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My Math Forum Plane in three-dimensional space

 Calculus Calculus Math Forum

 April 10th, 2019, 03:26 AM #1 Newbie   Joined: Apr 2019 From: Brazil Posts: 1 Thanks: 0 Plane in three-dimensional space Determine an equation of the plane whose points are equidistant from (2, -1, 1) and (3, 1, 5). -- Answer: x + 2y + 4z = 29/2
 April 10th, 2019, 09:00 AM #2 Newbie     Joined: Oct 2018 From: USA Posts: 19 Thanks: 13 Math Focus: Algebraic Geometry Since we want the plane to be equidistant, we know the plane passes through the midpoint of the line between the two points : $(2.5,0,3)$ Also, the plane has to be perpendicular to the line between the points, otherwise it won't be equidistant. To find the plane we need the vector between the two points: $\vec{u} = \langle 3-2 , 1-(-1) , 5-1 \rangle = \langle 1,2,4 \rangle$ The coefficients of planar equations are determined by the elements of their perpendicular vectors, so the equation for the plane is $1x + 2y + 4z = ?$. Since we know the midpoint is on the plane we can use it to calculate "?". $2.5 + 2(0) + 4(3) = 14.5 = \frac{29}{2}$. Which gives the full equation $x+2y+4z = \frac{29}{2}$ EDIT: Also, you can also just use the general form for a plane, where $\langle a,b,c \rangle$ is the normal vector and $(x_{0},y_{0},z_{0})$ is the starting point. $a\left( {x - {x_0}} \right) + b\left( {y - {y_0}} \right) + c\left( {z - {z_0}} \right) = 0$ Thanks from topsquark and wniemiec Last edited by Greens; April 10th, 2019 at 09:10 AM. Reason: Additional Info

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# Issue with caption inside measuredfigure environment

I need to write the figure sources under the figure themselves. As recommended in StackExchange, I used the caption package that I also used for the title of the figure, which comes over the figure. Because I did not want the source listed or numbered anywhere, I used \caption*{}.

I also wanted both the title and the source caption left aligned with the figure, meaning not starting from the begin of the line, but rather from the corner of the figure. To solve this problem, StackExchange recommended using package threeparttable and to put my figure in the measuredfigure environment.

Problem is, the asterisk in \caption*{} for the source does not work inside the measuredfigure as it is supposed to. How can I get rid of numeration/list Figure 0.1 written in my source caption?

The MWE is:

\documentclass[a4paper]{memoir}

\usepackage[T1]{fontenc}        % Selecao de codigos de fonte.
\usepackage{graphicx}           % Inclusão de gráficos
\usepackage{caption}
\usepackage{threeparttable}

\graphicspath{{./images/}}

\captionsetup{
font=normalsize,
justification=raggedright,
singlelinecheck=false,
format=hang,
labelsep=space
}

\begin{document}

\begin{figure}[h!]
\centering%
\begin{measuredfigure}%
\caption{Transmission system}%
\label{fig:Driveline}%
\includegraphics[width=.8\textwidth]{Driveline}%
\caption*{\footnotesize\textbf{Source}: Author}%%
\end{measuredfigure}%
\end{figure}

\listoffigures

\end{document}

I would simply use a minipage instead of the table.

\documentclass[a4paper]{memoir}

\usepackage[T1]{fontenc}        % Selecao de codigos de fonte.
\usepackage{graphicx}           % Inclusão de gráficos
\usepackage{caption}
%\usepackage{threeparttable}

\graphicspath{{./images/}}

\captionsetup{
font=normalsize,
justification=raggedright,
singlelinecheck=false,
format=hang,
labelsep=space
}

\begin{document}

\begin{figure}[htbp]
\centering
\begin{minipage}{.8\textwidth}
\caption{Transmission system}%
\label{fig:Driveline}%
\includegraphics[width=\textwidth]{example-image}%
\caption*{\footnotesize\textbf{Source}: Author}%%
\end{minipage}
\end{figure}

\listoffigures

\end{document}

I think it will be simpler to use the copyrightbox ppackage:

\documentclass[a4paper]{memoir}

\usepackage[T1]{fontenc} % Selecao de codigos de fonte.
\usepackage{graphicx} % Inclusão de gráficos
\usepackage{threeparttable}
\makeatletter
\footnotesize
\rmfamily
}
\graphicspath{{./images/}}

\captionsetup{
font=normalsize,
justification=raggedright,
singlelinecheck=false,
format=hang,
labelsep=space
}

\begin{document}

\begin{figure}[h!]
\centering%
\begin{measuredfigure}%
\caption{Transmission system}%
\label{fig:Driveline}%

• @Sebastiano: It is simpler to solve general problem: finding the number of solutions in non-negative integers of the equation: $$x_1+x_2+\dots+x_n= r$$. One proves by induction this number of solutions is the binomial coefficient $\;\biggl(\dfra{n+r-1}{r}\biggr)$. – Bernard Jan 17 '18 at 21:25


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# Made Easy Test Series

1 vote
605 views
Consider the following CFG.

S $\rightarrow$aAb|aBc|bAd|bBe
A$\rightarrow$g
B$\rightarrow$g

The number of states exist in DFA using LALR (1) construction for the above grammar  ____________??

(Doubt): In CLR(1) it takes 14 states and clubbing two states into one state will take 13 states in LALR(1). The LALR(1) construction takes 13 states for the construction but additional one more dead state is required as we are using DFA....!!! So 14 is the answer, I think.. But answer in Made Easy given as 13 Only.. Explain....???!!!

retagged
2
every dfa contain dead state ? No na.
0
every dfa is not having dead state,only some of them.
0

Just Consider Initial State I0, from that initial state on input g where does the next state goes.....?

As it is DFA at a particular state, state is defined for each and every input...?

0
In the CLR(1) table on every input symbol it performs either shift action or reduce action.

on particular input it is going to blank symbol,then system understands that is not valid string.and returns error.

## 2 Answers

1 vote
In LALR(1) minimal states are considered after clubbing the states which are differ only by lookahead symbol. If after clubbing,states are reduced then consider the reduced dfa .No need to consider dead state or anything.
0 votes
There is no clubing of states.LALR(1) is same as CLR(1).You please check once!!
0
clubbing of states means to combine those states those are differ by only lookahead symbol

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L1 = {an bm | n ≤ m ≤ 2n} L2 = {an bm│m≠n & m≠2n} Which of the following is true? A. Only L1 is CFG B. Only L2 is CFG C. Both are CFG D. None of them is CFG
1 vote
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Consider the following CFG. S → aSa | bSb | a | b | ε For the above CFG, the total number of strings generated whose length is less than or equal to 8 [exclude the empty string] is _____________.
1 vote
0 answers
4
608 views
$S\rightarrow aA|bAc|dc$ $A\rightarrow d$ Number of states in $CLR\left ( 1 \right )$ parser construction _______________ Is $S\rightarrow d.c|$ $A\rightarrow d.,a$ will be in $1$ state or in $2$ different states??


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# Estimate Integral w.r.t Dirac measure by Integral w.r.t Lebesgue measure

Given a bounded, nonnegative and measurable function $$f$$ and denote the Euclidean ball with center $$z$$ and radius $$r$$ by $$B_r(z)$$.

Is it somehow possible to estimate the Integral w.r.t. the Dirac Lebesgue measure by the Integral w.r.t the Lebesgue measure?

I.e. is something like $$\int_{B_r(z)} f(x) \delta_z (dx) \leq \int_{B_r(z)} f(x) dx$$ true (maybe with some positive constant on the r.h.s)?

I believe its false, because the l.h.s is simply $$f(z)$$ (which we can assume to be positive and not zero) while the r.h.s might be zero.

• a lower bound is possible, not an upper bound. – Carlo Beenakker Dec 5 '19 at 22:32
• @CarloBeenakker: I'm not sure what kind of lower bound you have in mind, but taking $f = a \cdot 1_{\{z\}^C}$ seems to rule out such a thing. – Nate Eldredge Dec 6 '19 at 4:30
• right, my mistake. – Carlo Beenakker Dec 6 '19 at 7:15


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## Intersection of 2 spheres

Hello,
I am calculating some integrals in 3 dimensions. However, the difficulties of such integrals lie in the determination of the boundaries of the variables integrated over.

