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# Share: Harry Potter and the Methods of Rationality

Is there some amazing rational thing you do when your mind’s running in all different directions?” she managed.
“My own approach is usually to identify the different desires, give them names, conceive of them as separate individuals, and let them argue it out inside my head. So far the main persistent ones are my Hufflepuff, Ravenclaw, Gryffindor, and Slytherin sides, my Inner Critic, and my simulated copies of you, Neville, Draco, Professor McGonagall, Professor Flitwick, Professor Quirrell, Dad, Mum, Richard Feynman, and Douglas Hofstadter.”
Hermione considered trying this before her Common Sense warned that it might be a dangerous sort of thing to pretend. “There’s a copy of me inside your head?”
“Of course there is!” Harry said. The boy suddenly looked a bit more vulnerable. “You mean there isn’t a copy of me living in your head?”
There was, she realized; and not only that, it talked in Harry’s exact voice.
“It’s rather unnerving now that I think about it,” said Hermione. “I do have a copy of you living in my head. It’s talking to me right now using your voice, arguing how this is perfectly normal.”
“Good,” Harry said seriously. “I mean, I don’t see how people could be friends without that.”
She continued reading her book, then, Harry seeming content to watch the pages over her shoulder.
She’d gotten all the way to number seventy, Katherine Scott, who’d apparently invented a way to turn small animals into lemon tarts, when she finally worked up the courage to speak.

# Regularization

Based on a small post found here.

One of the standard problems in ML with meta modelling algorithms(Algorithms that run multiple statistical models over given data and identifies the best fitting model. For ex: randomforest  or the rarely practical genetic algorithm) ,  is that they might favour overly complex models that over fit the given training data but on live/test data perform poorly.

The way these meta modelling algorithms work is they have a objective function(usually the RMS of error of the stats/sub model with the data)  they pick the model based on.(i.e: whichever model yields lowest value of the objective function).  So we can just add a complexity penalty(one obvious idea is the rank of the polynomial that model uses to fit, but how does that work for comparing with exponential functions?)  and the objective function suddenly becomes RMS(Error) + Complexity_penalty(model).

Now depending on the right choice of Error function and Complexity penalty this can find models that may perform less than more complex models on the training data, but can perform better in the live model scenario.

The idea of complexity penalty itself is not new, I don’t dare say ML borrowed it from scientific experimentation methods or some thing but the idea that the more complex a theory or a model it should be penalized over a simpler theory or model is very old. Here’s a better written post on it.

# Sleeper Theorems

This inspired me to compile a list:
Since, I’m not a mathematician(pure/applied) I just compiled things from the blog post combining
* Bayes Theorem $P(A|B) = P(B|A) *P(A)/P(B)$

• Jensen’s Inequality $\psi(E(X)) <= E(\psi(X))$ if $\psi$ is a convex function and X is
a random variable. Extends convexity from sums to integrals(aka discrete to continuous)
• lto’s lemma: aka(Merton, Black and Scholes option pricing formula)
• Complex analysis.. should i disqualify this as not a theorem??
• Standard error of the mean.details link
• Jordan Curve Theorem: A closed curve has an inside and an outside. (sounds obvious in 2D
and 3D, perhaps with time as 4D, keeping options open is staying outside closed curves??)
• kullback-leibler positivity:(no clue need to look up wolfram alpha or wikipedia)
• Hahn-Banach Theorem (again needs searching)
• Taylor’s theorem, (once again continuous function approximated by sum of discrete
components/expressions) Used in:
• Approximating any function with nth degree precision
• Bounding the error term of an approximation
• Decomposing functions into linear combinations of other functions
• Kolmogorov’s Inequality for the maximum absolute value of the partial sums of a sequence of IID random variables.( the basis of martingale theory)
• Karush-Kuhn-Tucker optimality conditions for nonlinear programming, link
here
• Envelope Theorem — from economics
• Zorn’s lemma , also Axiom of Choice
• Fourier Transform and Fast Fourier Transform

# Elbow Method

What is elbow method?:
Elbow method So elbowing is this mechanism of
aloud or is too subtle to try to find words for.

Okay, just kidding, while that’s kinda true, I was just pranking on y’all. What I want to
talk about is a stats/math/Machine Learning method used when trying to find clusters in a
given dataset. So [Elbow Method] (https://en.wikipedia.org/wiki/Elbow_method_(clustering))
is basically a measure/method for interpretation and validation of conistency of a cluster.
Ugh.. the original sentence in Wikipedia is so long with all 10-letter words, I couldn’t
even type it again.(Above attempt was simplified during typing-on-the-fly)

The basic issue is that, during a cluster analysis we need to settle on a few things:
* A measure for distance within, across and between clusters and points in the
clusters

• A method/algorithm for updating, re-assigning the points to clusters.
• Optional: A formula for guessing the number of algorithms. In most cases this is
optional, and parameterized.

In the case of elbow method it is a visual method for the third option. Basically, it’s a
ratio of variance (within clusters) divided by overall variance. So it explains how much(or
what %)of
the total variance is explained by choosing “n” number of clusters.

The name elbow method comes from visually plotting the number of clusters Vs the ratio(% of
variance explained) and finding that point where there’s an acute bend(if no.of.clusters is
in X-axis), picking the number of clusters at that point.

# Share: Harry Potter and the Methods of Rationality

The world around us redunds with opportunities, explodes with opportunities, which nearly all folk ignore because it would require them to violate a habit of thought; in every battle a thousand Hufflepuff bones waiting to be sharpened into spears. If you had thought to try a massed Finite Incantatem on general principles, you would have dispelled Mr. Potter’s suit of chainmail and everything else he was wearing except his underwear, which leads me to suspect that Mr. Potter did not quite realize his own vulnerability. Or you could have had your soldiers swarm Mr. Potter and Mr. Longbottom and physically wrest the wands from their hands. Mr. Malfoy’s own response was not what I would term well-reasoned, but at least he did not wholly ignore his thousand alternatives.” A sardonic smile. “But you, Miss Granger, had the misfortune to remember how to cast the Stunning Hex, and so you did not search your excellent memory for a dozen easier spells that might have proved efficacious. And you pinned all your army’s hopes on your own person, so they lost spirit when you fell. Afterward they continued to cast their futile Sleep Hexes, governed by the habits of fighting that had been trained into them, unable to break the pattern as Mr. Malfoy did. I cannot quite comprehend what goes through people’s minds when they repeat the same failed strategy over and over, but apparently it is an astonishingly rare realization that you can try something else. And so the Sunshine Regiment was wiped out by two soldiers.” The Defense Professor grinned mirthlessly. “One perceives certain similarities to how fifty Death Eaters dominated all of magical Britain, and how our much-loved Ministry continues in its rul

# F-test

We’ve already seen what F-score is. Now let’s see what
F-test. Side note: I came across it when I was writing
Elbow Method and my thoughts were, cool another F-word for my readers, so

## Here you go:

• F-test is any stats test that uses F-distribution

• It is often used when comparing stats models that have been fitted to a data set.. Ahh.. That
sounds no different from F-score then.. May be just different
fields(Statistics and Machine Learning) have different naming conventions?? Anyway two different
F-words.. So let’s just say what F-score/test?? Why two names for samething and move on…

## Examples:

• Null Hypothesis: Means of a given set of normally distributed populations all having same standard deviation being equal.(used in ANOVA)

• The hypothesis that a proposed regression model fits the data well.

• The hypothesis that a data set in a regression analysis follows the simpler of two proposed linear models that are nested within each other.

• It(non-regression type) is also a test of homoskedasticity

## Formula

• Formula: $explained variance/un-explained variance$ or $between-group-variability/within-group-variability$ Ok. That doesn’t sound like the F-score

• Formula(for regression models): $((RSS\_1 - RSS\_2) / (p_2 - p_1)/(RSS_2/(n-p_2)))$

# Visualization Grammar — VEGA

## VEGA:

A visualization grammar, a language for:
* — creating, saving and sharing interactive visualization designs
* — describe visual appearance and interactive behaviour of visualization in json
* — reactive signals that dynamically modify a visualization in response to input
event streams

## Key Semantics:

The key semantics are:
* — width, height, padding, autosize (all are for specifying the size of the
visualization)
* — data (an array of data definitions, can define type, name, stream, url, and values of the
data type)

• — scales (Configurations for as to map columns of data to pixel positions or
colors, or type of representation(for ex: categorical==> bands etc)).

