right hand side $(\rm La139 + Mo95+2n)$ of your equation.
• Thanks, is $202.2 \mathrm{MeV}$ or $211.3\mathrm{MeV}$ the correct answer? – Julia May 19 '17 at 7:26


text:
## Calculus (3rd Edition)

$$y'=7^{4x-x^2} (4-2x) \ln 7.$$
Recall that the derivative of $a^{f(x)}$ is $a^{f(x)} f'(x)\ln a$ Since $y=7^{4x-x^2}$, we have $$y'=7^{4x-x^2} (4-2x) \ln 7.$$


text:
## HW 1A.9 [ENDORSED]

$c=\lambda v$

Moderators: Chem_Mod, Chem_Admin

Henri_de_Guzman_3L
Posts: 88
Joined: Fri Sep 28, 2018 12:25 am

### HW 1A.9

For this problem, if I know the frequency and the wavelength, how do I find the energy of the photon? Is there a specific formula?

MaiaRodriguezChoi3E
Posts: 32
Joined: Fri Sep 28, 2018 12:25 am

### Re: HW 1A.9

I think you use E=hc/wavelength which was an equation we derived last lecture from E=hv and c=wavelength x v

Megan Gianna Uy 3L
Posts: 30
Joined: Fri Sep 28, 2018 12:26 am

### Re: HW 1A.9

In order to find the energy, use the formula E=hv, since the frequency is given.

Sana_Mian_3G
Posts: 30
Joined: Fri Sep 28, 2018 12:23 am

### Re: HW 1A.9

E = hf = hc/λ. This is the equation that is needed and the constant needed is h = 6.62608 × 10^–34 J.s

Fionna Shue 4L
Posts: 59
Joined: Fri Sep 28, 2018 12:18 am

### Re: HW 1A.9  [ENDORSED]

If you know the frequency (v), you can find the energy using the equation E=hv where h=6.626*10^-34 J.s. If you know the wavelength (λ), you can find the energy using the equation E=hc/λ where c=2.997*10^8m.s^-1.

Return to “Properties of Light”

### Who is online

Users browsing this forum: No registered users and 1 guest


text:
Karya, built on Mon Jul 24 11:39:07 PDT 2017 (patch 33511aca01257b76b88de7c7a2763b7a965c084e)

Derive.Call.Prelude.Articulation

Contents

Description

Calls that are similar to staff-notation articulations, or could be. This means calls that modify notes in relatively straightforward ways, either by adding an attribute or modifying their environment.

There is already general purpose syntax to add attributes to notes, e.g. attr = +x or n +x or just +x, and instruments may supply special calls for their attributes, but there are several attributes which look nice with their own calls and are used by many instruments.

TODO There are too many ways to apply attributes to notes, and they work in inconsistent ways.

Synopsis

# legato

I'm not really sure how fancy calls should be. On one hand, high level calls should get a nice result automatically. On the other hand, they're not very composable if they override things like %sus-abs.

This is not in note_calls, instruments that support this are expected to override ( with it.

# misc

This is the same as c_lengthen, but it's here for symmetry with c_sustain. Also, conceptually this is lower level, while c_lengthen is meant to be modified to whatever is locally appropriate.


text:
## A question on synchronization:

What is the largest a room can be before it is no longer possible to clap along to music?

## An iPad Mini Pays for Itself in Two and a Half Years

Hello Estimateers!

Our question for this entry has sort of a preamble. Skip to the bold text if I'm being boring.

As a New Year's/post-conference/pre-birthday present to myself, I just got an iPad mini. Now, until a month ago, I thought the same thing you thought: iPad minis are stupid giant phones that don't make calls. What the hell is the point? But I'd been thinking about getting an iPad for a while. My iPadded friends seemed to like them and everyone I talked to said iPad macros were great for reading and taking notes. Then, when I actually used my mom's new mini (which she got for Christmas) it actually seemed like the perfect size for those two things.

BUT EVERYONE THINKS THEY'RE SO STUPID!!! THEY MUST BE STUPID, RIGHT???

Because I am exposed to such a pervasive anti-mini bias, I've been really trying to convince myself that this was a good purchase. And then I thought of something...

Suppose my new iPad aided my productivity flawlessly. That is, I took every note for every talk on it and I never printed papers again. If this were the case, would my iPad mini actually be cost efficient? Or, put another way: How long does it take an iPad mini to pay for itself?

This is going to be a Julian-centric estimate, so all of these numbers are particular to me.

First off, we find the cost of the iPad. Just glancing at my receipts give me the following numbers:

• $390 - iPad mini (16 gigs, WiFi only) + screen cover + tax •$30 - a good stylus
• $20 - miscellaneous productivity improving apps That comes to a total of about$450.

What does it save me? Again, assuming it works perfectly (big assumption), I no longer need to buy notebooks, pens, printer paper, or ink. I'm going to consider these the major sources of savings.

NOTEBOOKS: Looking around my office, I see about 20 notebooks. I've been here for 2.5 years, so I average around 10 notebooks a year (legal pads, mostly). At 5 bucks a pop, that $50/year on notebooks. PENS: More of a guess for this one. I buy a couple pens each quarter, which comes out to (again) 10 a year. At a little over$2 per pen (Uniball Vision Elites on Amazon Prime) that's $20/year on pens and, interestingly, about a pen per notebook. PAPER: I almost always print out papers when I'm reading them so that I can take notes on the page (my iPad is changing that). I average around 10 sheets of paper a week, which comes to around 500 a year. That's about$10/year on paper (Amazon).

INK: This is an interesting number. I didn't actually know the cost of ink per page until I looked it up for this, but it's about 10 cents per page (according to this website). I print double sided, so that's $0.10 a page for 1000 pages a year, which gives$100/year on ink.

This brings us to a grand total of \$180/year on office supplies.

So that means an iPad mini (with perfect use) actually pays for itself after 2.5 years. Weirdly, this is right around what you'd expect the lifetime for a product like this to be, about 3ish to 4 years.

Since I don't buy my own office supplies, I suppose I should petition UChicago to reimburse me for my iPad...

## I've Returned!

Ahoy Estimateers!

After an extended hiatus, I've come back to make more estimates.

Ah... the sexy allure of a science blog that only 30ish people read... Who could resist its siren song? Not me, apparently.

Anyways, I've been thinking of re-starting this blog for a while now, but as a more casual thing. So I probably won't be posting with any sort regular period, just when I think of particularly interesting questions. But I always love getting suggestions! If you have a question or a cool estimate of your own, pass it on and I'll put it up.

Onwards to estimates!

## There is a New Source of Untapped Energy!

Hello Estimateers!

Sorry for the extended absence. I was sick last week and it sapped my ability to think of and type blog posts. But forging bravely ahead!

Instead of just thinking of it as a potential place for our doom fortresses, let's think of the Moon as a potentially harvestable source of energy. After all, we may as well have it do something useful instead of loafing around up there all day!

Okay, so how much energy is in the Moon? We've got two sources: kinetic energy and potential energy due to gravity. We'll do kinetic first.

Wikipedia go! The Moon weighs about $$10^{23}$$ kg and travels about $$1$$ km/s (!!!). That gives it a kinetic energy of

$$E_k= \frac{1}{2} m v^2 \approx 10^{29} \text{J}$$.

Potential energy is a bit trickier. Since gravity is pulling the Moon down, we can use the force of gravity on the moon to do work as we lower it to Earth (in the same way a weight powers a grandfather clock). The energy we can get from this is given by

$$E_p= \frac{G m M}{r_2}-\frac{G m M}{r_1}$$,

where the $$r$$'s are our initial and final radii and big $$M$$ is the mass of the Earth. $$r_1$$ is the orbital radius of the Moon ($$4 \times 10^5$$ km), $$r_2$$ is the radius of Earth ($$6\times 10^3$$ km), $$M$$ is $$6\times 10^{24}$$ km and $$G$$ is $$6\times 10^{-11}$$ N (m/kg)$$^2$$. Plugging in numbers givers us

$$E_p \approx 6\times 10^{30} \text{J}$$

$$E_p$$ is an order of magnitude larger than $$E_k$$ so we will ignore $$E_k$$.

Therefore, the amount of energy we could harvest from the Moon is about $$6 \times 10^{30}$$ J. To put this energy in context, the energy consumed in the US (from electricity) in 2009 was ten to the nineteen joules. So the Moon could power the (2009) US for 100,000,000,000 years.

## Question: The Lunar Generator

Hiya Estimateers,

This week, we're thinking about alternative energy: How much energy is stored in the moon?