$\int_{C} d^{3}\vec{t}$ e$^{-\vec{s}.\vec{t}}$
For example, if we consider (C) as the region of the intersection of 2 spheres:
C=|$\vec{s}$-$\vec{t}$|<1 and |$\vec{s}$+$\vec{t}$|<1
I want to solve these set of inequalities for fixed $\vec{s}$, using spherical coordinates.
i.e. determine the interval over |$\vec{t}$|, $\phi$ and $\vartheta$=angle($\vec{s}$,$\vec{t}$)

Does anyone have a strategy to deal with such inequalities?

Thanks in advance.$^{}$
 PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor
 Recognitions: Homework Help Use cylindrical-polar coordinates with the z axis perpendicular to the plane of intersection. You can treat it as a volume of rotation.


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# Is there a simple way to create a cross-shaped array in ConTeXt?

According to https://en.wikibooks.org/wiki/LaTeX/Mathematics#Matrices_and_arrays, the following code creates an array that has a cross-shape, with four items centered in each quadrant.

\begin{array}{c|c}
1 & 2 \\
\hline
3 & 4
\end{array}

The desired result is this, with the numbers centered vertically and horizontally within their quadrants.

1 | 2
-----
3 | 4

Since I'm placing text, not math, \startcombination seems to be the right code, but I don't see a way to add rules.

Is there a simple equivalent in ConTeXt? ConTeXt Garden mentions \startarray, but this command is reported as not found when I add it to my code. I can create this in MetaPost or with a table, but I wonder if there is a more proper way?

The equivalent of LaTeX's tabular in ConTeXt is \start...\stoptabulate. I'm not sure whether that is the best solution in your situation. Maybe you can clarify the question.
\starttext


text:
3 replaced http://electronics.stackexchange.com/ with https://electronics.stackexchange.com/

I try to connect an ESP8266-12 and a 12V RGB LED strip to 230V AC. Based on thisthis link, I've came to the following scheme. This will also be the first time I will etch a PCB myself.

The partlist will be as following:

Part      Value

C2        0.1uF
C3        0.1uF
C4        0.1uF
C5        0.1uF
D1        1N4004
D2        1N4004
D3        1N4004
D4        1N4004
F1        1A will be sufficient?
JP1       screw connectors for 230V AC
JP2       jumper for connecting GPIO15 to ground
LED_STRIP the rgb leddstrip
Q1        TIP120
Q2        TIP120
Q3        TIP120
R1        220 Ohms
R2        220 Ohms
R3        220 Ohms
S1        switch to reset ESP8266-12
SERIAL    header pins for connecting over serial
TR1       transfo
U$1 ESP12 U1 L7812 U2 LD1117V33  I'm still unsure about what transfo to use? I was thinking about the MYRRA 44090 TRANSFORMER 1.5VA 24V. I'd like to get some feedback on this pick. Also I'd like to gain some feedback if this scheme is safe to use. I assume the ESP8266-12 will be isolated from the net since I'm using a transfo? For completeness I add a link here to my GitHub repo where the eagle files can be found. I try to connect an ESP8266-12 and a 12V RGB LED strip to 230V AC. Based on this link, I've came to the following scheme. This will also be the first time I will etch a PCB myself. The partlist will be as following: Part Value C2 0.1uF C3 0.1uF C4 0.1uF C5 0.1uF D1 1N4004 D2 1N4004 D3 1N4004 D4 1N4004 F1 1A will be sufficient? JP1 screw connectors for 230V AC JP2 jumper for connecting GPIO15 to ground LED_STRIP the rgb leddstrip Q1 TIP120 Q2 TIP120 Q3 TIP120 R1 220 Ohms R2 220 Ohms R3 220 Ohms S1 switch to reset ESP8266-12 SERIAL header pins for connecting over serial TR1 transfo U$1       ESP12
U1        L7812
U2        LD1117V33

I'm still unsure about what transfo to use? I was thinking about the MYRRA 44090 TRANSFORMER 1.5VA 24V. I'd like to get some feedback on this pick.

Also I'd like to gain some feedback if this scheme is safe to use. I assume the ESP8266-12 will be isolated from the net since I'm using a transfo?

For completeness I add a link here to my GitHub repo where the eagle files can be found.

I try to connect an ESP8266-12 and a 12V RGB LED strip to 230V AC. Based on this link, I've came to the following scheme. This will also be the first time I will etch a PCB myself.

The partlist will be as following:

Part      Value

C2        0.1uF
C3        0.1uF
C4        0.1uF
C5        0.1uF
D1        1N4004
D2        1N4004
D3        1N4004
D4        1N4004
F1        1A will be sufficient?
JP1       screw connectors for 230V AC
JP2       jumper for connecting GPIO15 to ground
LED_STRIP the rgb leddstrip
Q1        TIP120
Q2        TIP120
Q3        TIP120
R1        220 Ohms
R2        220 Ohms
R3        220 Ohms
S1        switch to reset ESP8266-12
SERIAL    header pins for connecting over serial
TR1       transfo
U$1 ESP12 U1 L7812 U2 LD1117V33  I'm still unsure about what transfo to use? I was thinking about the MYRRA 44090 TRANSFORMER 1.5VA 24V. I'd like to get some feedback on this pick. Also I'd like to gain some feedback if this scheme is safe to use. I assume the ESP8266-12 will be isolated from the net since I'm using a transfo? For completeness I add a link here to my GitHub repo where the eagle files can be found. 2 edited tags 1 # Wi-Fi controlled light; 230VAC - 12VDC/3.3VDC I try to connect an ESP8266-12 and a 12V RGB LED strip to 230V AC. Based on this link, I've came to the following scheme. This will also be the first time I will etch a PCB myself. The partlist will be as following: Part Value C2 0.1uF C3 0.1uF C4 0.1uF C5 0.1uF D1 1N4004 D2 1N4004 D3 1N4004 D4 1N4004 F1 1A will be sufficient? JP1 screw connectors for 230V AC JP2 jumper for connecting GPIO15 to ground LED_STRIP the rgb leddstrip Q1 TIP120 Q2 TIP120 Q3 TIP120 R1 220 Ohms R2 220 Ohms R3 220 Ohms S1 switch to reset ESP8266-12 SERIAL header pins for connecting over serial TR1 transfo U$1       ESP12
U1        L7812
U2        LD1117V33

I'm still unsure about what transfo to use? I was thinking about the MYRRA 44090 TRANSFORMER 1.5VA 24V. I'd like to get some feedback on this pick.

Also I'd like to gain some feedback if this scheme is safe to use. I assume the ESP8266-12 will be isolated from the net since I'm using a transfo?

For completeness I add a link here to my GitHub repo where the eagle files can be found.


text:
## Is The Army racially egalitarian? (model this)

This paper links the universe of Army applicants between 1990 and 2011 to their federal tax records and other administrative data and uses two eligibility thresholds in the Armed Forces Qualification Test (AFQT) in a regression discontinuity design to estimate the effects of Army enlistment on earnings and related outcomes. In the 19 years following application, Army service increases average annual earnings by over $$4,000 at both cutoffs. However, whether service increases long-run earnings varies significantly by race. Black servicemembers experience annual gains of$$5,500 to 15,000 11–19 years after applying while White servicemembers do not experience significant changes. By providing Black servicemembers a stable and well-paying Army job and by opening doors to higher-paid postservice employment, the Army significantly closes the Black-White earnings gap in our sample.

Here is the full paper by Kyle Greenberg, et.al., via the excellent Kevin Lewis.