• — axes (Configuration of axes)

• — marks (Graphical primitives, which are used to encode data. Has properties
position, size, shape, color. Examples are: dot, circle, rectangle(bar-chart),
star etc..)

• — Have sub properties encode which marks the graphical primitives
• — Encode’s Sub property enter and exit configure interactive parts when
the mark is added or removed.
• — marks sub property hover, update configure overall interactive parts
• — each of the hover, update properties can be triggered/linked to signals
and changed accordingly
• — A special type of mark called group is present and can contain other
marks(for composition of graphical primitives to create complex ones)

• — signals (act as dynamic variables, or as event-listeners to use js parlance)

• — Has sub property event streams
• — Can set dynamically evaluated variables as values on events as
defined.
• — Events can be mouse over, mouse out, click,drag etc..
• — Event streams
• — Has sub properties source, type, marktype, between, consume, filetr etc.
• — Each sub property decides which mark to change/update, based on which
event type/user-action/data-change
• — Event streams also have CSS-style selectors

• — Legends

• — Can create legends for the visualizatinos
• — customize them with sub properties type, orient, fill, opacity, shape

• — Transforms

• — As the name implies it can transform data streams
• — Has sub properties ilke filter, stack, aggregate, bin, collect, fold,
impute etc

# Share: Harry Potter and the Methods of Rationality

There was a legendary episode in social psychology called the Robbers Cave experiment. It had been set up in the bewildered aftermath of World War II, with the intent of investigating the causes and remedies of conflicts between groups. The scientists had set up a summer camp for 22 boys from 22 different schools, selecting them to all be from stable middle-class families. The first phase of the experiment had been intended to investigate what it took to start a conflict between groups. The 22 boys had been divided into two groups of 11 –
– and this had been quite sufficient.
The hostility had started from the moment the two groups had become aware of each others’ existences in the state park, insults being hurled on the first meeting. They’d named themselves the Eagles and the Rattlers (they hadn’t needed names for themselves when they thought they were the only ones in the park) and had proceeded to develop contrasting group stereotypes, the Rattlers thinking of themselves as rough-and-tough and swearing heavily, the Eagles correspondingly deciding to think of themselves as upright-and-proper.
The other part of the experiment had been testing how to resolve group conflicts. Bringing the boys together to watch fireworks hadn’t worked at all. They’d just shouted at each other and stayed apart. What had worked was warning them that there might be vandals in the park, and the two groups needing to work together to solve a failure of the park’s water system. A common task, a common enemy.
Harry had a strong suspicion Professor Quirrell had understood this principle very well indeed when he had chosen to create three armies per year.


text:
chapter
20 Pages

## An Energy Principle for a Free Boundary Problem for Navier-Stokes Equations

WithRaja Dziri, Jean-Paul Zolésio

Abstract We study the existence of an optimal domain for an energy shape minimization problem.

By showing that the problem considered can be relaxed to measurable sets we avoid regularity hypotheses. The study leads, in the nonsmooth case, to a distributed optimality condition, which can be expressed, in the smooth case, by an extra-equation satisfied on the boundary of the optimal domain.

format: plain


text:
Article Contents
Article Contents
Early Access

Early Access articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Early Access publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Early Access articles via the “Early Access” tab for the selected journal.

# Pattern formation of Brusselator in the reaction-diffusion system

• * Corresponding author: Jianwei Shen
• Time delay profoundly impacts reaction-diffusion systems, which has been considered in many areas, especially infectious diseases, neurodynamics, and chemistry. This paper aims to investigate the pattern dynamics of the reaction-diffusion model with time delay. We obtain the condition in which the system induced the Hopf bifurcation and Turing instability as the parameter of the diffusion term and time delay changed. Meanwhile, the amplitude equation of the reaction-diffusion system with time delay is also derived based on the Friedholm solvability condition and the multi-scale analysis method near the critical point of phase transition. We discussed the stability of the amplitude equation. Theoretical results demonstrate that the delay can induce rich pattern dynamics in the Brusselator reaction-diffusion system, such as strip and hexagonal patterns. It is evident that time delay causes steady-state changes in the spatial pattern under certain conditions but does not cause changes in pattern selection under certain conditions. However, diffusion and delayed feedback affect pattern formation and pattern selection. This paper provides a feasible method to study reaction-diffusion systems with time delay and the development of the amplitude equation. The numerical simulation well verifies and supports the theoretical results.

Mathematics Subject Classification: Primary: 35K57, 35B36, 35Q92; Secondary: 34H20.

 Citation:

• Figure 1.  (a) Hopf bifurcation of $u$ about $b$ when $\theta = 0.05$ and $\tau = 0$. The time evolution corresponding to system (2) when $b = 1.5$(b), $b = 2.5$(c) and $b = 7.5$(d)

Figure 2.  The curve of the bifurcation critical point $b_{H}$ of the system (2) with the feedback strength $\theta$ when without diffusion and $\tau = 0$

Figure 3.  Concentration-time profiles of variables $u$ and $v$ in the system (2) for different $\tau$ when $d_1 = d_2 = 0$, $a = 1$, $\theta = 0.05$ and $b = 1.5$. The time delays are (a) $\tau = 1$, (b) $\tau = 1.5$ and (c) $\tau = 2$ respectively. (d) Bifurcation of the concentration $u$ versus $\tau$

Figure 4.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 1.5$, $d_1 = 0.004$, $\tau = 0$, $\theta = 0$, (a)(b) $d_2 = 0.3$; (c)(d) $d_2 = 0.4$; (e)(f) $d_2 = 0.5$

Figure 5.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 1.5$, $d_1 = 0.15$, $d_2 = 2.1$, (a)(b) $\tau = 0$, $\theta = 0$; (c)(d) $\tau = 0$, $\theta = 0.45$; (e)(f) $\tau = 0.1$, $\theta = 0.45$

Figure 6.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.04$, $d_2 = 0.2$, $\tau = 0$, $\theta = 0.35$

Figure 7.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.01$, $d_2 = 0.2$, $\tau = 0$, $\theta = 0.35$

Figure 8.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.01$, $d_2 = 0.8$, $\tau = 0, \theta = 0.35$

Figure 9.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.01$, $d_2 = 0.2$, $\tau = 0.05, \theta = 0.5$

Figure 10.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.04$, $d_2 = 0.2$, $\tau = 0.05, \theta = 0.5$

Figure 11.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.01$, $d_2 = 0.2$, $\tau = 5, \theta = 0.25$

Figure 12.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.04$, $d_2 = 0.2$, $\tau = 0.5, \theta = 0.25$

Figure 13.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.5$, $d_2 = 2$, $\tau = 0$ (a)(b) $\theta = 0.15$, (c)(d) $\theta = 0.25$, (e)(f) $\theta = 0.45$

Figure 14.  The pattern formation of $u$ and $v$ in the system(2) when $a = 1$, $b = 2.5$, $d_1 = 0.5$, $d_2 = 2$ and $\theta = 0.35$, (a)(b) $\tau = 0$; (c)(d) $\tau = 0.1$; (e)(f) $\tau = 1$

•  [1] H. Y. Alfifi, Feedback control for a diffusive and delayed Brusselator model: Semi-analytical solutions, Symmetry, 13 (2021), 725, 13 pp. [2] T. Biancalani, D. Fanelli and F. Di Patti, Stochastic Turing patterns in the Brusselator model, Phys. Rev. E, 8 (2010), 046215, 8 pp. [3] P. Clusella, M. C. Miguel and R. Pastor-Satorras, Amplitude death and restoration in networks of oscillators with random-walk diffusion, Commun. Phys., 4 (2021), 1-11. [4] G. Gambino, M. C. Lombardo, M. Sammartino and V. Sciacca, Turing pattern formation in the Brusselator system with nonlinear diffusion, Phys. Rev. E, 88 (2013), 042925, 12 pp. [5] A. A. Golovin, B. J. Matkowsky and V. A. Volpert, Turing Pattern Formation in the Brusselator Model with Superdiffusion, SIAM J. Appl. Math., 69 (2008), 251-272.  doi: 10.1137/070703454. [6] S. Guo and J. Wu, Bifurcation Theory of Functional Differential Equations, Applied Mathematical Sciences, 184. Springer, New York, 2013. doi: 10.1007/978-1-4614-6992-6. 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# A charge +Q and -2Q were placed on first and third of three very large parallel plates. The middle plate is earthed. Find the chargeon right extreem plate

