text:
### calculation of impact force

##### How Do You Estimate Impact Force? | WIRED

When calculating the work done by some force, Δr is the distance over which that force is applied and θ is the angle between the force and the displacement.

##### FALLING OBJECTS CALCULATIONS a - HazardControl.com

occur due to direct impact forces, or due to transferred energy to underlying structures when such impact force is transferred to other elements of the body, such as muscles, ligaments, bones, and joints. The time available for the absorption of impact forces …

##### Impulse of Force - HyperPhysics Concepts

Minimizing Impact Force. The process of minimizing an impact force can be approached from the definition of the impulse of force: . If an impact stops a moving object, then the change in momentum is a fixed quantity, and extending the time of the collision will decrease the time average of the impact force by the same factor. This principle is applied in many common-sense situations:

##### Force of Impact Equation Derivation - YouTube

Aug 25, 2016· Rearranging Newton’s Second Law to derive the force of impact equation. Want lecture notes? http://www.flippingphysics.com/impact-force.html This is an AP Ph...

##### How can i calculate impact force? - Quora

Your question doesn't mention a few important things we need to know, so let's assume: It falls vertically 3 metres then hits the screen (Note the spelling of metre (the distance) as this is not a meter that measures like a force meter,) It reboun...

##### How to Calculate Pendulum Force | Sciencing

How to Calculate Pendulum Force. When a pendulum moves away from its resting position, gravity forces it to swing back. This force is a function of the earth's constant acceleration due to gravity, the pendulum bob's mass and the angle between the pendulum and the vertical. Specifically, the force …

##### What is the equation for impact force? - Quora

The instantaneous impact force is F = ma (mass times acceleration) and thus the impact force varies over the collision duration, usually with an initial sharp increase, peaking and then gradually decreasing. There are 2 equations for average impac...

##### Physics I - Impact Force - YouTube

Nov 14, 2014· Physics I - Impact Force ... Calculating the Force of Impact when Stepping off a Wall ... Flipping Physics 12,761 views. 8:00. Changes in Momentum, Impact Forces, & Impulse | GCSE ...

##### Fall g-Force Calculator - VaultCanada - Equestrian Vaulting

This page provides a technical overview of how to calculate the force a vaulter experiences during a fall, including an introduction to g-force calculations with references and sources, an official test method that uses readily available tools, comparisons to other sports, and finally, recommendations specific to vaulting.

##### Jet Discharge Propulsion - Engineering ToolBox

Impact Force - Impact forces acts on falling objects hitting ground, crashing cars and similar Impulse and Impulse Force - Forces acting a very short time are called impulse forces Orifice, Nozzle and Venturi Flow Rate Meters - The orifice, nozzle and venturi flow rate meters use the Bernoulli Equation to calculate fluid flow rate using ...

##### Force on Driver in Example Car Crash

Force on Driver in Example Car Crash. For the car crash scenario where a car stops in 1 foot from a speed of 30 mi/hr, what is the force on the driver? Assume a 160 lb (mass = 5 slugs) driver. If firmly held in non-stretching seatbelt harness: Stopping distance 1 ft.

##### How to Calculate Force of Impact | Sciencing

Impact Force Calculator. Calculate an approximate average impact force and peak impact force from a collision of a moving body with output in Newtons (N, kN, MN, GN) and pound-force (lbf). The impact force calculator is versatile and can also be used to calculate the mass, velocity and either collision distance or duration.

##### The Splat Calculator - A Free Fall Calculator

The calculator uses the standard formula from Newtonian physics to figure out how long before the falling object goes splat: The force of gravity, g = 9.8 m/s 2 Gravity accelerates you at 9.8 meters per second per second. After one second, you're falling 9.8 m/s. …

##### Force Calculator F = ma

Calculate the unknown variable in the equation for force, where force equals mass multiplied by acceleration. ... Force Calculator. Force Calculator. Force Calculator . Choose a Calculation ... Calculator Use. This calculator will find the missing variable in the physics equation for force (F = M * a), when two of the variables are known. ...

##### Impact Force from Falling Object - HyperPhysics Concepts

Note that the above calculation of impact force is accurate only if the height h includes the stopping distance, since the process of penetration is further decreasing its gravitational potential energy.. The average impact force calculated here is the average over distance, which can be presumed to be proportional to, but not the same as, the average over time.

##### How to Calculate Bullet Impact | Sciencing

How to Calculate Bullet Impact ... momentum, kinetic energy, acceleration and force. The speed of the bullet is important, but so is its shape, e.g., its diameter. How To Calculate Bullet Impact. You can effectively calculate the impact of a bullet via the following series of steps. Collect the required information for the ammunition under ...

##### Analysis of Impact Force Equations

Analysis of Impact Force Equations Prepared for the International Technical Rescue Symposium, November 2002 By Chuck Weber Abstract This paper compares the actual impact forces measured during controlled testing to the values calculated by a commonly accepted rope force-predicting equation. All tests studied were

##### Impact Force Calculator - Best Free Online Calculator

The Impact Force Calculator an online tool which shows Impact Force for the given input. Byju's Impact Force Calculator is a tool which makes calculations very simple and interesting. If an input is given then it can easily show the result for the given number.

##### momentum - Calculating force of impact - Physics Stack ...

Since $\text{force = mass}\times\text{acceleration}$, is it right to say that an object traveling at a high constant velocity (zero acceleration), exerts zero force upon impact with a stationary object? I understand that upon impact, the projectile decelerates rapidly from initial velocity down to zero.

##### How to Calculate the Force of a Falling Object | Sciencing

The force is equal to the rate of change of momentum, so to do this you need to know the momentum of the object before and after the bounce. By calculating the change in momentum between the fall and the bounce and dividing the result by the amount of time between these two points, you can get an estimate for the impact force.

##### Car Crash Example - HyperPhysics Concepts

Impact force F = N = lb = tons!! You may change any data value. Clicking outside the box will then initiate a calculation of the impact force and conversion of the data value to the other types of units. Discussion of car crash scenario: Index Work-energy principle .

##### Unity 5 - Calculating impact force on collision - YouTube

Mar 15, 2017· Hello there, Today we will be calculating force on impact beetwen 2 objects as seen in the title. To finish it off we will fracture the object we ll be dropping. //PACKAGE : FracturedCube ...

##### Force of Impact | HowStuffWorks

Crumple zones also help redistribute the force of impact. All of the force has to go somewhere -- the goal is to send it away from the occupants. Think of the force involved in a crash as a force budget. Everything that happens to the car during an impact and every person inside of the car at the time of the impact spends some of the force.

##### Force Calculator - Smart Conversion

Force Calculator. Force Calculator. The force can be calculated by using the following formula: where p is the momentum, t is the time, m is the mass and a is the acceleration. Mass (m):

##### Impact Force - Engineering ToolBox

When a crumple zone deforms in a car crash the average impact force is designed to be as constant as possible. In an impact where the object is not deformed - the work made by the impact force slowing down the moving object equals to the work done by a spring force - and can be expressed as. W = 1/2 F max s = 1/2 k s 2 (2b) where

##### How to calculate approximate impact force of the pendulum ...

Jun 11, 2018· The problem is that to know the force that acts when one object strikes another requires knowing the time in which they are in contact with each other. For example, we can know the speed at which a pendulum bob strikes another object at the bottom...

##### Solve problem related to impact force from falling object

Initial PE = Final KE Impact velocity just before the impact is From work-energy principle, change in the kinetic energy of an object is equal to the net work done on the object. For a straight-line collision, the total work done is equal to the average force of impact times the distance traveled during the impact.

##### How to Calculate Crash Forces | Sciencing

Apr 29, 2018· According to Newton's Second Law of Motion, the force, in Newtons, that an object exerts on another object is equal to the mass of the object times its acceleration. How can this be applied to calculating the forces involved in a crash? Keep in mind that …

##### Pendulum Hammer Impact Force Calculation | Physics Forums

Jun 21, 2019· Find the duration of impact, then look up the equation for two masses impacting with a spring in between. Iterate the spring constant until the calculations match the video. You will then have the information to calculate the peak impact force. The hammer / anvil impact force is a useless number if you are interested in the effect on the SUT.

##### What is the best way to calculate impact time with collisions?

When calculating the force of this impact I need the momentum and the duration of the impact. The momentum is easy enough to calculate, but how is the duration of impact worked out? I know that it isn't referring to how long the objects are in contact, as this would mean that swords would harmlessly rub against a person if they were swung.

##### Fall factor and impact force - theory - Petzl USA

The impact force indicated on a rope corresponds to the maximum force measured on a metal mass (a climber) in the standard test conditions (see Impact force-standards). Theoretical fall factor. The fall factor is often used to quantify the severity of a climbing fall. It can have a …

##### Car Crash - Impact Force Calculator - Omni

Force of impact definition - impact force equation. Force of impact is the total force exerted on an object during a collision. To derive the impact force equation, you can consider the law of conservation of energy. At the beginning, a moving object possesses kinetic energy that reduces to zero after the collision (object stops).

##### What are some ways of calculating the force of impact? - Quora

Oct 04, 2016· The first thought that comes to mind is “Of What?” - But since you haven’t specified, I’m going to work off what you have - the first is force, the second is impact. So if two objects collide, with a change in momentum as a result, then force must...

##### Changes in Momentum, Impact Forces, & Impulse | GCSE ...

Dec 14, 2016· Learn about changes in momentum caused by an impulse. Learn about impact forces in collisions, specifically involving cars, and why increasing the impact time can reduce the impact force ...

##### Dropped Object Consequence Online Calculator ...

The Calculator assumes that full PPE is being worn and that the object is blunt (no sharp edges – outcome would be worse). Dropped Object Consequence Online Calculator Accuracy. The DROPS Calculator is a guide only and is intended to give a general idea of the potential severity of a …


text:
The statistical factors affecting the freezing of the road pavement

Title & Authors
The statistical factors affecting the freezing of the road pavement
Kim, Hyun-Ji; Lee, Jea-Young; Kim, Byung-Doo; Cho, Gyu-Tae;

Abstract
Due to the character of the climate of Korea, the pavement of a road is Influenced by freezing in winter season and thawing in thawing season. In the last few years, several articles have been devoted to the study to minimize the damage of freezing and thawing action. The purpose of this paper is to identify appropriacy of factors that influence road pavement thickness. We conduct the decision tree analysis on the field data of road pavement. The target variable is 'Frost penetration'. This value was calculated from the temperature data. The input variables are 'Region', 'Type of road pavement', 'Anti-frost layer', 'Month' and 'Air temperature'. The region was divided into 9 regions by freezing index $\small{350{\sim}450^{\circ}C{\cdot}day}$, $\small{450{\sim}550^{\circ}C{\cdot}day}$, $\small{550{\sim}650^{\circ}C{\cdot}day}$. The type of road pavement has three-section such as area of cutting, boundary area of cutting and bankin, lower area of banking. As the result, the variables that influence 'Frost penetration' are Month, followed by anti-frost layer, air temperature and region.
Keywords
Language
Korean
Cited by
References
1.
Berson, A., Smith, S. and Thearling, K. (2000). Building data mining applications for CRM, McGraw-Hill, New York.