## Marijuana Legalization and Fertility

State-level marijuana legalization has unintended consequences, including its effect on fertility. Marijuana use is associated with behaviors that increase fertility as well as physical changes that lower fertility. In this paper, I use a difference-in-differences design that exploits variation in medical and recreational marijuana legalization across states and over time to study the effects of marijuana legalization on fertility. This paper is the first to study the effects of recreational marijuana legalization on fertility. I find that legalizing recreational marijuana decreases a state’s birth rate by an average of 2.78% while increasing the probability that an individual is sexually active by 3.6 percentage points. [emphasis added by TC] Together, my findings show that the physical effects of marijuana use have the dominant effect on fertility. By contrast with the existing literature, I find that medical marijuana legalization does not affect the birth rate, although it increases the frequency of sexual activity by 1.6 sexual encounters per month. Neither type of marijuana legalization affects male gonorrhea cases or the probability of having sex with a stranger.

That is from a new paper by Sarah Papich, via the excellent Kevin Lewis.  And note that in this paper marijuana legalization predicts lower auto insurance premia.

## *Empires of Ideas*

The author is William C. Kirby and the subtitle is Creating the Modern University from Germany to America to China.  The shocker is that this is actually a good book.  In contrast, hardly any books on these topics are good.  This book is substantive on virtually every page, the author actually understands how universities work, and, get this…you have to read the book to know what is inside it.  The material covers why early German universities became so successful, why they declined and stayed low quality, why they revived somewhat in more recent times, which American universities have gotten better and richer and why (with respect to their governance), and what is going on with Chinese universities and their rise to eminence.  The latter part does feel a bit out of date, but overall an impressive performance.  Perhaps the sum total of all this work is a bit more desultory than what the author intends, but I will take desultory substance any day of the week.  Especially in such a “crummy book area” as this one.  The author by the way is a China specialist (good background for understanding universities!) and a former Dean at Harvard.

## Institutional Review Boards Should be Curtailed

A good piece on IRBs from CSPI by Willy Chertman:

Institutional Review Boards (IRBs) are ethics committees, ideally composed of scientific peers and lay community members, that review research before it can be conducted. Their ostensible purpose is to protect research subjects from research harms. But oftentimes, IRBs are costly, slow, and do more harm than good. They censor controversial research, invent harms where none exist, and by designating certain categories of subjects as “vulnerable,” cause a corresponding diminishment in research on those subjects. There is even a plausible legal argument that they violate researchers’ First Amendment rights. Because previous attempts to spur the responsible federal executive agencies into streamlining IRBs have been unsuccessful or only had limited success, a targeted legislative solution that does not depend on bureaucratic implementation is needed.

Chertman has a number of suggestions for reform. At the very least social science should not be under the purview of IRBs at all.

…a more sweeping approach would be removing social science from IRB jurisdiction altogether. Historian Zachary Schrag, who worked intensely to lobby federal agencies on the Common Rule revisions from 2009-2017, proposes this in his book, Ethical Imperialism. As he documents, the Belmont Report, and subsequent regulatory developments, were not designed with social science in mind. Congress could fix this historical oversight by changing the wording of HHS regulations. This would free IRBs to focus on truly high-risk research instead of wasting time on low-risk social science research. Since social science more often touches on political questions, this would also extricate government-mandated oversight boards (IRBs) from the delicate position of regulating politically charged research.

Removing IRBs from social science research is particulary important now because politically sensitive research can be crushed under the pretense that it could “harm” participants.

## Scottish Enlightenment vs. Irish Enlightenment

The Scottish Enlightenment seems like a real enlightenment to most observers, the 18th century Irish Enlightenment (Swift, Berkeley, Burke, toss in James Barry too) does not.  In my admittedly unorthodox view, I think the Irish Enlightenment simply had different concerns but was no less of an enlightenment.  Much of the Scottish Enlightenment was concerned with the following:

1. Increasing market size and division of labor

2. Martial virtue and security against foreign enemies

3. Sympathy

That all makes broad sense when you realize that Britain was indeed building the world’s largest economic market, and furthermore had to worry about its enemies on the Continent.  Regular social interactions were becoming normal enough that one could ask basic questions about sympathy, and assume that some degree of sympathy was present.

None of those conditions held true for Ireland.  Market size was small, and external market relations typically were controlled by the British.  As for military issues, Britain could dominate you in any case, so martial virtue was of secondary import, at least until later civil wars.  And sympathy was not to be assumed at all, for reasons of religious, political, and class prejudice.

My “standing on one foot” version of the Irish Enlightenment would be a concern with:

1. Is toleration at all possible?  Toleration needed before sympathy!

2. Can we expect there to be progress at all?  James Barry argues for the universality of progress, but Swift doubts whether moral progress is likely.  Burke wishes to take progress in baby steps.  Berkeley is skeptical altogether.  If you are ruled by the Brits, the richest society to date, but they are still bastards to you, maybe you will be more skeptical about moral progress.

3. A sense of terror from difference, as mirrored both in Burke’s aesthetics of the sublime and the voyages in Swift’s Gulliver’s Travels.  Everyone is running around deeply afraid of “the other,” and this concern surfaces also in Burke’s fears for the French aristocrats.  The enthusiasms of the French revolutionaries reminded Burke all too much of the earlier Irish civil wars and rebellions and massacres, even though in both cases he knew the privileges of the nobles were not deserved.  Swift is consistently asking whether one culture can understand the other at all.

I view the two Enlightenments as embodying different kinds of skepticism.  The Scots, such as Hume and Smith, hold a deep epistemic skepticism, which led them to recipes for decentralization and mechanism design.  The Irish had a more practical skepticism, doubting whether moral progress in human beings was all that likely.

The Irish and Scottish Enlightenments perhaps clashed most directly when Burke took issue with David Hume’s accounts of the Catholic 1641 “massacres” in Ireland, arguing that a more nuanced understanding of Irish history was needed.  Burke considered writing his own history of Ireland.

Burke, like Swift, understood the point of view of “the settled” fairly well, arguably better than the Scots did:

Beyond Irish affairs, Burke also began the impeachment of Warren Hastings over his actions as governor-general of India. The fourteen-year impeachment clearly displayed his obsessive nature, but it also finds him arguing against the imposition of British laws and manners on India. Instead, he defends the native civilisations, their institutions and religious beliefs.

Bishop Berkeley is a more complicated fit in this story, and might require a blog post of his own.  But think of him as telling everyone that everything they think they know is wrong, and they actually exist in a simulation in the mind of God.  A prospect to strike terror into the hearts of many!  Even the supposed truths of mathematics and the calculus melt away on close examination.  As for politics, Berkeley worried a great deal about corruption and factions, and he favored extensive government interventions, both social and economic, to make life stable again and human beings virtuous.  He feared that perhaps progress was not possible, as growing wealth would lead to luxurious and corrupted tastes.

Overall, the Irish Enlightenment wasn’t nearly as optimistic as its Scottish counterpart.  But it was far more mindful of the perspective of the victim, presaging more modern developments.  And later in the 19th century, the Irish Enlightenment turned its attention to themes of depopulation and excessively high land rents, both extremely relevant to current times as well…

The Irish Enlightenment is, dare I say, underrated?

To assess the importance of unequal access to medical expertise and services, we estimate the causal effects of having a child who is a doctor on parents’ mortality and health care use. We use data from parents of almost 22,000 participants in admission lotteries to medical school in the Netherlands. Our findings indicate that informal access to medical expertise and services is not an important cause of differences in health care use and mortality.

That is from “Do Doctors Improve the Health Care of Their Parents? Evidence from Admission Lotteries,” by Elisabeth Artmann, Hessel Oosterbeek, and Bas van der Klaauw, in the new American Economic Journal: Applied Economics.  Here are earlier, ungated versions.

## What Caused the Murder Spike?

I think there’s clear evidence that the current murder spike was caused primarily by the 2020 BLM protests. The timing matches the protests well, and the pandemic poorly. The spike is concentrated in black communities and not in any of the other communities affected by the pandemic. It matches homicide spikes corresponding to other anti-police protests, most notably in the cities where those protests happened but to a lesser degree around the country. And the spike seems limited to the US, while other countries had basically stable murder rates over the same period.

I agree with Scott Alexander, although I would emphasize a little more the mediating factor of the police pullback.