17,079 questions, page 10
1. ## physics

An object carries a charge of -7.8 µC, while another carries a charge of -2.0 µC. How many electrons must be transferred from the first to the second object so that both objects have the same charge?

asked by john hamon on February 17, 2019

#include int main() { char ch; printf("Enter Your State Name : "); scanf("%c",&ch); if(ch == 'malacca') printf("Shipping Charge : $25"); else if(ch == 'pahang') printf("Shipping Charge :$50"); else if(ch == 'terengganu') printf("Shipping Charge : $65"); asked by Borhan on February 15, 2016 3. ## physics Subjects Art Business Computers English Foreign Languages Health Home Economics Mathematics Music Physical Education Science Social Studies Features Contribute Download Experts Forum Job Openings Homework Tips Libraries.Jiskha Link to Us Reference School asked by leesa on February 23, 2008 4. ## physics A 2.20 µF capacitor (#1) is charged to 942 V and a 6.41 µF capacitor (#2) is charged to 657 V. These capacitors are then disconnected from their batteries. Next the positive plates are connected to each other and the negative plates are connected to each asked by Conor on February 9, 2012 5. ## Statistics The soccer team's shirts have arrived in a big box and people start grabbing them. The box contains 7 medium, 12 Large, and 11 extra-large shirts. What is the probability that the first 4 shirts are all extra large? I have been struggling with the problem asked by Nick on October 1, 2013 6. ## physics 2 small conducting spheres are identical except that sphere x has a charge of -10 microcoulombs and sphere y has a charge of +6 microcoulombs after the spheres are brought and then separated what is the charge on each sphere in miicrocoulombs? asked by Anonymous on January 17, 2012 7. ## math grd 10 a trapiziod has vertices A(-2,3) B(4,1) C(-1,-1) and D(2,-2). prove that the line joining the midpoints of the non-parallel sides is the average length of the two parallel sides of the trapaziod. asked by GAGAN on October 12, 2011 8. ## maths the area of trapezium is 276cm2 and its height is 24cm.if one of its parallel side is longer than other by 7cm.find the length of parallel side. asked by ravi on January 15, 2015 9. ## Math The area of trapezium is 270cmsq. Nd its height is 6cm.if one of parallel sides is double the other,find the two parallel sides. Ans is 30nd60cm asked by Simran kaur on September 15, 2012 10. ## Math a trapiziod has vertices A(-2,3) B(4,1) C(-1,-1) and D(2,-2). prove that the line joining the midpoints of the non-parallel sides is the average length of the two parallel sides of the trapaziod. asked by GAGAN on October 12, 2011 11. ## geometry What is the area of a trapezoidal piece of land if the shorter parallel side is 52 ft long, the other parallel side is 130 ft and the altitude of the trapezoid is 75 ft ? asked by kimama on November 8, 2009 12. ## new mexico Kara drew a horizontal dashed line through the middle of a trapezoid parallel to the parallel sides.Did she create a line of symmetry? asked by jacob on November 29, 2012 13. ## need help asap, plz help! math10 a trapiziod has vertices A(-2,3) B(4,1) C(-1,-1) and D(2,-2). prove that the line joining the midpoints of the non-parallel sides is the average length of the two parallel sides of the trapaziod. asked by GAGAN on October 12, 2011 14. ## Geometry In a quadrilateral ABCD, AB is parallel to DC and AD is parallel to BC. Find the perimeter of ΔCOD if the diagonals of the quadrilateral intersect each other at pointOand AC = 20 in, BD = 20 in, AB = 13 in Can You Add the Answer, asked by Gracie on March 24, 2017 15. ## Physics!! Help!!!!! . A neutral conducting sphere contains a spherical cavity. A point charge +q is located at the |center of the cavity. A. What is the total surface charge on the interior surface of the conductor? B. What is the total charge on the exterior surface of the asked by Melissa on February 3, 2012 16. ## business Calc A real estate developer would like to analyze his revenue,cost and profit for a specific hosing project that is under construction.last month he sold 20 large houses for m$ 250000 and 10 small houses for $150000.The cost build large houses was asked by joe on November 17, 2013 17. ## physics 2 Three charges are placed on the y axis. One charge of -3.2 micro-Coulombs is placed at y = 0, another charge of +2.6 micro-Coulombs is placed at y = -0.29 meters, and another unknown charge is placed at y = +0.51 meters. The total force on the charge at y asked by Jessica on January 18, 2013 18. ## physics A 35 micro coulomb point charge is placed 32 cm from an identical 35 micro coulomb charge. How much work would be required to move a 0.50 micro coulomb test charge from a point midway between them to a point 12 cm closer to either of the charges? i got an asked by lauren on February 11, 2016 19. ## 12th grade calculus find points on the curve x^2+xy+y^2=7 (a) where the tangen is parallel to the x-axis and (b) wehre the tangent is parallel to athe y-axis. (in this case, dy/dx is not defined, but dx/dy is. what value does dx/dy have at these point?) asked by - on October 19, 2008 20. ## science Two wires if the same metal and of the same dia. And same length are connected in series 1st n then parallel, the ratio of energy produced during series n parallel connection will be ..... A. 1:2 B. 2:1 C. 1:4 D. 4:1 asked by sanjay on February 10, 2016 21. ## science Two wires if the same metal and of the same dia. And same length are connected in series 1st n then parallel, the ratio of energy produced during series n parallel connection will be ..... A. 1:2 B. 2:1 C. 1:4 D. 4:1 asked by sanjay on February 10, 2016 22. ## science Two wires if the same metal and of the same dia. And same length are connected in series 1st n then parallel, the ratio of energy produced during series n parallel connection will be ..... A. 1:2 B. 2:1 C. 1:4 D. 4:1 asked by sanjay on February 11, 2016 23. ## physics A wire of uniform thickness with a resistance of 27 ohm is cut into three equal pieces and are joint in parallel.find the resistance of the parallel combination. asked by archit on May 1, 2014 24. ## physics (1) A helium atom consists of two protons (charge +2e) and two electrons (charge -2e) that are an average of 4.3 x 10^-11 m apart. Find the electrical force between them. Find the gravitational force between them. What is the ratio of gravitational to asked by Fred on April 17, 2009 25. ## physics Three point charges, A=2.00 uC, B=7.00 uC, C=-4.00 uC, are located at the corners of an equilateral triangle. a) Find the magnitude and direction of the electric field position of the 2.00 uC charge. b) How would the eletric field be affected if the charge asked by Ella on November 7, 2012 26. ## Math Hi SOCK is a parrallelogram .through a variable point H of[SC] draw the parallel to [OS]which cuts [SK]in E and [OC] in F. the parallel to [OC]cuts [OS]in M and [KC]in N. Find the locus of I midpoint of [HM]. asked by suha on March 14, 2008 27. ## algebra Need help with this The area of a trapezoid is 240 cm2. The height is 20 cm and the length of one of the parallel sides is 10 cm. Find the length of the second parallel side asked by jennifer on October 4, 2016 28. ## algebra Need help with this The area of a trapezoid is 240 cm2. The height is 20 cm and the length of one of the parallel sides is 10 cm. Find the length of the second parallel side asked by jennifer on October 4, 2016 29. ## geometry If an object is reflected twice over parallel lines, and corresponding points of the original and final translation image are 30 centimeters apart, how far apart are the parallel lines? asked by devona on November 8, 2010 30. ## math If an object is reflected twice over parallel lines, and corresponding points of the original and final translation image are 30 centimeters apart, how far apart are the parallel lines? asked by nelson on March 24, 2011 31. ## algebra the line "l" passes through the point P=(1,-1,1) and has a direction vector d=[2,3,-1], for the following plane Pl, determine whether l and P is parallel, perpendicular, or neither. a) 2x + 3y - z = 1 could you tell me also how it would differ if it was asked by Reen on January 12, 2011 32. ## math For the pairs of lines defined by the following equations indicate with an "I" if they are identical, a "P" if they are distinct but parallel, an "N" (for "normal") if they are perpendicular, and a "G" (for "general") if they are neither parallel nor asked by jp on January 26, 2015 33. ## math Which of the following equations represents the equation for the line that is parallel to the given line and passes through the given point? y= 1/5 x - 10; (15, -16) A. y = -5x +19 B. y = 1/5x + 91/5 C. y = 1/5 x - 19 D. y = 5x - 19 I do know that to be asked by Jane on April 11, 2012 34. ## geometry A trapezoid has a lower base which is twice as long as its parallel upper base. The upper base is 21 cm long. One non-parallel side is 20 cm long and the other non-parallel side is 6 cm longer than the shorter non-parallel side. What is the perimeter of asked by kimama on November 8, 2009 35. ## science A 2.75-gram air inflated balloon is given an excess negative charge, q1 = -3.00 × 10-8 C, by rubbing it with a blanket. It is found that a charged rod can be held above the balloon at a distance of d = 5.80 cm to make the balloon float. In order for this asked by Kels on February 19, 2013 36. ## plz help now, chemistry How do you write chemical formulas? For example how so you right a chemical formula for calcium fuoride? Calcium flouride would be CaF2 This is because .. Calcium symbol - Ca Flourine symbol - F you would write CaF BUT you must consider charges calcium has asked by Beautiful on December 21, 2006 37. ## physics A particle travels horizontally between two parallel walls separated by 18.4 m. It moves toward the opposing wall at a constant rate of 5.8 m/s. Also, it has an acceleration in the direction parallel to the walls of 1.4 m/s2 . asked by Anonymous on September 7, 2010 38. ## physics A particle travels horizontally between two parallel walls separated by 18.4 m. It moves toward the opposing wall at a constant rate of 5.8 m/s. Also, it has an acceleration in the direction parallel to the walls of 1.4 m/s2 . asked by Anonymous on September 7, 2010 39. ## pre cal Electricity Rates in Florida. Florida Power & Light Company supplies electricity to residential customers for a monthly customer charge of$5.69 plus 8.48 cents per kilowatt-hour for up to 1000 kilowatt-hours. (a) Write a linear equation that relates the