2.
Freund, Y. and Mason, L. (1999). The alternating decision tree learning algorithm. In ICML, 99, 121-133.

3.
Heo, M. H. and Lee, Y. G. (2008). Data mining modeling and example, Hannarae, Seoul.

4.
Kwon, G. B. (2003). Bearing capacity estimation of subgrade for frost heaving effect, Incheon National University, Incheon.

5.
Kim, N. S., Nam, Y. K., Cho, G. T. and Lee, B. W. (2011). An establishment of database for effective design of anti-frost heave layer using field data. Korean Society of Hazard Mitigation, 11, 43-47.

6.
Kim, Y. J., Yu, J. and Kim, H. M. (1999). A study on the frost penetration depth and insulation methods in pavement, Korea Institute of Civil Engineering and Building Technology, Goyang.

7.
Lee, J. Y. and Kim, H. J. (2014). Identification of major risk factors association with respiratory diseases by data mining. Journal of the Korean Data & Information Science Society, 25, 373-384.

8.
Lee, M. S., Heo, T. Y., Park, H. M. and Kim, B. I. (2012). Development of model for structural evaluation of anti-freezing layer. Journal of the Korean Society of Road Engineers, 14, 25-32.

9.
Quinlan, J. R. (1993). C4.5: Programs for machine learning, Morgan-Kaufmann Publishers, San Mateo, CA.

10.
Shin, E. C., Lee, J. S. and Cho, G. T. (2011). A study on the frost penetration depth of pavement with field temperature data. Journal of the Korean Society of Road Engineers, 13, 21-32.

11.
Nam, Y. K., Park, C. B., Cho, G. T. and Jin, J. H. (2002). The field data on behavior characteristics of anti-frost heave layer. International Journal of Highway Engineering, 4, 19-23.

format: plain


text:
## CryptoDB

### Paper: Making Masking Security Proofs Concrete (Or How to Evaluate the Security of Any Leaking Device), Extended Version

Authors: Alexandre Duc Sebastian Faust François-Xavier Standaert DOI: 10.1007/s00145-018-9277-0 Search ePrint Search Google We investigate the relationship between theoretical studies of leaking cryptographic devices and concrete security evaluations with standard side-channel attacks. Our contributions are in four parts. First, we connect the formal analysis of the masking countermeasure proposed by Duc et al. (Eurocrypt 2014) with the Eurocrypt 2009 evaluation framework for side-channel key recovery attacks. In particular, we re-state their main proof for the masking countermeasure based on a mutual information metric, which is frequently used in concrete physical security evaluations. Second, we discuss the tightness of the Eurocrypt 2014 bounds based on experimental case studies. This allows us to conjecture a simplified link between the mutual information metric and the success rate of a side-channel adversary, ignoring technical parameters and proof artifacts. Third, we introduce heuristic (yet well-motivated) tools for the evaluation of the masking countermeasure when its independent leakage assumption is not perfectly fulfilled, as it is frequently encountered in practice. Thanks to these tools, we argue that masking with non-independent leakages may provide improved security levels in certain scenarios. Eventually, we consider the tradeoff between the measurement complexity and the key enumeration time complexity in divide-and-conquer side-channel attacks and show that these complexities can be lower bounded based on the mutual information metric, using simple and efficient algorithms. The combination of these observations enables significant reductions of the evaluation costs for certification bodies.
##### BibTeX
@article{jofc-2019-30115,
title={Making Masking Security Proofs Concrete (Or How to Evaluate the Security of Any Leaking Device), Extended Version},
journal={Journal of Cryptology},
publisher={Springer},
volume={32},
pages={1263-1297},
doi={10.1007/s00145-018-9277-0},
author={Alexandre Duc and Sebastian Faust and François-Xavier Standaert},
year=2019
}


text:
• Status: Solved
• Priority: Medium
• Security: Public
• Views: 425

# how to create a VB script or a bat file with waiting period

I need to create a bat file or a VB script which will ask a question with a big banner
Is this a Master Y/N
(warning Y=Do not do anything, N= start cloning process)
if user responds Yes it shouldn't do anything and just exit.
If user DOES NOT RESPOND for 2 minutes or respond N then it should run command  “c:\windows\system32\XYZ.exe"
0
wajhiuddin
• 11
• 8
• 5
• +2
3 Solutions

Commented:
You need to use choice command in a batch file, the syntax is :

CHOICE  [ /C[:]choices ]  [ /N ]  [ /S ]  [ /T[:]c,nn ] text

/C:choices      Specifies allowable keys.
Default for English versions is YN
/N   Do not display choices an ? at end of prompt string.
/S or /CS   Treat choice keys as case sensitive.
Up to (and including) the Resource Kit versions, use /S.
In Windows 7 use /CS.
/T:c,nn   Default choice to c after nn seconds.
text   Prompt string to display.

e.g.:

CHOICE /C:AB /N /T:N,10 Format drive A:, B:, or None?
IF ERRORLEVEL 1 SET DRIVE=drive A:
IF ERRORLEVEL 2 SET DRIVE=drive B:
IF ERRORLEVEL 5 SET DRIVE=None
ECHO You chose to format %DRIVE%

-Rahul
0

Commented:
Here's a shot at a BAT approach to give you the idea. The formatting and messaging could be adjusted, but just to give you the basic idea.

@echo off

echo **********************************************************************************
echo **********************************************************************************
echo **********************************************************************************
echo *****                                                                        *****
echo *****                         I M P O R T A N T                              *****
echo *****                                                                        *****
echo *****  Please indicate below if this is the MASTER or not.                   *****
echo *****                                                                        *****
echo *****  W A R N I N G :                                                       *****
echo *****                                                                        *****
echo *****     Y = Do not do anything                                             *****
echo *****     N = start cloning process                                          *****
echo *****                                                                        *****
echo **********************************************************************************
echo **********************************************************************************

choice /C YN /N /T 120 /D N /M "Is this a Master (Y/N): "
if %ERRORLEVEL% EQU 1 exit /b

c:\windows\system32\XYZ.exe

~bp
0

Commented:
Also not that if the actual program path you want to execute contains spaces then you will need to quote it as in:

"c:\windows\system32\XYZ.exe"

~bp
0

Author Commented:
billprew,
Only yes option works "N" doesn't do do anything, it should run  command from c:\windows\system32when user etihter select N or don't do any thing
Thanks
0

Commented:

@echo off

echo **********************************************************************************
echo **********************************************************************************
echo **********************************************************************************
echo *****                                                                        *****
echo *****                         I M P O R T A N T                              *****
echo *****                                                                        *****
echo *****  Please indicate below if this is the MASTER or not.                   *****
echo *****                                                                        *****
echo *****  W A R N I N G :                                                       *****
echo *****                                                                        *****
echo *****     Y = Do not do anything                                             *****
echo *****     N = start cloning process                                          *****
echo *****                                                                        *****
echo **********************************************************************************
echo **********************************************************************************

choice /C YN /N /T 120 /D N /M "Is this a Master (Y/N): "
if %ERRORLEVEL% EQU 2 GOTO No
if %ERRORLEVEL% EQU 1 GOTO Yes
GOTO END

:Yes
ECHO DOING SOMETHING COMMAND LINE
GOTO END

:No
ECHO DOING NOTHING COMMAND LINE
GOTO END

:END
PAUSE
EXIT

0

Commented:
I should have payed more attention.

@echo off

echo **********************************************************************************
echo **********************************************************************************
echo **********************************************************************************
echo *****                                                                        *****
echo *****                         I M P O R T A N T                              *****
echo *****                                                                        *****
echo *****  Please indicate below if this is the MASTER or not.                   *****
echo *****                                                                        *****
echo *****  W A R N I N G :                                                       *****
echo *****                                                                        *****
echo *****     Y = Do not do anything                                             *****
echo *****     N = start cloning process                                          *****
echo *****                                                                        *****
echo **********************************************************************************
echo **********************************************************************************

choice /C YN /N /T 120 /D N /M "Is this a Master (Y/N): "
if %ERRORLEVEL% EQU 2 GOTO No
if %ERRORLEVEL% EQU 1 GOTO Yes
GOTO END

:Yes
ECHO DOING NOTHING
GOTO END

:No
ECHO DOING SOMETHING COMMAND LINE
"c:\windows\system32\XYZ.exe"
GOTO END

:END
PAUSE
EXIT

0

Commented:
If my version, build on Bill's script works, please just give me few thanks points and give most to Bill. As he did all the work.
0

IT ConsultancyCommented:
Just for a change here is a quick VBScript which does similar:
REM VBScript version of display of Yes/No with timeout for EE question 27424321
REM Steve Knight (dragon-it) - 31/10/2011

Const Yes = 6
Const No = 7
Const YesNoDialog = 4
Const QuestionMark = 32

Dim objShell, answer, Delay, Title, Question

Delay=120 'Delay In seconds

Question=_
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10) & _
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10) & _
chr(10) & _
"                          IMPORTANT" & chr(10) & _
chr(10) & _
"  Please choose whether this is the MASTER" & chr(10) & _
chr(10) & _
"  YES = Do nothing" & chr(10) & _
"   NO = Start cloning process" & chr(10) & _
chr(10) & _
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10) & _
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10)

Set objShell = CreateObject("Wscript.Shell")

answer = objShell.Popup(Question, Delay, Title, YesNoDialog + QuestionMark)

Wscript.quit
Else
objShell.Run "%SystemRoot%\System32\xyz.exe",,False
End If

PopUp.vbs
0

IT ConsultancyCommented:
Or I suppose better using built-in constants and making it appear "always on top":

Steve
REM VBScript version of display of Yes/No with timeout for EE question 27424321
REM Steve Knight (dragon-it) - 31/10/2011

Dim objShell, answer, Delay, Title, Question

Delay=120 'Delay In seconds

Question=_
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10) & _
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10) & _
chr(10) & _
"                          IMPORTANT" & chr(10) & _
chr(10) & _
"  Please choose whether this is the MASTER" & chr(10) & _
chr(10) & _
"  YES = Do nothing" & chr(10) & _
"   NO = Start cloning process" & chr(10) & _
chr(10) & _
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10) & _
"+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+" & chr(10)

Set objShell = CreateObject("Wscript.Shell")

answer = objShell.Popup(Question, Delay, Title, vbYesNo + vbQuestion + vbDefaultButton2 + vbSystemModal)

Wscript.quit
Else
objShell.Run "%SystemRoot%\System32\xyz.exe",,False
End If

0

Commented:
@wajhiuddin

==> Only yes option works "N" doesn't do do anything, it should run  command from
==> c:\windows\system32when user etihter select N or don't do any thing

I just tested it again here, and that is not the case.  It works as you asked, if they enter N, or if they enter nothing for 2 minutes it runs the executable.  I just did a test and got this result (displaying the EXE name rather than actually running it for my test).  So I think the code works as requested.