No, not in terms of harvestable fuel, I'm talking mechanical energy. If I attached a giant crank to the moon so that it turned a motor, how much energy could I possibly get out of it? Enough to blow up all major US cities with my death ray? Err... I mean enough to HEAL all the major US... sick people... with some kind of... health ray...?

Find out Wednesday!

## A Plot for the Brainy-and-Lovely Claire

M'buddy said she wanted to see which countries were the top-spenders, suggesting that the GDP-spending correlation might actually both be symptoms of a country being resource-rich.

Here, we've zoomed in to the top right corner of that log-log plot. The colors are meaningless. I again apologize for the plot quality. Steinberg would be furious.

## You Gotta Spend Money to Make Money

Hi there Estimateers!

We're doing something sort of different today at WET. Instead of the usual fare (ask a question, dimensionally analyze your way to an answer) we're instead going to generate two interesting plots. But first, a recap of our problem statement.

Government spending: good for the economy? Taxes: bad for the economy? That's pretty much it. I hear a lot politicians say things like "Taxes stifle business" or "We need to cut these fat government budgets. Government spending hurts the free market!" (I need to start going to different parties...) Anyway, I hear a lot of words and ideas, but words are weak and numbers are strong. Where the hell is the data on this stuff? If I were going to look at this analytically, I would start by plotting some indicator of economic health vs. tax rate and government spending for a bunch of different countries.

Well, let's start looking analytically:

 Fig. 1: GDP per capita as a function of government spending per capita. Note the log-log scales on the axes. US highlighted in red.
 Fig. 2: GDP per capita as a function of tax rate. Note the log scale on only the y-axis. US highlighted in red
First order of business: I apologize for the quality of these plots. If this were something I was doing professionally, they'd look nicer. But this being a weird semi-public thought journal, it is what it is.

Okay, next we'll do some bookkeeping. Fig. 1 uses Mathematica's built in country data (Wolfram), whereas the data in Fig. 2 is the data from GapMinder, a graphical-world-data analyzing website that all readers should check out. Fig. 2 also uses data from 2006.

Whew! On to more interesting stuff. There are three main things I noticed from these plots:

1. GDP/capita is strongly correlated with government spending.
2. GDP/capita is weakly correlated with tax rate.
3. Both correlations are positive.
This means good economies tend to have spend-y governments and good economies (weakly) tend to tax more. We can compute correlation coefficients for these plots and find that the correlation is about .79 between GDP/C and GS/C and about .20 between GDP/C and TR.

I'm tempted to ramble on about these, but really I just wanted to see the plots and I wouldn't exactly say anything that isn't already there. So I think I'll back slowly away from this post...

But first some a caveat. Correlation ain't causation, as all you smart people know. This says high government spending and high GDP go hand-in-hand, but not that one creates the other.

To close: Government spending is quite positively correlated with GDP. Taxes are also positively correlated with GDP, but not as strongly. So good news for advocates of big government, I suppose.  But seriously, I made this plot in one afternoon. Surely an intern can make them, too. Why don't politicians use plots like these to make arguments? Blerg!


text:
# The magnetic energy stored in an inductor is ______ current.

Directly proportional to

Inversely proportional to

Directly proportional to the square of

Inversely proportional to the square of


text:
# Leo Mace conducts revival

while t i n g g c t s K\ on Price Two Weeks R e \ i \ a l A two w e t k s i e \ i \ staited Monda\ n i g h t Octobei t h i o u g h Oitobci 22 at the house I - l i s t G c n e i a l C ' h u c l i Ewngehst Re\ I of Dcxtci w i l l c o n d i c t Rt\ \rnos Denton the pastoi ext ext i n d a c01 dial weleome one


text:
# Should the intercept be included when you check the condition index?

Many sources state that a condition index >30 constitutes a multicollinearity problem. When I've tried to implement this check in practice, I've realized that the condition index (and VIFs) change depending on whether or not the intercept is included in the model. Is the standard approach to include the intercept? Does it matter if there is collinearity between the intercept and the predictors?

• You should probably include the intercept. If collinearity is a problem, that must also include variables that is close to a constant, that is, collinear with the intercept – kjetil b halvorsen Sep 17 '17 at 17:32


text:
# Quadratic Equation Questions for IBPS PO PDF

0
7302

## Quadratic Equation Questions for IBPS PO PDF

Download Top-15 Banking Exams Quadratic Equation Questions PDF. Banking Exams Quadratic Equation questions based on asked questions in previous exam papers very important for the Banking  exams.

Take a IBPS PO free mock test

Instructions

In the following questions two equations numbered I and II are given. You have to solve both the equations and
Give answer a: if x > y
Give answer b: if x ≥ y
Give answer c: if x < y
Give answer d: if x ≤ y
Give answer e: if x = y or the relationship cannot be established.

Question 1: I.  $x^{2}-3x-88=0$
II. $y^{2}+8y-48=0$

a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or the relationship cannot be established.

Question 2: I.  $5x^{2}+29x+20=0$
II. $25y^{2}+25y+6=0$

a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or the relationship cannot be established.

Question 3: I.  $2x^{2}-11x+12=0$
II. $2y^{2}-19y+44=0$

a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or the relationship cannot be established.

Question 4: I.  $3x^{2}+10x+8=0$
II. $3y^{2}+7y+4=0$

a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or the relationship cannot be established.

Question 5: I.  $2x^{2}+21x+10=0$
II. $3y^{2}+13y+14=0$

a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or the relationship cannot be established.

Instructions

In the following questions two equations numbered I and II are given. You have to solve both equations and

a. x ˃ y
b. x ≥ y
c. x ˂ y
d. x ≤ y
e. x = y or the relationship cannot be established

Question 6: I. ${x^2}$ – 7x + 10 = 0
II. ${y^2}$ + 11y + 10 = 0

a) x ˃ y

b) x ≥ y

c) x ˂ y

d) x ≤ y

e) x = y or the relationship cannot be established

Question 7: I. ${x^2}$ + 28x + 192 = 0
II. ${y^2}$ + 16y + 48 = 0

a) x ˃ y

b) x ≥ y

c) x ˂ y

d) x ≤ y

e) x = y or the relationship cannot be established

Question 8: I.2x – 3y = – 3.5
II. 3x + 2y = – 6.5

a) x ˃ y

b) x ≥ y

c) x ˂ y

d) x ≤ y

e) x = y or the relationship cannot be established

Question 9: I. ${x^2}$ + 8x + 15 = 0
II. ${y^2}$ + 11y + 30 = 0

a) x ˃ y

b) x ≥ y

c) x ˂ y

d) x ≤ y

e) x = y or the relationship cannot be established

Question 10: I. x = $\sqrt {3136}$
II.${y^2}$ = 3136

a) x ˃ y

b) x ≥ y

c) x ˂ y

d) x ≤ y

e) x = y or the relationship cannot be established

Instructions

In each of these questions two equations numbered I and II are given. You have to solve both the equations and –
Give answer a: if x < y
Give answer b: if x ≤ y
Give answer c: if x > y
Give answer d: if x ≥ y
Give answer e: if x = y or the relationship cannot be established.

Question 11: I.  $x^{2}+13x+42=0$
II. $y^{2} +19y+90=0$

a) if x < y

b) if x ≤ y

c) if x > y

d) if x ≥ y

e) if x = y or the relationship cannot be established.

Question 12: I.   $x^{2}-15x+56=0$
II. $y^{2} -23y+132=0$

a) if x < y

b) if x ≤ y

c) if x > y

d) if x ≥ y

e) if x = y or the relationship cannot be established.

Question 13: I. $x^{2}+7x+12=0$
II. $y^{2} +6y+8=0$

a) if x < y

b) if x ≤ y

c) if x > y

d) if x ≥ y

e) if x = y or the relationship cannot be established.

Question 14: I. $x^{2}-22x+120=0$
II. $y^{2} -26y+168=0$

a) if x < y

b) if x ≤ y

c) if x > y

d) if x ≥ y

e) if x = y or the relationship cannot be established.

Question 15: I.$x^{2}+12x+32=0$
II. $y^{2} +17y+72=0$

a) if x < y

b) if x ≤ y

c) if x > y

d) if x ≥ y

e) if x = y or the relationship cannot be established.

I.$x^{2} – 3x – 88 = 0$

=> $x^2 + 8x – 11x – 88 = 0$

=> $x (x + 8) – 11 (x + 8) = 0$

=> $(x + 8) (x – 11) = 0$

=> $x = -8 , 11$

II.$y^{2} + 8y – 48 = 0$

=> $y^2 + 12y – 4y – 48 = 0$

=> $y (y + 12) – 4 (y + 12) = 0$

=> $(y + 12) (y – 4) = 0$

=> $y = -12 , 4$

$\therefore$ No relation can be established.