asked by kisha on January 15, 2014
40. ## physics

consider three identical metal spheres a b and c. sphere a carries a charge of +5q. sphere b carries a charge of -q. sphere c carries no net charge. spheres a and b are touched together and then separated. sphere c is touched to sphere a and separated from

asked by lara on April 22, 2010
41. ## Physics

A positive test charge is moving between two oppositely charged plates. As the charge moves toward the negative plate, its potential energy? does it decrease, increase, or remain the same?

asked by TomTom on February 27, 2012
42. ## physics

Two particles each have a mass of 6.7 x 10-2 kg. One has a charge of +7.3 x 10-6 C, and the other has a charge of -7.3 x 10-6 C. They are initially held at rest at a distance of 1.1 m apart. Both are then released and accelerate toward each other. How fast

asked by kim taylor on September 18, 2011
43. ## science(physics)

hi -- thank you for your help before-- that makes sense-- also, im stuck on this: if there is a negative2.5 microcoulomb charge 1 m away from a 6microcoulomb charge, then at what point (other than infinity) is the electric field = zero? Sorry, i have no

asked by APPRECIATIVE STUDENT on January 20, 2011

Thompson assumed that the amount of positive charge and negative charge in an atom was equal. Was this a reasonable assumption? I really do not understand this. I tried looking up on the site, but information there wasn't so clarified.

asked by Anonymous on November 1, 2010
45. ## Physics

A rod has a charge of -2.0 ìC. How many electrons must be removed so that the charge becomes +3.3 ìC

asked by Arnold Manguy on April 19, 2010
46. ## kwabhanya secondary school

Scıence What ıs a charge on A charge after touchıng each other A and B charges?

asked by zama on July 21, 2015
47. ## physics

A 5.75 µC and a -2.61 µC charge are placed 19.8 cm apart. Where can a third charge be placed so that it experiences no net force?

asked by Jose on January 25, 2011
48. ## Physics

What is the magnitude of the force a +29 charge exerts on a +3.3 charge 48 away?

asked by Allison on January 26, 2013
49. ## physics

What is the magnitude of the force a +23 µC charge exerts on a +3.5 mC charge 49 cm away?

asked by Jose on January 25, 2011
50. ## physics

What is the magnitude of the force a +29 \mu C charge exerts on a +3.5 mC charge 35 cm away?

asked by cach on January 22, 2010
51. ## physics

An object has a charge of −2.4 ìC. How many electrons must be removed so that the charge becomes +2.8 ìC

asked by Anonymous on January 18, 2013
52. ## Physics

How when light rays travel outward from their light source in all directions, they are not parallel to each other, but when they approach an object they are parallel to each other?

asked by Emily on May 1, 2010
53. ## Maths

A and B are points on the parallel of latitude 58.4N their longitudes being 148W and 32E respectively.What is their distance apart (a)along the parallel of latitude (b)along a great circle

asked by Rilwan on February 18, 2018
54. ## maths

The area of trapezium is 1586Sq.cm and the distance between its parallel sides is 26cm. If one of the parallel sides is 84cm,find the other.

asked by jaivesh on January 21, 2016
55. ## Physics

A 0.7 um-diameter droplet of oil, having a charge of +e, is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a

asked by Lauren on February 6, 2011
56. ## PHYSICS

Three small spheres are placed at fixed points along the x-axis, whose positive direction points towards the right. Sphere A is at x = 23.0 cm, with a charge of -10.00 ìC. Sphere B is at x = 55.0 cm, with a charge of 2.00 ìC. Sphere C is at x = 57.0 cm,

asked by Jay on May 3, 2010
57. ## Physics last question

A charge of 23.6 is located at (4.37 m, 5.94 m), and a charge of -10.7 is located at (-4.53 m, 6.77 m). What charge must be located at (2.19 m, -2.91 m) if the electric potential is to be zero at the origin?

asked by rudi on November 10, 2010
58. ## Physics

The drawing shows a large cube (mass=42 kg) being accelerated across a horizontal table by a horizontal force P. The coefficient of kinetic friction between the table and large cube is 0.24. A small cube (mass= 5.0 kg) is in contact with the front surface

asked by Anonymous on February 3, 2011
59. ## Physics

The drawing shows a large cube (mass=42 kg) being accelerated across a horizontal table by a horizontal force P. The coefficient of kinetic friction between the table and large cube is 0.24. A small cube (mass= 5.0 kg) is in contact with the front surface

asked by Anonymous on February 1, 2011
60. ## programming

Assume the input to be the charge for the food, draw a flowchart that will compute the total amount of a meal purchased at a restaurant. The output should be the charge for the food, the amount of a 15 percent tip, the amount of the 7 percent sales tax (on

asked by stephanie on August 20, 2014
61. ## Physics: Manitude of Surface Charge on Dielectric

An empty capacitor has a capacitance of 1.86 μF and is connected to a 12-V battery. A dielectric material (κ = 4.5) is inserted between the plates of this capacitor. What is the magnitude of the surface charge on the dielectric that is adjacent to either

asked by Phil-- HELP NEEDED ASAP on May 10, 2013
62. ## physics

please check: Two point charges, initially 1 cm apart, are moved to a distance of 3 cm apart. By what factor do the resulting electric and gravitational forces between them change? a. 9 b. 3 c. 1/3 d. 1/9 D Two positive charges, each of magnitude q, are on

asked by physics on March 14, 2009
63. ## URGENT Physics help

Positively charged Object A is brought close to neutral Object B but does not touch it. The two objects begin to attract each other. What is this process called? (Points : 1) grounding charge polarization conduction repulsion 4. How many coulombs could be

asked by Hannah on April 21, 2014
64. ## physics

If you stand 3.0 m in front of a flat mirror, how far away from you would yourimage be in the mirror? 6.0 m If light waves are coherent, a. they shift over time b. their intensity is less than that of incoherent light c. they remain in phase d. they have

asked by physics on March 13, 2009
65. ## chemistry

an ezyme -catalysed reaction was carried out in a solution buffered with 0.05 M phosphate ph 7.2 . As a result of the reaction ,0.06M of acid was formed. (phosphoric acid has three pka values. The one required for this calculation is pka2=7.2). 1) what was

