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## November 24, 2011

### Signed Integers Considered Stupid (Like This Title)

Unrelated note: If you title your article "[x] considered harmful", you are a horrible person with no originality. Stop doing it.

Signed integers have always bugged me. I've seen quite a bit of signed integer overuse in C#, but it is most egregious when dealing with C/C++ libraries that, for some reason, insist on using for(int i = 0; i < 5; ++i). Why would you ever write that? i cannot possibly be negative and for that matter shouldn't be negative, ever. Use for(unsigned int i = 0; i < 5; ++i), for crying out loud.

But really, that's not a fair example. You don't really lose anything using an integer for the i value there because its range isn't large enough. The places where this become stupid are things like using an integer for height and width, or returning a signed integer count. Why on earth would you want to return a negative count? If the count fails, return an unsigned -1, which is just the maximum possible value for your chosen unsigned integral type. Of course, certain people seem to think this is a bad idea because then you will return the largest positive number possible. What if they interpret that as a valid count and try to allocate 4 gigs of memory? Well gee, I don't know, what happens when you try to allocate -1 bytes of memory? In both cases, something is going to explode, and in both cases, its because the person using your code is an idiot. Neither way is more safe than the other. In fact, signed integers cause far more problems then they solve.

One of the most painfully obvious issues here is that virtually every single architecture in the world uses the two's complement representation of signed integers. When you are using two's complement on an 8-bit signed integer type (a char in C++), the largest positive value is 127, and the largest negative value is -128. That means a signed integer can represent a negative number so large it cannot be represented as a positive number. What happens when you do (char)abs(-128)? It tries to return 128, which overflows back to... -128. This is the cause of a host of security problems, and what's hilarious is that a lot of people try to use this to fuel their argument that you should use C# or Java or Haskell or some other esoteric language that makes them feel smart. The fact is, any language with fixed size integers has this problem. That means C# has it, Java has it, most languages have it to some degree. This bug doesn't mean you should stop using C++, it means you need to stop using signed integers in places they don't belong. Observe the following code:
  if (*p == '*')
{
++p;
total_width += abs (va_arg (ap, int));
}

This is retarded. Why on earth are you interpreting an argument as a signed integer only to then immediately call abs() on it? So a brain damaged programmer can throw in negative values and not blow things up? If it can only possibly be valid when it is a positive number, interpret it as a unsigned int. Even if someone tries putting in a negative number, they will serve only to make the total_width abnormally large, instead of potentially putting in -128, causing abs() to return -128 and creating a total_width that is far too small, causing a buffer overflow and hacking into your program. And don't go declaring total_width as a signed integer either, because that's just stupid. Using an unsigned integer here closes a potential security hole and makes it even harder for a dumb programmer to screw things up1.

I can only attribute the vast overuse of int to programmer laziness. unsigned int is just too long to write. Of course, that's what typedef's are for, so that isn't an excuse, so maybe they're worried a programmer won't understand how to put a -1 into an unsigned int? Even if they didn't, you could still cast the int to an unsigned int to serve the same purpose and close the security hole. I am simply at a loss as to why I see int's all over code that could never possibly be negative. If it could never possibly be negative, you are therefore assuming that it won't be negative, so it's a much better idea to just make it impossible for it to be negative instead of giving hackers 200 possible ways to break your program.

1 There's actually another error here in that total_width can overflow even when unsigned, and there is no check for that, but that's beyond the scope of this article.

## November 7, 2011

### Why Kids Hate Math

They're teaching it wrong.

And I don't just mean teaching the concepts incorrectly (although they do plenty of that), I mean their teaching priorities are completely backwards. Set Theory is really fun. Basic Set Theory can be taught to someone without them needing to know how to add or subtract. We teach kids Venn Diagrams but never teach them all the fun operators that go with them? Why not? You say they won't understand? Bullshit. If we can teach third graders binary, we can teach them set theory. We take forever to get around to teaching algebra to kids, because its considered difficult. If something is a difficult conceptual leap, then you don't want to delay it, you want to introduce the concepts as early as possible. I say start teaching kids algebra once they know basic arithmetic. They don't need to know how to do crazy weird stuff like x * x = x² (they don't even know what ² means), but you can still introduce them to the idea of representing an unknown value with x. Then you can teach them exponentiation and logs and all those other operators first in the context of numbers, and then in the context of unknown variables. Then algebra isn't some scary thing that makes all those people who don't understand math give up, its something you simply grow up with.

In a similar manner, what the hell is with all those trig identities? Nobody memorizes those things! You memorize like, 2 or 3 of them, and almost only ever use sin² + cos² = 1. In a similar fashion, nobody ever uses integral trig identities because if you are using them you should have converted your coordinate system to polar coordinates, and if you can't do that then you can just look them up for crying out loud. Factoring and completing the square can be useful, but forcing students to do these problems over and over when they almost never actually show up in anything other than spoon-fed equations is insane.

Partial Fractions, on the other hand, are awesome and fun and why on earth are they only taught in intermediate calculus?! Kids are ALWAYS trying to pull apart fractions like that, and we always tell them to not do it - why not just teach them the right way to do it? By the time they finally got around to teaching me partial fractions, I was thinking that it would be some horrifically difficult, painful, complex process. It isn't. You just have to follow a few rules and then 0 out some functions. How can that possibly be harder than learning the concept of differentiation? And its useful too!

Lets say we want to teach someone basic calculus. How much do they need to know? They need to know addition, subtraction, division, multiplication, fractions, exponentiation, roots, algebra, limits, and derivatives. You could teach someone calculus without them knowing what sine and cosine even are. You could probably argue that, with proper teaching, calculus would be about as hard, or maybe a little harder, than trigonometry. Trigonometry, by the way, has an inordinate amount of time spent on it. Just tell kids how right triangles work, sine/cosine/tangent, SOHCAHTOA, a few identities, and you're good. You don't need to know scalene and isosceles triangles. Why do we even have special names for them? Who gives a shit if a triangle has sides of the same length? Either its a right triangle and its useful or its not a right triangle and you have to do some crazy sin law shit that usually means your algorithm is just wrong and so the only time you ever actually need to use it you can just look up the formula because it is a obtuse edge case that almost never comes up.

Think about that. We're grading kids by asking them to solve edge cases that never come up in reality and grading how well they are in math based off of that. And then we're confused when they complain about math having no practical application? Well duh. The sheer amount of time spent on useless topics is staggering. Calculus should be taught to high school freshman. Differential equations and complex analysis go to the seniors, and by the time you get into college you're looking at combinatorics and vector analysis, not basic calculus.

I have already seen some heavily flawed arguments against this. Some people say that people aren't interested in math, so this will never work. Since I'm saying that teaching kids advanced concepts early on will make them interested in math, this is a circular argument and invalid. Other people claim that the kids will never understand because of some bullshit about needing logical constructs, which just doesn't make sense because you should still introduce the concepts. Introducing a concept early on and having the student be confused about it is a good thing because it means they'll try to work it out over time. The more time you give them, the more likely it will click. Besides, most students aren't understanding algebra with the current system anyway, so I fail to see the point of that argument. It's not working now so don't try to change it or you'll make it worse? That's just pathetic.

TL;DR: Stop teaching kids stupid, pointless math they won't need and maybe they won't rightfully conclude that what they are being taught is useless.


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## Archive for the ‘evolution’ category: Page 12

The super app, synonymous with popular mobile apps like WeChat, Grab, GoTo and Paytm, has enjoyed noteworthy success in Asian countries, but is relatively absent in other markets. CNBC’s Nessa Anwar, joined by Arjun Kharpal, explains the strategies and evolution behind the world’s biggest super apps.

Mysterious strands of DNA that seemingly assimilate genes from many different organisms in their surrounding environment have been discovered in a Californian backyard.

Scientists have named these elements “Borgs”, and their discovery could help us not just understand the evolution of microorganisms, but their interactions within their ecosystems, and their role in the broader environment.

According to geomicrobiologist Jill Banfield from the University of California, Berkeley, Borgs could make for a tremendously significant discovery.

Viruses that infect bacteria may drive the evolution of drug-resistant superbugs by inserting their genes into the bacterial DNA, a new study suggests.

The bacteria-attacking viruses, called phages, act as parasites in that they depend on their hosts for survival. The viral parasites often kill off their microbial hosts after infiltrating their DNA, said senior study author Vaughn Cooper, director of the Center for Evolutionary Biology and Medicine at the University of Pittsburgh School of Medicine. But sometimes, the phages slip into the bacterial genome and then lay low, making sneaky changes to the bacterium’s behavior, Cooper said.