I.$5x^{2} + 29x + 20 = 0$

=> $5x^2 + 25x + 4x + 20 = 0$

=> $5x (x + 5) + 4 (x + 5) = 0$

=> $(x + 5) (5x + 4) = 0$

=> $x = -5 , \frac{-4}{5}$

II.$25y^{2} + 25y + 6 = 0$

=> $25y^2 + 10y + 15y + 6 = 0$

=> $5y (5y + 2) + 3 (5y + 2) = 0$

=> $(5y + 3) (5y + 2) = 0$

=> $y = \frac{-3}{5} , \frac{-2}{5}$

Therefore $x < y$

I.$2x^{2} – 11x + 12 = 0$

=> $2x^2 – 8x – 3x + 12 = 0$

=> $2x (x – 4) – 3 (x – 4) = 0$

=> $(x – 4) (2x – 3) = 0$

=> $x = 4 , \frac{3}{2}$

II.$2y^{2} – 19y + 44 = 0$

=> $2y^2 – 8y – 11y + 44 = 0$

=> $2y (y – 4) – 11 (y – 4) = 0$

=> $(y – 4) (2y – 11) = 0$

=> $y = 4 , \frac{11}{2}$

$\therefore x \leq y$

I.$3x^{2} + 10x + 8 = 0$

=> $3x^2 + 6x + 4x + 8 = 0$

=> $3x (x + 2) + 4 (x + 2) = 0$

=> $(x + 2) (3x + 4) = 0$

=> $x = -2 , \frac{-4}{3}$

II.$3y^{2} + 7y + 4 = 0$

=> $3y^2 + 3y + 4y + 4 = 0$

=> $3y (y + 1) + 4 (y + 1) = 0$

=> $(y + 1) (3y + 4) = 0$

=> $y = -1 , \frac{-4}{3}$

$\therefore x \leq y$

I.$2x^{2} + 21x + 10 = 0$

=> $2x^2 + x + 20x + 10 = 0$

=> $x (2x + 1) + 10 (2x + 1) = 0$

=> $(x + 10) (2x + 1) = 0$

=> $x = -10 , \frac{-1}{2}$

II.$3y^{2} + 13y + 14 = 0$

=> $3y^2 + 6y + 7y + 14 = 0$

=> $3y (y + 2) + 7 (y + 2) = 0$

=> $(y + 2) (3y + 7) = 0$

=> $y = -2 , \frac{-7}{3}$

$\therefore$ No relation can be established.

I.$x^{2} – 7x + 10 = 0$

=> $x^2 – 5x – 2x + 10 = 0$

=> $x (x – 5) – 2 (x – 5) = 0$

=> $(x – 5) (x – 2) = 0$

=> $x = 5 , 2$

II.$y^{2} + 11y + 10 = 0$

=> $y^2 + 10y + y + 10 = 0$

=> $y (y + 10) + 1 (y + 10) = 0$

=> $(y + 10) (y + 1) = 0$

=> $y = -10 , -1$

$\therefore x > y$

I.$x^{2} + 28x + 192 = 0$

=> $x^2 + 16x + 12x + 192 = 0$

=> $x (x + 16) + 12 (x + 16) = 0$

=> $(x + 16) (x + 12) = 0$

=> $x = -16 , -12$

II.$y^{2} + 16y + 48 = 0$

=> $y^2 + 12y + 4y + 48 = 0$

=> $y (y + 12) + 4 (y + 12) = 0$

=> $(y + 12) (y + 4) = 0$

=> $y = -12 , -4$

$\therefore x \leq y$

I : $2x – 3y = -3.5$

II : $3x + 2y = -6.5$

Multiplying eqn(I) by 2 and eqn(II) by 3, and then adding both equations, we get :

=> $(4x + 9x) + (-6y + 6y) = (-7 -19.5)$

=> $13x = -26.5$

=> $x = \frac{-26.5}{13} \approx -2$

=> $y = \frac{3x + 6.5}{2} = 0.25$

Hence $x < y$

I.$x^{2} + 8x + 15 = 0$

=> $x^2 + 5x + 3x + 15 = 0$

=> $x (x + 5) + 3 (x + 5) = 0$

=> $(x + 5) (x + 3) = 0$

=> $x = -5 , -3$

II.$y^{2} + 11y + 30 = 0$

=> $y^2 + 5y + 6y + 30 = 0$

=> $y (y + 5) + 6 (y + 5) = 0$

=> $(y + 6) (y + 5) = 0$

=> $y = -6 , -5$

$\therefore x \geq y$

I. $x = \sqrt {3136}$

=> $x = 56$

II.${y^2} = 3136$

=> $y = \sqrt{3136} = \pm 56$

$\therefore x \geq y$

I.$x^{2} + 13x + 42 = 0$

=> $x^2 + 7x + 6x + 42 = 0$

=> $x (x + 7) + 6 (x + 7) = 0$

=> $(x + 7) (x + 6) = 0$

=> $x = -7 , -6$

II.$y^{2} + 19y + 90 = 0$

=> $y^2 + 9y + 10y + 90 = 0$

=> $y (y + 9) + 10 (y + 9) = 0$

=> $(y + 9) (y + 10) = 0$

=> $y = -9 , -10$

$\therefore x > y$

I.$x^{2} – 15x + 56 = 0$

=> $x^2 – 8x – 7x + 56 = 0$

=> $x (x – 8) – 7 (x – 8) = 0$

=> $(x – 8) (x – 7) = 0$

=> $x = 8 , 7$

II.$y^{2} – 23y + 132 = 0$

=> $y^2 – 11y – 12y + 132 = 0$

=> $y (y – 11) – 12 (y – 11) = 0$

=> $(y – 11) (y – 12) = 0$

=> $y = 11 , 12$

$\therefore x < y$

I.$x^{2} + 7x + 12 = 0$

=> $x^2 + 3x + 4x + 12 = 0$

=> $x (x + 3) + 4 (x + 3) = 0$

=> $(x + 3) (x + 4) = 0$

=> $x = -3 , -4$

II.$y^{2} + 6y + 8 = 0$

=> $y^2 + 4y + 2y + 8 = 0$

=> $y (y + 4) + 2 (y + 4) = 0$

=> $(y + 4) (y + 2) = 0$

=> $y = -4 , -2$

Because $-2 > -4$ and $-3 > -4$

Therefore, no relation can be established.

I.$x^{2} – 22x + 120 = 0$

=> $x^2 – 10x – 12x + 120 = 0$

=> $x (x – 10) – 12 (x – 10) = 0$

=> $(x – 10) (x – 12) = 0$

=> $x = 10 , 12$

II.$y^{2} – 26y + 168 = 0$

=> $y^2 – 12y – 14y + 168 = 0$

=> $y (y – 12) – 14 (y – 12) = 0$

=> $(y – 12) (y – 14) = 0$

=> $y = 12 , 14$

$\therefore x \leq y$

I.$x^{2} + 12x + 32 = 0$

=> $x^2 + 8x + 4x + 32 = 0$

=> $x (x + 8) + 4 (x + 8) = 0$

=> $(x + 8) (x + 4) = 0$

=> $x = -8 , -4$

II.$y^{2} + 17y + 72 = 0$

=> $y^2 + 9y + 8y + 72 = 0$

=> $y (y + 9) + 8 (y + 9) = 0$

=> $(y + 9) (y + 8) = 0$

=> $y = -9 , -8$

$\therefore x \geq y$

We hope this Quadratic Equation Questions for IBPS PO  will be highly useful for your preparation.


text:
# Simplify (13/4)÷1 3/4

Convert to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Combine and .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Simplify (13/4)÷1 3/4

Scroll to top


text:
# The band structure of Weyl Semimetals

Weyl semimetals are topological quantum materials whose low energy excitations emerges as massles Weyl Fermions. They have a band touching point near the Fermi level called Weyl node.

What is actually the energy dispersion relation of Weyl Fermions? More specifically, do we have to consider the band as a linear dispersion relation or as a conduction and valence band which takes the shape of two cones?

I came up with this doubt because if we consider the band dispersion relation as linear, then

$$E_k=C\times (k-k_0)$$(For convenience consider 1D. but I know that Weyl semimetals are three dimensional)

then the effective mass is given by $$m*=\frac{\hbar^2}{\frac{\partial^2E_k}{\partial k^2}}$$

that gives

$$m*=\frac{\hbar^2}{0}=\infty$$

Which contradicts the fact that Weyl Fermions are massless.

But If we consider it as the latter one then the derivative is not defined at the Weyl node? Where am I wrong in my calculations and concepts?