[Tue 11/01/2011  9:38:02.86 c:\ee]ee27424321
**********************************************************************************
**********************************************************************************
**********************************************************************************
*****                                                                        *****
*****                         I M P O R T A N T                              *****
*****                                                                        *****
*****  Please indicate below if this is the MASTER or not.                   *****
*****                                                                        *****
*****  W A R N I N G :                                                       *****
*****                                                                        *****
*****     Y = Do not do anything                                             *****
*****     N = start cloning process                                          *****
*****                                                                        *****
**********************************************************************************
**********************************************************************************
Is this a Master (Y/N): N
c:\windows\system32\XYZ.exe

~bp
0

Commented:
@ReneGe,

What was your intent in rearranging my code slightly, seems to provide basically the same solution but with more work?

~bp
0

Commented:
And to cover the base where the user presses CTRL-C and then sayes N to "Terminate batch job?" I'll assume you would not want to run the EXE in that odd case, and adjust my code as follows to cover this.

@echo off

echo **********************************************************************************
echo **********************************************************************************
echo **********************************************************************************
echo *****                                                                        *****
echo *****                         I M P O R T A N T                              *****
echo *****                                                                        *****
echo *****  Please indicate below if this is the MASTER or not.                   *****
echo *****                                                                        *****
echo *****  W A R N I N G :                                                       *****
echo *****                                                                        *****
echo *****     Y = Do not do anything                                             *****
echo *****     N = start cloning process                                          *****
echo *****                                                                        *****
echo **********************************************************************************
echo **********************************************************************************

choice /C YN /N /T 120 /D N /M "Is this a Master (Y/N): "
if %ERRORLEVEL% LEQ 1 exit /b

c:\windows\system32\XYZ.exe

~bp
0

IT ConsultancyCommented:
Perhaps he hasn't got choice.exe ... only in Win 7, resource kit, 2003 R2, 2008 wasn't it?
0

Commented:
@dragon-it

Fair point Steve, although the statement:

==> Only yes option works "N" doesn't do do anything, it should run  command from

didn't make me think he was getting an error on the CHOICE command.
@wajhiuddin

Can you clarify exactly what you are seeing?
~bp
0

IT ConsultancyCommented:
@billprew Good point.  If choice.exe wasn't present I suppose it may trigger an error which does the "Y" process, don't know off hand what error is returned when an EXE gives a "not recogniszed as a command" error but don't suppose it is 1.

Will see what feedback we get....

Did you try the VBScript one above too :-) http:#37059750 revised slightly in next post

Steve
0

Commented:
Of course I tried yours :-).  Seemed to work for me.  Although I wouldn't pad the Title with leading spaces, messes up the task bar icon text (IMHO).

~bp
0

IT ConsultancyCommented:
It centred it (ish!).... though tend to agree!
0

IT ConsultancyCommented:
(I meant did wajhiuddin try mine btw, not you Bill!)
0

Commented:
Yup, I knew what you were after in the dialog box title area, and that was okay, but in the taskbar icon it pushes the text far to the right and looks odd or truncates.  I'd stick with it left justified...

~bp
0

Commented:
(I think maybe you're trying to hard to be "artistic" Steve :-) ).

~bp
0

Author Commented:
thanks to billprew,ReneGe and dragon-it it works as  you all sugested
0

Commented:
@wajhiuddin:
Glad I could somehow help and thanks for the points.

@billprew:

I do not understand the nature of your question.  I thought that by adding these few lines, it would make it visually easyer to understand for the poster.

Cheers,
Rene

0

Commented:
@ReneGe

I think I'll just drop my question, I felt a bit like all you did was reformat my code and repost it, and for me that isn't in the spirit of EE.  That being said, it's sometimes a hard line to walk, and I know that.  So I guess it is what it is, if that's your style in responding to questions then so be it, live and let live.

~bp
0

IT ConsultancyCommented:
0

IT ConsultancyCommented:
Bill, Rene did say "If my version, build on Bill's script works, please just give me few thanks points and give most to Bill. As he did all the work. "
0

Commented:
Thanks Steve :)

Bill, I have the most respect for you, and I owe what I know in regards to Batch File scripting to mostly you, Steve, the Qs, and just a few other highly skilled Experts. Your contribution permit me to develop great and powerfull tools that made my life a lot easyer. If I offended you in some way, please forgive my innocence and sometimes lack of humain skills. Helping and receiving a note of some gratitude or points makes me feel good, and, I don't see the difference.

I hope you'll understand my nature and assume the best.

Truly,
Rene

0

Commented:
Guys, it's all good. That's why I said I'm not gonna flame off on this, but did want to at least share a thought or two.  You guys know I enjoy the interaction with you here, and I know we all take pride in our work.  I'll keep my ego in check...

~bp
0
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text:
## what is the distance in meters?

Two archers shoot arrows in the same direction from the same place with the same initial speeds, but at different angles. One shoots at 45.0 degrees above the horizontal, while the other shoots at 60.0 degrees.

If the arrow launched at 45.0 degrees lands 225 m from the archer, how far apart are the two arrows when they land? (You can assume that the arrows start at essentially ground level.)


text:
1
AIEEE 2003
+4
-1
If the sum of the roots of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the sum of the squares of their reciprocals, then $${a \over c},\,{b \over a}$$ and $${c \over b}$$ are in
A
Arithmetic - Geometric Progression
B
Arithmetic Progression
C
Geometric Progression
D
Harmonic Progression
2
AIEEE 2003
+4
-1
The value of '$$a$$' for which one root of the quadratic equation $$\left( {{a^2} - 5a + 3} \right){x^2} + \left( {3a - 1} \right)x + 2 = 0$$\$
is twice as large as the other is
A
$$- {1 \over 3}$$
B
$${2 \over 3}$$
C
$$- {2 \over 3}$$
D
$${1 \over 3}$$
3
AIEEE 2003
+4
-1
The number of real solutions of the equation $${x^2} - 3\left| x \right| + 2 = 0$$ is
A
3
B
2
C
4
D
1
4
AIEEE 2003
+4
-1
The real number $$x$$ when added to its inverse gives the minimum value of the sum at $$x$$ equal to
A
-2
B
2
C
1
D
-1
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text:
# Catalan objects associated to a univariate polynomial

Given a monic degree $n$ polynomial $f(z)$ with no double roots, and a phase $0\leq \theta < \pi$, there are natural constructions which associate to this data:

a noncrossing matching on $2n$ vertices, and

a triangulation of an $n+2$-gon.

These objects are both counted by Catalan numbers, leading me to feel that there should be some connection. It is not the case that the fibres of the two maps are the same, and I will say more below about how they are clearly different. My question is: what is the connection?

Let me now explain the constructions. Consider the points $z$ in $\mathbb C$ such that arg($\pm f(z)$)$=\theta$. Generically, this consists of $n$ unbounded curves, which, for large $|z|$, are evenly-spaces spokes of a wheel (with $2n$ spokes), and therefore can be interpreted as giving rise to a noncrossing matching. See Martin, Savitt, Singer and Savitt. As you tune $\theta$, the matchings change in a nicely controlled way, as pairs of components meet and reconnect. Tuning from $\theta=0$ to $\theta=\pi$ results in $n-1$ of these reconnections, and the total effect is to rotate the diagram by one step.

Now we consider how to produce the triangulation. I found out about this from a sequence of papers by Cecotti, Vafa, and a varying list of others, studying a connection between BPS states of 4d supersymmetric quantum field theories and cluster algebras. For the present topic see, in particular, Sections 4 and 5 of Cecotti, Córdova, Vafa. I found background provided in Section 4 of Mulase and Penkava helpful. The idea is to define a foliation of $\mathbb C$, where a curve $p(t)$ lies on a leaf of the foliation if $(p'(t))^2f(p(t))e^{2\theta i}$ is always real and positive. From a zero of $f$, there will be three equally-spaced curves coming out, and generically they will connect to points at infinity. For $|z|$ very large, the trajectories approach spokes of a wheel, with $n+2$ spokes. By connecting into a triangle the endpoints (on the circle at infinity) of the three curves coming out from each zero of $f$, you get a triangulation of an $n+2$-gon. As you tune $\theta$, the triangulation changes by diagonal flips. Again, the total effect of tuning from 0 to $\pi$ is to rotate the diagram by one step (though note that the "step" is a different fraction of $2\pi$ from the step that appears in the noncrossing matching).

(Edited to add: I should mention that, in the terminology of the people who study these flows, $f(z)dz$ is called a "quadratic differential", though these are often considered in more complicated situations, where there might be poles, for instance.)

If you prefer to complicate matters rather than simplifying them, you could also consider the question of whether there are any other Catalan objects associated to a monic polynomial and a phase (with different fibres than the above maps).

-
This reminds me of the article "On Stokes Sets", by Yuliy Baryshnikov [springerlink.com/content/lg2p8l0447n86075/], where Catalan numbers appear in a similar context. –  F. C. Feb 5 '12 at 13:18
Yes, absolutely. Thanks for pointing out the reference! For anyone who wants to get a better handle on the triangulation picture that I referred to, that's an excellent place to look. –  Hugh Thomas Feb 5 '12 at 14:13
About Baryshnikov's paper, I should add (because it confused me) that he is mainly interested in fixing theta, and letting the polynomial vary, whereas I asked about is fixing the polynomial and letting theta vary. (While in the paper by Cecotti et al, they actually vary both at once.) –  Hugh Thomas Feb 8 '12 at 12:44


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# Math Help - basic Rational Expression simplifying help

1. ## basic Rational Expression simplifying help

ok so I have the following problem:

4x+2
-------- (fraction line, i thought this would be easier)
12x^2+14x+4

I can get pretty close to this but i get stuck along the way

i end up with:
2(2x+1)
-------------
3x(2x+1)+2(2x+1)

I dont know what to do, if I cancel out the 2x+1's im still left with a 2 as the numerator, if i cancel out the 2(2x+1) I feel like im breaking a rule because its part of addition (3x+2)

thanks for any help

2. Originally Posted by NecroWinter
ok so I have the following problem:

4x+2
-------- (fraction line, i thought this would be easier)
12x^2+14x+4

I can get pretty close to this but i get stuck along the way

i end up with:
2(2x+1)
-------------
3x(2x+1)+2(2x+1)

I dont know what to do, if I cancel out the 2x+1's im still left with a 2 as the numerator, if i cancel out the 2(2x+1) I feel like im breaking a rule because its part of addition (3x+2)

thanks for any help
note the denominator ... 3x(2x+1)+2(2x+1) = (2x+1)(3x+2)

$=\displaystyle\frac{2x+1}{6x^2+7x+2}$
$=\displaystyle\frac{2x+1}{(2x+1)(3x+2)}$


text:
Question
Sun March 02, 2008 By:

# doubts

Thu May 08, 2008

alpha decay:

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (two protons and two neutrons bound together into a particle identical to a helium nucleus) and transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. For example:

${}^2{}^{38}_{92}\hbox{U}\;\to\;{}^2{}^{34}_{90}\hbox{Th}\;+\;{}^4_2\hbox{He}^{2+},$[1]

although this is typically written as:

${}^{238}\hbox{U}\;\to\;^{234}\hbox{Th}\;+\;\alpha.$ An alpha particle is the same as a helium-4 nucleus, and both mass number and atomic number are the same.

beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. In the case of electron emission, it is referred to as "beta minus" (β ), while in the case of a positron emission as "beta plus" (β+ ).