For the first time ever, researchers from the University of Pittsburgh School of Medicine discovered that phages — tiny viruses that attack bacteria — are key to initiating rapid bacterial evolution leading to the emergence of treatment-resistant “superbugs.” The findings were published today in Science Advances.

The researchers showed that, contrary to a dominant theory in the field of evolutionary microbiology, the process of adaptation and diversification in bacterial colonies doesn’t start from a homogenous clonal population. They were shocked to discover that the cause of much of the early adaptation wasn’t random point mutations. Instead, they found that phages, which we normally think of as bacterial parasites, are what gave the winning strains the evolutionary advantage early on.

“Essentially, a parasite became a weapon,” said senior author Vaughn Cooper, Ph.D., professor of microbiology and molecular genetics at Pitt. “Phages endowed the victors with the means of winning. What killed off more sensitive bugs gave the advantage to others.”

A tachyon field might be responsible for cosmological inflation at an early time and contribute to cosmological dark matter at a later time. We investigate tachyonic inflation by analyzing a tachyon field with different potentials in the framework of loop quantum cosmology. No matter which tachyon field energy dominates at the bounce, the evolution of the background can be divided into three phases: super-inflation, damping, and slow-roll inflation. The duration of each phase depends on the initial condition. During the slow-roll inflation, when the initial condition is $$V(T_\mathrm{B})/\rho _\mathrm{c}\ge 10^{-6}$$ V(TB)/ρc≥10–6, the number of e-folds is very high ($$N\gg 60$$ N≫60) for $$V\propto T^{-n}$$ V∝T-n with $$n=1$$ n=1 and 1 / 2. For an exponential potential, to get enough e-folds, $$V(T_\mathrm{B})/\rho _\mathrm{c}$$ V(TB)/ρc should be greater than $$7.802\times 10^{-4}$$7.

This animated map shows the last billion years of Earth’s tectonic plate movement in just 40 seconds, showing how continents formed.

Data collected can be used to provide new insights into the evolution of the Kuiper Belt, and the larger solar system.

Trans-Neptunian Objects (TNOs), small objects that orbit the sun beyond Neptune, are fossils from the early days of the solar system which can tell us a lot about its formation and evolution.

A new study led by Mohamad Ali-Dib, a research scientist at the NYU Abu Dhabi Center for Astro, Particle, and Planetary Physics, reports the significant discovery that two groups of TNOs with different surface colors also have very different orbital patterns. This new information can be compared to models of the solar system to provide fresh insights into its early chemistry. Additionally, this discovery paves the way for further understanding of the formation of the Kuiper Belt itself, an area beyond Neptune comprised of icy objects, that is also the source of some comets.

Finding the hypothetical particle axion could mean finding out for the first time what happened in the Universe a second after the Big Bang, suggests a new study published in Physical Review D.

How far back into the Universe’s past can we look today? In the electromagnetic spectrum, observations of the Cosmic Microwave Background — commonly referred to as the CMB — allow us to see back almost 14 billion years to when the Universe cooled sufficiently for protons and electrons to combine and form neutral hydrogen. The CMB has taught us an inordinate amount about the evolution of the cosmos, but photons in the CMB were released 400000 years after the Big Bang making it extremely challenging to learn about the history of the universe prior to this epoch.

To open a new window, a trio of theoretical researchers, including Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) Principal Investigator, University of California, Berkeley, MacAdams Professor of Physics and Lawrence Berkeley National Laboratory senior faculty scientist Hitoshi Murayama, Lawrence Berkeley National Laboratory physics researcher and University of California, Berkeley, postdoctoral fellow Jeff Dror (now at University of California, Santa Cruz), and UC Berkeley Miller Research Fellow Nicholas Rodd, looked beyond photons, and into the realm of hypothetical particles known as axions, which may have been emitted in the first second of the Universe’s history.

The star is only a little bit larger than Earth’s Moon, but more massive than the Sun and might be a Frankenstein zombie star.

Astronomers discovered the smallest and most massive white dwarf star, about the same size as Earth’s Moon with a mass greater than the Sun.

An international group of astronomers has created images with never-before-seen detail of a galaxy cluster with a black hole at its center, traveling at high speed along an intergalactic “road of matter.” The findings also support existing theories of the origins and evolution of the universe.

The concept that roads of thin gas connect clusters of galaxies across the universe has been difficult to prove until recently, because the matter in these ‘roads’ is so sparse it eluded the gaze of even the most sensitive instruments. Following the 2020 discovery of an intergalactic thread of gas at least 50 million light-years long, scientists have now developed images with an unprecedented level of detail of the Northern Clump—a cluster of galaxies found on this thread.

By combining imagery from various sources including CSIRO’s ASKAP radio telescope, SRG/eROSITA, XMM-Newton and Chandra satellites, and DECam , the scientists could make out a large galaxy at the center of the clump, with a black hole at its center.

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• Volume 122, Issue 2

May 2012,   pages  153-311

• Farey Sequences and Resistor Networks

In this article, we employ the Farey sequence and Fibonacci numbers to establish strict upper and lower bounds for the order of the set of equivalent resistances for a circuit constructed from 𝑛 equal resistors combined in series and in parallel. The method is applicable for networks involving bridge and non-planar circuits.

• On Non-Frattini Chief Factors and Solvability of Finite Groups

A subgroup 𝐻 of a group 𝐺 is said to be a semi $CAP^∗$-subgroup of 𝐺 if there is a chief series $1 = G_0$ < $G_1$ <$\cdots$ < $G_m = G$ of 𝐺 such that for every non-Frattini chief factor $G_i/G_{i-1},H$ either covers $G_i/G_{i-1}$ or avoids $G_i/G_{i-1}$. In this paper, some sufficient conditions for a normal subgroup of a finite group to be solvable are given based on the assumption that some maximal subgroups are semi $CAP^∗$-subgroups.

• Permutation Groups with Bounded Movement having Maximum Orbits

Let 𝐺 be a permutation group on a set 𝛺 with no fixed points in 𝛺 and let 𝑚 be a positive integer. If no element of 𝐺 moves any subset of 𝛺 by more than 𝑚 points (that is, $|𝛤^g\backslash𝛤|≤ m$ for every $𝛤\subseteq𝛺$ and $g\in G$), and also if each 𝐺-orbit has size greater than 2, then the number 𝑡 of 𝐺-orbits in 𝛺 is at most $\frac{1}{2}(3m-1)$. Moreover, the equality holds if and only if 𝐺 is an elementary abelian 3-group.

• Split Malcev Algebras

We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras 𝑀 is of the form $M=\mathcal{U}+\sum_jI_j$ with $\mathcal{U}$ a subspace of the abelian Malcev subalgebra 𝐻 and any $I_j$ a well described ideal of 𝑀 satisfying $[I_j, I_k]=0$ if 𝑗 ≠ 𝑘. Under certain conditions, the simplicity of 𝑀 is characterized and it is shown that 𝑀 is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras.

• Discretization of Continuous Frame

In this paper we consider the notion of continuous frame of subspaces and define a new concept of continuous frame, entitled continuous atomic resolution of identity, for arbitrary Hilbert space $\mathcal{H}$ which has a countable reconstruction formula. Among the other results, we characterize the relationship between this new concept and other known continuous frames. Finally, we state and prove the assertions of the stability of perturbation in this concept.

• On the Uniqueness of Meromorphic Functions that Share Three or Two Finite Sets on Annuli

• On Cohomology Theory for Topological Groups

We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of the identity. We show that if 𝐺 and 𝐴 are locally compact and second countable, then the second cohomology group based on locally continuous measurable cochains as above parametrizes the collection of locally split extensions of 𝐺 by 𝐴.

• Absolutely Continuous Spectrum and Spectral Transition for some Continuous Random Operators

In this paper we consider two classes of random Hamiltonians on $L^2(\mathbb{R}^d)$: one that imitates the lattice case and the other a Schrödinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also know the existence of dense pure point spectrum for some disorder thus exhibiting spectral transition valid for the Bethe lattice and expected for the Anderson model in higher dimension.