Weyl semimetals (WSMs) are realized when non-degenerate bands cross at isolated points in the Brillouin zone. Consider the simplest example of a time-reversal symmetry broken WSM modeled by the hamiltonian $$H = t' \sin{k_x} \sigma_x + t'' \sin{k_y} \sigma_y + t (\cos{k_x} + \cos{k_y}+ \cos{k_z} - M) \sigma_z.$$ This hamiltonian admits 2 bands ($$\sigma_j$$ are the Pauli matrices). When $$1 < M < 3$$ a WSM phase is realized with Weyl points (i.e. points where the two bands cross) at $$(k_x, k_y, k_z) = (0, 0, \pm \cos^{-1}(M-2))$$.
If you zoom-in close to one of the Weyl points (say the one at $$k_z >0$$), Taylor expand the terms in the hamiltonian in terms of the deviations $$\delta k_j$$, and keep only the leading order term in each expansion, then you'll find the following effective hamiltonian $$H_+ = t' \delta k_x~ \sigma_x + t'' \delta k_y~ \sigma_y - t \sin\cos^{-1}(M-2) ~\delta k_z~ \sigma_z.$$
At zero density, the Fermi level will intersect the Weyl points, and the low energy excitations will be described by $$H_+$$ (here, "low" implies energies at which the quadratic terms that were dropped in the Taylor expansion are small compared to the linear terms). Notice that these excitations disperse linearly, and has 2 branches. In this sense the low energy excitations emulate Weyl fermions.
If one ignores the higher order terms in the Taylor expansion entirely, then the low energy excitations appear to be massless owing to an absence of terms $$\propto \delta k_j^2$$. In reality there is a finite but small mass. Here, we need to distinguish between the 'band mass' ($$m_*$$), which is a measure of the local curvature of a band, from the particle-like excitation's mass which is the energy gap in the excitation spectrum: If the excitation spectrum is described by $$E(k) = \sqrt{k^2 + \mu^2}$$, then $$\mu$$ is the mass/energy gap. It is $$\mu$$ that is usually alluded to when the term massless is invoked in the context of semi-metals or multiband insulators.
It is instructive to check these limiting behaviors with the eigenvalues (bands) of the microscopic hamiltonian, $$H$$. Make special note of the terms being dropped from the Taylor expansion.


text:
# Adhesive Leaf Created by a Corona Discharge

## Abstract

Here, we report a new concept of both the adhesive manner and material, named “adhesive leaf (AL),” based on the leaf of the plant Heteropanax fragrans. The treatment of the corona discharge on the leaf surface can cause the nano-/microdestruction of the leaf epidermis, resulting in an outward release of sap. The glucose-containing sap provided the AL with a unique ability to stick to various substrates such as steel, polypropylene, and glass. Moreover, we reveal that the AL adhesion strength depends on the AL size, as well as the corona-discharge intensity. Conventional adhesives, such as glue and bond, lose their adhesive property and leave dirty residues upon the removal of the attached material. Unlike the conventional methods, the AL is advantageous as it can be repeatedly attached and detached thoroughly until the sap liquid is exhausted; its adhesive ability is maintained for at least three weeks at room temperature. Our findings shed light on a new concept of a biodegradable adhesive material that is created by a simple surface treatment.

## Introduction

Evolutionary processes have created the diverse adhesive methods of the organisms in nature1,2,3,4,5,6. For instance, on each footpad of the gecko animal, hundreds of thousands of setae with a density of 5300/m2 exist7. Each seta consists of hundreds of spatulas, and each microspatula applies approximately 20 μN using a number of forces including the van der Waals, dipole, and capillary forces1,2. All of the forces are congregated and contribute to the adhesion of the gecko onto walls. In contrast to the manner of the gecko foot, chemical adhesive methods are also used in nature; for example, mussels can attach to all surfaces4,6. Mussels produce hair-like fibers that are composed of amino acids including 3,4-dihydrxy-L-phenylalanine and lysine, and the fibers allow the mussels to adhere to sea-rock surfaces. Another interesting organism, the Onychophora, squeezes out a slime known as a food web that overcomes its slow migration speed to obtain feed (prey); an adhesive property of the slime is enough to entangle the organism’s prey8.

Taking advantage of nature-developed techniques, the ancient Egyptians made paper from papyrus, which possesses an adhesive property without any additives9; since then, it appears that researchers have continuously studied the adhesive method of organisms for many centuries1,2,3,5,6,7. Today, this research area is called biomimetics10. By using the morphological benefit of the gecko footpad, for example, gecko tape has been developed to ensure a collective adhesion; a method of the microfabrication of dense arrays of flexible plastic pillars is used to make the gecko tape7. A mimicking of the high-strength adhesive material that is produced by mussels has shown that it is nontoxic to living cells, thereby suggesting its potential suitability for surgical and other biomedical applications11. Besides, many studies are currently underway to mimic the techniques in nature effectively in terms of biocompatible applications.

Meanwhile, the corona-discharge is generated by the application of a high voltage at high frequency to an electrode tip. The corona-treated surface becomes stiff, whereby often induces physical damage (surface degradation) of insulating materials (e.g., rubber)12. When the corona-discharge is exerted, the materials are discharged through the circumjacent fluid such as water and air. Corona-discharge treatment has been widely used to activate the surface of materials using high energy levels13,14,15. For instance, corona-discharged polydimethylsiloxane can strongly adhere to other materials such as glass, plastic, or itself without the additional use of adhesives16,17. In the present study, a report is presented on the leaves of Heteropanax fragrans for the attainment of an adhesive property as a corona discharge is treated. The treatment of the corona discharge changes not only the leaf epidermal structure, but it also alters the leaf adhesive functionality, thereby creating the adhesive leaf (AL).

The corresponding mechanism is as follows: As the leaves are treated by the corona discharge, sap oozes from the leaves through the damaged epidermis, which is a phenomenon that is similar to a snail’s secretion of its adhesive mucus throughout its body18. Snail mucus plays a central role in the attachment regarding various surfaces as well as self-defense. Organic-compound mixtures such as polysaccharides, the proteins in the snail mucus, provide snails with a surface-attachment ability. It is confirmed here that the AL adhesion strength is augmented as the AL surface area is increased. Moreover, tests of the AL adhesive ability for various substrates such as steel, polymer, and glass were conducted. It is believed that the AL represents a novel concept of a biodegradable and eco-friendly adhesive material.

## Results and Discussion

When the corona discharge was applied to a Heteropanax fragrans leaf, the leaf adhered to the wall surfaces, as shown in Fig. 1(a) and (b); accordingly, the “adhesive leaf” name was derived. Because of the liquid leakage from the AL surface, it was predicted that the AL adhesive force is due to the fine sap flow through the micropores that is formed by the corona-discharge destruction of the leaf epidermal structure, as shown in Fig. 1(c). To verify whether this prediction is valid, a needle was used to puncture holes with diameters of a few millimeters into the leaves; however, the sap did not leak out due to its viscosity19, and the punctured leaves did not display an adhesive property (data not shown). In contrast, it was confirmed that the corona-discharge-created ALs could attach to the walls due to the adherence of the sap to the leaves, and the ALs were even patterned with alphabets, as shown in Fig. 1(d). In addition, the AL adhesive strength can persist until the sap is exhausted. Note that the number of attachments/detachments is dependent on the AL size and the quantity of sap inside the leaf; this will be discussed later. Even if the AL on the wall is dried, the adhesive ability can be maintained for at least three weeks. These results imply that the AL adhesive force is attributed to the flow of the sap through the micropores that are formed by the corona-induced destruction of the leaf epidermal structure.

FTIR experiments were conducted to analyze the sap components that are the result of the corona treatment, as shown in Fig. S2. The subtraction of the sap wavelength band from the deionized (DI)-water wavelength band revealed that glucose is present in the sap20. The leakage of the sap from the AL was confirmed by the temperature changes in the corona-treated spots. Using an infrared camera, direct measurements of the temperature changes on the leaf surface before and after the corona discharge were performed. Prior to the corona treatment, the mean temperature of the leaf surface was measured as approximately 27 °C, as can be seen in Fig. 2(a). Immediately after the corona treatment, the temperature of a corona-treated spot on the leaf surface rose sharply up to approximately 33 °C, as shown in Fig. 2(b). After approximately 20 s, the spot temperature gradually decreased to a temperature that is even slightly lower than the pre-corona-treatment measurement, as shown in Fig. 2(c) and (d). The lowered temperature remained unchanged for at least 120 s, and this is evident in Fig. 2(e). As represented in Fig. S3, the temperature curve obeys the Boltzmann sigmoid model. These temperature changes imply that the corona treatment induced a highly thermal energy to destruct the leaf surface, and the sap flowed out from the damaged structures and was evaporated upon its contact with air. It was subsequently speculated that the AL corona-treated spots would show a lower temperature than those of the pristine leaves.