asked by josh on January 12, 2016
66. ## Physics

Consider three conducting spheres each 10 cm in diameter. “A” has a net charge of 5 C, “B” has a net charge of 10 C, and “C” has a net charge of zero, but is placed in an electric field of 1000 V/m. Rank the electric field strength inside the

asked by Beth on June 13, 2012
67. ## Organic Chemistry

Would a C-Cl bond be polar or nonpolar in a molecule if both have a formal charge of 0? I thought at first that it would be polar just due to their electronegativities (just by looking at the periodic table), but if they both have a formal charge of 0,

asked by Este on September 2, 2016
68. ## physics

Two particles are fixed on an x axis. Particle 1 of charge 47.9 μC is located at x = -5.87 cm; particle 2 of charge Q is located at x = 32.3 cm. Particle 3 of charge magnitude 52.8 μC is released from rest on the y axis at y = 15.1 cm. What is the value

asked by Anonymous on December 13, 2012
69. ## calculus

Find a number x0 between 0 and pi such that the tangent line to the curve y = sin x at x = x0 is parallel to the line y = -x=2. I get that for both lines to be parallel to each other their slopes need to be the same. I found -1/2 = cos(x) but I get stuck

asked by asdf on December 1, 2012
70. ## Geometry

Which best describes the relationship between the lines with equations -16x+2y=0 and -x-8y=-2? a. neither parallel nor perpendicular b. parallel c. same line d. perpendicular

asked by alan on October 26, 2007
71. ## Math

Which best describes the relationship between the lines with equations 8x+y=6 and 16x+2y=0 (a) perpendicular (b) parallel (c) same line (d) neither parallel nor perpendicular

asked by Bria on September 4, 2007
72. ## physics

An object's velocity vector and linear momentum vector are always... a)parallel b)anti-parallel c)perpendicular d)none of the above

asked by barry324 on October 30, 2012
73. ## algebra

give the slop of each line and then determine whether two lines are parallel, perpendicular, or neither parallel nor perpendicular. 2x+5y=5, 4x+10y=0

asked by Chandresh on November 24, 2014
74. ## Physics

A point particle that has a charge of 12.5 µC is located at x = 0, y = 0 and a point particle that has a charge q is located at x = 10.0 cm, y = 0. The electric force on a point particle that has a charge of 5.0 µC at x = 20.0 cm, y = 0 is -(19.7) N .

asked by Kevin on January 29, 2013
75. ## Physics

A point particle that has a charge of 12.5 µC is located at x = 0, y = 0 and a point particle that has a charge q is located at x = 10.0 cm, y = 0. The electric force on a point particle that has a charge of 5.0 µC at x = 20.0 cm, y = 0 is -(19.7) N .

asked by Kevin on January 29, 2013
76. ## Chemistry

Hello everybody, I'm having difficulty understanding the rationalization behind the strengths of Bronstend Lowry acids and bases and my textbook isn't too helpful. Can someone please expalin to me: (1) What exactly is effective negative charge density? (2)

asked by John Peterson on July 16, 2007
77. ## physics

Three point charge of 2NC 7NC and - 4NC are located at the corners of an equilateral triangl as shown below. Caculate the magnitude and direction of the net force on the 7uc charge.

asked by james on May 9, 2016
78. ## physics

Three point charge of 2NC 7NC and - 4NC are located at the corners of an equilateral triangl as shown below. Caculate the magnitude and direction of the net force on the 7uc charge.

asked by james on May 9, 2016
79. ## Physics

On the lower left corner of a square is a fixed charge qLL = 1.5x10^-9 C and on the loser right corner is a fixed charge qLR = 4.0x10^-9 C. The square has a side length L = 0.25 meters. a) Find the electric potential energy of a third charge q = -6x10^-9 C

asked by Diane on January 26, 2010
80. ## Calculus

You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 165 guests per night. The next week you charged$10 per guest and averaged 150

asked by Sydney on August 29, 2013
81. ## physics

A uniform electric field of magnitude 250 V/m is directed in the positive x direction. A +12.0-ìC charge moves from the origin to the point (x, y) = (20.0 cm, 50.0 cm). (a) What is the change in the potential energy of the charge–field system? (b)

asked by sammy on April 30, 2007
82. ## Physics

The large disk-shaped flywheel illustrated below has a radius R of 0.25 m. It is made to spin by the small wheel that contacts it at its rim. The small wheel applies a constant force of 1430 N. Friction in the bearing exerts a retarding torque 22 Nm on the

asked by Beth on November 7, 2016
83. ## phys101

a hydraulic press contains oil of density=800kg/meter cube,and the areas of the large cylinder=0.5meter squad and area of small cylinder=0.0001meter squad.the mass of the large piston is 51kg,while the small piston has unknown mass m.If an additonal mass

asked by KABELO on April 19, 2010
84. ## math

the lions gate bridge in vancuver BC, is a suspension bridge that spans 1516m. Large cables are attached to the tops of the towers, 50m above the road. the road is suspended from the large cables with small vertical cables, the smallest one being 2m. find

asked by Navroz on April 18, 2010

#include int main() { char ch; printf("Enter Your State Name : "); scanf("%c",&ch); if(ch == 'a') printf("Shipping Charge : $25"); else if(ch == 'b') printf("Shipping Charge :$50"); else if(ch == 'c') printf("Shipping Charge : $65"); else printf("The asked by Borhan on February 13, 2016 86. ## Programming #include int main() { char ch; printf("Enter Your State Name : "); scanf("%c",&ch); if(ch == 'a') printf("Shipping Charge :$25"); else if(ch == 'b') printf("Shipping Charge : $50"); else if(ch == 'c') printf("Shipping Charge :$65"); else printf("The

asked by Borhan on February 14, 2016
87. ## Biology

Consider the following pairs of organisms: large predators and small predators: large herbivores and small herbivores: and migratory animals and non-migratory animals. The two animals most likely to suffer the most from habitat fragmentation are the A.

asked by kathy on July 29, 2009
88. ## physics

Consider point charges + Q and +9Q, which are separated by 12 meters. At what point, on a line between the two charges, would it be possible that the electric field would be zero. A. There is no such point possible B. 9 meters from the +Q charge C. 9

asked by TJ on July 21, 2009
89. ## physics

A point charge of -8.4 µC is at the origin. a)What is the electric potential due to this charge at (x,y) = (3.5 m, 0 m) b) What is the electric potential due to this charge at (x,y) = (-3.5 m, 0 m) c) What is the electric potential to this charge at (x,y)

asked by sonia on September 16, 2011
90. ## Bio

In spite of factors that tend to restrict cell size, some plant cells are very large. For example, some marine algae have cells almost as large as a chicken egg which of the following characteristics would favor the growth of large cells? 1- thin layer of

asked by bubba on October 25, 2009
91. ## Bio

In spite of factors that tend to restrict cell size, some plant cells are very large. For example, some marine algae have cells almost as large as a chicken egg which of the following characteristics would favor the growth of large cells? 1- thin layer of

asked by bubba on October 26, 2009
92. ## Physics

A capacitor consisting of two parallel plates of area A = 4.6 m2 and spacing d = 0.150 m is filled with two parallel slabs of dielectric material of equal thickness and with dielectric constants 1 = 2.20 and 2 = 5.50, respectively. What is the total

asked by Meghan on February 26, 2012
93. ## Physics

Two identical 2 ohm resistors are connected in parallel to a 1 ohm resistor in the circuit.the potential difference across the cell is 6 v and internal resistance is negligible.calculate the effect across the parallel combination

asked by Kholo on May 16, 2015
94. ## Biochemistry

1. What is the overall charge of the tripeptide below pH 1.0? 2. What is the overall charge of the tripeptide at pH 12? 3. What type of intermolecular attractions could the side chains of the amino acids make with the solvent (water) at pH 7.4? (Note that

asked by Aria on October 5, 2013
95. ## physics

In the rectangle in the drawing, a charge is to be placed at the empty corner to make the net force on the charge at corner A point along the vertical direction. What charge (magnitude and algebraic sign) must be placed at the empty corner? (the rectangle

asked by Sarah on September 6, 2013
96. ## Physics repost

Neutral metal sphere A, of mass 0.10kg, hangs from an insulating wire 2.0m long. An identical metal sphere B, with charge -q is brought into contact with sphere A. Sphere A goes 12 degrees away from Sphere B and there is a 90 degree angle at Sphere B

asked by Alex on April 21, 2008
97. ## Physics

A point charge (m = 1.0 g) at the end of an insulating string of length L = 46 cm (Fig. 16-66) is observed to be in equilibrium in a uniform horizontal electric field of E = 8800 N/C, when the pendulum's position is as shown in Fig. 16-66, with the charge

asked by kjipper on January 28, 2013
98. ## Math

The diagram: it is a large triangle labelled ACD(AC a line horizontal, then AD and CD joining at the tip going down-so the triangle is "upside down" with the base up) with a line drawn that connects point E, which intersects segment CD at the middle(a

asked by Winnie on March 18, 2015
99. ## chemistry

Decide if each of the following principles were first discovered during Thompson's cathode ray tube experiments, Rutherford's gold foil experiment, Millikan's oil drop experiment or none of these. Label each one with either Thompson, Rutherford, Milikan,

asked by chris on April 14, 2011


text:
## How To Write Ordinal Numbers In Word

How To Write Ordinal Numbers In Word – A vast array of sets can be enumerated using ordinal numbers to serve as a tool. They can also be used as a method to generalize ordinal numbers. 1st One of the most fundamental concepts of mathematics is the ordinal numbers. It is a number that indicates … Read more