• On the Extrema of Dirichlet's First Eigenvalue of a Family of Punctured Regular Polygons in Two Dimensional Space Forms

Let $\wp 1,\wp 0$ be two regular polygons of 𝑛 sides in a space form $M^2(𝜅)$ of constant curvature 𝜅=0,1 or -1 such that $\wp 0\subset\wp 1$ and having the same center of mass. Suppose $\wp 0$ is circumscribed by a circle 𝐶 contained in $\wp 1$. We fix $\wp 1$ and vary $\wp 0$ by rotating it in 𝐶 about its center of mass. Put $𝛺 =(\wp 1\backslash\wp 0)^0$, the interior of $\wp 1\backslash\wp 0$ in $M^2(𝜅)$. It is shown that the first Dirichlet’s eigenvalue 𝜆 1(𝛺) attains extremum when the axes of symmetry of $\wp 0$ coincide with those of $\wp 1$.

• Asymptotic Behavior of Stochastic Two-Dimensional Navier-Stokes Equations with Delays

The paper proves the 𝐿2-exponential stability of weak solutions of two-dimensional stochastic Navier–Stokes equations in the presence of delays. The results extend some of the existing results.

• On the Limit Distribution of Lower Extreme Generalized Order Statistics

In a wide subclass of generalized order statistics $(gOs)$, which contains most of the known and important models of ordered random variables, weak convergence of lower extremes are developed. A recent result of extreme value theory of $m-gOs$ (as well as the classical extreme value theory of ordinary order statistics) yields three types of limit distributions that are possible in case of linear normalization. In this paper a similar classification of limit distributions holds for extreme $gOs$, where the parameters $𝛾_j,j=1,\ldots,n$, are assumed to be pairwise different. Two illustrative examples are given to demonstrate the practical importance for some of the obtained results.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 127 | Issue 5
November 2017


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# What is the activation energy of a Daniell cell?

I'm having trouble finding a posted literature value for the activation energy for the Daniell cell redox reaction:

$$\ce{Cu^2+ + Zn -> Cu + Zn^2+}$$

Where might I be able to find this information?

• Electron transfer is extremely fast, that finding its rate constant is not a trivial exercise. – M. Farooq Feb 12 at 1:10
• The equation is the summary of 2 processes ongoing on 2 different places, while activation energy applies on a single elementary reaction step. – Poutnik Feb 12 at 4:41
• An activation energy has a sense in a homogeneous mixture. This is not the case in a Daniell cell – Maurice Feb 12 at 8:51
• @Maurice, "An activation energy has a sense in a homogeneous mixture. This is not the case in a Daniell cell" is a misconception. Electrode kinetics is very vast field and people do report activation energy, see e.g., pubs.acs.org/doi/abs/10.1021/jp9721309 – M. Farooq Feb 12 at 13:47


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# Charge Density of Styrofoam

A 8.2 g piece of Styrofoam carries a net charge of -0.700 µC and floats above the center of a large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet?

Ive solved some other related questions with charge densities, but I can't figure out where to start on this one.
None of Gauss's Laws seem to have anything to do with mass and the area is underminable using basic algebra.

8.2g carrying -0.0000007 C
so the charge per unit area will be with units C / m^2

the flux should be equal to the charge divided by Eo

any help about solving this would be appreciated

Gyroscope
brunie, you can apply Gauss's Law to find the electric field created by the large horizontal sheet of plastic, and if this sheet infinite, the electric field calculated is uniform.
You also know that the piece of styrofoam is in equilibrium, so what is the net force on it. I have already talked too much. :)

brunie, you can apply Gauss's Law to find the electric field created by the large horizontal sheet of plastic, and if this sheet infinite, the electric field calculated is uniform.
You also know that the piece of styrofoam is in equilibrium, so what is the net force on it. I have already talked too much. :)

i dont understand how the electric field can be calculated if the area is infinite, also where would the mass be taken into account?

Doc Al
Mentor
There are two things to understand:
(1) The field from a uniform (and infinite) plane of charge (which will be a function of the charge density). You can use Gauss's law to derive it. Hint: Start by drawing a Gaussian box around a section of the plane of charge.
(2) What field strength is required to support the piece of styrofoam? Hint: What force must the field exert on the charge styrofoam?

There are two things to understand:
(1) The field from a uniform (and infinite) plane of charge (which will be a function of the charge density). You can use Gauss's law to derive it. Hint: Start by drawing a Gaussian box around a section of the plane of charge.
(2) What field strength is required to support the piece of styrofoam? Hint: What force must the field exert on the charge styrofoam?

im not very good at deriving the equations, most of the stuff weve been doing on gauss's law has been pretty basic
could u walk me thu a few steps

should the field strength have to balance the gravitational force?

Doc Al
Mentor
im not very good at deriving the equations, most of the stuff weve been doing on gauss's law has been pretty basic
You'll find this pretty basic as well. I'd be surprised if it wasn't in your book. Anyway, see here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html#c1"

should the field strength have to balance the gravitational force?
To be suspended, the net force on the styrofoam must be zero: The upward electric force must balance the downward force of gravity.

Last edited by a moderator:
ok so

mg = ∂ / 2 Eo
(8.2/1000)*9.8 = ∂ / 2 (8.85 x 10^-12)

then do i solve for ∂ ?
y doesnt the given net charge come into account?

can n e 1 help?

Doc Al
Mentor
Careful. The electric field from a sheet of charge is:

$$E = \sigma / 2 \epsilon_0$$

What force does that field exert on the styrofoam? (That's where the charge comes in.)

ok, im just having trouble seeing the big picture
we have a electric field, a electric force and gravitational force

the net force should be zero since it is suspended

but i just dont understnad how to balance or equate these forces/fields

Doc Al
Mentor
First things first. What force does an electric field exert on a charge? (Hint: Look up the definition of electric field.)

ok
so should the expression be F / q = ∂ / 2Eo
where F = mg ?

Doc Al
Mentor
Now you're cooking.

great, thanks 4 ur help


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# Import a given column from an excel file? [closed]

It seems that I can get the first column of excle data, say "test.xls", if I know the total length...

data = Table[{i}, {i, 6}];
Export["test.xls", data];
Import["test.xls", {"Data",1,Range[len],1}]

But the problem is, If I don't know the total length, can I do the same thing? especially consider the data scale is quite large.

## closed as off-topic by Öskå, gpap, m_goldberg, Jens, Oleksandr R.Jan 15 '15 at 11:18

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – Öskå, gpap, m_goldberg, Jens, Oleksandr R.
If this question can be reworded to fit the rules in the help center, please edit the question.

• Can you provide a small example xls to ease answering? – Philipp Jan 13 '15 at 16:03
• @Philipp updated with data filled in test.xls. – van abel Jan 13 '15 at 16:07
• @Öskå the real range is set by Range[len],1 thus this will import first column with row from 1 to the len. Although the results is a row, quite strange. – van abel Jan 13 '15 at 16:26
• Saving as csv is no option? – Philipp Jan 13 '15 at 16:28
• @Öskå Aha, yes, your code work for me and solved my problem. But why my Import["test.xls", {"Data", 1, ;; , 1}] don't work??? – van abel Jan 13 '15 at 16:29

The answer you are looking for is here: Import a Spreadsheet.

Thus you can use:

Import["~/test.xls", {"Data", 1, All, 2}]

The syntax in your case is {"Data", # of sheet(s), # of row(s), # of column(s)}.

Its easy: just look at the structure of your imported data. Since you did not provide a file, we will use example data from Wolfram:

tab = Import["ExampleData/elements.xls"]
{{{"AtomicNumber", "Abbreviation", "Name", "AtomicWeight"}, {1., "H",
"Hydrogen", 1.00793}, {2., "He", "Helium", 4.00259}, {3., "Li",
"Lithium", 6.94141}, {4., "Be", "Beryllium", 9.01218}, {5., "B",
"Boron", 10.8086}, {6., "C", "Carbon", 12.0107}, {7., "N",
"Nitrogen", 14.0067}, {8., "O", "Oxygen", 15.9961}, {9., "F",
"Fluorine", 18.9984}}}'

Now you see, there is a first bracket spreading the tables of the spreadsheet. Here only one. Then rows and then columns. Hence, what you want is the first column of the first table in the spreadsheet:

tab[[1, All, 1]]
{"AtomicNumber", 1., 2., 3., 4., 5., 6., 7., 8., 9.}

to look at the example spreadsheet, you can save it by using:

Export["test.xls", Import["ExampleData/elements.xls"]]

• @Öskå exactly!! – van abel Jan 13 '15 at 16:11
• Can't you just save as csv and then read until you leave the first column? – Philipp Jan 13 '15 at 16:14


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What's the main difference between the Schnorr identification scheme and its Smart-Card implementation?

This question arises because I couldn't find any official paper for the Schnorr identification scheme, but only for the Smart-Card implementation of it. Also, it seems that everyone, when talking about the SIS links the paper for the Smart-Card implementation. So I'm kinda confused, especially 'cause English isn't my native language and I can't figure it out by myself. I don't understand if they are the same thing, or if they differ just for a simple particular reason that didn't need a dedicated paper. If so... what's that difference? Thank you very much!