An scanning electron microscopy (SEM) analysis of an AL corona-treated spot was performed to examine the damaged structures. The SEM images revealed that the corona discharge could create micropore structures (tens-of-μm sizes) on the AL surfaces compared with the pristine-leaf surfaces (control), and this can be seen in Fig. 3(a) and (b). The AL micropore structures were randomly created on the corona-treated spots, which may have played a role in the sap-leakage pathways contained inside the leaves. Similarly, the leaf surfaces before and after the corona treatment were observed using an optical microscope. Microsize pores became apparent as white dots after the corona treatment, and these are shown in Fig. 4(a) and (b). The white color of the dots may be due to the sap light reflection. Moreover, the AL surface, except for the white-dot structure, became very deteriorated compared with the pristine-leaf surface. A quantification of the degree of the damaged leaf surface was calculated using the normalized surface roughness with a different corona energy. To calculate the normalized surface roughness, the AL surface roughness was divided by the surface roughness of the pristine surface (before the corona treatment).

Also, the corona energy depends on either the distance (dcorona) between the tip of a corona discharge and the sample (leaves) or between the tip of a corona discharge and the treatment time (tcorona)15. Three different dcorona values of 5, 10 and 15 mm and two different tcorona values of 30 and 60 s were considered. The results show that the surface roughness was increased as the dcorona became closer and the tcorona was increased, as shown in Fig. 4(c). Interestingly, these results imply that the dcorona of 5 mm and the tcorona of 60 s are more effective for the formation of the damaged structures including the micropores compared with the other conditions.

It was predicted that the AL surface roughness is directly correlated to the amount of sap that flows out through the damaged structure. As such, it is thought that the AL adhesion strength depends on the amount of flowed-out sap. In fact, it is difficult to quantitatively measure the volume of the sap released as a function of corona-discharge. The reasons are as follows: First, although the volume of sap contained in leaves usually depends on the sizes of the leaves, there should be individual differences between the leaves according to the plant’s health. Second, in the attachment process of an AL, it is necessary to press the AL to a certain substrate (Fig. 1). The volume of the released sap might differ in that process. Nevertheless, we can predict the relationship between the volume of the sap released as a function of corona-discharge and the experimental condition of corona-discharge. The ALs were attached to a wall and then pulled with the Instron tensile-force tester to measure the AL adhesive strength (Fig. 5). The corona-treatment conditions (i.e., dcorona and tcorona) are the same as those from the surface-roughness analysis. The adhesion-strength data were acquired from the force–distance (F–D) curve. Specifically, at tcorona = 30 s, the F–D curves are not significantly different regardless of the dcorona, as can be seen in Fig. 5(a). In contrast, it seems that the F–D curves at tcorona = 60 s are slightly larger than those that at tcorona = 30 s, which is shown in Fig. 5(b). Interestingly, the AL adhesion at tcorona = 60 s is the largest at dcorona = 5 mm. This trend can be clearly seen in the surface plot of Fig. 5(c) that exhibits the relationship between the three factors, the AL adhesion strength, the dcorona, and the tcorona. We found that the adhesion force of AL increases when the distance between the electrode and the leaf surface gets closer or the corona-treatment time gets longer. Under an assumption that the adhesion force of AL is proportional to the volume of sap, the results represent that the volume of released sap tends to be proportional to the time of corona-treatment and be inversely proportional to the distance between the electrode and the leaf surface.

To confirm whether the AL adheres effectively to other materials, experiments were conducted to measure the AL adhesive strength and the adhesive force per single area using polypropylene, glass, and steel (Fig. 6). In all of the experiments, the AL was created with a dcorona of 10 mm. In the condition of dcorona = 5 mm, the corona-discharge often causes too much destruction of the surface of AL. It may be attributed to the high intensity of corona-discharge due to the short distance15. As the distance dcorona increases, we confirmed that the phenomenon decreases remarkably. We empirically determined that the dcorona = 10 mm is proper.

Notably, the AL performance could often be varied not only due to the AL size; indeed, in the tests with various substrate materials, the AL ability showed a sensitivity to the spot size, but it is too difficult to control the spot size with a handheld corona-discharge device. As an alternative to the making of the ALs with one corona-treated spot, a corona-discharge treatment was applied to the entire leaf surfaces. In the experiment, the time of corona-treatment depended on the size of the leaves and was usually less than 2~3 min per one AL. The results show that the AL adhesive strength is seemingly higher in the sequential order of glass, polypropylene, and steel. Specifically, both the AL area and adhesion showed the linear characteristics of 1.964, 1.848 and 2.345 mN/mm2 for steel, polypropylene, and glass, respectively. We speculate on the reasons for the variations along the linear curve. The fact that every leaf has distinctive vein means each leaf has different sap content and distribution20,21. The randomness of poration characteristics could also be the reason. Every corona-treated leaf shows diverse pore structure, location, and number. Nevertheless, the results indicate that the AL that is produced by the corona discharge can be attached to various substrates. Together, Fig. 6 represents two findings: First, the area of the AL is proportional to the adhesion strength. Second, AL can be attached to various types of surfaces. In this experiment, we made AL with leaves from a species of plant (Heteropanax fragrans) and measured its adhesion properties on only three types of surfaces. To better understand the adhesion properties of AL, we need a further study using more species of leaf on various substrates.

In this study, to make AL, we have treated corona-discharge only on the upper epidermis of leaves. Because the lower epidermis has protruding structures such as primary and secondary veins, we have thought that the veins could affect the adhesion properties of AL. To compare the effect of corona-discharge treatment on plant leaf surface between upper and lower epidermis, we prepared two kinds of leaves with different structures (a curved leaf: Dracaena reflexa – Song of Jamaica; a flat leaf: Schefflera arboricola). The distance between the electrode and leaf surface was approximately 10 mm and the time of corona-treatment was 60 s. The curved leaf can be attached to the wall (of a fume hood) after corona-treatment regardless of the external structure of the leaves (Fig. S5). In addition, regardless of whether the leaves were treated front or back (i.e., upper or lower epidermis), the sap exudes through the damaged epidermis. What we found was that the attachment duration was shortened when the lower epidermis was treated; it only lasted few seconds (Fig. S5b). We thought that the curved structure might hinder the leaves from stably being attached. We also conducted the same experiment using flat leaves to see if our thoughts are correct (Fig. S5c). As a result, AL stayed well on the wall regardless of whether the leaves were treated front or back. However, the lower epidermis-treated AL could not last more than 10 s (Fig. S5d). We believe that the protruding primary vein structure of the lower epidermis affects the adhesion of AL. To verify our hypothesis, we proceeded the same experiment using leaf fragments (of Schefflera arboricola) that do not contain the primary vein (Fig. S5e). As a result, both cases (upper or lower epidermis) showed stable adhesion ability. Taken together, it is fair to say that the adhesion ability of AL is stable regardless of whether the leaves were treated front or back, only if the leaves are flat without any protruding parts like a primary vein.

In conclusion, an investigation of the adhesion of the corona-treated leaves was first conducted, thereby demonstrating the adhesion mechanism. Specifically, the corona discharge can delicately destroy the leaf-surface structure, and the sap flows out through the destroyed structure to form an adhesive force on the leaf surface. This adhesion force is sufficient to withstand the weight of the leaf itself (several milligrams) and results in an attachment to various substrate materials, such as steel, polymer, and glass. The authors believe that an adhesive mechanism that is due to the leakage of a viscous liquid through a micropore surface can be applied in the development of a novel bandage for applications like the treatment of wounds.

## Methods

### Corona-discharge treatment

The BD-10A hand-held corona-discharge device with a 230-V high-frequency generator (Electro-Technic Products, U.S.A.) was used to create the AL. The corona-discharge, brought on by the ionization of air, was performed near the center of the leaves as much as possible to minimize the deviation of the plasma stream from the leaf area (Fig. S1). (Caution: Because the corona discharge produces high voltages and electrical currents, any conductive materials that are around the experimental environments need to be removed.) The distances between the electrode and the leaf surface were kept 5, 10, and 15 mm away and the treatment times for corona-discharge were 30 and 60 s. Immediately after the corona-treatment, ALs can be attached to various substrates such as cement wall, glass, steel, and polymers by a simple clicking motion to the center of AL.