## How To Write Ordinal Numbers

How To Write Ordinal Numbers – An endless number of sets can be easily enumerated using ordinal numerals as a tool. They can also be utilized as a tool to generalize ordinal figures. 1st The ordinal number is one of the most fundamental concepts in mathematics. It is a number that identifies the location of … Read more


text:
1. Extensions
3. Install and set-up
4. Install via the command line

You can install the Series 3 versions of the Excel Add-in via the command line. This is useful if you want to install the Excel Add-in for many users consistently.

The MSI file for the relevant version of the Excel Add-in is required to install the Excel Add-in via the command line. See Downloads.

You should be proficient with the command prompt before you install the Excel Add-in with it. This information is intended for IT teams who want to install the Excel Add-in for multiple users.

You must have administrator permissions for Windows Installer in order to install the Excel Add-in via the command line. Ensure that you open the command prompt as an administrator.

## View the full list of installation options

A large number of installation options are available when you install the Anaplan Excel Add-in via the command line. You can use a universal Windows command to see the options in Windows Installer.

To view the full list of options:

1. Open Command Prompt.
Right-click Command Prompt and select Run as administrator to ensure you have administrator permissions.
2. Navigate to the folder that contains the MSI file for the version of the Excel Add-in you want to install. This is the Downloads folder by default.
Alternatively, you can specify the full file path for the installer after the msiexec command in the next step.
3. Use the command msiexec to run the MSI file.
The Windows Installer dialog displays. It contains a full list of the options you can use for your installation.

An example command for this procedure is msiexec "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi"

### Useful installation options

This table contains some useful installation options from the full list. Some are universal options in Windows, and some apply only to the Excel Add-in.

 Installation option Purpose Example /i Install the add-in. msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" /q Perform a quiet installation of the add-in, with no installation wizard. msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" /q /qr Perform a quiet installation of the add-in, with only a progress bar and no final window. Also enables installation without administrator permissions. msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" /qr /x Uninstall the add-in. msiexec /x "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" APPDIR="" Install the add-in to a specified directory. msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" APPDIR="C:/Users/Anaplan/Add-in Folder" AUTH_SELECTION="" TXT_SSONAME="" Select authentication type (SSO or username and password) and provide SSO Friendly URL for installation. If you do not provide this option, installation defaults to username and password authentication. Msiexec /i “C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi” AUTH_SELECTION=“Auth_SSO” TXT_SSONAME="SSO Friendly URL" /qr ALLUSERS="" MSIINSTALLPERUSER="" Specify which users in Windows to install the add-in for. Learn more about ALLUSERS and MSIINSTALLPERUSER. Msiexec /i “C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi” ALLUSERS="2" MSIINSTALLPERUSER="1"

## Command line installation with the MSI file

You can simply double-click the MSI file in Windows to perform a standard installation. However, if you use the command line, you can customize your installation with further options explained on this page.

Use this procedure as a basis for other types of installation:

1. In the start menu, right-click Command Prompt and select Run as administrator.
2. Locate the MSI file for the version of the Excel Add-in you want to install. This is the Downloads folder by default.
You can hold shift and right-click the file to copy its path.
3. Use the command msiexec and additional tags to run the MSI file.
The type of installation depends upon the tags you use.

### Quiet installation with reduced UI

you can perform a quiet installation of the add-in. This means that the Excel Add-in installs with no installation wizard, only a progress bar. This type of installation does not require administrator permissions.

Use the command msiexec and the additional tags /i and /qr to perform a quiet installation of the Excel Add-in with reduced UI.  Only a progress bar displays, with no installation wizard, because the /qr tag is used.

An example command for this procedure is:

msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" /qr

### Installation to a specific directory

The default installation location of the Excel Add-in is C:/ProgramData/Anaplan/ExcelAddIn. However, you can install the Excel Add-in to any location.

Use the command msiexec and the additional tags /i and APPDIR="" to install the Excel Add-in to a specific directory. Enter the directory to install the Excel Add-in to between the quotation marks. When you execute the command, the ExcelAddin Setup wizard displays.

An example command for this procedure is:

msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" APPDIR="C:/Users/AnaplanUser/Add-in Folder"

### Install for all users with SSO preconfigured

It's possible to install the add-in for all users in a Windows configuration with SSO preconfigured. Use this to simplify configuration of the add-in for users.

Use the command msiexec and the additional tags  /i, ALLUSERS="", MSIINSTALLPERUSER="", AUTH_SELECTION="Auth_SSO", TEXT_SSONAME="SSO Friendly Name" and /qr to run the MSI file. Replace SSO Friendly Name with the SSO Friendly Name for your SSO configuration. Only a progress bar displays, with no installation wizard, because the /qr tag is used.

An example command for this procedure is:

msiexec /i "C:\Users\AnaplanUser\Downloads\AnaplanExcelAddin.Release.msi" ALLUSERS="2" MSIINSTALLPERUSER="1" AUTH_SELECTION=“Auth_SSO” TXT_SSONAME=YourSSOFriendlyName /qr


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# Gaussian integral over logarithm of shifted error function

Suppose we have the following integral:

$$\int^{\infty}_{-\infty} \frac{dz}{\sqrt{2\pi}}e^{\frac{-z^2}{2} } \log\left( \text{erf} \, a (z-b) +1 \right), \ \ \ \ a,b \in \mathbb{R}$$ Does a closed-form solution of this integral exist? If it does not exist, does it exist for $b=0$?

What I tried so far

Even numerical evaluation of the problem for given $a,b$ is difficult, since the error-function becomes -1 for large negative z causing the logarithm to diverge.

On Wikipedia I found the following solution for a related problem: $$\int^{\infty}_{-\infty} \frac{dz}{\sqrt{2\pi d^2}}\text{exp}\left[{\frac{-(z+c)^2}{2 d^2} }\right] \text{erf}(az+b)=\text{erf}\left[\frac{b-ac}{\sqrt{1+2a^2d^2}} \right],$$ which makes me suggest that something similar might exist for the stated problem.

• Googling “Ng Geller Erf Nist” will get you two tables of erf-related integrals. The integral you want may not exist, but you already found the one that seems to be helpful most often, and you can see if any of their other results help. Apr 14 '18 at 19:48
• even for $b=0$, $a=1$ a closed-form solution is not forthcoming Apr 14 '18 at 20:14


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# Is a Black Hole in Thermal Equilibrium with its Thermal Atmosphere?

A Schwarzchild black hole has a "thermal atmosphere" in the region $$r_{s} < r < (3/2)r_{s}$$ where $$r_{s}$$ is the Schwarzchild radius [1, 2]. The thermal atmosphere is comprised of radiation quanta that are entangled with quanta behind the horizon [1, 3]. The radiation quanta that slowly leak out of the atmosphere constitute the radiation that Hawking found (Hawking radiation) [1, 4]. Far from the black hole, the radiation has a temperature $$T_{hawking} = \frac{1}{8 \pi M}$$. The temperature of the thermal atmosphere is $$T_{atm} = \frac{1}{2 \pi \rho}$$ where $$\rho$$ is the proper distance to the horizon. This shows that the temperature of the thermal atmosphere diverges as one approaches the horizon [1, 2, 3]

Hawking showed that a Schwarzchild black hole can be in thermal equilibrium with blackbody radiation at a temperature $$T_{eq} = \frac{5}{32 \pi M} = \frac{5}{4}T_{hawking}$$, if the "size" (radius) of the total (black hole + radiation) system does not exceed $$\frac{3}{2}r_{s}$$ [1, 2]. This implies that a black hole in thermal equilibrium with blackbody radiation has the same size as a black hole surrounded by its thermal atmosphere.