• I already did actually. I've already found this paper and here they link the Smart-Card implementation. Oct 24 '21 at 20:35
• Could you next time please provide links and textual references to the documentation you are mentioning in the question? Oct 25 '21 at 11:54
• Of course, sorry Oct 25 '21 at 12:50

The standard paper used as reference for the Schnorr identification protocol and associated signature scheme is Claus-Peter Schnorr, Efficient Signature Generation by Smart Cards (alternative version), in Journal of Cryptology, 1991.

Differences between this and the Schnorr identification protocol as in a modern textbook:

• The original exposition uses a Schnorr group of large prime order $$q$$, that is a subgroup of the group $$\mathbb Z_p^*$$ for a huge prime $$p$$ with $$q$$ a divisor of $$p-1$$. It's now customary to reason in an abstract group of order $$q$$, which can be implemented e.g. as an elliptic curve group.

• The group's notation is multiplicative in the original, and is now often additive.

• In the original, the verifier's secret $$e$$ is random in $$[0,2^t)$$ with $$2^t\ll q$$, for efficiency reasons. Many modern expositions make $$e$$ random in $$[0,q)$$ or similarly large interval.

• The original is unclear about if in the identification protocol itself the prover A sends group element $$x$$ (text) or it's hash $$h(x)$$ (figure 1), an optimization reducing communication size. Modern expositions tend to use no hash in the identification protocol.

• The original (in both text and figure 1) makes it part of the identification protocol to verify A's public key $$v$$ and it's association with A's identity $$I$$ using a signature $$S$$:

• in 2.: “…the KAC’s signature $$S$$ for $$(I,v)$$,…”
• in 3.: “B verifies the signature $$S$$…”
• in 5.: “B verifies $$(I,v)$$ either by checking the signature $$S$$ or by verifying $$(I,v)$$ on–line”.

But modern expositions often make that an external preliminary. Some remove $$I$$ and $$S$$, and A supplying it's public key $$v$$ in the first step.

• In some parts of the original article A is a Smart Card, when some other expositions are mum on how computations are made, or assimilate computation means with their owner/operator.

• The original exposition emphasizes that A drawing $$r$$ and computing $$x$$ (in step 2.) can be an offline preliminary.

Using the original notation and steps numbering (contrary to many textbooks), a minimal modern exposition could go

• We work in a suitable public group of prime order $$q$$ and generator $$\alpha$$, noted multiplicatively. The group's $$q$$ elements are thus $$\alpha^b$$ for $$b\in[0,q)$$.
• Prover A wants to demonstrate knowledge of $$s\in[0,q)$$ such that $$v=\alpha^s$$, with public $$v$$ assumed known to verifier B. It uses four exchanges:
1. A draws $$r\in_R[0,q)$$, computes $$x:=\alpha^r$$, sends $$x$$
1. B draws $$e\in_R[0,q)$$, sends $$e$$
1. A computes $$y:=r+s\,e\bmod q$$, sends $$y$$
1. B verifies $$x=\alpha^y\,v^e$$.

Is the Schnorr identification scheme and the Smart Card implementation actually the same identical thing?

No: a scheme is not an implementation, much like an algorithm is not the same as a program using that algorithm written for a particular type of computer. The implementation makes choices like the computing mean being a Smart Card; using a Schnorr group with certain size parameters; further limiting the number of bits in $$e$$ to parameter $$t$$. It sends hash $$h(x)$$ rather than $$x$$ in step 2, with the verification step 5 correspondingly changed to $$h(x)=h(\alpha^y\,v^e)$$. It defines what $$v$$ is in the context, and towards that introduces $$I$$ and $$S$$.

When a modern text refers to the Schnorr identification scheme, it tends to be to the abstract protocol reduced as in the above section, without Smart Card, $$t$$, $$h$$; and often without $$I$$, $$S$$.

In work making use of the Schnorr identification scheme, I'd cite the JoC paper and independently state the protocol I use, so that there's no ambiguity about what I mean with Schnorr identification scheme.

• Thanks for the explanation, but my question was simpler: is the Shnorr identification scheme and the Smart Card implementation actually the same identical thing? That's the part I can't really tell 'cause english isn't my native language... But I did understand the actual protocol without looking at the paper, I just need to figure out if those are two different things and something changes, or there's just "one" schnorr identification scheme and the Smart Card thing is just the context, because I have to cite the paper. Oct 25 '21 at 6:45
• You're putting way too much stock into the paper's title. The linked paper is the journal version of the paper that introduced Schnorr signatures. There's an older conference version as well. One or both is what you would cite. As @fgrieu explained the exact instantiation is likely not what people mean when they refer to Schnorr signatures or the Schnorr identification scheme but it's nevertheless the work that introduced them. The smart card bit was nothing more than an early 90s sales pitch for an efficient signature scheme. Oct 25 '21 at 14:48
• Thank you very much to both of you, now everything's clear! Thanks @fgrieu Oct 25 '21 at 17:55


text:
# SSC CHSL 18 Jan 2017 Morning Shift

Instructions

For the following questions answer them individually

Question 81

A shopkeeper, sold dried apricots at the rate Rs 1,310 a kg and bears a loss of 13%. Now if he decides to sell it at Rs 1,441 per kg, what will be the result?

Question 82

If cos 240° = x, then value of x is

Question 83

3 hrs after a goods train passed a station, another train travelling at a speed of 88 km/hr following that goods train passed through that station. If after passing the station the train overtakes the goods train in 8 hours. What is the speed of the goods train?

Question 84

If a + b = 9 and $$a^{2} + b^{2}$$ = 61, then ab is

Question 85

Reflection of the point (2,5) in the x axis is

Question 86

The price of an article is discounted by 25%, to restore to its original value, the new price must be increased by

Question 87

If 1/√(1+$$tan^{2}$$A) = x, then value of x is

Question 88

20% discount is offered on an item. By applying a promo code the customer wins 5% cash back. What is the effective discount?

Question 89

A wooden bowl is in shape of a hollow hemisphere of internal radius 8 cm and thickness 1 cm. Find the total surface area of the bowl?

Question 90

If 6A = 7B = 5C; find A : B : C

OR


text:
2 Parallel Wires
MMMMMMMMMM

Parallel Wires

This page is for transmission lines which consist of two cylindrical conductors, which run parallel to each other. In the most general case, the conductors may be different diameter, and have a hollow core, as shown below.

It is common for the conductors to be the same diameter, and to be solid rather than hollow - for example, they may be two conventional round wires.

A hollow core example is given because at high frequencies, even conductors which are solid metal, can appear to have an insulating core, due to the skin effect.

Capacitance
Different Diameter, Any Separation

Consider the case where two cylindrical, parallel, conductors form a transmission line

Using electromagnetic field theory, one can calculate the capacitance of two parallel wires. The details will be omitted here, but are available many places for those interested $C' = \frac{{{\varepsilon _r}{\varepsilon _0}2\pi }}{{{{\cosh }^{ - 1}}\left( {\frac{{4{s^2} - d_1^2 - d_2^2}}{{2{d_1}{d_2}}}} \right)}}$ Where

• $$C'$$ is the capacitance per unit length of the wire pair, usually measured in farads per meter
• $${\varepsilon _0}$$ is the electric constant (also known as the permittivity of free space), which is approximately 8.85 × 10-12 farads per meter. Note that the units on this parameter will match the units on $$C'$$.
• $${\varepsilon _r}$$ is the relative permittivity of the space surrounding the wires, unitless. This was at one time called the dielectric constant, but that term is now depreciated.
• $$D$$ length of each wire, usually measured in meters, so it is compatible with the units of the electric constant.
• $$s$$ distance from center of one conductor, to center of the other. It can be measured in any units of length, provided the same unit is used for the $${d_1}$$ and $${d_2}$$ distances.
• $${d_1}$$ outer diameter of one conductor. It can be measured in any units of length, provided the same unit is used for the $$s$$ and $${d_2}$$ distances.
• $${d_2}$$ outer diameter of the other conductor. It can be measured in any units of length, provided the same unit is used for the $$s$$ and $${d_1}$$ distances.
• $$C$$ is the total capacitance of the transmission line,and is given by $$C=C'D$$, where $$D$$ is the length of the transmission line. Notice that current will flow through both conductors, traveling a total distance of $$2D$$. When measuring $$D$$, it is best to use meters, so it is compatible with the denominator of the units of the electric constant.