Gamma rays are often produced alongside other forms of radiation such as alpha or beta. When a nucleus emits an α or β particle, the daughter nucleus is sometimes left in an excited state. It can then jump down to a lower level by emitting a gamma ray in much the same way that an atomic electron can jump to a lower level by emitting visible light or ultraviolet radiation.

Related Questions
Sat November 04, 2017

# from boards point of view is it important to learn speed of emmitted alpha particle from the topic alpha decay?

Mon October 30, 2017

Home Work Help


text:
Glossary

Gap deletion

A gap deletion is the deletion of a contiguous interval (gap) from a genetic string, typically in the context of alignment problems. If we view an alignment as transforming $s$ into $t$, then a gap deletion corresponds to an interval of gap symbols in $t$ aligned with non-gap symbols in $s$.

Gap insertions are the inverse operations of gap deletions.


text:
## Data Structure 2

Points: 2
Time limit: 1.0s
Memory limit: 64M

Author:
Problem type
Allowed languages
C++, Python3

This practice problem will require you to utilise Stack to solve the bracket matching problem.

Brackets are used in many places, and in this task your job is to make sure the three types of brackets are syntactically correct. The rules are very simple, matching pairs of brackets are considered valid.

E.g. the following brackets are valid:

()[{}]
[[]]

The following is invalid:

[]]
({)}

OJ question csci125p020 only asks you to detect validity for a single type of bracket. In this question you will need to do so for all three types using Stack. You will need to implement a stack as you like first, then use it to solve this question.

#### Input Specification

The first line contain a single number $$N$$ ($$N<1000$$), indicating the number of test cases.

Each line will contain a single test case. Each case will contain no more than 200 characters without whitespace.

#### Output Specification

The output should contain the $$N$$ lines, each line either Valid or Invalid, indicating whether the sequence is valid.

#### Sample Input

5
]([((]((({)]}
[]()(({}[(())])[])
[]}}())][[
{)[(}()){[((]}{
{{[{{}}[]]{[[]]()}}}

#### Sample Output

Invalid
Valid
Invalid
Invalid
Valid


text:
# A number when divided by 296 leaves, 75 as remainder. If the same number is divided by 37 the remainder obtained is : Option 1) Option 2) Option 3) Option 4) 5Option 5)

$Number= 296k+75$
$37\times 8k+37*2+1$
$37(8k+2)+1$
$Remainder=1$


text:
• D

F Nous contacter

0

# Documents  37K15 | enregistrements trouvés : 2

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Sélection courante (0) : Tout sélectionner / Tout déselectionner

P Q

## Post-edited  Various aspects of the dynamics of the cubic Szegö solutions Grellier, Sandrine (Auteur de la Conférence) | CIRM (Editeur )

The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform analyticity for a large set of initial data, turbulence phenomenon for a dense set of smooth initial data in large Sobolev spaces.
From joint works with Patrick Gérard.
The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform ...

## Multi angle  Soliton resolution for derivative NLS equation Sulem, Catherine (Auteur de la Conférence) | CIRM (Editeur )

We consider the Derivative Nonlinear Schrödinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities). We prove global wellposedness and give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. Our analysis provides explicit formulae for the multi-soliton component as well as the correction dispersive term. We use the inverse scattering approach and the nonlinear steepest descent method of Deift and Zhou (1993) revisited by the $\bar{\partial}$-analysis of Dieng-McLaughlin (2008) and complemented by the recent work of Borghese-Jenkins-McLaughlin (2016) on soliton resolution for the focusing nonlinear Schrödinger equation. This is a joint work with R. Jenkins, J. Liu and P. Perry. We consider the Derivative Nonlinear Schrödinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities). We prove global wellposedness and give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. Our analysis provides explicit formulae for the multi-soliton component as well as ...

##### Codes MSC

Nuage de mots clefs ici

Z


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The Additive Heuristic for POCL Planning

The key assumption behind the additive heuristic is subgoal independence. We give a recursive definition of the additive heuristic for POCL planning, starting at the level of literals and working towards a definition of heuristic cost for a partial plan.

Given a literal q, let (q) be the set of ground actions having an effect that unifies with q. The cost of the literal q can then be defined as

hadd(q) = .

A positive literal q holds initially if it is part of the initial conditions. A negative literal ¬q holds initially if q is not part of the initial conditions (the closed-world assumption). The cost of an action a is

hadd(a) = 1 + hadd(Prec(a)),

where Prec(a) is a propositional formula in negation normal form representing the preconditions of action a. A propositional formula is in negation normal form if negations only occur at the level of literals. Any propositional formula can be transformed into negation normal form, and this is done for action preconditions by VHPOP while parsing the domain description file.

Existentially quantified variables in an action precondition can be treated as additional parameters of the action. The cost of an existentially quantified precondition can then simply be defined as follows:

hadd(x.) = hadd()

We can deal with universally quantified preconditions by making them fully instantiated in a preprocessing phase, so in order to complete the definition of heuristic cost for action preconditions we only need to add definitions for the heuristic cost of conjunctions and disjunctions. The cost of a conjunction is the sum of the cost of the conjuncts:

hadd() = hadd()

The summation in the above formula is what gives the additive heuristic its name. The definition is based on the assumption that subgoals are independent, which can lead to overestimation of the actual cost of a conjunctive goal (i.e. the heuristic is not admissible). The cost of a disjunction is taken to be the cost of the disjunct with minimal cost:

hadd() = hadd()

The additive heuristic cost function for POCL plans can now be defined as follows:

hadd() = hadd(q)

As with the cost function for conjunction, the above definition can easily lead to overestimation of the number of actions needed to complete a plan, since possible reuse is ignored. We propose a remedy for this below.

The cost of ground literals can be efficiently computed through dynamic programming. We take conditional effects into account in the cost computation. If the effect q is conditioned by p in action a, we add hadd(p) to the cost of achieving q with a. We only need to compute the cost for ground literals once during a preprocessing phase, leaving little overhead for evaluating plans during the planning phase. When working with lifted actions, there is extra overhead for unification. It should also be noted that all lifted literals are independently matched to ground literals without considering interactions between open conditions of the same action. For example, two preconditions (a ?x) and (b ?x) of the same action can be unified to ground literals with different matchings for the variable ?x.

Håkan L. S. Younes
2003-08-26


text:
$$\require{cancel}$$

# 20.1: The Interstellar Medium

Learning Objectives

By the end of this section, you will be able to:

• Explain how much interstellar matter there is in the Milky Way, and what its typical density is
• Describe how the interstellar medium is divided into gaseous and solid components

Astronomers refer to all the material between stars as interstellar matter; the entire collection of interstellar matter is called the interstellar medium (ISM). Some interstellar material is concentrated into giant clouds, each of which is known as a nebula (plural “nebulae,” Latin for “clouds”). The best-known nebulae are the ones that we can see glowing or reflecting visible light; there are many pictures of these in this chapter.

Interstellar clouds do not last for the lifetime of the universe. Instead, they are like clouds on Earth, constantly shifting, merging with each other, growing, or dispersing. Some become dense and massive enough to collapse under their own gravity, forming new stars. When stars die, they, in turn, eject some of their material into interstellar space. This material can then form new clouds and begin the cycle over again.

About 99% of the material between the stars is in the form of a gas—that is, it consists of individual atoms or molecules. The most abundant elements in this gas are hydrogen and helium (which we saw are also the most abundant elements in the stars), but the gas also includes other elements. Some of the gas is in the form of molecules—combinations of atoms. The remaining 1% of the interstellar material is solid—frozen particles consisting of many atoms and molecules that are called interstellar grains or interstellar dust (Figure $$\PageIndex{1}$$). A typical dust grain consists of a core of rocklike material (silicates) or graphite surrounded by a mantle of ices; water, methane, and ammonia are probably the most abundant ices.

If all the interstellar gas within the Galaxy were spread out smoothly, there would be only about one atom of gas per cm3 in interstellar space. (In contrast, the air in the room where you are reading this book has roughly 1019 atoms per cm3.) The dust grains are even scarcer. A km3 of space would contain only a few hundred to a few thousand tiny grains, each typically less than one ten-thousandth of a millimeter in diameter. These numbers are just averages, however, because the gas and dust are distributed in a patchy and irregular way, much as water vapor in Earth’s atmosphere is often concentrated into clouds.

In some interstellar clouds, the density of gas and dust may exceed the average by as much as a thousand times or more, but even this density is more nearly a vacuum than any we can make on Earth. To show what we mean, let’s imagine a vertical tube of air reaching from the ground to the top of Earth’s atmosphere with a cross-section of 1 square meter. Now let us extend the same-size tube from the top of the atmosphere all the way to the edge of the observable universe—over 10 billion light-years away. Long though it is, the second tube would still contain fewer atoms than the one in our planet’s atmosphere.

While the density of interstellar matter is very low, the volume of space in which such matter is found is huge, and so its total massis substantial. To see why, we must bear in mind that stars occupy only a tiny fraction of the volume of the Milky Way Galaxy. For example, it takes light only about four seconds to travel a distance equal to the diameter of the Sun, but more than four years to travel from the Sun to the nearest star. Even though the spaces among the stars are sparsely populated, there’s a lot of space out there!

Astronomers estimate that the total mass of gas and dust in the Milky Way Galaxy is equal to about 15% of the mass contained in stars. This means that the mass of the interstellar matter in our Galaxy amounts to about 10 billion times the mass of the Sun. There is plenty of raw material in the Galaxy to make generations of new stars and planets (and perhaps even astronomy students).