Given the fact that the radiation in the thermal atmosphere leaks away very slowly, can we conclude black hole is approximately in thermal equilibrium with its thermal atmosphere?

References:

1. Susskind, Leonard and Lindesay, James, An Introduction to Black Holes, Information and the String Theory Revolution. The Holographic Universe}, World Scientific, 1st Edition, 2005.

1. Jacobson, Ted Introductory Lectures on Black Hole Thermodynamics http://www.physics.umd.edu/grt/taj/776b/lectures.pdf

2. Harlow, Daniel Jerusalem Lectures on Black Holes and Quantum Information arxiv:1409.1231v4

3. Preskill, John Black holes and information: A crisis in quantum physics http://www.theory.caltech.edu/people/preskill/talks/blackholes.pdf


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# how to view homology of affine Grassmannian as a subring of symmetric function

Let $G=SL_n$, it is proven that $R:=H_*(Gr_G)\cong \mathbb{C}[\sigma_1,...,\sigma_{n-1}]$ where $\sigma_i$ are of degree $2i$ as a polynomial ring generated by $n-1$ variables and the ring structure comes from the fact the $Gr_G$ is homotopic to $\Omega K$ ($K$ is the maximal compact subgroup of $G$) and $\Omega K$ has a group structure. It is known that $R$ can be viewed as a subring of symmetric function $Sym$ by mapping each $\sigma_i$ to $h_i$ ($i$-th complete homogeneous symmetric function of degree $i$ ).

My question is: Why should we view $R$ as a subring in $Sym$ in such way? What is the geometric reason behind it?

You should look at the book of Lam, Lapointe, Morse, Schilling, Shimozono and Zabrocki. More specifically, under k-Schur functions and how/why they constitute a basis of $$H_*(Gr_{SL_k})$$. They mainly work in K-theory, but one of the main results in loc. cit originally proved by Lam is that there is a natural Hopf algebra isomorphism between the Hopf subalgebra of k-Schur functions $$\Lambda_{(k)}:=\mathbb{Q}[h_1,\ldots,h_{k-1}]\subset \Lambda$$ and $$H_*(Gr_{SL_k})$$. See the references therein for the Hopf algebra structures.
Geometrically the k-Schurs are just the Schubert basis in the (K-)homology of the affine Grassmannian. Multiplication by $$h_i$$ is more interesting in this basis, it's given by the k-Pieri rule.


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# moment generating function of a summation

Suppose the time between independent incoming calls to a call center is well modeled by an exponential distribution having $\lambda = 0.025$. Let $T_i$ be the time between the $i$th and the $(i-1)$st call, and define $S_k = \sum^k_{i=1} T_i$. What are:

(a) The moment generating function of $T_4$?

(b) The moment generating function of $S_6$?

(c) $E[S_6]$?

I did (a) by solving $E(e^{tX}) = \int^\infty_00.025e^{tx}e^{-0.025x}dx$ and got that the mgf of $T_4 = \frac{0.025}{0.025-t}$, defined for $t<0.025$.

I'm not quite sure how to solve (b), but I think that since all $T_i$ are independent, then the mgf of $S_6$ should be the product of all the individual mgf of $T_1,T_2,...,T_6$. Since the mgf of all $T_i$ should be the same, then should the mgf of $S_6 = {(\frac{0.025}{0.025-t})}^6$?

And for (c), I should just find the first moment of $S_6$ right?

-

If $X\sim \exp(\lambda)$ for $i=1,\ldots k$, then \begin{align} M_X(t)&=E[e^{tX}]=\int_0^\infty e^{tx}\lambda e^{-\lambda x}\,\mathrm dx=\lambda\int_0^\infty e^{x(t-\lambda)}\,\mathrm dx\\ &= \begin{cases} \infty,\quad &\text{for }t\geq \lambda,\\ \lambda(t-\lambda)^{-1},&\text{for }t<\lambda, \end{cases} \end{align} so you're right about (a). Since $T_1,\ldots, T_6$ are independent, we have $$M_{S_6}(t)=E\left[e^{tS_6}\right]=E\left[e^{tT_1}\cdots e^{tT_6}\right]=E\left[e^{tT_1}\right]\cdots E\left[e^{tT_6}\right]=M_{T_1}(t)\cdots M_{T_6}(t),$$ where we have used that also $e^{tT_1},\ldots, e^{tT_6}$ are independent. So your answer is correct here as well.
And yes, (c) just asks for the first moment of $S_6$, but note that this can be calculated via its moment-generating function, i.e. $$E\left[S_6\right]=M_{S_6}'(0).$$


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Migrating to MacOS for work

Some annoyances; a different kind of friction; ultimately a bit meh

I’m a long time Microsoft DOS/WFW/95/NT/2000/XP/Vista/7/10 user on the desktop; I can make it sing and dance exactly to my tune. Where other people complain about Windows, or get frustrated by it; I never have a problem. Now, Windows isn’t perfect, far from it, but it’s a basically a tool that causes me minimal friction, letting me get on and solve interesting problems; I don’t use it in production, just for my desktop. Last summer, I got so annoyed with the corporate build of Windows 10 that I submitted a requisition for a Macbook Pro; I’m not actually sure which model it is, but it has a touch bar and 16Gb of RAM. Now that I’ve been using it for about 5 months I thought I’d jot down my thoughts about the transition. My last long-term experience of the Mac was back in 2007/2008; does it create more or less friction a decade later?

Applications

There are going to be things that you must have to help you transition; mine are Spectacle - since windows left/right arrow key is something I use a lot, and completely missing from the Mac; Karabiner Elements as it’s hard to stop using ctrl-shift-c/v when that’s your muscle memory reflex; Sensible Side Buttons because extra buttons are an actual thing on mice, and I want to use them.

MacBrew has made my life a lot easier but I had to do some dodgy hacks to get it to install on the Mac; this is all to do with how the powers that be have set up the Mac (not how I would…) rather than anything else. The BSD shell tools like tar and readlink are subtly different to the GNU equivalents so I’ve had to end up doing stuff to make things portable-ish…

function findReadlink()
{
if [ \$? == 0 ]; then
else
fi
}

The Good

Things haven’t really changed all that much, I still have the toolchain that I need to get stuff done, albeit with some caveats. This is the key thing here, it doesn’t actually bother me all that much that I’m using a Mac or Windows; it generally takes me ~10 minutes to switch between the two in the mornings (I make a conscious decision which one to use at the start of the day).

The touchpad is excellent compared to the equivalent Lenovo/Dell/Asus offerings.

Getting the love from all the other developers is nice; now I don’t have to google-fu and figure out how to do the stuff on Windows. This was already on the wane because of docker but it always made me a trifle sad that if you didn’t’t have any skin in the Microsoft development enviroment game (after all my primary development platform is the JVM), but you had to use Windows, you weren’t a trendy developer, and as such, not worthy of developer love.

Docker desktop works with the Cisco VPN, whereas on Windows 10, it never did. This is actually a big plus since I have to be on the VPN all the time now because reasons…

It has forced me to be more platform neutral; I’m now using docker to host tiddywiki (which I use to write notes); I will probably end up using docker to host javadocs so that I can work offline.

The keyboard is still my biggest gripe; I’m just not happy with it; the layout is wrong and chiclet keys are shit and will always be shit. I grew up with the BBC Model B; learnt to touch type on a british layout typewriter; so this counts as friction. I can map the keyboard to British PC when I have an external keyboard plugged in. I can even have it mapped to British PC keyboard with just the laptop keyboard but of course Apple in its infinite wisdom thinks that the laptop keyboard is special and the backtick key should stay as labelled (bottom left of a Mac UK keyboard screen) when it should really be where the paragraph mark key is (top left). The paragraph mark key is the \ key when on the laptop; when I have an external keyboard plugged in everything is in the right place. At least I suppose the @ key is mapped correctly so I don’t make loads of mistakes typing email addresses.