Notice the thickness of the conductors is not labeled in the figure above, and is not used in the calculations of capacitance. While the thickness is important for resistance measurements, it makes no difference capacitance. A pair of very thin cylinders will have the same capacitance as a pair of solid conductors of the same external diameter.

Same Diameter, Any Separation

Many transmission lines use the same gauge, or diameter, wire in both conductors.

This simplifies the expression of capacitance to $\begin{array}{c} {d_1} = {d_2} = d\\ C' = \frac{{{\varepsilon _r}{\varepsilon _0}\pi }}{{{{\cosh }^{ - 1}}\left( {\frac{s}{d}} \right)}} \end{array}$ Where

• $${d}$$ outer diameter of either conductor. It can be measured in any units of length, provided the same unit is used for $$s$$.
• All other terms are described in the previous section, above.

Same Diameter, Wide Separation

In some applications, the separation of the wires is far greater than the diameter of either one.

In this case, the hyperbolic function in the capacitance expression can be avoided, by using a large angle approximation, and obtaining $\begin{array}{c} {d_1} = {d_2} = d\\ d \ll s\\ C' \cong \frac{{{\varepsilon _r}{\varepsilon _0}\pi }}{{\ln \left( {\frac{{2s}}{d}} \right)}} \end{array}$ Where

• $$s$$ distance from one conductor, to the other. $$s$$ must be much larger than $$d$$, so it does not make much difference if one measures from center-to-center or edge-to-edge of the conductors.
• $$d$$ outer diameter of either conductor. It can be measured in any units of length, provided the same unit is used for $$s$$.
• All other terms are described in the previous section, above.
The error in the above approximation is about 5% for $$s=2d$$, and is under 1% when $$s=4d$$.

If the wires are different diameters, then replace $$d$$ in the expression above, with the geometric mean of the two diameters. But if you need to go to that much work, you may just want to return to the expression for conductors of different diameters, and any separation.

Volume That Influences Capacitance

The capacitance of two parallel conductors is affected by the relative permittivity, $${\varepsilon _r}$$, of the region which is external to both conductors.

We do not typically speak of the relative permittivity of the conductors themselves, or else call the permittivity of conductors infinity. Either way, it does not impact the capacitance of the transmission line.

If the conductors are hollow (have a center region which acts like an insulator), then the permittivity of the core has no impact on the capacitance calculations.

Inductance

If the wires are connected to circuits at either end that allow current to pass around the loop they form, then the wires will have an inductance. We normally think of inductors as being loops of wire wound close together, often around some magnetic material such as iron. However any loop of wire will have inductance.

Using electromagnetic field theory, one can calculate the inductance of this loop, $$L$$, or the inductance per unit length, $$L'$$. The details will be omitted here, but are available many places. $L' = \frac{{{\mu _r}{\mu _0}}}{{2\pi }}{\cosh ^{ - 1}}\left( {\frac{{4{s^2} - d_1^2 - d_2^2}}{{2{d_1}{d_2}}}} \right)$ Where

• $$L'$$ is the inductance per unit length of the wire pair, usually measured in henries per meter
• $${\mu _0}$$ is the magnetic constant (also known as the permeability of free space), which is approximately $$4\pi × 10-7 henries per meter. Note that the units on this parameter will match the units on \(C'$$.
• $${\mu _r}$$ is the relative permeability of the space surrounding the wires, unitless.
• $$s$$ distance from center of one conductor, to center of the other. It can be measured in any units of length, provided the same unit is used for the $${d_1}$$ and $${d_2}$$ distances.
• $${d_1}$$ outer diameter of one conductor. It can be measured in any units of length, provided the same unit is used for the $$s$$ and $${d_2}$$ distances.
• $${d_2}$$ outer diameter of the other conductor. It can be measured in any units of length, provided the same unit is used for the $$s$$ and $${d_1}$$ distances.
• $$L$$ is the total capacitance of the transmission line,and is given by $$L=L'D$$, where $$D$$ is the length of the transmission line. When measuring $$D$$, it is best to use meters, so it is compatible with the denominator of the units of the magnetic constant.

Many cables use the same gauge (diameter) wire in both conductors. This simplifies the inductance equation to $\begin{array}{c} {d_1} = {d_2} = d\\ L' = \frac{{{\mu _r}{\mu _0}}}{\pi }{\cosh ^{ - 1}}\left( {\frac{s}{d}} \right) \end{array}$ If the wires are the same gauge, and the separation is much greater than the diameter, then the hyperbolic function can be avoided with the approximation $\begin{array}{c} {d_1} = {d_2} = d\\ s \gg d\\ L' \cong \frac{{{\mu _r}{\mu _0}}}{\pi }\ln \left( {\frac{{2s}}{d}} \right) \end{array}$ The error in the above approximation is about 5% for s=2d, and is under 1% when s=4d. If the wires are different diameters, and the spacing is large compared to both diameters, then the $$d$$ term in the equation above should be replaced with the geometric mean of the wire diameters. It may be just as easy to return to the formula above for wires of any diameter and any separation.

Volume that Affects Inductance

The relative permeability, $${\mu _r}$$, in all regions in the vicinity of two parallel conductors affect the inductance calculations. This includes the value of $${\mu _r}$$ of the conductors themselves, $${\mu _r}$$ outside the conductors, and if they are hollow, the value of $${\mu _r}$$ in the interior of the conductors.

Many electrical insulators have a $${\mu _r}$$ very close to one. This includes a vacuum, nearly all gasses, glass and many ceramic materials, and many electrical insulators made from petrochemical products. If the conductors are hollow, then the calculations on this page assumed the interior of the conductors was an insulator with a $${\mu _r}$$ of one. Note that some conductors use a steel core, which has a $${\mu _r}$$ significantly greater than one. The calculations on this page do not address this kind of conductor.

Electrical conductors carrying alternating current can see a substantial increase in their resistance due to the skin effect. This can be minimized by selecting conductors which have a $${\mu _r}$$ of one. Many commonly used conductors, including aluminium and copper have $${\mu _r}$$ of one, as does material such as gold and water. Iron based alloys, such as steel are a notable exception, with $${\mu _r}$$ which can reach into the thousands and above. The calculations on this page assume the conductor has a $${\mu _r}$$ of one.

The $${\mu _r}$$ in all areas surrounding the conductors impact their inductance. The calculations above assume the $${\mu _r}$$ was uniform in all regions near the conductors.

Many tools, machines, office furniture, enclosures, and buildings are fabricated using iron based alloys, such as steel. Notice that inductance of a parallel set of conductors will be strongly influenced by passing near these objects.


text:
# [texworks] Problem with line mangling

Stefan Löffler st.loeffler at gmail.com
Thu Jul 7 10:12:13 CEST 2011

Hi,

On 2011-07-07 08:30, Paul A Norman wrote:
>> in particular for
>> long (1000+ lines) documents
> I had it happening to me while recently testing for it, in a second
> re-opened document (a letter) where \end{document} is at only line 192

Are you talking about 0.4.3 (or a later version), or about the recent
attempt in r862, or something else?
TL'11 contains AFAIK 0.4.4, in which this should be partly resolved. At
least the latest reports (yours and Alain's) I got all included line
numbers close to or about 1000. If there were other cases in recent
versions of Tw that weren't reported (or that I forgot) of course it's
not problem to remove the "long (1000+ lines)" part... it would be a bit
disturbing for me, though, as it doesn't fit my current hypothesis ;).

> I'll look at cleaning up and posting my (auto)back-up scripts, can be
> run manually or on hooks, and allows for remembered' custom
> directories for backup location.

for the software to say 'hey, we ship with a backup script, because we
know our program crashes or causes problems' ;).

> I am also wondering if this could have happened to me in the past when
> line numbers were turned off, as I have found areas later on a reopen,
> where I have re-typed almost identical text on a previous edit, in the
> same general location areas as the original text, which I might have
> previously been putting down to bad work habits due to late night
> work—now I am not so sure it was the late nights.

I can't say, of course. My current hypothesis is that the problem
appears when Qt is trying to put text into a window that has not been
shown. Maybe it is even some kind of race condition that occurs only
when the window is shown while the text is not yet fully ready. But I
haven't been able to make heads or tails of the Qt internals yet.
Anyway, this is consistent with my tests (opening a file from the file
manager vs. opening it into an empty, unmodified document (in which case
the empty window is reused and thus shown already)). Plus, the race
condition would explain why this is fickle (different computer work
loads cause different processing times), and why it happens
predominantly in long documents (if that's the case).