I would also add that each step in the mechanism–protests lead to police pullback which leads to an increase in murders–is well supported on its own in the academic literature. Step one, for example, is that protests lead to police pullback. In The effect of highly publicized police killings on policing: Evidence from large U.S. cities Cheng and Long document exactly this:

Our regression discontinuity and difference-in-differences estimates provide consistent and strong evidence that those high-profile killings reduced policing activities, including police self-initiated activities and arrests.

That’s step one. Step two is that police on the street reduce crime which you can find from my research using the terror alert level as well as that of many others. Step one plus step two leads to a spike in murders following the 2020 BLM protests.

As Alexander noted, we also have plenty of evidence on a micro level. For example, I showed clear evidence of police pullback–a “blue strike”–and consequent increase in crime in Baltimore after the Freddie Gray protests. Put it all together along with the timing and other evidence and the case is strong that the 2020 BLM protests led to police pullback which led to a spike in murders, especially in black communities.

## My Conversation with Barkha Dutt

Here is the link, and here is part of the CWT summary:

Barkha joined Tyler to discuss how Westerners can gain a more complete picture of India, the misogyny still embedded in Indian society, why family law should be agnostic of religious belief, the causes of declining fertility in India, why relations between Hindus and Muslims seem to be worsening, how caste has persisted so strongly in India, the success of India’s subsidized institutes of higher education, the best city for Indian food, the power of Amar Chitra Katha’s comics, the influence of her English liberal arts education, the future of Anglo-American liberalism in India, the best ways to use Twitter, and more.

And from the conversation:

COWEN: Many outsiders have the impression that relations between Hindus and Muslims and the aggregate in India have become worse over the last 10 to 15 years. If you put aside particular actions of particular political personalities, and you try to think of a structural reason why that might be true — because normally the intuition is, people grow richer, they’re more tolerant, there’s more commercial interaction, there’s more intermingling — what would be your structural account of why, in some ways, that problem has become worse?

DUTT: You just spoke of intermingling, Tyler. I think that one of the biggest reasons for the worsening relations, or the othering, as it were, of communities that are not your own is the ghettoization of how people live. For example, if there were neighborhoods where people live cheek by jowl — that still happens, of course, in many cities, but it also happens less than it used to, and that is true. We are seeing a Muslim quarter, to give an example, or a Christian quarter in a way that we wouldn’t have before our cities were so ghettoized.

I think that kind of intermingling, of living in the same housing societies or neighborhoods, participating in each other’s festivals as opposed to just tolerating them — those are the structural changes or shifts that we are witnessing. It’s also true that it is tougher for a person from a religious minority — in particular, an Indian Muslim — to get a house as easily as a non-Muslim. I think I would be lying if I did not acknowledge that. Also, the last point is interfaith marriages or interfaith love. This is a deeply politicized issue as well.

While I’m talking to you, in the last 24 hours in the Southern city of Hyderabad, one of our big technology hubs, we’ve had reports of a Muslim family that attacked a Hindu man for marrying a Muslim woman. In reverse, we see Muslim women also targeted all the time if they choose to marry Hindus. This is not helped by the fact that you’ve had several states now talking about what they call love jihad. That’s the phrase they use for marriages that are across religious communities, in particular between Hindus and Muslims.

The percentage of Indians marrying not just outside their religion but also outside their caste — which in Hinduism is a hierarchical system of traditional occupation that you’re born into — is woefully low. I don’t know if I remember my data correctly, but I think less than 5 percent of Indians actually marry outside of their own communities. I would need to go back to that number and check it, but that’s what I remember off the top of my head.

Those are the structural reasons: the fact that people don’t love or have relationships outside of their community, don’t live enough with people of diverse faiths, and don’t participate in each other’s lives.

We used to have this politically correct phrase called tolerance, which I actually just hate, and I keep nudging people towards the Indian military. The Indian military actually has a system of the commanding officer taking on the faith of his troops during religious prayers. The military has multireligious places of worship. It even has something called an MMG, which is not just a medium machine gun but a Mandir Masjid Gurdwara, which is all the different faiths praying together at the same place. We don’t see a lot of that kind of thing happening outside of the military.

Another survey done by Pew reinforced this when it spoke of Indians today being more like a thali than khichri. Let me just explain that. A thali is a silver tray where you get little balls of different food items. Pew found that Hindus and Muslims — when surveyed, both spoke of the need for religious diversity as being a cornerstone of India. They like the idea of India as a thali, where there were different little food items, but separate food items. The khichri is rice and lentils all mixed up and eaten with pickle. The khichri is that intermingling, the untidy overlapping.

We are just seeing less and less of that overlapping. In my opinion, that is tragic. Where there is social interdependence, where there is economic interdependence, where there is personal interdependence is when relationships thrive and flourish and get better. But when they remain ghettos, separations just tolerating each other — that, I think, remains in the realm of othering.

Recommended, interesting throughout.

## Why have college completion rates increased?

Jeffrey T. Denning, Eric R. Eide, Kevin J. Mumford, Richard W. Patterson and Merrill Warnick tell us why: grade inflation:

We document that college completion rates have increased since the 1990s, after declining in the 1970s and 1980s. We find that most of the increase in graduation rates can be explained by grade inflation and that other factors, such as changing student characteristics and institutional resources, play little or no role. This is because GPA strongly predicts graduation, and GPAs have been rising since the 1990s. This finding holds in national survey data and in records from nine large public universities. We also find that at a public liberal arts college grades increased, holding performance on identical exams fixed.

That is from the new American Economic Journal: Applied Economics.  And here are earlier ungated versions.

## George Washington Can Be Proud

In recent years formerly proud universities such as Georgetown, Princeton, and MIT have cravenly failed to defend liberal principles.

Justice, however, is about more than punishing and condemning evil. It is even more important to defend and laud the good. So I want to laud the clear, concise, principled, and measured but forceful letter from George Washington University Provost Christopher Alan Bracey and Law School Dean Dayna Bowen Matthew responding to calls to condemn and fire one of their professors.

Dear Members of the George Washington University Community,

Since the recent U.S. Supreme Court ruling to overturn Roe v. Wade, we have heard from members of our community who have expressed feelings of deep disagreement with this decision.

We also have received requests from some members of the university and external communities that the university terminate its employment of Adjunct Professor and Supreme Court Justice Clarence Thomas and cancel the Constitutional Law Seminar that he teaches at the Law School. Many of the requests cite Justice Thomas’ concurring opinion in Dobbs v. Jackson Women’s Health Organization, in which he called the substantive due process doctrine a “legal fiction.” Justice Thomas has been a consistent critic of the Court’s legal philosophy on substantive due process for many years. Because we steadfastly support the robust exchange of ideas and deliberation, and because debate is an essential part of our university’s academic and educational mission to train future leaders who are prepared to address the world’s most urgent problems, the university will neither terminate Justice Thomas’ employment nor cancel his class in response to his legal opinions.

Justice Thomas’ views do not represent the views of either the George Washington University or its Law School. Additionally, like all faculty members at our university, Justice Thomas has academic freedom and freedom of expression and inquiry. Our university’s academic freedom guidelines state: “The ideas of different faculty members and of various other members of the University community will often and quite naturally conflict. But it is not the proper role of the University to attempt to shield individuals within or outside the University from ideas and opinions they find unwelcome, disagreeable, or even deeply offensive.

Just as we affirm our commitment to academic freedom, we affirm the right of all members of our community to voice their opinions and contribute to the critical discussions that are foundational to our academic mission.

## New York City fact of the day

The top 1 percent of earners, who make more than $804,000 a year, contributed 41 percent of the city’s personal income taxes in 2019. About one-third of the people who left moved from Manhattan, and had an average income of$214,300. No other large American county had a similar exodus of wealth.

Here is more from the NYT.


text:
# Dry Gas

Written by Jerry Ratzlaff. Posted in Properties

A natural gas with with very little liquid hydrocarbons or water vapor. It consists of almost 100 of methane $$(CH4)$$.


text:
# Thread: Find an injective map

1. ## Find an injective map

Hey,

I am considering the set $\displaystyle \mathcal{P}_{k}(\mathbb{N})$ which is the set of subsets of $\displaystyle \mathbb{N}$ with $\displaystyle k$ elements.