### Thermal imaging of the AL

The corona-treatment-driven temperature changes in the ALs were quantitatively analyzed using thermal imaging and the corresponding FLIR ONE software (FLIR, U.S.A.). After a 30-s corona treatment, time-lapse images of a leaf were immediately acquired for 2 min with a 3-s time interval at room temperature. The leaves were on a sheet of laboratory paper on a table without any fixation.

### SEM imaging of the AL

The morphology and structure of the AL before and after the corona treatment were characterized using the JSM-6701F field-emission scanning electron microscopy (FE-SEM) device (JEOL, Japan). A platinum (Pt)-coating application was conducted for 120 s before the experiment. The SEM was operated at 10 kV, and the imaging spots were randomly selected on the AL surfaces. The SEM micrographs for each spot were collected at different magnifications (×50, ×250, and ×900).

### Optical imaging of the AL

An inverted microscope (AE31E, Shinhan Scientific, Korea) was used to observe the AL surfaces before and after the corona treatment. Calculation of surface roughness (R q ) of the leaves is performed using ImageJ (NIH, USA) with SurfCharJ plugin22 by the following equation:

$${R}_{q}={(\frac{1}{{N}_{x}{N}_{y}}\sum _{i=1}^{{N}_{x}}\sum _{j=1}^{{N}_{y}}{z}_{ij}^{2})}^{1/2},$$

where z is height values of the surface, N is the direction of outward surface normal vector, and x and y are the coordinates in the plane direction. For quantitative analysis of damaged structures of leaf surfaces after corona-treatment, the value of R q that calculated after corona-treatment was normalized by the value of R q that calculated before corona-treatment (Fig. 4c).

### FTIR analysis of the AL

The Fourier-transform infrared (FTIR) spectra of the sap were acquired using an FTIR spectrometer (Spectrum 100 FT-IR Spectrometer, Perkin Elmer, USA) at a resolution of 4 cm−1. The sap was extracted from the surface of several ALs using the corona discharge and was gathered by applying a gentle squeezing. The final sap volume is approximately 2 ml. The spectra of the sap and the control (i.e., distilled water) were recorded in the range of 500–4000 cm−1. The absorbance was plotted by subtracting the measured sap spectrum from the control-sample spectrum.

### Measurement of the AL adhesive force using a tensile-force tester

Immediately after the corona treatment, the AL petiole was mounted in the Model 4502 tensile testing machine (Instron, U.S.A.) to determine the AL adhesive force. Accordingly, the lamina part of the AL was attached to the base surface that is well aligned with the load axis, as can be seen in Fig. S4. An initial load of 1 N was applied by changing the clamp-to-clamp distance at which the initial gauge length was defined as zero. The specimens were stretched at the stretching velocity of 150 mm/min until a failure occurred. The effect of the corona-discharge treatment on the AL performance was tested using a comparison of the AL adhesive forces that were measured on a metal surface depending on the corona-treatment time (i.e., 30 and 60 s) and the distances between the tip and the leaves (i.e., 5, 10, and 15 mm). In addition, the AL adhesive force was evaluated on different substrates (i.e., steel, polypropylene, and glass). The adhesive force was normalized by the AL surface area.

## References

1. 1.

Autumn, K. et al. Adhesive force of a single gecko foot-hair. Nature 405, 681–685 (2000).

2. 2.

Autumn, K. et al. Evidence for van der Waals adhesion in gecko setae. Proceedings of the National Academy of Sciences 99, 12252–12256, https://doi.org/10.1073/pnas.192252799 (2002).

3. 3.

Sahni, V., Blackledge, T. A. & Dhinojwala, A. A Review on Spider Silk Adhesion. The Journal of Adhesion 87, 595–614, https://doi.org/10.1080/00218464.2011.583588 (2011).

4. 4.

Lee, H., Dellatore, S. M., Miller, W. M. & Messersmith, P. B. Mussel-Inspired Surface Chemistry for Multifunctional Coatings. Science 318, 426 (2007).

5. 5.

Lee, H., Lee, B. P. & Messersmith, P. B. A reversible wet/dry adhesive inspired by mussels and geckos. Nature 448, 338–341, http://www.nature.com/nature/journal/v448/n7151/suppinfo/nature05968_S1.html (2007).

6. 6.

Lee, H., Scherer, N. F. & Messersmith, P. B. Single-molecule mechanics of mussel adhesion. Proceedings of the National Academy of Sciences 103, 12999–13003, https://doi.org/10.1073/pnas.0605552103 (2006).

7. 7.

Geim, A. K. et al. Microfabricated adhesive mimicking gecko foot-hair. Nat. Mater. 2, 461–463 (2003).

8. 8.

Concha, A. et al. Oscillation of the velvet worm slime jet by passive hydrodynamic instability. Nature Communications 6, 6292, 10.1038/ncomms7292https://www.nature.com/articles/ncomms7292#supplementary-information (2015).

9. 9.

Scora, P. E. & Scora, R. W. Some observations on the nature of papyrus bonding. Journal of Ethnobiology 11, 193–202 (1991).

10. 10.

Vincent, J. F. V., Bogatyreva, O. A., Bogatyrev, N. R., Bowyer, A. & Pahl, A.-K. Biomimetics: its practice and theory. Journal of The Royal Society Interface 3, 471 (2006).

11. 11.

Jeon, E. Y. et al. Rapidly light-activated surgical protein glue inspired by mussel adhesion and insect structural crosslinking. Biomaterials 67, 11–19, https://doi.org/10.1016/j.biomaterials.2015.07.014 (2015).

12. 12.

Zhu, Y., Haji, K., Otsubo, M. & Honda, C. Surface Degradation of Silicone Rubber Exposed to Corona Discharge. IEEE Transactions on Plasma Science 34, 1094–1098, https://doi.org/10.1109/TPS.2006.876498 (2006).

13. 13.

Farris, S. et al. The fundamentals of flame treatment for the surface activation of polyolefin polymers – A review. Polymer 51, 3591–3605, https://doi.org/10.1016/j.polymer.2010.05.036 (2010).

14. 14.

Lawson, D. F. Corona Discharge Activation and Reconstruction of Elastomer Surfaces. Rubber Chemistry and Technology 60, 102–110, https://doi.org/10.5254/1.3536111 (1987).

15. 15.

Wei, K., Rudy, M. S. & Zhao, Y. Systematic investigation of the benchtop surface wrinkling process by corona discharge. RSC Advances 4, 59122–59129, https://doi.org/10.1039/C4RA10732B (2014).

16. 16.

Haubert, K., Drier, T. & Beebe, D. PDMS bonding by means of a portable, low-cost corona system. Lab on a Chip 6, 1548–1549, https://doi.org/10.1039/B610567J (2006).

17. 17.

Liu, K., Gu, P., Hamaker, K. & Fan, Z. H. Characterization of bonding between poly(dimethylsiloxane) and cyclic olefin copolymer using corona discharge induced grafting polymerization. Journal of Colloid and Interface Science 365, 289–295, http://dx.doi.org/10.1016/j.jcis.2011.09.004 (2012).

18. 18.

Newar, J. & Ghatak, A. Studies on the Adhesive Property of Snail Adhesive Mucus. Langmuir 31, 12155–12160, https://doi.org/10.1021/acs.langmuir.5b03498 (2015).

19. 19.

Kim, W. Mechanics of xylem sap drinking. Biomedical Engineering Letters 3, 144–148, https://doi.org/10.1007/s13534-013-0104-0 (2013).

20. 20.

Jensen, K. H. et al. Sap flow and sugar transport in plants. Reviews of Modern Physics 88, 035007 (2016).

21. 21.

Roth-Nebelsick, A., Uhl, D., Mosbrugger, V. & Kerp, H. Evolution and Function of Leaf Venation Architecture: A Review. Annals of Botany 87, 553–566, https://doi.org/10.1006/anbo.2001.1391 (2001).

22. 22.

Chinga, G., Johnsen, P. O., Dougherty, R., Berli, E. L. & Walter, J. Quantification of the 3D microstructure of SC surfaces. Journal of Microscopy 227, 254–265, https://doi.org/10.1111/j.1365-2818.2007.01809.x (2007).

## Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A11034311) and by Korea University Grant. This work was also supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (No. NRF-2016R1A2B4010269 and 2017R1A2B2002076).

## Author information

Authors

### Contributions

W.L. and G.L. conceived the research. W.L., J.S., S.K., D.Y. and S.C. experimented. W.L., J.S., S.C., R.A.W., K.S.H., S.W.L., G.L. and D.S.Y. analyzed data. W.L., J.S., S.K., G.L. and D.S.Y. wrote the first version of the manuscript. W.L. and G.L. finalized the manuscript.