>> TeXworks crashes
> I haven't had an actual crash from this for a long time (months).

It seems to crash only if you move the cursor into and out of such a
hidden line with the arrow keys. From the looks of the debugging
backtrace I did a while ago, some pointers of the line are not
initialized correctly (they are NULL), and those are probably accessed
without proper safe-guarding, resulting in the crash. But as long as you
don't touch those lines, no crash happens.

HTH
Stefan
`


text:
# 6.8. Cumulative Distributions¶

Figure 6.4: CDF of degree in the Facebook dataset along with the WS model (left) and the BA model (right), on a log-x scale.

Figure 6.4 represents the degree distribution by plotting the probability mass function (PMF) on a log-log scale. That’s how Barabási and Albert present their results and it is the representation used most often in articles about power law distributions. But it is not the best way to look at data like this.

A better alternative is a cumulative distribution function (CDF), which maps from a value, x, to the fraction of values less than or equal to x.

Given a Pmf, the simplest way to compute a cumulative probability is to add up the probabilities for values up to and including x:

def cumulative_prob(pmf, x):
ps = [pmf[value] for value in pmf if value<=x]
return np.sum(ps)

For example, given the degree distribution in the dataset, pmf_fb, we can compute the fraction of users with 25 or fewer friends:

>>> cumulative_prob(pmf_fb, 25)
0.506

The result is close to 0.5, which means that the median number of friends is about 25.

CDFs are better for visualization because they are less noisy than PMFs. Once you get used to interpreting CDFs, they provide a clearer picture of the shape of a distribution than PMFs.

The thinkstats module provides a class called Cdf that represents a cumulative distribution function. We can use it to compute the CDF of degree in the dataset.

from thinkstats2 import Cdf

And thinkplot provides a function called Cdf that plots cumulative distribution functions.

thinkplot.Cdf(cdf_fb)

Figure 6.4 shows the degree CDF for the Facebook dataset along with the WS model (left) and the BA model (right). The x-axis is on a log scale.

Figure 6.5: Complementary CDF of degree in the Facebook dataset along with the WS model (left) and the BA model (right), on a log-log scale.

Clearly the CDF for the WS model is very different from the CDF from the data. The BA model is better, but still not very good, especially for small values.

In the tail of the distribution (values greater than 100) it looks like the BA model matches the dataset well enough, but it is hard to see. We can get a clearer view with one other view of the data: plotting the complementary CDF on a log-log scale.

The complementary CDF (CCDF) is defined

$CCDF(x) ≡ 1 − CDF(x)$

This definition is useful because if the PMF follows a power law, the CCDF also follows a power law:

$CCDF(x) ∼ (x/x_m)^-\ ^α$

where $$x_m$$ is the minimum possible value and $$α$$ is a parameter that determines the shape of the distribution.

Taking the log of both sides yields:

$logCCDF(x) ∼ −α (logx − logx_m)$

So if the distribution obeys a power law, we expect the CCDF on a log-log scale to be a straight line with slope −α.

Figure 6.5 shows the CCDF of degree for the Facebook data, along with the WS model (left) and the BA model (right), on a log-log scale.

With this way of looking at the data, we can see that the BA model matches the tail of the distribution (values above 20) reasonably well. The WS model does not.


text:
[latexpage]

I had the interesting realization recently while tutoring one of my students. As he worked on his solution for solving a system of equations, I suggested that his work would be much more clear if he outlined what he was doing and showed steps to his process instead of simply writing a bunch of equations and having the answer pop out at the end.

He bemoaned having to be so complete with the work, not seeing the point of having to add these small elements to his solution, but I held my viewpoint. I knew it was important for him to write the entire solution in a clear manner, but he didn’t seem to care about achieving this level of perfection. He thought the elements I suggested were more or less superfluous, since the core of his solution was correct.

So what was my realization?

It was that, ironically, I do the same thing as he does in my own mathematics classes.

## The quest for one hundred

As I’ve mentioned a few times in my writing, I’ve had the same professor for all of my mathematics courses in CÉGEP. During this time, I had a bit of a personal goal: get a perfect score on one of my tests.

Unfortunately, I never met this goal, though I did get close. My best mark was 69.5/70, which is over 99%. Other than that, my tests usually hovered around the lower nineties.

What becomes clear though as you look at my exams is that, apart from silly errors, most of my work is correct, but is lacking a small clarification or a point of completion. As you can probably see (and like I said, I only just made the connection), my situation is remarkably close to that of my student who I tutor.

Every time I saw this kind of error on my exam, I’d shake my head, not really even knowing how I could have been expected to write that anyway. I took solace in the fact that almost no one in my classes ever included the little things, and so I was just like the rest of the class.

In regards to my own performance, I didn’t fully appreciate what these little clarifications for completeness would do to my solution. Instead, I told myself to be happy that I got the core part of the problem and just forgot a little thing of almost no consequence. This is obviously the wrong view to take, but I didn’t make the connection.

The reality is that mathematics is a sort of logic. Therefore, all parts of a solution to a problem are important if the final answer is to be believed. Whether or not the final answer works is entirely dependent on the small and big details of the solution. Omitting a detail means the foundation isn’t rock solid. Sure, it might happen to be the correct answer now, but it is only in spite of the lack of detail, not because of it.

For example, I lost points on one of my tests because I failed to identify the curve I was using as a cylinder. I was dealing with the classic $x^2+y^2=1$ representation of the cylinder, but I failed to mention that the previous equation was for all z values. I thought this was an implicit assumption from the equation, but it’s actually important to explicitly declare it. This is because the equation I wrote is actually a circle in two dimensions, yet is a sphere or solid in three dimensions.

Therefore, what I thought was a harmless extra point of completeness was actually very relevant to the solution. It was the difference between a circle and a cylinder. Consequently, I now fully understand why my professor took away points in the question. Of course she knew I was talking about a cylinder, but the equation I wrote was really that of a circle, so further clarification was needed,

What I’ve learned from this is that there is no small detail that you should leave out from a mathematics problem. Simply put, it’s much more advantageous to be explicit about the work you’re doing than to make a bunch of implicit assumptions and hope everyone gets it. You will rarely lose points for being complete, but you definitely will on the other side.

I’ve found that this occurs for me just as it does others. Even with over a decade of doing mathematics in class, I struggle to be perfectly complete. However, it does give me a bit of inspiration to include all the important points of a solution as they come up.

Remember: the little frustrations are annoying, yet they will instruct one to be more complete in their mathematical pursuits.


text:
## Homework Problem B.5

$E=hv$

Savannah Mance 4G
Posts: 107
Joined: Fri Aug 30, 2019 12:17 am

### Homework Problem B.5

In this problem, the given information is that a y-ray has energy of 140.11 keV and I'm supposed to find the wavelength. I know I'm supposed to use Einstein's equation. But, what is keV? What is this unit? I've never seen it before so I have no idea how to convert it or if I even have to.

christabellej 1F
Posts: 109
Joined: Sat Aug 17, 2019 12:17 am

### Re: Homework Problem B.5

KeV is a unit of energy. It is equivalent to 1000 eV because of the prefix kilo. From there, you can convert this unit to another energy unit - Joules by using the constants and equations sheet. 1 eV is equivalent to 1.6022*10^-19 J, so you can then use stoichiometry to convert KeV to Joules. After that, you can use the 2 equations we learned: E = hv and c = (wavelength) (frequency) to find the overall wavelength.

Kayli Choy 2F
Posts: 100
Joined: Sat Aug 24, 2019 12:17 am

### Re: Homework Problem B.5

An electron-volt (eV) is a unit of energy that is equal to the energy an electron gains after being accelerated across 1 volt. This unit is typically used when discussing energy on an atomic/sub-atomic level (very small amounts of energy).


text:
$$\require{cancel}$$

# 1.P Exercises

1. According to classical physics, a non-relativistic electron whose instantaneous acceleration is of magnitude radiates electromagnetic energy at the rate

where is the magnitude of the electron charge, the permittivity of the vacuum, and the electron mass. Consider a classical electron in a circular orbit of radius around a proton. Demonstrate that the radiated energy would cause the orbital radius to decrease in time according to

where is the Bohr radius, the reduced Planck constant, and

Here, is the velocity of light in a vacuum, and the fine structure constant. Deduce that the classical lifetime of a hydrogen atom is .

2. Demonstrate that

in a finite dimensional ket space.

3. Demonstrate that in a finite dimensional ket space: Here, , are general operators.

1.

2.

3.

4.