I want to find a injective function $\displaystyle \phi_{k}:\mathcal{P}_{k}(\mathbb{N}) \rightarrow \mathbb{N}^{k}$.

Suggestions ppreciated.

2. ## Re: Find an injective map

Originally Posted by detalosi
Hey,

I am considering the set $\displaystyle \mathcal{P}_{k}(\mathbb{N})$ which is the set of subsets of $\displaystyle \mathbb{N}$ with $\displaystyle k$ elements.

I want to find a injective function $\displaystyle \phi_{k}:\mathcal{P}_{k}(\mathbb{N}) \rightarrow \mathbb{N}^{k}$.

Suggestions ppreciated.
What does the notation $\mathbb{N}^{k}$ mean? I hate to guess and be wrong. That is a waste of effort.

3. ## Re: Find an injective map

I understand it to be the set of subsets of $\displaystyle \mathbb{N}$ with no more than $\displaystyle k$ elements.

4. ## Re: Find an injective map

Originally Posted by detalosi
I understand it to be the set of subsets of $\displaystyle \mathbb{N}$ with no more than $\displaystyle k$ elements.
Well, I would never have guessed that. If that is correct then $\mathcal{P}_k(\mathbb{N})\subset \mathbb{N}^k$.
So that the problem is trivial, use the identity mapping.

BTW I doubt that is what the notation means.

5. ## Re: Find an injective map

I have the following.

Consider the set of k natural numbers $\displaystyle B= \left\{ 1,2,3,...,k \right\}$ where $\displaystyle x_{1}<x_{2}<x_{3}<...<x_{k}$.

Then I define the function $\displaystyle \psi_{k}(B)= (x_{1},x_{2},x_{3},...,x_{3})$.

This function is injective.

Questions: what is the difference betjene the set $\displaystyle \mathcal{P}_{k}(\mathbb{N})$ and the set $\displaystyle \mathbb{N}^{k}$?

6. ## Re: Find an injective map

Originally Posted by detalosi
Questions: what is the difference betjene the set $\displaystyle \mathcal{P}_{k}(\mathbb{N})$ and the set $\displaystyle \mathbb{N}^{k}$?
I told you that I doubted that your understanding of that notation was correct.

If I were guessing, $\prod\limits_{i = 1}^k \mathbb{N}$, i.e. the set of all k-tuples with natural number entries.

7. ## Re: Find an injective map

Yes, I might have been wrong, but I searched the internet for the explanation. It is not possible for me to ask my instructor for the time being.

I don't understand you answer. Allow me to state the problem in order to avoid any misunderstanding on my part.

The exercise states the following:

Q1)
Explain that the set $\displaystyle \mathcal{P}(\mathbb{N})$ of all subsets of $\displaystyle \mathbb{N}$ is unacountable.

A1)
I have shown this using Cantor's diagonal method.

Q2)
Let $\displaystyle \mathcal{P}_{fin}(\mathbb{N})$ be the set of all finite subsets of $\displaystyle \mathbb{N}$. Furthermore let $\displaystyle \mathcal{P}_{k}(\mathbb{N})$ for $\displaystyle k>0$ be the set of subsets of $\displaystyle \mathbb{N}$ with exactly $\displaystyle k$ elements.
Find an injective map $\displaystyle f_{k}: \mathcal{P}(\mathbb{N}) \rightarrow \mathbb{N}^{k}$ for every $\displaystyle k>0$

A2)
This is where I need help.
You stated, that I could use the identity map. So if I consider a map which takes members of $\displaystyle \mathcal{P}_{fin}(\mathbb{N})$ (say a set with 3 subsets) then the map would give back the ordered triple $\displaystyle (x_{1}, x_{2}, x_{3})$. This would constitute an identity-map which is injective. By construction the map I presented above is injective.

Would you agree with this?

8. ## Re: Find an injective map

You have a set of $k$ elements. You are calling them $x_1<x_2<\cdots < x_k$. This is the set $\{x_1,x_2,\ldots, x_k\}$. Plato suggested the map:

$$\{x_1,x_2,\ldots, x_k\} \mapsto (x_1,x_2,\ldots, x_k)$$

The question is, is this function injective? You want to show that

$$\{x_1,x_2,\ldots, x_k\} \mapsto (z_1,z_2,\ldots, z_k)$$

and

$$\{y_1,y_2,\ldots, y_k\} \mapsto (z_1,z_2,\ldots, z_k)$$

Then

$$\{x_1,x_2,\ldots, x_k\} = \{y_1,y_2,\ldots, y_k\}$$

This is trivial because of the well-ordering principle of Natural Numbers. You can put any subset of natural numbers in order, and that ordering allows the mapping to be injective. Basically, the process takes the least element of the set and put it in the first position of the tuple. Then, you drop that element and consider the subset with one fewer elements. It will again have a least element, and that gets mapped to the second spot. Keep going until you get the $k$-th spot of the tuple to complete the mapping.


text:
# Question about a proof in Junod's paper about the Blum-Blum-Shub generator

I am reading Junod's paper about the Blum-Blum-Shub generator. There is one thing I just do not understand about his proof of Lemma 4. On page 17 he writes:

We conclude that $$x=-x_0$$ and from Lemma 1 we know that $$x \ne x_0$$

(So far I understand.)

, so they must have different parities (Why is this the case?), $$n$$ beeing odd, which is a contradiction.

Could you please explain that to me?

If $$x_0$$ is odd, then $$-x_0 = n - x_0$$ must be even (and versa-visa).


text:
Q

# Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is: (iii) coincident lines

Q6.    Given the linear equation $2x + 3y -8 =0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(iii) coincident lines

Views

Given the equation,

$2x + 3y -8 =0$

As we know that the condition for the coincidence  of the lines  $a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0$, is,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

So any line with this condition can be  $4x+6y-16=0$

Here,

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-8}{-16}=\frac{1}{2}$

As

$\frac{1}{2}=\frac{1}{2}=\frac{1}{2}$   the line satisfies the given condition.

Exams
Articles
Questions


text:
# Deduction of contraposition propositional logic

I have to find a deduction whose conclusion is the law of contraposition: $(\varphi \rightarrow \psi) \rightarrow (\neg \psi \rightarrow \neg \varphi)$.

In particular it is suggested we use the following axioms:

1. $\varphi \rightarrow (\psi \rightarrow \varphi)$
2. $(\varphi \rightarrow \psi) \rightarrow ((\varphi \rightarrow \neg \psi) \rightarrow \neg \varphi)$

This is as far as I've gotten, but in the end the result is a tautology and not my intended formula:

1. $\varphi \rightarrow \psi \vdash \neg \psi \rightarrow \neg \varphi$ [Deduction theorem]
2. $(\neg \psi \rightarrow \neg \varphi) \rightarrow ((\varphi \rightarrow \psi) \rightarrow (\neg \psi \rightarrow \neg \varphi))$ [Iteration of 1.]
3. $\varphi \rightarrow \psi$ [Assumption]
4. $(\neg \psi \rightarrow \neg \varphi) \rightarrow (\neg \psi \rightarrow \neg \varphi)$ [Modus ponens of 2 and 3]

How can I get from $(\neg \psi \rightarrow \neg \varphi) \rightarrow (\neg \psi \rightarrow \neg \varphi)$ to $(\neg \psi \rightarrow \neg \varphi)$?

Thank you very much in advance!

• I'm uncomfortable with using the deduction theorem, since it is in itself stronger than the law of contraposition. – Mark Fischler Oct 25 '16 at 21:31
• This was just my idea, I'm sure there is a better and more elegant solution. – Francesco Carzaniga Oct 26 '16 at 7:08

Assume the antecedent of (($\phi$$\rightarrow$$\psi$)$\rightarrow$($\lnot$$\psi$$\rightarrow$$\lnot$$\phi$)).

Then apply 2. and detach something, which I'll call "something".

Now assume the second antecedent of the above '$\lnot$$\psi$'. Then apply axiom 1 and detach something that matches the antecedent of "something".