Example $$\PageIndex{1}$$: Estimating Interstellar Mass

You can make a rough estimate of how much interstellar mass our Galaxy contains and also how many new stars could be made from this interstellar matter. All you need to know is how big the Galaxy is and the average density using this formula:

$\text{total mass } = \text{ volume } \times \text{ density of atoms } \times \text{ mass per atom } \nonumber$

You have to remember to use consistent units—such as meters and kilograms. We will assume that our Galaxy is shaped like a cylinder; the volume of a cylinder equals the area of its base times its height

$V=\pi R^2h \nonumber$

where $$R$$ is the radius of the cylinder and $$h$$ is its height.

Suppose that the average density of hydrogen gas in our Galaxy is one atom per cm3. Each hydrogen atom has a mass of 1.7 × 10−27 kg. If the Galaxy is a cylinder with a diameter of 100,000 light-years and a height of 300 light-years, what is the mass of this gas? How many solar-mass stars (2.0 × 1030 kg) could be produced from this mass of gas if it were all turned into stars?

Solution

Recall that 1 light-year = 9.5 × 1012 km = 9.5 × 1017 cm, so the volume of the Galaxy is

$V= \pi R^2 h = \pi \left( 50,000 \times 9.5 \times 10^{17} \text{ cm} \right)^2 \left( 300 \times 9.5 \times 10^{17} \text{ cm} \right) = 2.0×10^{66} \text{ cm}^3 \nonumber$

The total mass is therefore

$M=V \times \text{ density of atoms } \times \text{ mass per atom} \nonumber$

$2.0 \times 10^{66} \text{ cm}^3 \times \left(1 \text{ atom/cm}^3 \right) \times 1.7 \times 10^{–27} \text{ kg} =3.5 \times 10^{39} \text{ kg} \nonumber$

This is sufficient to make

$N= \frac{M}{\left( 2.0 \times 10^{30} \text{ kg} \right)}=1.75 \times 10^9 \nonumber$

stars equal in mass to the Sun. That’s roughly 2 billion stars.

Exercise $$\PageIndex{1}$$

You can use the same method to estimate the mass of interstellar gas around the Sun. The distance from the Sun to the nearest other star, Proxima Centauri, is 4.2 light-years. We will see in Interstellar Matter around the Sun that the gas in the immediate vicinity of the Sun is less dense than average, about 0.1 atoms per cm3. What is the total mass of interstellar hydrogen in a sphere centered on the Sun and extending out to Proxima Centauri? How does this compare to the mass of the Sun? It is helpful to remember that the volume of a sphere is related to its radius:

$V=(4/3) \pi R^3 \nonumber$

The volume of a sphere stretching from the Sun to Proxima Centauri is:

$V=(4/3) \pi R^3=(4/3) \pi \left( 4.2 \times 9.5 \times 10^{17} \text{ cm} \right)^3=2.7×10^{56} \text{ cm}^3 \nonumber$

Therefore, the mass of hydrogen in this sphere is:

$M=V \times \left( 0.1 \text{ atom/cm}^3 \right) \times 1.7 \times 10^{–27} \text{ kg } = 4.5 \times 10^{28} \text{ kg} \nonumber$

This is only $$\left(4.5 \times 10^{28} \text{ kg} \right)/ \left(2.0 \times 10^{30} \text{ kg} \right) = 2.2 /%$$ the mass of the Sun.

NAMING THE NEBULAE

As you look at the captions for some of the spectacular photographs in this chapter and The Birth of Stars and the Discovery of Planets outside the Solar System, you will notice the variety of names given to the nebulae. A few, which in small telescopes look like something recognizable, are sometimes named after the creatures or objects they resemble. Examples include the Crab, Tarantula, and Keyhole Nebulae. But most have only numbers that are entries in a catalog of astronomical objects.

Perhaps the best-known catalog of nebulae (as well as star clusters and galaxies) was compiled by the French astronomer Charles Messier (1730–1817). Messier’s passion was discovering comets, and his devotion to this cause earned him the nickname “The Comet Ferret” from King Louis XV. When comets are first seen coming toward the Sun, they look like little fuzzy patches of light; in small telescopes, they are easy to confuse with nebulae or with groupings of many stars so far away that their light is all blended together. Time and again, Messier’s heart leapt as he thought he had discovered one of his treasured comets, only to find that he had “merely” observed a nebula or cluster.

In frustration, Messier set out to catalog the position and appearance of over 100 objects that could be mistaken for comets. For him, this list was merely a tool in the far more important work of comet hunting. He would be very surprised if he returned today to discover that no one recalls his comets anymore, but his catalog of “fuzzy things that are not comets” is still widely used. When Figure $$\PageIndex{1}$$ refers to M4, it denotes the fourth entry in Messier’s list.

A far more extensive listing was compiled under the title of the New General Catalog (NGC) of Nebulae and Star Clusters in 1888 by John Dreyer, working at the observatory in Armagh, Ireland. He based his compilation on the work of William Herschel and his son John, plus many other observers who followed them. With the addition of two further listings (called the Index Catalogs), Dreyer’s compilation eventually included 13,000 objects. Astronomers today still use his NGC numbers when referring to most nebulae and star groups.

# Summary

About 15% of the visible matter in the Galaxy is in the form of gas and dust, serving as the raw material for new stars. About 99% of this interstellar matter is in the form of gas—individual atoms or molecules. The most abundant elements in the interstellar gas are hydrogen and helium. About 1% of the interstellar matter is in the form of solid interstellar dust grains.

## Glossary

interstellar dust
tiny solid grains in interstellar space thought to consist of a core of rocklike material (silicates) or graphite surrounded by a mantle of ices; water, methane, and ammonia are probably the most abundant ices
interstellar medium (ISM)
(or interstellar matter) the gas and dust between the stars in a galaxy
nebula
a cloud of interstellar gas or dust; the term is most often used for clouds that are seen to glow with visible light or infrared


text:
Correcting the Bootstrap Resampling
By Elijah Bernstein-Cooper, September 2, 2015, 0 comments.

## Number of bootstrap resamplings

The number of simulations we run can seem somewhat arbitrary. However the simplest way to determine whether or not we have chosen enough samples is if our estimated confidence interval changes at all between several bootstrap simulations. In the paper I will quote the change in the confidence intervals from different bootstrap runs. A rule of thumb is bootstrap resampling should include at least 10,000 samples.

## Bootstrap Resampling Probabilities

In yesterday’s post I showed the linear fits to each cloud. The bootstrap fits seemed to show too shallow of a slope given the distribution of the data. Today I identified this a mistake I implemented in the bootstrap resampling.

I was assigning the probability of a measurement to be resampled as the inverse of the measurements error. This mean that the vast majority of bootstrap resamples included only low $A_V$ measurements where the error is small. Weighting the resampling led to a biased bootstrap measruement. My initial reasoning for this was to favor more precise measurements in the bootstrap.

The bootstrap resampling now gives an equal probability to any measurement to be resampled. The more precise measurements are still favored, as I perform a weighted least-squares fit to the bootstrapped data. Below are the results using the corrected bootstrap scheme.

##### Figure 1

$A_V$ vs N(HI) relationships for each cloud. The contour levels are now the same in each cloud: 0.99, 0.98, 0.95, 0.86, 0.59% of the data. The bootstrap fit is dominated by the lower $A_V$ data with relatively smaller error, however with the corrected resampling, the DGRs for each cloud rose from previous iterations. The DGR in California went from 4.4 to 7.2. The slopes now seem to trace the bulk of the data more reasonably now.

The scatter plot with error bars shows the high $A_V$ data points do not contribute significantly to the fit because of their larger error.

##### Figure 2

$A_V$ vs N(HI) relationships for each cloud, showing only every 1 out of every 100 data points. After correcting the bootstrap resampling, the fitted relationship now follows a trend more like we would expect, as opposed to before.


text:
## Writing a Linear Equation to Solve an Application

### Learning Outcomes

• Write a linear equation to express the relationship between unknown quantities.
• Write a linear equation that models two different cell phone packages.
• Use a linear model to answer questions.

## Contribute!

Did you have an idea for improving this content? We’d love your input.


text:
CMStatistics 2018: Start Registration
View Submission - CMStatistics
B0799
Title: Comparing several adaptive multiple testing methods for discrete uniform homogeneous $p$-values Authors:  Marta Cousido Rocha - University of Vigo (Spain) [presenting]
Jacobo de Una-Alvarez - University of Vigo (Spain)
Sebastian Doehler - Darmstadt University of Applied Science (Germany)
Abstract: Large-scale discrete uniform homogeneous $p$-values arise in many applications, for example, in genome wide association studies. Several multiple testing procedures for such $p$-values are compared through simulations. Specifically, we consider the $q$-value approach based on several estimators for the proportion of true null hypotheses $\pi_0$: the usual estimator for continuous and possibly heterogeneous $p$-values, and two estimators proposed recently for discrete $p$-values. One of these two proposals is focused on discrete uniform homogeneous $p$-values while we adapt the other one, originally valid for discrete heterogeneous $p$-values to uniform $p$-values. The simulated scenario is that of the two-sample problem with low sample size, along a large number of locations or genes. The considered test statistics are the standard student's $t$ test, a permutation test based on the absolute deviation between the sample means, the Kolmogorov-Smirnov two-sample test, and a permutation test based on the $L_2$ distance between the empirical characteristic functions pertaining to the two samples. The main conclusion is that the specific estimator for $\pi_0$ influences the power a lot, and that the approaches for discrete $p$-values may or may not improve the $q$-value procedure based on the continuous estimator of $\pi_0$.