The touch bar is pointless; I have it setup to only show the expanded control strip (which gives me basically the media keys) with overrides for certain apps where I do use the function keys a lot; a non-tactile esc key doesn’t help with VI. I only see the touch bar when I’m using the laptop without additional monitors.

Outlook; required by policy since Mail.app can’t be started; isn’t as good as the Windows version. I’m making do, but I’m really missing quick actions and being able to edit the toolbar. Being able to edit the toolbar would allow me to fit things into my workflow, such as creating appointments from emails (rather than meetings) since I use appointments to remind me to reply to emails. Interestingly because Mail can’t be started, it actually causes a bunch of other problems because of the nature of the default application (which I can’t change, again, not the Mac, but more a corporate-policy-issue),

I’ve actually gone back to using midnight commander and vifm on the commandline because Finder is so rubbish. I don’t think Windows Explorer is actually good but compared to Finder it’s like being in charge of a machine-gun nest against a cavalry charge.

Grab is just not as good as Snipping Tool; the Windows version with its built in annotation/highlight makes it easy to do mark-up screenshots and the like, it’s just not as easy with Grab.

USB-C doesn’t float my boat at all; having to buy extra peripherals and cables to get dual monitor support makes me sad; I accept that this is because I’m stuck in USB-A land but equally how many webcams have you seen that come native with a USB-C cable?

The dock seems like a bit of an afterthought, espcially with the menu bar at the top it squashes the vertical real estate (more so since the laptop screen isn’t 1080p anyway). I’ve got it on the right hand side of the screen but I’m not convinced by it. It’s a niggle; if you have dual monitors then you get the added bonus of having to look for the menu bar on the wrong screen sometimes, but that’s probably just me.

The Ugly

The ugly is all down to how the Macs are managed within our corporate environment; corporate IT seems to be quite Windows centric, so perhaps this is unsurprising; I’m sure there are fixes and workarounds, but life is too short to spend my time trying to fix problems which shouldn’t really be problems if people actually did their fucking job.

I can’t use Skype for Business / Teams / Outlook without being on the VPN; everything gets horribly confused and breaks. I could never use Outlook on Windows without the VPN, but I could certainly use Teams and Skype.

Even though I have administrative access, my administrative access doesn’t work well unless I’m on the VPN.

Single sign on is completely broken; I have to sign on multiple times with Safari (or Chrome) whereas on Windows 10 this wouldn’t be the case since Edge knows about my domain credentials. Firefox doesn’t play well with domain credentials on either platform.

Summary

Having a Mac is useful, since my team is fully on Windows 10, so I get a different point of view. It has a different kind of friction; it’s different as opposed to bad; on the whole it doesn’t make me want to scream. Given the choice I wouldn’t a swap a properly configured Microsoft Surface Pro or the Dell XPS13 Linux edition for a Macbook.

For my personal stuff, I will still continue to use Windows 10. With WSL I get a full linux shell and toolchain; with WinGit I get a good-enough linux-style toolchain; it doesn’t cause me any friction and gets out of my way.

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## Multi angle  Towards ternary Goldbach's conjecture Helfgott, Harald (Auteur de la Conférence) | CIRM (Editeur )

The ternary Goldbach conjecture (1742) asserts that every odd number greater than $5$ can be written as the sum of three prime numbers. Following the pioneering work of Hardy and Littlewood, Vinogradov proved (1937) that every odd number larger than a constant $C$ satisfies the conjecture. In the years since then, there has been a succession of results reducing $C$, but only to levels much too high for a verification by computer up to $C$ to be possible $(C>10^{1300})$. (Works by Ramare and Tao have solved the corresponding problems for six and five prime numbers instead of three.) My recent work proves the conjecture. We will go over the main ideas of the proof.
ternary Goldbach conjecture - sums of primes - circle method
The ternary Goldbach conjecture (1742) asserts that every odd number greater than $5$ can be written as the sum of three prime numbers. Following the pioneering work of Hardy and Littlewood, Vinogradov proved (1937) that every odd number larger than a constant $C$ satisfies the conjecture. In the years since then, there has been a succession of results reducing $C$, but only to levels much too high for a verification by computer up to $C$ to be ...

##### Audience

Nuage de mots clefs ici

Z


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# Figures on left pages, text on right ones with class book (cont.)

In addition to the very useful discussion Figures on left pages, text on right ones with class book, numbering only on right pages, I would like to handle 2 other features:

• the suppression of blank pages automatically inserted by book,
• the possibility to switch between figure and table captions.

Regarding the first, 3 blank pages are added before a new chapter (probably also before a new part) where only 1 should be. I managed to remove one redefining \chapter as follows (removing the first line involving \clearpage) but not the other.

\renewcommand\chapter{
\thispagestyle{plain}%
\global\@topnum\z@
\@afterindentfalse
\secdef\@chapter\@schapter}

For the second, I defined a new command \switchcaption as follows which I call before and after a table respectively with "table" and "figure" as argument.

\newcommand\switchcaption[1]{\def\@captype{#1}}

By the way, I would be very interested in better understanding

• when it is needed to work within \makeatletter \makeatother (apparently \newcommand works differently in both cases: it "reads" the new command name with subsequent braces outside \makeatletter \makeatother and without braces otherwise),
• why \addfig definition needs two statements (one for \@addfig and another apparently for its argument).

• I'm afraid you're asking two completely different questions here, and that they should be asked separately. Anyway, as far as I know for question (2a): don't use \def, and for (2b): it's needed when you tamper with TeX internal macros which have @ in their names. – Axioplase Oct 27 '11 at 0:48
• For your first two btw's see tex.stackexchange.com/questions/655/… and tex.stackexchange.com/questions/8351/…. – Caramdir Oct 27 '11 at 0:50
• Thank you for your fast follow-up! By the way I finally worked out more elegant (and suitable) solutions to the above-mentionned issues. The blank pages were actually linked to the page break inserted by \include (I am writing a thesis...). Using \input instead solves the problem (without redefining \chapter). In addition, I managed to avoid blank pages at the end of the document redefining \blankpage to stop recursion (\renewcommand{\blankpage}{}). To define table captions, I realised that I could use the command \captionof provided by the caption package I am using anyway. – Benoît Bidaine Oct 27 '11 at 0:51
• Regarding your choice of \include or \input, also see: tex.stackexchange.com/questions/246/… – Werner Oct 27 '11 at 1:45

After viewing the comments, it seems like the only thing left (even though it is actually not in question form), is to efficiently switch between table and caption. You mention that you currently do this manually:

\switchcaption{table}% Switch to table caption
\begin{table}[..]
...
\end{table}
\switchcaption{figure}% Switch to figure caption

This manual interaction could be avoided by adding some code to the beginning and ending of the table environment. Such "patching" is possible using the etoolbox package. It provides \AtBeginEnvironment{<env>}{<code>} and \AtEndEnvironment{<env>}{<code>} (also \BeforeBeginEnvironment{<env>}{<code>} and \AfterEndEnvironment{<env>}{<code>}) to insert <code> at the beginning/end of environment <env>. A little bit more efficient would be to just add:

\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\makeatletter
\AtBeginEnvironment{table}{\def\@captype{table}}% Switch to table captions at beginning of table environment
\AtBeginEnvironment{figure}{\def\@captype{figure}}% Switch to figure captions at beginning of figure environment
\makeatother

to your document preamble that should switch as needed depending on the environment used.

Edit: The above "solution" may be moot if you are using the figure environment for all your figures and tables. If that is the case, the your \switchcaption combination will still be necessary.

To that end, note that you can still use the table environment within the command \addfig, which necessarily modifies the caption to read Table x: .... This is a common misinterpretation of the table and figure environments, stemming from their respective names. They are merely wrappers for any content, allowing you to place \includegraphics commands inside table and a tabular (say) inside figure.

• When the caption package is used please don't use \def\@captype{table} but \captionsetup{type=table} instead. This latter one will not only define \@captype but also apply table-local caption options, set an hyperref anchor (if hyperref is used), prepare the environment for sub-figures resp. sub-captions etc. – Axel Sommerfeldt Oct 27 '11 at 6:11