And I hope you can then find the last step.

Edit:

In Polish notation we have the following as axioms:

1. CaCba
2. CCabCCaNbNa

Here's a diagram:

    CCabCCaNbNa    Cab   C a  C b a
\           /        |    | |
\         /         --   | --
\       / Nb     C Nb C a Nb
\     /   \    /
CCaNbNa  CaNb
\    /
Na

• I'm not sure I understand what you mean. By "assuming the antecedent" I think you mean what I did in the first step with the deduction theorem, and I could also assume $\neg \psi$, as you seem to suggest in your answer, but this doesn't get me anywhere. If you could be a bit more precise also in your usage of "detach" I would be very grateful. – Francesco Carzaniga Oct 26 '16 at 7:11
• Clarification: By following your steps it seems to me you're implying that implication is associative. – Francesco Carzaniga Oct 26 '16 at 7:21
• By "detach" I mean infer using modus ponendo ponens. – Doug Spoonwood Oct 26 '16 at 8:11
• @FrancescoCarzaniga I've added a diagram. – Doug Spoonwood Oct 26 '16 at 8:22
• Thank you very much now it is perfectly clear. – Francesco Carzaniga Oct 26 '16 at 11:05


text:
# Multiple isset block going from more specific to more generic

I have a data structure that allows for inheritance of properties, in such a way that if a property is not defined within a context, the second most specific context is checked until said property is found. Simplified it's basically the following:

function getCarPartColor($carData,$owner, $brand,$part) {
$color = false; if(isset($carData->{$owner}->{$brand}->{$part})) {$color = $carData->{$owner}->{$brand}->{$part};

} else if(isset($carData->{$owner}->{$brand}->allparts)) {$color = $carData->{$owner}->{$brand}->allparts; } else if(isset($carData->{$owner}->allbrands->allparts)) {$color = $carData->{$owner}->allbrands->allparts;

} else if(isset($carData->allowners->allbrands->allparts)) {$color = $carData->allowners->allbrands->allparts; } return$color;
}

Where $carData is the data structure and the rest are the querying variables. If I were to call: getCarPartColor($carData, "AnthonyNewel", "opel", "engine");

But I hadn't defined any color for $carData->AnthonyNewel->opel->engine, then it checks if a color is set on $caraData->AnthonyNewel->opel->allparts, and fetches this one instead if it exists. If it's not there, it then checks if it's defined for allbrands, and it goes on.

While the code above works, one can't help but notice the repetition. Is there a less verbose way to write this while still being maintanable (i.e. not a long ternary operator)?

• What are the expected returns of each scenario? – Brett Santore Jul 28 '14 at 17:41
• @BrettSantore the same kind of value, only within a different "context" of the data. Think of it as the following: somebody asks what color is the engine of AnthonyNewel's Opel car. The function replies well I don't know the color of specifically the engine, but I know that all AnthonyNewel's Opel car engines are blue, so take blue. OR Well I don't know about his opel cars specifically but I know that all engines of all the cars AnthonyNewel owns are blue, so take blue. It's a little bit like class inheritance, but for data. – Mahn Jul 28 '14 at 19:57
• So imagine the string "blue" as the return value in all of the possible scenarios (for the sake of simplicity), only in some cases it will be defined in more specific data paths than others (depending on the arguments passed) – Mahn Jul 28 '14 at 20:02
• @EliasVanOotegem No it will not. PHP does not generate notices, warnings or errors on unset properties when isset is used (that's the whole point of using isset first). With the code above there can never be an scenario where PHP throws notices, warning or errors because every single path is tested with isset before any usage. – Mahn Jul 29 '14 at 8:51
• I'm sorry, i guess more specifically, what is returned when the function fails to find a string? – Brett Santore Jul 29 '14 at 12:44

Expanding on k_smd's suggestion of using a loop, you could easily make this function a tad more generic using an array as a second argument.
I'd also strongly recommend you use type-hints, and doc-blocks to make your code more maintainable. And as ever looking at the coding standards never hurts.

Anyway, here's a slightly more concise version of your function:

/**
* @param \stdClass $car * @param array$properties
* @return mixed|bool
*/
function getCarPartColor(stdClass $car, array$properties)
{
$defaults = array('allowners', 'allbrands', 'allparts'); //ensure numeric indexes:$properties = array_values($properties);$current = $car;//current object to evaluate for ($i=0, $j=count($properties);$i<$j;++$i) { if (isset($current->{$properties[$i]}))//given property exists
$current =$current->{$properties[$i]};
elseif (isset($current->{$defaults[$i]}))//default exists$current = $current->{$defaults[$i]}; else//none exist, return false return false; } return$current;
}

With minimal effort, you can make this function even more generic (and re-usable). It would suffice to pass the defaults as third argument, and you can use this function as a generic pseudo-recursive getter:

/**
* @param \stdClass $car * @param array$properties
* @param array $defaults * @return mixed|bool * @throws \InvalidArgumentException */ function getSubProperty(stdClass$obj, array $properties, array$defaults)
{
//make sure the size of both arrays match
$j = count($properties);
if (!$j ||$j > count($defaults)) throw new \InvalidArgumentException( sprintf( 'Default argument should contain at least %d values, instead saw %d',$j,
count($defaults) ) ); //call array_values on array arguments, to ensure numeric indexes$current = $obj; for ($i=0, $j=0;$i<$j;++$i)
{
if (isset($current->{$properties[$i]}))//given property exists$current = $current->{$properties[$i]}; elseif (isset($current->{$defaults[$i]}))//default exists
$current =$current->{$defaults[$i]};
else//none exist, return false
return false;
}
return $current; }  Of course, you might have spotted a "feature" you might not care for too much. Suppose you pass an object like this: $foo = (object) array(
'foobar' => (object) array(
'property' => (object) array(
'value' => 123
)
)
);//$foo->foobar->propery->value  You could then call this last function, trying to get $foo->something->property->value and pass array('foobar', 'foobar', 'foobar') as the $defaults array. The result would be that, during the first iteration of the for loop, the $properties[$i] value (something) would not be found, and instead, the $defaults value (foobar) will be used. The next iterations would then pan out just fine, and in the end, the function will return $foo->foobar->property->value. This, then, is a potential source of mysterious, and difficult to trace bugs. But don't worry. It's a fairly easy thing to fix: /** * @param \stdClass$car
* @param array $properties * @param array$defaults
* @return mixed|bool
* @throws \InvalidArgumentException
*/
function getSubProperty(stdClass $obj, array$properties, array $defaults) { //same as above for ($i=0, $j=0;$i<$j;++$i)
{
if (!isset($current->{$properties[$i]})) break;//break the loop!$current = $current->{$properties[$i]}; } for ($i;$i<$j;++$i) {//only use defaults from here on end if (!isset($current->{$defaults[$i]}))
return false;
$current =$current->{$defaults[$i]};
}
return $current; }  Putting it all together: Finally, it might be useful to have the ability to switch back and forth between the $properties and $defaults provided in some cases. So in an ideal world, you might want to add another argument to your function, that allows the caller to decide what the appropriate course of action is, using something like this: /** * @param \stdClass$car
* @param array $properties * @param array$defaults
* @param bool $switch = false * @return mixed|bool * @throws \InvalidArgumentException */ function getSubProperty(stdClass$obj, array $properties, array$defaults, $switch = false) {$j = count($properties); if (!$j || $j > count($defaults))
throw new \InvalidArgumentException(
sprintf(
'Default argument should contain at least %d values, instead saw %d',
$j, count($defaults)
)
);
$current =$obj;
if ($switch === true) {//switch is true, function can switch back and forth for ($i=0, $j=0;$i<$j;++$i)
{
if (isset($current->{$properties[$i]}))//given property exists$current = $current->{$properties[$i]}; elseif (isset($current->{$defaults[$i]}))//default exists
$current =$current->{$defaults[$i]};
else//none exist, return false
return false;
}
return $current; } //No switching: if the$properties value can't be found, try defaults, or fail
for ($i=0,$j=0;$i<$j;++$i) { if (!isset($current->{$properties[$i]}))
break;//break the loop!
$current =$current->{$properties[$i]};
}
for ($i;$i<$j;++$i)
{
if (!isset($current->{$defaults[$i]})) return false;$current = $current->{$defaults[$i]}; } return$current;
}

• I'm going to mark it as the accepted answer because I think this is the best alternative that the language would allow, though I think I will stick with the original since for the time being I find more maintainable (in that a new developer can grab the code and get what's going on fairly quick). But good thinking nonetheless! – Mahn Jul 30 '14 at 11:11

Long time reader, first time poster, welcoming of critique.