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# 9.8 Superconductivity  (Page 5/12)

 Page 5 / 12

## Key equations

 Electrostatic energy for equilibrium separation distance between atoms ${U}_{\text{coul}}=-\frac{k{e}^{2}}{{r}_{0}}$ Energy change associated with ionic bonding ${U}_{\text{form}}={E}_{\text{transfer}}+{U}_{\text{coul}}+{U}_{\text{ex}}$ Critical magnetic field of a superconductor ${B}_{\text{c}}\left(T\right)={B}_{\text{c}}\left(0\right)\left[1-{\left(\frac{T}{{T}_{\text{c}}}\right)}^{2}\right]$ Rotational energy of a diatomic molecule ${E}_{r}=l\left(l+1\right)\frac{{\hslash }^{2}}{2I}$ Characteristic rotational energy of a molecule ${E}_{0r}=\frac{{\hslash }^{2}}{2I}$ Potential energy associated with the exclusion principle ${U}_{\text{ex}}=\frac{A}{{r}^{n}}$ Dissociation energy of a solid ${U}_{\text{diss}}=\alpha \frac{k{e}^{2}}{{r}_{0}}\left(1-\frac{1}{n}\right)$ Moment of inertia of a diatomic molecule with reduced mass $\mu$ $I=\mu {r}_{0}^{2}$ Electron energy in a metal $E=\frac{{\pi }^{2}{\hslash }^{2}}{2m{L}^{2}}\left({n}_{1}^{2}+{n}_{2}^{2}+{n}_{3}^{2}\right)$ Electron density of states of a metal $g\left(E\right)=\frac{\pi V}{2}{\left(\frac{8{m}_{e}}{{h}^{2}}\right)}^{3\text{/}2}\phantom{\rule{0.2em}{0ex}}{E}^{1\text{/}2}$ Fermi energy ${E}_{\text{F}}=\frac{{h}^{2}}{8{m}_{e}}{\left(\frac{3N}{\pi V}\right)}^{2\text{/}3}$ Fermi temperature ${T}_{\text{F}}=\frac{{E}_{\text{F}}}{{k}_{\text{B}}}$ Hall effect ${V}_{\text{H}}=uBw$ Current versus bias voltage across p-n junction ${I}_{\text{net}}={I}_{0}\left({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1\right)$ Current gain ${I}_{c}=\beta {I}_{B}$ Selection rule for rotational energy transitions $\text{Δ}l=±1$ Selection rule for vibrational energy transitions $\text{Δ}n=±1$

## Conceptual questions

Describe two main features of a superconductor.

How does BCS theory explain superconductivity?

BSC theory explains superconductivity in terms of the interactions between electron pairs (Cooper pairs). One electron in a pair interacts with the lattice, which interacts with the second electron. The combine electron-lattice-electron interaction binds the electron pair together in a way that overcomes their mutual repulsion.

What is the Meissner effect?

What impact does an increasing magnetic field have on the critical temperature of a semiconductor?

As the magnitude of the magnetic field is increased, the critical temperature decreases.

## Problems

At what temperature, in terms of ${T}_{C}$ , is the critical field of a superconductor one-half its value at $T=0\phantom{\rule{0.2em}{0ex}}\text{K}$ ?

$T=0.707\phantom{\rule{0.2em}{0ex}}{T}_{\text{c}}$

What is the critical magnetic field for lead at $T=2.8\phantom{\rule{0.2em}{0ex}}\text{K}$ ?

A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a $50\text{-}\text{Ω}$ resistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?

61 kV

A tightly wound solenoid at 4.0 K is 50 cm long and is constructed from Nb wire of radius 1.5 mm. What maximum current can the solenoid carry if the wire is to remain superconducting?

Potassium fluoride (KF) is a molecule formed by an ionic bond. At equilibrium separation the atoms are ${r}_{0}=0.255\phantom{\rule{0.2em}{0ex}}\text{nm}$ apart. Determine the electrostatic potential energy of the atoms. The electron affinity of F is 3.40 eV and the ionization energy of K is 4.34 eV. Determine dissociation energy. (Neglect the energy of repulsion.)

$\begin{array}{ccc}\hfill {U}_{\text{coul}}& =\hfill & -5.65\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \\ \hfill {E}_{\text{form}}& =\hfill & -4.71\phantom{\rule{0.2em}{0ex}}\text{eV},\phantom{\rule{0.2em}{0ex}}{E}_{\text{diss}}=4.71\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \end{array}$

For the preceding problem, sketch the potential energy versus separation graph for the bonding of ${\text{K}}^{+}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{\text{Fl}}^{\text{−}}$ ions. (a) Label the graph with the energy required to transfer an electron from K to Fl. (b) Label the graph with the dissociation energy.

The separation between hydrogen atoms in a ${\text{H}}_{2}$ molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV.

${E}_{0r}=7.43\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{eV}$

The characteristic energy of the ${\text{Cl}}_{2}$ molecule is $2.95\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}\text{eV}$ . Determine the separation distance between the nitrogen atoms.

how can we say dirac equation is also called a relativistic equation in one word
what is the electronic configration of Al
what's the signeficance of dirac equetion.?
what is the effect of heat on refractive index
As refractive index depend on other factors also but if we supply heat on any system or media its refractive index decrease. i.e. it is inversely proportional to the heat.
ganesh
you are correct
Priyojit
law of multiple
Wahid
if we heated the ice then the refractive index be change from natural water
Nepal
can someone explain normalization condition
Swati
yes
Chemist
1 millimeter is How many metres
1millimeter =0.001metre
Gitanjali
The photoelectric effect is the emission of electrons when light shines on a material.
What is photoelectric effect
it gives practical evidence of particke nature of light.
Omsai
particle nature
Omsai
photoelectric effect is the phenomenon of emission of electrons from a material(i.e Metal) when it is exposed to sunlight. Emitted electrons are called as photo electrons.
Anil
what are the applications of quantum mechanics to medicine?
Neptune
application of quantum mechanics in medicine: 1) improved disease screening and treatment ; using a relatively new method known as BIO- BARCODE ASSAY we can detect disease-specific clues in our blood using gold nanoparticles. 2) in Genomic medicine 3) in protein folding 4) in radio theraphy(MRI)
Anil
Quantam physics ki basic concepts?
why does not electron exits in nucleaus
electrons have negative
YASH
Proton and meltdown has greater mass than electron. So it naturally electron will move around nucleus such as gases surrounded earth
Amalesh
.......proton and neutron....
Amalesh
excuse me yash what negative
Rika
coz, electron contained minus ion
Manish
negative sign rika shrestha ji
YASH
electron is the smallest negetive charge...An anaion i.e., negetive ion contains extra electrons. How ever an atom is neutral so it must contains proton and electron
Amalesh
yes yash ji
Rika
yes friends
Prema
koantam theory
Laxmikanta
yes prema
Rika
quantum theory tells us that both light and matter consists of tiny particles which have wave like propertise associated with them.
Prema
proton and nutron nuclear power is best than proton and electron kulamb force
Laxmikanta
what is de-broglie wave length?
Ramsuphal
plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
expression for photon as wave
Are beta particle and eletron are same?
yes
mari
how can you confirm?
Amalesh
sry
Saiaung
If they are same then why they named differently?
Amalesh
because beta particles give the information that the electron is ejected from the nucleus with very high energy
Absar
beta particle is of two kind beta plus and beta minus ,beta minus is electron and beta plus is positron
Nepal
beta particles are none but positive charged electron
Priyojit
which is ejected from nucleus
Priyojit
when nutron converts to proton it splits to two part one proton and the minus part ejected as beta
Priyojit
both are same things only the difference is that beta partical ejected from the neuclus and electrons revolves round the neuclus.
Sibghat
what is meant by Z in nuclear physic
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
miss sanjana your question is wrong...question should be no of nucleus present in an atom...and answer is 1...
Owais
Owaise is right
Gitanjali
Z = number of protons in a nucleus of an atom
Shashikanth
Note on spherical mirrors


text:
# Source code for pysteg.features.bsm

##  $Id$
## -*- coding: utf-8 -*-

"""
Calculate the BSM features of Avcibas et al (2005).

The paper present the features in 3 groups (i)-(iii), where the
features within each group are calculated in very similar ways,
based on the same basic statistics.  These groups are recognised
as subvectors in the :class:bsmVector object.

:Module:    pysteg.features.bsm
:Date:      $Date$
:Revision:  $Revision$
:Author:    © 2012: Hans Georg Schaathun <georg@schaathun.net>
"""

import numpy as np
from .cm import splitMatrix

__all__ = [ "bsmraw", "bsm12", "bsm3", ]

# Group (i)-(ii) Preliminaries
# ----------------------------

# The first two groups, totalling 16 features, are based on four
# statistics a, b, c, d from each of the two bit planes, defined in
# Eq (2) in the paper.  These four statistics are calculated by
# :func:chiavg below.  First we define the auxiliary function
# :func:chi defining the \chi_{r,s} values from Eq (1).
#
# .. autofunc:: pysteg.analysis.sfeatures.chi
#
# ::

def chi(X,dir):
"""
This function calculates the texture type \chi_{r,s} for each pixel r,
according to (1) in Avcibas' paper.  The input dir is the direction s.
The result is a numpy array, giving the type for each pixel of X with
respect to the given direction.

Although Avcibas uses the range 1..4 for the type, we use 0..3 because
this makes implementation easier.
"""
(A,B) = splitMatrix(X,dir)
return 2*A + B

# .. autofunc:: chiavg
#
# ::

def chiavg(X):
"""
This function returns a numpy array [a,b,c,d], where a,b,c,d
are given by (2) in Avcibas' paper.
"""
h = np.zeros(4)
dlist = [ (0,1), (1,0), (-1,0), (0,-1) ]
for d in dlist:
h += np.histogram( chi(X,d), range(5) )[0]
return h.astype(float) / X.size

# Group (i)
# ---------
#
# Group (i) is based on a 10-D features vector from each of the bit
# planes.  The ten features used for the image is the vector difference
# of the features from the two bitplanes.
#
# .. autofunction:: g1
#
#    calculates the 10-D feature vector from a binary image.
#    The input is the output of the :func:chiavg function.
#
# ::

def g1(h):
a,b,c,d = h
bc = b + c
m2 = a / ( a + 2*bc )
m3 = a / bc
m5 = ( a/(a+b) + a/(a+c) + d/(b+d) + d/(c+d) ) / 4
m6 = a*d / np.sqrt( (a+d)*(a+c)*(b+d)*(c+d) )
m7 = np.sqrt( (a/(a+b)) * (a/(a+c)) )
m8 = bc / (2*a + b + c)
m9 = b*c / S ** 2
m10 = bc / 4*S
return np.array( [ m1,m2,m3,m4,m5,m6,m7,m8,m9,m10 ] )

# Group (ii)
# ----------
#
# The calculation of group (ii) can be made significantly simpler
# than the presentation in the paper.  Firstly, we observe that
# the probability estimates p_i^j are equal to the a/4, b/4, c/4, and
# d/4, and can thus be calculated easily directly from the output of
# :func:chiavg from Group (i).
#
# Group (ii) consists of four features calculated from a pair of
# lists [a,b,c,d] calculated by :func:chiavg for each of the two
# binary image.  Each of the feature uses one one of the following
# basic similarity function, which we define as global variables
# because they are used also for Group (iii).
#
# ::

f11 = lambda (p7,p8) : min(p7,p8)
f12 = lambda (p7,p8) : abs(p7-p8)
f13 = lambda (p7,p8) : - p7 * np.log(p8)
f14 = lambda (p7,p8) : - p7 * np.log(p7/p8)
basefunc = [ f11, f12, f13, f14 ]

def g2(h1,h2):