### Corresponding authors

Correspondence to Gyudo Lee or Dae Sung Yoon.

## Ethics declarations

### Competing Interests

The authors declare that they have no competing interests.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Lee, W., Son, J., Kim, S. et al. Adhesive Leaf Created by a Corona Discharge. Sci Rep 8, 1737 (2018). https://doi.org/10.1038/s41598-018-19328-8

• Accepted:

• Published:

• ### Bioinspired Micro Glue Threads Fabricated by Liquid Bridge-to-Solidification as an Effective Sensing Platform

• Woong Kim
• , Wonseok Lee
• , Hyunsung Choi
• , Gyudo Lee
• , Jongsang Son
• , Sang Won Lee
• , Joohyung Park
• , Woochang Kim
• , Minwoo Kim
• , Dae Sung Yoon
• , Doyeon Bang
• , Sungsoo Na
•  & Jinsung Park

ACS Sensors (2020)


text:
The Mathematical Pirate took one look at the piece of paper attached to the dock.

“They’re BANNING formula triangles?! By order of @srcav?!” He swished his sword around. “Let me figure out where he lives, I’ll show him.”

“He lives… inshore, cap’n” said the $n$th mate. “It’s too dangerous.”

“Can we send Ninja-chops?” He was pretty sure the Mathematical Ninja wasn’t within earshot, but lowered his voice all the same.

“I’ll see what we can do,” said the $n$th mate.

The scene went wibble-wibble-wibble as the Mathematical Pirate thought back to his time at Pirate Maths school. The Pirate Teacher was sneakily asking physics questions: “What’s the potential difference? You, yes, you?”

“$V$?” said the young Mathematical Pirate. “… Aye! Arrr!”

“Well done,” said the Pirate Teacher. “$V = IR$. So what’s $I$? You, there!” He pointed at the $n$th mate.

“$\frac{V}{R}$,” he said without even a beat.

“Blistering barnacles!” said the Mathematical Pirate. “How did you rearrange that so quickly?”

The $n$th mate drew out a formula triangle, like this:

“How does that help?”

“If two things are on the same line, you can multiply them together to get the other.”

“So, $V=IR$. I knew that.”

“But if they’re on different lines, you can divide the top one by a lower one to get the third.”

“So $I = \frac{V}{R}$, like you said.”

“Exactly. And it works any time you have $a = bc$ (whatever is alone goes on top) or $d = \frac{e}{f}$ (whatever’s on top stays on top) - so you can use it for SOH CAH TOA, density, speed, constant acceleration… all of the things you need in your day-to-day pirating adventures.”

“Arr,” said the Mathematical Pirate. “I think I’ll steal that.”

The Mathematical Pirate is a passionate - you might say violent - advocate of the formula triangle, but it’s not as well-received - generally - among teachers, several of whom would ban them given the chance. There are reasons for this antipathy, some better than others - which I thought I’d put to the Mathematical Pirate.

### I don’t like them

“Arr. That’s just stupid,” said the Mathematical Pirate. “I don’t like the difference of two squares (just learn to factorise properly!) but I realise it works for some people. They’re welcome to use it. Doesn’t bother me. I’m a pirate, not a fascist.”

“Right”, I said, “you could make the same argument about learning $7 \times 8 = 56$ when you ‘should’ be working it out as $(10-2) (10-3)$ every time.”

### They can go wrong

The Mathematical Pirate tapped his cutlass, absent-mindedly, on the table. “And algebra never does, I suppose?”

“They say algebra, done properly, is infallible.”

A derisive snort. “A formula triangle, used appropriately, works just fine. It’s based on algebra.”

### They’re gimmicky

“@shahlock says he doesn’t teach them because they’re gimmicky, like singing the quadratic equation.”

The Mathematical Pirate looked slightly hurt. “That’s my favourite shanty! Hoist up the minus b’s sails! See how the square root’s set!

“Ahem.”

“Erm… yeah, sorry. Is that one of those Nix the Tricks arguments? That gimmicks are harmful and we should only work from a spirit of true understanding? Because that’s bollocks in the real world.”

“Language!”

“Oh!” said the Mathematical Pirate. “C’est débile en réalite.”

“That’s better. I agree, in an ideal world, every student would generate the rules of algebra starting from a few self-evident axioms and apply them rigorously to appropriate problems, but that’s not how it works, however much we’d like it to. ‘Gimmicks’ like the triangle, the Table of Joy ((See Basic Maths For Dummies, available at all good bookstores and some rotten ones)) , subtracting simultaneous equations, difference of two squares, and dozens of others, make some problems accessible to students who’ll otherwise get discouraged and think “I’ve no idea what’s going on here, I must be stupid and rubbish at maths.”

“Arr.”

### They avoid understanding and cementing algebraic skills

“Wait, what?” said the Mathematical Pirate. “The mechanical shuffling of abstract symbols around an equals sign somehow shows more ‘understanding’ than setting up a triangle? Give me a break.”

“Well, I’m sure some teachers would argue that students ought to know what the equals sign means, and that whatever you do to one side you need to do to the other.”

“They ought to, aye,” said the Mathematical Pirate. “And I can see that it’s just for a special case - but it’s a special case that crops up ALL THE SODDING TIME.”

“Thinking about it, there’s one big distinction that got missed in the whole twitter spat the other day: the difference between numeracy and maths. The triangle is a great tool for numeracy: it gives you the right answer quickly. It’s not quite so great if you’re trying to train a mathematician (or someone who’ll use mathematical skills for science or whatever) as they really ought to be able to rearrange.”

“But does that mean they avoid understanding?”

“I use formula triangles to rearrange things all the time, especially something like $a = \frac bc$ - if I want $c$, I can visualise the triangle much more quickly than multiplying by $c$ and dividing by $a$. And I like to think that I understand algebra pretty well, thank you very much.”

### They avoid interconnectivity

“So, one method that works for problems across maths, physics, chemistry, biology, economics, navigation and 3,000 other things is somehow anti-connectivity? I don’t get it.”

“I think the argument is that using a triangle isn’t connected to the rest of algebra.”

“Except that it’s based on algebra and a nifty way of dealing with a special case, like all the ones we outlined earlier? Except that it gives a second check on an algebraic method? Except that it gives students a hook to see that algebra works the same way as another method they’re comfortable with?”

“I know. The whole thing smacks of people wanting to teach the One True Path To Mathematics - but there’s no such thing. By necessity, maths teaching involves a hodge-podge of methods that start out as mystical recipes before eventually, with any luck, taking part of a strong mathematical structure.”

### They eliminate the need for thinking

“Arrr!” said the Mathematical Pirate. “That they do. I’ve got better things to do with my brain than think about the mechanics of simple algebraic equations. Like give sanity checks to my answers. The first thing I learned in my navigation PhD was that the correct order of thinking is a: dredge it up from memory, b: look it up; c: work it out. That frees your brain up to do important things like interpret the question, interpret the answer, swash buckles, and so on.”

“Isn’t the whole point of maths to make things simpler? Saying ‘thou shalt rearrange’ feels like one of those arbitrary school rules that, even though there might have been good reasons for putting them in place, just serve to annoy people and end up being ignored.”

“Rules?” said the Mathematical Pirate, with a quizzical look on his face.

“In any event, taking a perfectly valid method a student knows how to use and labelling it ‘wrong’ is a sure-fire way to kill their confidence and mathematical creativity.”

### They’re not proper maths

The cutlass handle wobbled, as its blade was several centimetres deep in the fo’c’s’le. “Arr,” said the Mathematical Pirate, “I’ll never get that out now. Proper maths? PROPER MATHS? Exploiting a recurring pattern isn’t proper maths?” He breathed out.

“I know, I know. It’s a bizarre argument: one of the main ideas of ‘proper’ maths is to take something tricky, spot a pattern you know how to deal with, and use it to make the tricky thing simpler.”

“Hello, the @srcav residence?” said the voice on the phone.

“The Mathematical Pirate tells me you want to ban formula triangles.”

“… well, not nece…”

“SHUT IT! They’re not my preferred way of doing things, either. But they’re really useful to some students.”

“I didn’t me…”

“THE MATHEMATICAL NINJA HAS SPOKEN.”

Click.

* Edited 2014-10-15 to put in missing image, and again to stop the author confusing Ninjas with Pirates.


text:
# Primes Less than 100

Sporcle game here.   Name all the primes less than 100 in 3 minutes.