You could create an array populated with each variant of the property you're looking for:

    $is_set = array ($carData->{$owner}->{$brand}->{$part},$carData->{$owner}->{$brand}->allparts,
$carData->{$owner}->allbrands->allparts,
$carData->allowners->allbrands->allparts );  And then check each value in the array using a foreach loop which ends when the condition isset evaluates to true. The first property to evaluate to true is then returned which in turn breaks you out of the function (credit to Brett for the insight).  foreach ($is_set as $this_set) { if isset($this_set) {
return $this_set; } }  Putting it all together would look like: function getCarPartColor($carData, $owner,$brand, $part) {$is_set = array (
$carData->{$owner}->{$brand}->{$part},
$carData->{$owner}->{$brand}->allparts,$carData->{$owner}->allbrands->allparts,$carData->allowners->allbrands->allparts
);

foreach ($is_set as$this_set) {
if isset($this_set) { return$this_set;
}
}
}

• I would wrap this in the original function getCarPartColor($carData,$owner, $brand,$part), you would than remove the break since the return would exit the function. – Brett Santore Jul 28 '14 at 17:43
• could you explain this a little more please? (edit it into the post) – Malachi Jul 28 '14 at 17:49
• Neat, but the problem here is that PHP would throw a warning if for instance $carData->{$owner}->{$brand}->{$part} isn't set at all, and the data structure I'm working with is built under the assumption that not setting a property at all is okay to inherit the property of the parent context. – Mahn Jul 28 '14 at 20:02


text:
## College Physics (4th Edition)

$\rho = 2.3 \times 10^{17} kg/m^3$
The radius of nucleus is given by $r = r_0 A^{1/3}$ To find the density, $\rho$ $\rho = \frac{M}{V}$ $\rho = \frac{M}{\frac{4}{3} \pi r^3 }$ substitute $r = r_0 A^{1/3}$ and $M = Au$ into the $r$ in density equation $\rho = \frac{Au}{\frac{4}{3} \pi (r_0 A^{1/3})^3 }$ simplify the equation $\rho = \frac{1u}{\frac{4}{3} \pi (r_0^3) }$ Now solve for $\rho$ $\rho = \frac{1.66\times 10^{-27} kg}{\frac{4}{3} \pi (1.2 \times 10^{-15} m)^3 }$ $\rho = 2.3 \times 10^{17} kg/m^3$


text:
## LaTeX forum ⇒ Others ⇒ TikZ + Beamer: Placing text immediately under images

Information and discussion about other tools not listed above.
kaiserkarl13
Posts: 582
Joined: Tue Mar 25, 2008 5:02 pm
Location: Columbia, Missouri, USA

### TikZ + Beamer: Placing text immediately under images

There are many times when I'm making a beamer-based presentation and I want to include an image that is accompanied, right below it (either centered or left-aligned), by a caption denoting where I got the image. In in-line images, I can work around this with line breaks, but what I really want is something like this:
\begin{tikzpicture}  \node (main) at (0,0) {\includegraphics{myimage}};  \node [below of=main] {My caption};  \node (second) at (3,0.5) {\includegraphics{myotherimage}};  \node [below of=second] {My second caption};\end{tikzpicture}

This will, unfortunately, result in "captions" that overlay the pictures or are too far from them. It works perfectly if I specify [anchor=south west] for the main image and [anchor= north west] for the first caption, but if I try that for the second image, the second caption is right on top of the first one, regardless of what I specify for the second image.

What I'm really trying to do is avoid specifying "node distance=XXX" by trial-and-error or laying out each picture/caption set with exact coordinates (i.e., what I want is to move one and the other moves with it, but they're always right below the images).

Any suggestions?

Tags:

Stefan Kottwitz
Posts: 8208
Joined: Mon Mar 10, 2008 9:44 pm
Location: Hamburg, Germany
Contact:
Hi,

did you solve this challenge in the meantime?

I think it may not be hard. It's just that there was no actual code here, to try, so it was a bit too theoretical for me to answer.

Stefan


text:
# Demixing Structured Signal form their Nonlinear Superposition

We study the problem of *demixing* a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,m$, where $x = \Phi w+\Psi z$ denotes the superposition signal, $\Phi$ and $\Psi$ are orthonormal bases in $\mathbb{R}^n$, and $w, z\in\mathbb{R}^n$ are sparse coefficient vectors of the constituent signals, and $e_i$ represents the noise. Moreover, $g$ represents a nonlinear *link* function, and $a_i\in\mathbb{R}^n$ is the $i$-th row of the measurement matrix, $A\in\mathbb{R}^{m\times n}$. Problems of this nature arise in several applications ranging from astronomy, computer vision, and machine learning. We make some concrete algorithmic progress for the above demixing problem. Specifically, we consider two scenarios: (i) the case when the demixing procedure has no knowledge of the link function, and (ii) the case when the demixing algorithm has perfect knowledge of the link function. In both cases, we provide fast algorithms for recovery of the constituents $w$ and $z$ from the observations. Moreover, we support these algorithms with a rigorous theoretical analysis, and derive (nearly) tight upper bounds on the sample complexity of the proposed algorithms for achieving stable recovery of the component signals.

Publications
1. M. Soltani and C. Hegde, Fast Algorithms for Demixing Sparse Signals from Nonlinear Observations, IEEE Transactions on Signal Processing, vol. 65, no. 16, p4209-4222, Aug 2017. [Paper]

2. M. Soltani and C. Hegde, Stable Recovery from Random Sinusoidal Feature Maps, International Conference on Acoustics, Speech, and Signal Processing (ICASSP), March 2017 [Paper]

3. M. Soltani and C. Hegde, Iterative Thresholding for Demixing Structured Superpositions in High Dimensions, NIPS Workshop on Learning in High Dimensions with Structure (LHDS), December 2016. [Paper]

4. M. Soltani and C. Hegde, A Fast iterative Algorithm for Demixing Sparse Signals from Nonlinear Observations, IEEE GlobalSIP Symposium on Compressed Sensing and Deep Learning, Dec 2016. [Paper]


text:
See an introductory tutorial on logic gates: NetOps, also referred to as NetOps 2.0, is a networking approach that encompasses the use of DevOps tools, methods and techniques to create an agile, scalable and programmable infrastructure capable of delivering business-critical applications and services rapidly and efficiently. The output is "false" if both inputs are "false" or if both inputs are "true."

{\displaystyle (A\cdot B)+({\overline {A}}\cdot {\overline {B}})}

An XNOR gate is also called exclusive NOR gate or EXNOR gate.In a two input XNOR gate, the output is high (logic 1 or true) when two inputs are same.

If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. 4 pictures 1 word 4 desserts 2 on a plate 2 in a cone 6 letter word? On the app 4 pics 1 word, what is the answer to the one with the presidental mic.

it is not..? (

Or if you're especially insane, you can develop your own logic symbol keyboard utility. .

If the Subset box is available, click a character subset. Word | Zeichen darstellen.

( How do i type Boolean algebra symbols in word? A

Graphical characteristics:Symmetric, Closed shape, Monochrome, Contains both straight and curved lines, Has crossing lines. Click Close. Note: If you are using an expanded font, such as Arial or Times New Roman, the Subset list appears. where is the magnifier glass symbol in word?

Four pics one word game whats the word, music symbol, chello, chello case and a plate with 3 fish on it?

The Private Use set-up undoubtedly prevents a lot older documents from breaking. The NAND gate operates as an AND gate followed by a NOT gate. ( A A logical inverter, sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. Instead, you can type '1U+B5' and press ALT+X, or you can type '1B5', select 'B5', and press ALT+X. with a fifth NAND gate).