# The input include two lists h1 and h2 representing the two bit planes
# to be compared.  We divide each of them by four, and zip them together
# to a single list of pairs (p7^j,p8^j).
#
#   ::

L = zip(list( h1 / 4 ), list( h2 / 4 ) )

# Each of the features applies a simple function to a pair of the list
# L, and add the result over all the pairs in the list.  These four basic
# are defined in the global basefunc list.  The actual features can be
# calculated by applying each function f on each pair from L (using
# :func:map) and then add over the elements of L.
#
#   ::

return [ sum( map(f,L) ) for f in basefunc ]

# Group (iii)
# -----------
#
# The structure of Group (iii) is very similar to Group (ii),
# but it is not based on the same base statistics a,b,c,d.
# Instead each possible value for a 3x3 binary submatrix is
# enumerated (range 0..511), and for each pixel, the corresponding
# type of its 3x3 neighbourhood is recorded.  The histogram of
# these neighbourhood types is used as the underlying statistics.
# This histogram, for a binary image X, is calculated using the
# following :func:shist function.
#
# ::

def shist(X):
(M,N) = X.shape

# To take care of the boundary, we need to pad the array with a
# zero frame.
#
#   ::

Y = np.zeros((M+2,N+2))
Y[1:-1,1:-1] = X

# We generate the new array by multiplying submatrices of Y with
# the mask filter, and then take the histogram of this array.
#
#   ::

mask = np.array( [[ 1,2,4] , [2**7, 2**8, 2**3], [2**6, 2**5, 2**4]] )
Z = np.array( [ [ np.sum( mask * Y[x:(x+3),y:(y+3)] )
for y in xrange(N) ] for x in xrange(M) ] )
return np.histogram( Z, range(513) )[0].astype(float)

# The main function :func:g3 is implemented very similarly to
# :func:g2, except that the input is two binary images, and
# the histogram to be used is calculated internally.
#
# ::

def g3(X7,X8):
L = zip( shist(X7), shist(X8) )
return [ sum( map(f,L) ) for f in basefunc ]

# The :class:bsmVector class
# ----------------------------

def _bitplanes(I):
return ( (I>>1) % 2 , I % 2 )

[docs]def bsmraw(I):
"Return the raw BSM features underlying groups (i) and (ii)."
if I == None:
return namesraw
X7,X8 = _bitplanes(I)
return list(chiavg(X7)) + list(chiavg(X8))

[docs]def bsm3(I):
"Return group (iii) of the BSM features."
if I == None:
return names3
X7,X8 = _bitplanes(I)
return g3(X7,X8)

featureDic = {
"BSM-12" : [ ("Raw 7",), ("Raw 8",), ("(iii)",) ],
"BSM-18" : [ ("(i)",), ("(ii)",), ("(iii)",) ],
}

dlist = [ (0,1), (1,0), (-1,0), (0,-1) ]
names1 = [ "BSM[i]m%s" % (x,) for x in range(1,11) ]
names2 = [ "BSM[ii]" + s for s in [ "f1", "f2", "f3", "f4" ] ]
names3 = [ "BSM[iii]" + s for s in [ "f1", "f2", "f3", "f4" ] ]
namesraw = [ "BSMR7(%s,%s)" % (x,y) for (x,y) in dlist ] + \
[ "BSMR8(%s,%s)" % (x,y) for (x,y) in dlist ]

[docs]def bsm12(I):
"Return groups (i) and (ii) of the BSM features."
if I == None:
return names1 + names2
X7,X8 = _bitplanes(I)
h7 = chiavg(X7)
h8 = chiavg(X8)
return  list( g1(h7) - g1(h8) ) + g2(h7,h8)


text:
# Mutation in the α-Synuclein Gene Identified in Families with Parkinson's Disease

@article{Polymeropoulos1997MutationIT,
title={Mutation in the $\alpha$-Synuclein Gene Identified in Families with Parkinson's Disease},
author={M. Polymeropoulos and C. Lavedan and E. Leroy and S. Ide and A. Dehejia and A. Dutra and B. Pike and H. Root and J. Rubenstein and R. Boyer and E. Stenroos and S. Chandrasekharappa and A. Athanassiadou and T. Papapetropoulos and W. Johnson and A. Lazzarini and R. Duvoisin and G. Iorio and L. Golbe and R. Nussbaum},
journal={Science},
year={1997},
volume={276},
pages={2045-2047}
}
Parkinson's disease (PD) is a common neurodegenerative disorder with a lifetime incidence of approximately 2 percent. A pattern of familial aggregation has been documented for the disorder, and it was recently reported that a PD susceptibility gene in a large Italian kindred is located on the long arm of human chromosome 4. A mutation was identified in the α-synuclein gene, which codes for a presynaptic protein thought to be involved in neuronal plasticity, in the Italian kindred and in three… Expand
6,398 Citations
No pathogenic mutations in the β-synuclein gene in Parkinson's disease
11 families consistent with autosomal dominant inheritance of probable Parkinson's disease (PD) are presented, and Sequencing the translated exons of the β-synuclein gene failed to identify any pathogenic mutation. Expand
Point Mutations in the α-Synuclein Gene.
• Biology, Medicine
• Methods in molecular medicine
• 2001
It was concluded that this mutation is the cause of PD in this family, and the first report of a mutation causing clinically and pathologically defined idiopathic PD associated with the critical pathologic finding, the intraneuronal inclusions in brainstem nuclei including the substantia nigra. Expand
The role of the α-synuclein gene mutation in patients with sporadic Parkinson’s disease in the United Kingdom
• Biology, Medicine
• Journal of neurology, neurosurgery, and psychiatry
• 1998
DNA from 70 patients with Parkinson's disease was screened for the G209A mutation, suggesting that it is not relevant for most patients with sporadic idiopathic Parkinson’s disease. Expand
Low frequency of α‐synuclein mutations in familial Parkinson's disease
Primers and methods for exonic sequencing of this gene were developed and the entire coding region of the gene was sequenced and no genetic variation was found, suggesting that NACP is not the chromosome 4 locus for disease. Expand
Absence of mutations in the coding region of the α-synuclein gene in pathologically proven Parkinson's disease
• Biology, Medicine
• Neurology
• 1998
Using reverse transcribed-polymerase chain reaction (RT-PCR) technique, the entire coding region of the α-synuclein gene is sequenced using brain tissue from 24 pathologically proven Parkinson's disease cases, suggesting that a mutation at the coding region is unlikely to be responsible for nigrostriatal degeneration in typical sporadic Parkinson's Disease. Expand
Causal relation between α-synuclein locus duplication as a cause of familial Parkinson's disease
The results indicate that SNCA is more frequently associated with familial Parkinson's disease than previously thought, and that there is a clear dosage effect according to the number of supernumerary copies of this gene. Expand
Sequencing of the α-Synuclein Gene in a Large Series of Cases of Familial Parkinson's Disease Fails to Reveal any Further Mutations
It is concluded that the A53T change described in the alpha-synuclein gene is a rare cause of PD or may even be a rare variant. Expand
Evaluation of the γ-synuclein gene in German Parkinson's disease patients
The results do not support a major role of the γ-synuclein gene in Parkinson's disease and no evidence for an increased risk of combined genotypes of polymorphisms in theγ- synuclein and the α-syn nuclein gene was found. Expand
Genetic dissection of familial Parkinson's disease.
• Biology, Medicine
• Molecular medicine today
• 1998
The elucidation of polygenic changes in the dopamine pathway, mitochondrial dysfunction, and metabolism of xenobiotics is now technically possible by means of association and genotype studies and will have important implications for the development of individual therapeutic strategies to prevent disease progression. Expand
Genetic Analysis of Synphilin-1 in Familial Parkinson's Disease
Two-point genetic linkage analysis of a dinucleotide repeat within the synphilin-1 gene initially implicated this locus as a cause of Parkinson's disease in three of nine families, but subsequent haplotype, sequencing, and association analyses suggest that variability within the locus does not confer susceptibility to Parkinson's Disease. Expand

#### References

SHOWING 1-10 OF 18 REFERENCES
Mapping of a Gene for Parkinson's Disease to Chromosome 4q21-q23
Parkinson's disease (PD) is the second most common neurodegenerative disorder after Alzheimer's disease, affecting approximately 1 percent of the population over age 50. Recent studies have confirmedExpand
A familial Alzheimer's disease locus on chromosome 1
A 112-base pair allele of D1S479 co-segregated with the disease in five of seven families, which is consistent with a common genetic founder. Expand
A mutation in Alzheimer's disease destroying a splice acceptor site in the presenilin-1 gene
The intron/exon structure of the PS-1 gene has been determined and this information has been used to identify a mutation in the splice acceptor site for exon 9 in a family with early onset Alzheimer's disease. Expand
The human NACP/alpha-synuclein gene: chromosome assignment to 4q21.3-q22 and TaqI RFLP analysis.
The chromosome localization of the NACP gene was determined using PCR and Southern blotting analyses of somatic cell hybrids and in situ chromosome hybridization, and a two-allele RFLP was identified by screening genomic DNA from unrelated Caucasian individuals by using Southern blot analysis. Expand
Familial Alzheimer's disease in kindreds with missense mutations in a gene on chromosome 1 related to the Alzheimer's disease type 3 gene
Analysis of the nucleotide sequence of the open reading frame of the E5-1 gene led to the discovery of two missense substitutions at conserved amino-acid residues in affected members of pedigrees with a form of familial AD that has a later age of onset than the AD3 subtype (5070 years versus 3060 years for AD3). Expand
A large kindred with autosomal dominant Parkinson's disease
• Medicine
• Annals of neurology
• 1990
It is concluded that what is probably a single gene without an additional environmental insult can cause the pathological changes typical of PD and will enhance the likelihood of significant genetic component in the cause of sporadic PD. Expand
Linkage of a prion protein missense variant to Gerstmann–Sträussler syndrome
It is shown here that PrP codon 102 is linked to the putative gene for the syndrome in two pedigrees, providing the best evidence to date that this familial condition is inherited despite also being infectious, and that substitution of leucine for proline at PrPcodon 102 may lead to the development of Gerstmann–Sträussler syndrome. Expand
High-resolution mapping of SNCA encoding α-synuclein, the non-Aβ component of Alzheimer’s disease amyloid precursor, to human chromosome 4q21.3→q22 by fluorescence in situ hybridization
• Biology
• 1995
The human α-synuclein gene (SNCA) was previously identified as the non-Aβ component of Alzheimer’s disease amyloid precursor (NACP). A cosmid clone containing this gene has been isolated and mapped by
A clinical genetic study of Parkinson's disease
The cumulative risk of Parkinson's disease in relatives of patients seen consecutively for 1 year and the proportion of secondary cases of PD as a function of pedigree completeness was assessed, suggesting significant familial aggregation in a subset of randomly ascertained families. Expand
The anterior olfactory nucleus in Parkinson's disease
• Medicine, Biology
• Movement disorders : official journal of the Movement Disorder Society
• 1995
It is shown that the presence of Lewy bodies in the olfactory bulb and tract is associated with significant neuronal loss in patients with idiopathic Parkinson's disease. Expand


text:
# Daedalus' Ninth Challenge

## Recommended Posts

I was reminiscing about a problem that my Calculus 3 professor gave us, and decided to modify the problem to make it a little more challenging to solve. Although the problem isn't hard to figure out, it does have some interesting consequences. So without further adieu, I give you my ninth challenge.