4. If , are Hermitian operators then demonstrate that is only Hermitian provided and commute. In addition, show that is Hermitian, where is a positive integer.

5. Let be a general operator. Show that , , and are Hermitian operators.

6. Let be an Hermitian operator. Demonstrate that the Hermitian conjugate of the operator is .

7. Let the be the eigenkets of an observable , whose corresponding eigenvalues, , are discrete. Demonstrate that

where the sum is over all eigenvalues, and denotes the unity operator.

8. Let the , where , and , be a set of degenerate eigenkets of some observable . Suppose that the are not mutually orthogonal. Demonstrate that a set of mutually orthogonal (but unnormalized) degenerate eigenkets, , for , can be constructed as follows:

This process is known as Gram-Schmidt orthogonalization.

9. Demonstrate that the expectation value of a Hermitian operator is a real number. Show that the expectation value of an anti-hermitian operator is an imaginary number.

10. Let be an Hermitian operator. Demonstrate that .

11. Consider an Hermitian operator, , that has the property that , where is the unity operator. What are the eigenvalues of ? What are the eigenvalues if is not restricted to being Hermitian?

12. Let be an observable whose eigenvalues, , lie in a continuous range. Let the , where

be the corresponding eigenkets. Demonstrate that

where the integral is over the whole range of eigenvalues, and denotes the unity operator.


text:
# Calculating Real Budget Deficit, given Nominal Deficit and Inflation

I am doing this course on Coursera. In the context of explaining what Budget Deficits are, the professor puts up the following formula:

Real Deficit = Nominal Deficit - (Inflation*Total Debt)

My confusion is, where is the Total Debt coming from? Shouldn't Real Deficit be just a function of Nominal Deficit and Inflation? i.e.,

Real Deficit = Nominal Deficit - (Inflation*Real Deficit)

My understanding is that Total Debt is just the accumulated debt over the years (including the current year's budget deficit incurred so far). Is that understanding wrong?

The professor goes on to give a numerical example to explain the concept of inflating the debt. That's when the effective burden of debt falls due to inflation.

If Nominal Deficit = \$100 billion, inflation =10% and Total Debt =$5 trillion, then

Real Deficit = 100 - (0.10*5000) = -\$800 billion.

I don't get it.

Edit: This is the direct link to the 6 minute lecture where he talks about it.

Basically the argument is that if in year $$t$$ deficit was 100mil but the same year the total debt 5billion and inflation was 10% that means that in real terms the value of debt is 500mill less and the teacher of that course treats this as 500mill revenue so under that definition even though you had 100mill deficit you would end up with 400mill surplus because thanks to inflation the net real debt decreased.


text:
CryptoDB

Paper: Unifying Leakage Models on a Rényi Day

Authors: Thomas Prest Dahmun Goudarzi Ange Martinelli Alain Passelègue DOI: 10.1007/978-3-030-26948-7_24 Search ePrint Search Google In the last decade, several works have focused on finding the best way to model the leakage in order to obtain provably secure implementations. One of the most realistic models is the noisy leakage model, introduced in [PR13, DDF14] together with secure constructions. These works suffer from various limitations, in particular the use of ideal leak-free gates in [PR13] and an important loss (in the size of the field) in the reduction in [DDF14].In this work, we provide new strategies to prove the security of masked implementations and start by unifying the different noisiness metrics used in prior works by relating all of them to a standard notion in information theory: the pointwise mutual information. Based on this new interpretation, we define two new natural metrics and analyze the security of known compilers with respect to these metrics. In particular, we prove (1) a tighter bound for reducing the noisy leakage models to the probing model using our first new metric, (2) better bounds for amplification-based security proofs using the second metric.To support that the improvements we obtain are not only a consequence of the use of alternative metrics, we show that for concrete representation of leakage (e.g., “Hamming weight + Gaussian noise”), our approach significantly improves the parameters compared to prior works. Finally, using the Rényi divergence, we quantify concretely the advantage of an adversary in attacking a block cipher depending on the number of leakage acquisitions available to it.
BibTeX
@article{crypto-2019-29877,
title={Unifying Leakage Models on a Rényi Day},
booktitle={Advances in Cryptology – CRYPTO 2019},
series={Lecture Notes in Computer Science},
publisher={Springer},
volume={11692},
pages={683-712},
doi={10.1007/978-3-030-26948-7_24},
author={Thomas Prest and Dahmun Goudarzi and Ange Martinelli and Alain Passelègue},
year=2019
}