Tags: ,


text:
## Judging a book by its cover

It seems to me, that judging a prediction model by graphing the results is akin to judging a book by its cover. Random forest was used to fit the regression model, which then was used for prediction. The predicted and actual

## Autocorrelation - A Brief Overview Using R

Definition of Autocorrelation Given a time series , where  denotes the observation at time , the time series is said to show autocorrelation if there is correlation between the lagged values of the time series. The autocorrelation coefficient is the


text:
# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 4th 2013

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 4th 2013

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 4th 2013

have copied that paragraph also into the entry stable homotopy groups of spheres (which is badly in need of some genuine content)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 4th 2013
• (edited Nov 4th 2013)

have added the list of values of $\vert J(\pi_{4k-1}(O))\vert$ for low $k$.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 11th 2013
• (edited Nov 11th 2013)

I have added some more comments to J-homomorphism – Definition – On groups meant to be careful about the argument of how the continuous action of the topological group $O(n)$ on the topological space $S^n$ turns into an $\infty$-action of the homotopy type of the stable orthogonal group on the sphere spectrum.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 12th 2013

added the characterization of the image of J in terms of chromatic homotopy theory (in the $E(1)$-local sphere spectrum) to Image of J – In terms of chromatic homotopy theory

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 17th 2013
• (edited Nov 17th 2013)

added a few more pointers to discussion of the image of J in terms of $K(1)$/$E(1)$-localization of the sphere spectrum:

Is there anything else?

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 30th 2014

added pointer to Gaudens-Menichi 07 for expressing the canonical $O(n)$-action on general $n$-fold loop spaces in terms of the J-homomorphisms.

If anyone has more pointers for this, let me know.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMar 21st 2019


text:
• Corpus ID: 56012431

# Bordered Floer homology for manifolds with torus boundary via immersed curves

@article{Hanselman2016BorderedFH,
title={Bordered Floer homology for manifolds with torus boundary via immersed curves},
author={Jonathan Hanselman and Jacob Rasmussen and Liam Watson},
journal={arXiv: Geometric Topology},
year={2016}
}
• Published 12 April 2016
• Mathematics
• arXiv: Geometric Topology
This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If $M$ is such a manifold, we show that the type D structure $\widehat{\mathit{CFD}}$ may be viewed as a set of immersed curves decorated with local systems in $\partial M$. These curves-with-decoration are invariants of the underlying three-manifold up to regular homotopy of the curves and isomorphism of the local systems. Given two such manifolds and a homeomorphism $h$ between…
Immersed curves in Khovanov homology
• Mathematics
• 2019
We give a geometric interpretation of Bar-Natan's universal invariant for the class of tangles in the 3-ball with four ends: we associate with such 4-ended tangles $T$ multicurves
Heegaard Floer homology for manifolds with torus boundary: properties and examples
• Mathematics
• 2018
This is a companion paper to earlier work of the authors, which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We prove a
Bordered invariants of pairs of sutured manifolds with torus boundary
We establish a framework for extending invariants of sutured manifolds to invariants of pairs of sutured manifolds who differ by attaching a basic slice along a torus boundary component. In the
Order-detection of slopes on the boundaries of knot manifolds
• Mathematics
• 2022
. Motivated by the L -space conjecture, we investigate various notions of order-detection of slopes on knot manifolds. These notions are designed to characterise when rational homology 3-spheres
Instanton Floer homology, sutures, and Heegaard diagrams
• Mathematics
Journal of Topology
• 2022
This paper establishes a new technique that enables us to access some fundamental structural properties of instanton Floer homology. As an application, we establish, for the first time, a relation
Fukaya categories of surfaces, spherical objects and mapping class groups
• Mathematics
Forum of Mathematics, Sigma
• 2021
Abstract We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least $2$ whose Chern character represents a nonzero Hochschild homology class is
Integral Klein bottle surgeries and Heegaard Floer homology
We study gluings $X$ of the twisted $I$-bundle over the Klein bottle to knot complements, and investigate which gluings can be realizable as integral Dehn surgery along a knot in $S^3$. Closed,
Taut foliations in branched cyclic covers and left-orderable groups
• Mathematics
Transactions of the American Mathematical Society
• 2019
We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred
• Mathematics
• 2020
When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal δ-grading. This leads to the broader class of thin links that one would like to
Almost $\iota$-complexes as immersed curves
Here the existence of a new homomorphism $P_{\omega} : \Theta_{\mathbb{Z}}^3 \to \mathbb{Z}$ is proven and the existence of a $\mathbb{Z}^{\infty}$ summand in $\Theta_{\mathbb{Z}}^3$ is reproven.

## References

SHOWING 1-10 OF 42 REFERENCES
A calculus for bordered Floer homology
• Mathematics
• 2015
We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint
Bordered Heegaard Floer homology
• Mathematics
Memoirs of the American Mathematical Society
• 2018
We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with
Bimodules in bordered Heegaard Floer homology
• Mathematics
• 2010
Bordered Heegaard Floer homology is a three-manifold invariant which associates to a surface F an algebra A(F) and to a three-manifold Y with boundary identified with F a module over A(F). In this
The decategorification of bordered Heegaard Floer homology
Bordered Heegaard Floer homology is an invariant for 3-manifolds, which associates to a surface F an algebra A(Z), and to a 3-manifold Y with boundary, together with an orientation-preserving
Bordered Floer homology and existence of incompressible tori in homology spheres
Let $Y$ be a homology sphere which contains an incompressible torus. We show that $Y$ cannot be an $L$ -space, i.e. the rank of $\widehat{\text{HF}}(Y)$ is greater than $1$ . In fact, if the homology
On L-spaces and left-orderable fundamental groups
• Mathematics
• 2011
Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions
AN INTRODUCTION TO KNOT FLOER HOMOLOGY
This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid dia- grams, and
Fukaya categories of the torus and Dehn surgery
• Mathematics
Proceedings of the National Academy of Sciences
• 2011
It is shown that A∞-structures on the graded algebra A formed by the cohomology of two basic objects in the Fukaya category of the punctured 2-torus are governed by just two parameters (m6, m8), extracted from the Hochschild cohmology of A.


text:
# Math-in-HTML Examples

### How to add high-quality, scalable math formulas to web pages.

$$\pi/4 = 1-1/3+1/5-1/7+1/9-1/11+\cdots$$ $$x(t)=\sum_{k=0}^{\infty}a_k \cos(2\pi kt/T)+b_k \sin(2\pi kt/T)$$

Web Development section >

This Math-in-HTML Examples page

! Note !
More MathJax info and examples may be added,

 in the 'head' section of this web page. You may have to adjust the directory location of 'MathJax.js' to be compatible with your web site structure. Some MathJax (and MathML) Examples : From the Wikipedia page on MathML, the code :

Example of MathML embedded in an HTML5 file :

The area of a circle is
$<mi>π</mi> <mo></mo> <msup> <mi>r</mi> <mn>2</mn> </msup>$.

is rendered as :

#### Example of MathML embedded in an HTML5 file :

The area of a circle is $\pi {r}^{2}$.

You can see from this that MathML is quite 'wordy' --- although it usually does not require the installation (or remote access to) a large group of files. The MathML interpreter is built into most modern (post-2011) web browsers.

On the other hand, the following MathJax examples use a more compact notation --- so that a one-line math formula can usually be coded using one line of MathJax syntax.

A MathJax TeX example :

The TeX-like code :

When $$a \ne 0$$, there are two solutions to $$ax^2 + bx + c = 0$$
and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$

 renders as : When $$a \ne 0$$, there are two solutions to $$ax^2 + bx + c = 0$$ and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ A few MathJax examples from an AMS web page : In the 2015 April ams.org web page www.ams.org/news/math-in-the-media/04-2015-media, we can see MathJax examples like the following (by looking at the web page source HTML). The string $$\pi$$  causes a greek letter pi to be shown ... centered like this $$\pi$$ The line $$\pi/4 = 1-1/3+1/5-1/7+1/9-1/11+\cdots$$  displays a representation of the infinite series that connects all odd numbers to pi, namely $$\pi/4 = 1-1/3+1/5-1/7+1/9-1/11+\cdots$$ The line $$x(t)=\sum_{k=0}^{\infty}a_k \cos(2\pi kt/T)+b_k \sin(2\pi kt/T)$$  presents the equation for a Fourier series of the function x(t): $$x(t)=\sum_{k=0}^{\infty}a_k \cos(2\pi kt/T)+b_k \sin(2\pi kt/T)$$ More examples It is my intent that the discussion and examples above will help people (relatively) quickly understand how to render math formulas in web pages. There are more examples in about 20 '.html' files in the 'test' directory of the MathJax installation. To find more MathJax or MathML examples, you can do WEB SEARCHES on keywords such as: You can find examples involving calculus symbols for integration and differentiation.

Bottom of this
Math-in-HTML Examples page.