A Moth to a Flame

It is common knowledge that certain insects, such as moths, are attracted to light sources. Let's consider that a moth navigates the world by maintaining a constant angle to the sun, which can be considered an infinite light source. Furthermore, let's say that at night the moth uses any light source that is available, and for all intents and purposes our light source is a bug zapper. Since the bug zapper is not an infinite light source, the moth will spiral into the bug zapper due to maintaining a constant angle with respect to radial lines from the center of the bug zapper that define the path of the spiral.

The goal of this challenge is to identify the type of spiral, and to find the simplified equation for the curvature of the spiral in terms of the radial distance $d$ and the angle of the moth $\phi$ with respect to radial lines from the center of the bug zapper. Several clues have been given that should help you solve this challenge. Reputation awaits for the one who solves it first.

Edited by Daedalus

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"Reputation awaits for the one who solves it first."

How? I don't think he has posted here since he died n years ago

Incidentally n-2 is a square number.

However I guess solving the problem by knowing one of the names of that spiral and googling it doesn't count.

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"Reputation awaits for the one who solves it first."

How? I don't think he has posted here since he died n years ago

Incidentally n-2 is a square number.

However I guess solving the problem by knowing one of the names of that spiral and googling it doesn't count.

The problem has two parts. You have to know the type of spiral so you can get it's equation to find the curvature. The equation for it's curvature must be in terms of $d$ and $\phi$. If you know the name of the spiral, go ahead and post it John. Perhaps someone will find the answer by googling it.

Edited by Daedalus

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Why does your diagram show an r but your wording a d?

Is this intentional misdirection?

Edited by studiot

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Why does your diagram show an r but your wording an d?

Is this intentional misdirection?

It's actually a clue that I provided hinting at the way I solved the problem. Nice attention to the details!

Edited by Daedalus

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It would be more fun to solve the way Descartes originally did.

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It would be more fun to solve the way Descartes originally did.

True, it would be more fun, but the challenge only requires that one provides the equation for the curvature in terms of $d$ and $\phi$.

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I'd like to point out that moths do not navigate by the Sun...

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I'd like to point out that moths do not navigate by the Sun...

Lol... They sure don't. It's just a set up for the problem as was given to me by my Calc 3 professor. Just to speed things up a little, the spiral is known as a logarithmic or equiangular spiral.

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I'd like to point out that moths do not navigate by the Sun...

With mathematics, sometimes the illogical is needed to solve the logical.

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Who actually gave neg rep to Moontanman? Don't worry I'll counter it...

Edited by Daedalus

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Who actually gave neg rep to Moontanman? Don't worry I'll counter it...

Because of my willingness of opinion, I did. I didn't see it as a joke rather as a criticism that was unnecessary, therefore I stated that the logic he was presenting was unneeded because it doesn't help solve the problem. The point of a mathematical problem with seemingly illogical parts is to help to solve the problem.

Just my opinion. I will take up the challenge and see if I can solve it.

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Well, at least you're honest Unity Moontanman and I are friends, and I took his response as a joke. It's always hard to tell someone's intentions just through text. Feel free to solve the challenge. I found it quite interesting when I worked the problem many years ago, but I love mathematics.

Edited by Daedalus

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This curve has some remarkable geometric properties as well as calculus ones. Calculus had not been invented when Descartes discovered it in 1638.

Jacob Bernoulli had one engraved on his tomb along with the words "Eadem metata resurgo"

Because of the constant angle property, if you roll the curve along a straight line, its centre or pole describes another straight line at an angle to the first. Erect a perpendicular from the pole to the first straight line and the length from where it cuts, back along back the first straight line to the starting point is equal to the length of the spiral.

Edited by studiot

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This curve has some remarkable geometric properties as well as calculus ones. Calculus had not been invented when Descartes discovered it in 1638.

Jacob Bernoulli had one engraved on his tomb along with the words "Eadem metata resurgo"

Because of the constant angle property, if you roll the curve along a straight line, its centre or pole describes another straight line at an angle to the first. Erect a perpendicular from the pole to the first straight line and the length from where it cuts, back along back the first straight line to the starting point is equal to the length of the spiral.

That's actually pretty cool studiot. The professor who gave us this problem is a good friend of mine. However, he didn't want an equation for the answer. He gave us the distance $d$ and the angle of the moth $\phi$ with respect to radial lines from the center of the bug zapper and wanted the curvature of the logarithmic spiral at that point. So, as usual, I derived the equation and plugged in the numbers. It's actually a pretty neat problem with an interesting result once you try to solve it.

I figured this challenge would be a nice break from my usual type of problems that can be tough to solve. Don't get me wrong. This problem can be challenging too. If you don't know the type of spiral, you would have to search for it online in order to get the equations, which was intended. I didn't expect anyone to go to a library and research the problem to solve it. However, the problem is no where near as tough as my other challenges.

Edited by Daedalus

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What made you think I went to a Library?

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What made you think I went to a Library?

I never thought you went to a library. The comment was intended towards John's statement in the second post:

However I guess solving the problem by knowing one of the names of that spiral and googling it doesn't count.

It's ok to research the problem online, but one would still have to solve for the equation of the curvature in terms of $d$ and $\phi$, which is the whole point of the challenge.

Edited by Daedalus

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Like JC, I didn't want to spell out the name of the curve, until you did, in order not to spoil it for others.

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One of the (not very original) names of that curve is the equiangular spiral.

If you have heard of that and Google it, you get a lot of information about it.

Unfortunately, my maths isn't very good. Can I get some credit for the particular case where = 90 degrees?

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Like JC, I didn't want to spell out the name of the curve, until you did, in order not to spoil it for others.

I'm not sure if you seen post #9, but I went ahead and gave everyone the name of the spiral to help speed things up.

One of the (not very original) names of that curve is the equiangular spiral.

If you have heard of that and Google it, you get a lot of information about it.

Unfortunately, my maths isn't very good. Can I get some credit for the particular case where = 90 degrees?

Yeah, there is quite a bit of information on the internet concerning logarithmic spirals, but oddly enough I haven't seen the equation for this particular derivation of the curvature. You will find other equations, but they are not in terms using only $d$ and $\phi$. However, that doesn't mean you won't find it, but that it's not listed on the usual sites one would go to look. As for the case when $\phi = 90^\circ$, I included that in the graph I posted as a clue...

Edited by Daedalus

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Hint the polar form is best.

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Hint the polar form is best.

Most definitely. I ended up converting from polar to parametric to derive the equation for the curvature because I like working with vector valued functions.

Edited by Daedalus

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It has been over two weeks and no one has provided the solution. So, here is the answer to this challenge:

A logarithmic spiral is defined by the polar equation:

$r=a\,e^{b\,\theta}$

The following definition as provided by Wikipedia will allow us to solve for $b$ in terms of $\phi$:

$\phi=\text{cos}^{-1}\frac{\left\langle r(\theta),\,r'(\theta)\right\rangle}{\left\|r(\theta)\right \|\,\left\|r'(\theta)\right\|}=\text{tan}^{-1}\frac{1}{b}$

Solving for $b$, we get:

$b=\text{cot}\,\phi$

Now that we have $b$ in terms of $\phi$, we'll substitute the result into the polar equation:

$r=a\,e^{\theta\,\text{cot}\,\phi}$

Now if it isn't obvious what to do with that $a$ to get $d$ into the equation, you can always rewrite the equation using $d$. We'll even add an angle $\varphi$ where the radial distance will be equal to $d$:

$d=a\,e^{\varphi\,\text{cot}\,\phi}$

Solving for $a$, we get:

$a=d\,e^{-\varphi\,\text{cot}\,\phi}$

Substitute the result into the original equation and simplify:

$r=\left(d\,e^{-\varphi\,\text{cot}\,\phi}\right)e^{\theta\,\text{cot}\,\phi}$

$r=d\,e^{(\theta-\varphi)\,\text{cot}\,\phi}$

We can clearly see that when $\theta$ is equal to $\varphi$, the function simplifies to $r=d$. This brings us to the realization that $a$ is just a scaling factor and we didn't need $\varphi$. We could've just defined $r=d$ when $\theta=0$. Next, we'll define the polar function as a vector valued function in order to find the curvature:

$R(\theta)=\left\langle d\,e^{\theta\,\text{cot}\,\phi}\text{cos}\,\theta,\,d\,e^{\theta\,\text{cot}\,\phi}\text{sin}\,\theta\right\rangle$

The curvature of our function $R$ is defined by:

$k(\theta)=\frac{\left\vert T'(\theta)\right\vert}{\left\vert R'(\theta)\right\vert}$

The magnitude of $R'(\theta)$ is equal to:

$\left\vert R'(\theta)\right\vert=d\,e^{\theta\,\text{cot}\,\phi}\text{csc}\,\phi$

Solving for the unit tangent vector $T$, we get:

$T(\theta)=\frac{R'(\theta)}{\left\vert R'(\theta)\right\vert}=\left\langle\text{cos}(\theta+\phi),\,\text{sin}(\theta+\phi)\right\rangle$

The magnitude of $T'(\theta)$ is equal to one:

$\left\vert T'(\theta)\right\vert=\sqrt{\left(-\text{sin}(\theta+\phi)\right)^2+\left(\text{cos}(\theta+\phi)\right)^2}=1$

Now that we have $\left\vert R'(\theta)\right\vert$ and $\left\vert T'(\theta)\right\vert$, we can define the curvature:

$k(\theta)=\frac{1}{d\,e^{\theta\,\text{cot}\,\phi}\text{csc}\,\phi}$

As stated, when $\theta=0$ the function simplifies to $r=d$. So, we can set $\theta=0$ and arrive at the solution for the challenge:

$k=\frac{1}{d\,\text{csc}\,\phi}=\frac{\text{sin}\,\phi}{d}$

A circle also has this equiangular property and its curvature is $k=1/d$, which is what we expect for $\phi=\pi/2$ or $90^\circ$:

$k=\frac{\text{sin}(\pi/2)}{d}=\frac{1}{d}$

Ninth Challenge.zip

Edited by Daedalus

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