text: D. 27%. % C = 12.01/44.01 =0.2729= 27.29% (we will divide0.2729 with 100 to take the percentage. if 5.76 grams of co2 forms when 4.00 grams of c2h6 reacts, what is the percent yield for 2c2h6+7o2=4co2+6h2o . As a can is around 12 fluid ounces, or 355 ml, the amount of $\ce{CO2}$ in a can is: $$\text{2.2 g} \ \ce{CO2}* \frac{\text{1 mol} \ \ce{CO2}}{\text{44 g} \ \ce{CO2} } = 0.05 \ \text{mol}$$ In March 2011, carbon dioxide levels were at 391 ppm, which is 0.0391 percent of the atmosphere. Plants and other photoautotrophs use solar energy to produce carbohydrate from atmospheric … They tell us that levels of carbon dioxide (CO 2) in the atmosphere are higher than they have been at any time in the past 400,000 years. chemistry _H3PO4+_KOH->_K3PO4+_H2O if 49.0 g of H3PO4 is reacted with excess KOH, determind the percent yield of K3PO4 if you produce 49.0 g of K3PO4. Chemistry. The graphs show monthly mean carbon dioxide measured at Mauna Loa Observatory, Hawaii. QuestionThe Occupational Safety and Health Administration has set the limit on the maximum percentage of carbon dioxide (CO2… So , % C in CO2 … Question: What Is The Percent By Mass Of Sodium Bicarbonate Percent In The Mixture Based On :2NaHCO3 ----> Na2CO3 + CO2 + H2O When We Heat The Mixture Carbon Dioxide And Water Are Lost.So Mass Of CO2 + H2O Lost = 5.128 - 4.256= 0.872 GMolar Mass Of NaHCO3 Is = 84 G /molMolar Mass Of CO2 = 44 G / … (calculate the… It is calculated as the mass of the component divided by the total mass of the mixture and then multiplied by 100 to get the percent. I am often asked how carbon dioxide can have an important effect on global climate when its concentration is so small – just 0.041 percent … O2 = 31.99886 g/mol (31.99886 g/mol) / (44.00964 g/mol) = 0.7270875 = 72.70875% O by mass Relevance. Two … The carbon dioxide data on Mauna Loa constitute the longest record of direct measurements of CO 2 in the atmosphere. 8. 1 2 g r a m s of Carbon are present in 4 4 g r a m s of Carbon Dioxide. A nucleus spontaneously splits and absorbs energy. The CO2 that nature emits (from the ocean and vegetation) is balanced by natural absorptions (again by the ocean and vegetation). What Is Mass Percent? The global average atmospheric carbon dioxide in 2019 was 409.8 parts per million (ppm for short), with a range of uncertainty of plus or minus 0.1 ppm. 1 Answers. CO2 in the air reacts with seawater and forms carbonic acid that acidifies the ocean. Asked By adminstaff @ 19/10/2019 01:11 PM. C. 33%. ; CO2 Broadcasts Resource hub for broadcasters, publishers, bloggers and others who are share the CO2 … 50%. B. Carbon dioxide (chemical formula CO 2) is a colorless gas with a density about 53% higher than that of dry air. The mass of the elements that are not oxygen equals 194.8g. • The US has had declining CO2 for two years running, the last time the US had declining CO2 for 3 years running was in the 1980s • The UK is down one place to tenth on the list, 8% on the year. If 4.1 kg of CO2 are produced during a combustion reaction, how many molecules of CO2 would be produced? Percent Composition Calculation What is the C in CO2 Determine the molar mass from CHE 1110 at St. John's University CS2+O2-->CO2 +SO2 a) What is the percent yield? Solution for What is the percent yield of CO2 if the reaction of 10.0 grams of CO with excess O2 produces 12.8 grams of CO2? Solution for 30) What is the percent yield of CO2 if the reaction of 10.0 grams of CO with excess O2 produces 12.8 grams (actual yield) of CO2? Percent Composition Of Compounds. Mass percent is a method of expressing the concentration of a substance in a mixture or element in a compound. 4. Carbon dioxide (CO 2) is an important trace gas in Earth's atmosphere.It is an integral part of the carbon cycle, a biogeochemical cycle in which carbon is exchanged between the Earth's oceans, soil, rocks and the biosphere. 75%. A. About 99 percent of the atmosphere is made of oxygen and nitrogen, which cannot absorb the infrared radiation the Earth emits. (atomic mass of C = 12, O = 16) A. What is the percent by mass of oxygen in a gaseous mixture whose molar composition is 0.500% CO2 and 99.500% air? Related Questions in Chemistry. What is the mass of one mole of the compound? So, we will multiply 2 with 16.00 which is the weight of the oxygen. Problem: The solubility of CO2 in water at 25 °C and 1 atm is 0.034 mol/L. The composition of air is 21% mole O2 70% mole N2 and has an average molar mass of 29.0 g/mol. Mass percentage of Oxygen is 72.7% Mass percentage of Carbon is 27.3% Let us consider we begin with one mole of Carbon dioxide molecules. Carbon dioxide levels today are higher than at any point in at least the past 800,000 years. Mass percent of oxygen = 35.2g O/230g x 100 = 15% O 2 CO (g) + O2 (g) ---> 2 CO2 (g) a.… This is the total weight of CO2. This roughly corresponds to a mass of 3 trillion tons. One mole of Carbon Dioxide has one mole of carbon atoms in all and 2 moles of Oxygen atoms as the ratio of Carbon to Oxygen in carbon Dioxide is 1:2. what is the mass percentage of carbon in CO2? 81% (238 ratings) Problem Details. Learn More About Atmospheric CO2 Readings & Stabilization. As acidification increases, pH falls. Of the remaining 1 percent, the main molecules that can absorb infrared radiation are CO2 and water vapor, because their atoms are able to vibrate in just the right way to absorb the … Favorite Answer. In fact, human emit 26 gigatonnes of CO2 per year while CO2 in the atmosphere is rising by only 15 gigatonnes per year - much of human CO2 … The percent by mass of oxygen is the same for any sample of CO2, regardless of the sample's mass: CO2 = 44.00964 g/mol. ; CO2 Q&As Questions and answers on all thing CO2: From measurements and tracking to targets and solutions. What is the mass percent of water in IrBr3-4 H2O? After nitrogen, oxygen, water vapor and argon, carbon dioxide is the fifth most abundant gas in the atmosphere. (atomic mass of C = 12, O = 16)? Submit your answer. What is its solubility under atmospheric conditions where the partial pressure of CO2 is 0.003 atm? The post What is the percent by mass of oxygen in a gaseous mixture whose molar composition is 0.500% CO2 and 99.500% air? When correctly balanced, the coefficient for water is 16. Do you know the better answer! The mass of oxygen is 230g - 194.8g = 35.2g of oxygen. LOGIN TO VIEW ANSWER. what is the mass percentage of carbon in CO2? ››More information on molar mass and molecular weight. Chemistry C3Hg + 02 → CO2 + H2O This chemical equation represents the combustion of propane. This is the total weight of CO2. 2 Answers. Molecular weight of C O 2 is 4 4 g r a m s that is [1 2 + (2 × 1 6)]. What is the percent of O in Cr2O3? oxygen has a mass number of 16, as it as 8 protons, 8 neutrons. hydrogen has a mass number of 1, there are 2 hydrogens in water so 1+1=2. One mole of … The masses of the elements in one mole of the compound are: mass N = 28.0 g mass H = 4.0 g mass O = 48.0 g The molar mass of the compound is 80.0 g/mol. Calculate the empirical … % C = 12.01/44.01 = 0.2729= 27.29% (we will divide 0.2729 with 100 to take the percentage). Since pre-industrial times, the average pH of ocean surface water fell from 8.21 to 8.10. Chemistry. FLY6789. Because the mass of CO2 is … Therefore human emissions upset the natural balance, rising CO2 to levels not seen in at least 800,000 years. appeared first on Nursing Research Essays. Which best describes nuclear fission? As a logarithmic scale, this change equates to a 30 percent increase in acidity. In chemistry, the formula weight is a quantity computed by multiplying the atomic weight (in atomic mass units) of each element in a chemical formula by the number of atoms of that element present in the formula, then adding all of these products together. To calculate percent … General estimates have placed a can of Coca-Cola to have 2.2 grams of $\ce{CO2}$ in a single can. Now, to know the percent composition of Carbon and Oxygen .We will divide their weight with the total weight of CO2. 1 Answer SCooke Apr 15, 2018 Yield = #1.06%# Excess #O_2 = 17.6g# Explanation: First, we calculate the theoretical yield from the balanced equation. Reader question: I heard that carbon dioxide makes up 0.04 percent of the world's atmosphere.Not 0.4 percent or 4 percent, but 0.04 percent! Find the mass percents for the elements present in H mass of H = 2 mol H x 1.008g/mol = 2.016 g mass of S = 1 mol S x 32.00g /mol = 32.00 g mass of O = 4 mol O x 16.00g/mol = 64.00 g Calculate the mass % of the elements present in glucose, C When chemists have an unknown … I think it would be 27%. 2. Now, to know the percent composition of Carbon and Oxygen .We will divide their weight with the total weight of CO2. They were started by C. David Keeling of the Scripps Institution of Oceanography in March of 1958 at a … Carbon dioxide molecules consist of a carbon atom covalently double bonded to two oxygen atoms. Thus, percentage by weight of Carbon in C O 2 is 4 4 1 2 × 1 0 0 , which is almost equal to 2 7 % How can it be so important in global warming if it's such a small percentage? B. so 16(oxygen mass number)+2 (hydrogen mass number)=18 this is … 1 decade ago. The last step is to calculate the percent by mass of each element in ammonium nitrate (NH4NO3). Ancient air bubbles trapped in ice enable us to step back in time and see what Earth's atmosphere, and climate, were like in the distant past. CO2 Records Track the all-tim e highs reached by atmospheric CO2 and compare them with the latest CO2 levels. FREE Expert Solution Show answer. It occurs naturally in Earth's atmosphere as a trace gas.The current concentration is about 0.04% (412 ppm) by … b) Calculate the mass in grams of the excess reactant. Answer Save. The composition of air is 21% mole O2 70% mole N2 and has an average molar mass of 29.0 g/mol. A compound was analyzed and found to contain the following percent composition: 2.056% hydrogen, 32.69% S, and 65.26% oxygen. 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# Circular shift and reflection

I know that in a circulant matrix(C) all other rows are (right) shifted versions of first row. Let $x = [c_{0},c_{N-1},c_{N-2},...,c_{1}]$ be the first row. Then $x(n-j) = [c_{j},c_{j-1},c_{j-1},...,c_{j+1}]$ will be the $j^{th}$ row, where $j = 0,1,...,N-1$. The reflection of x(n) = $\hat{x}(n) = x(-n) = x(N-n)$. How can I find the expression for $i^{th}$ column of C in terms of reflection and delay operators on $x$. I am trying to prove circulant matrices are commutative. Is there any other way to prove this.

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How is a "delay operator" defined? –  Guess who it is. May 12 '11 at 15:44
@JM,delay operator is $x(n-j)$.Shifting each component of x by j units to the right. –  Vinod May 12 '11 at 15:47

I think you'll find it's easier to express these things using modular arithmetic. For two circulant matrices $A$ and $B$ with entries $a_{ij}$ and $b_{ij}$, respectively, you can write $a_{ij}=\alpha_{i-j}$ and $b_{ij}=\beta_{i-j}$, where the indices on $\alpha$ and $\beta$ are understood mod $N$. Then the two products are

$$\begin{eqnarray} (AB)_{ik} &=& \sum_ja_{ij}b_{jk}\\ &=& \sum_j\alpha_{i-j}\beta_{j-k} \end{eqnarray}$$

and

$$\begin{eqnarray} (BA)_{ik} &=& \sum_jb_{ij}a_{jk}\\ &=& \sum_j\beta_{i-j}\alpha_{j-k} \;. \end{eqnarray}$$

Now you can rename the summation index in one of the products as $j=i+k-j'\pmod{N}$ to see that the two are the same.

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A circulant matrix is determined by its first row. Take the usual basis for the space of row vectors, and extend each row vector to a circulant matrix. You get a basis for the space of circulant matrices.

Each of these basis matrices is a power of the circulant matrix whose first row is $[0\ 1\ 0\ \dots\ 0]$, so these basis matrices commute with one another. So linear combinations of them also commute; that is, any two circulant matrices commute.

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In "the usual basis for the space of row matrices", I think you mean "row vectors"? –  joriki May 12 '11 at 16:08
Thanks! Fixed now. –  mac May 12 '11 at 16:11