( ¯ How can i insert a computer power symbol into ms word? how to make a pentagram symbol on the keyboard If both inputs are "false," then the output is "false." + Please paste the youtube video url in the field below: This site is best viewed while logged in. +

( you can normally type 4, yo How to type a cross symbol on your computer keyboard? My i phone shows a plug symbol instead of a bolt symbol when charging, what does that mean? [11.06] a cone has a base area of 45 inÂ² and a lateral area which is 2.2 times bigger than the base area.

Cloud disaster recovery (cloud DR) is a combination of strategies and services intended to back up data, applications and other ... A storage area network (SAN) is a dedicated high-speed network or subnetwork that interconnects and presents shared pools of ... FCoE (Fibre Channel over Ethernet) is a storage protocol that enable Fibre Channel (FC) communications to run directly over ... A Fibre Channel switch is a networking device that is compatible with the Fibre Channel (FC) protocol and designed for use in a ... All Rights Reserved, Otherwise, the output is "false.". Das will ich haben! But in practice, there is a limit to the number of gates that can be packed into a given physical space.

Microsoft word xnor symbol There is a rupee symbol on the keyboard of dell inspiron laptop.

If the input is 1, then the output is 0. both represent the XNOR gate with inputs A and B. What does tm symbol on top of a word indicate? Most logic gates take an input of two binary values, and output a single value of a 1 or 0. random letters: ozzmrlroaxqh?

Please paste the youtube video url in the field below: This site is best viewed while logged in. What does the numeric symbol mean when it is typed before a word? when i try to install it it says "updatetool.exe" cannot find or called different?

What does the numeric symbol mean when it is typed before a word? Otherwise, the output is "true. mother in law is panicking..this is a new thing/problem. S Like the and, the Insert Symbol tool lets you insert single characters into a document so you can change 'P implies Q' to the logical formulation P ⊃ Q or P → Q depending on your symbolism (and you can also switch between 'P and Q,' P & Q or P ∧ Q). How to type a cross symbol on your computer keyboard? There are two ways that can enable you to. If ALT+X is converting the wrong character code, you may select the correct character code before pressing ALT+X, or you can precede the code with the letters 'U+'. Another way of looking at this circuit is to observe that the output is 1 if the inputs are different, but 0 if the inputs are the same. ⋅ .

Hello:) i want to try and make a guitar symbol or some kind of rockstar symbol with the keyboard..do you know how to do that and help? Please note that there are no 7 basic gates but there are ONLY and ONLY 2 basic gates that are AND and OR and an INVERTER with using AND, OR and INVERTOR you can create any type of gate, perhaps author was confused with 7 colors of white lights, but digital binary world is a way different than the Analog business. B provide an explanation f... 4 pic 1 word 6 letter word. If the four NOR gates are replaced by NAND gates, this results in an XOR gate, which can be converted to an XNOR gate by inverting the output or one of the inputs (e.g. ¯ CMOS, or Complementary Metal-Oxide-Silicon, ICs are constructed from MOSFET or JFET type Field Effect Transistors.

Click the character that you want to insert, and then click Insert. {\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)} ) Insert a special character. How to change voice and video symbol in gmail chat to original symbol? = Like us to stay up to date However, this approach requires five gates of three different kinds. How to make an illuminati symbol on word? )
For 2-input gate, it can be interpreted as when both of the inputs are same, then the output is High state and when the inputs are different , then the output is Low state “ 0 ”.

Use this list to choose from an extended list of language characters, including Greek and Russian (Cyrillic), if available. TTL, or Transistor-Transistor Logic, ICs will use NPN and PNP type Bipolar Junction Transistors. when both of p and q are false.In grammar, nor is a coordinating conjunction..

I cant get the watsapp icon symbol whn msgg arives i only get notify sound not symbol on my picrmax canvas 4 destop will u guys plz help meee? Otherwise, the output is "false." im now using a different computer but cant get into facebook a lock symbol appears near the f icon for faceboo... How to type rupee symbol from hp keyboard in windows 7 desktop? U+2299 ⊙ CIRCLED DOT OPERATOR the sign for the XNOR operator (negation of exclusive disjunction).

An alternative arrangement is of five NAND gates in a topology that emphasizes the construction of the function from In a Boolean comparison, the Xor operator always evaluates both expressions, which could include making procedure calls.

In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately five volts positive (+5 V).

What does the symol "hide im" on the skype bar code under the face symbol means.

B My iphone 4s wont come on its just stuck on a itunes symbol and a charger import symbol any ideas how to get my phone back on? i see nba players doit after a three point shot.. i see it done by a street gang called the b. Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.
Couple Handprint Painting Tiktok, Bluetooth Jammer Diy, Leisure Travel Unity Murphy Bed For Sale, Dog Chew Treats, Masterminds Show Gsn, Gelati Vs Gelato Strain, Pat Priest Lds, Johnny Gargano New Theme Song, Sous Vide Woodcock, Xm42 Backpack For Sale, St Louis County Police Blotter, Serveur Ark Gratuit, Huffy Torex Utv Parts, Edam Entertainment Website, Sons Of Guns Game, Agathe Cléry Film Complet, The Theme Best Expressed In Both Excerpts Is, Rever D'une Star Islam, F2 Boiling Point, How Old Is Vikas Vasu, Best Frozen Food At Safeway, Quinn Bradlee Net Worth, Epic Mickey Nintendo Switch, Alex Scott Parents, Victoria 2 Hpm Formable Nations, Virginia Slaghekke Wikipedia, " />
See an introductory tutorial on logic gates: NetOps, also referred to as NetOps 2.0, is a networking approach that encompasses the use of DevOps tools, methods and techniques to create an agile, scalable and programmable infrastructure capable of delivering business-critical applications and services rapidly and efficiently. The output is "false" if both inputs are "false" or if both inputs are "true."

{\displaystyle (A\cdot B)+({\overline {A}}\cdot {\overline {B}})}

An XNOR gate is also called exclusive NOR gate or EXNOR gate.In a two input XNOR gate, the output is high (logic 1 or true) when two inputs are same.

If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. 4 pictures 1 word 4 desserts 2 on a plate 2 in a cone 6 letter word? On the app 4 pics 1 word, what is the answer to the one with the presidental mic.

it is not..? (

Or if you're especially insane, you can develop your own logic symbol keyboard utility. .

If the Subset box is available, click a character subset. Word | Zeichen darstellen.

( How do i type Boolean algebra symbols in word? A

Graphical characteristics:Symmetric, Closed shape, Monochrome, Contains both straight and curved lines, Has crossing lines. Click Close. Note: If you are using an expanded font, such as Arial or Times New Roman, the Subset list appears. where is the magnifier glass symbol in word?

Four pics one word game whats the word, music symbol, chello, chello case and a plate with 3 fish on it?

The Private Use set-up undoubtedly prevents a lot older documents from breaking. The NAND gate operates as an AND gate followed by a NOT gate. ( A A logical inverter, sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. Instead, you can type '1U+B5' and press ALT+X, or you can type '1B5', select 'B5', and press ALT+X. with a fifth NAND gate).

( ¯ How can i insert a computer power symbol into ms word? how to make a pentagram symbol on the keyboard If both inputs are "false," then the output is "false." + Please paste the youtube video url in the field below: This site is best viewed while logged in. +

( you can normally type 4, yo How to type a cross symbol on your computer keyboard? My i phone shows a plug symbol instead of a bolt symbol when charging, what does that mean? [11.06] a cone has a base area of 45 inÂ² and a lateral area which is 2.2 times bigger than the base area.

Cloud disaster recovery (cloud DR) is a combination of strategies and services intended to back up data, applications and other ... A storage area network (SAN) is a dedicated high-speed network or subnetwork that interconnects and presents shared pools of ... FCoE (Fibre Channel over Ethernet) is a storage protocol that enable Fibre Channel (FC) communications to run directly over ... A Fibre Channel switch is a networking device that is compatible with the Fibre Channel (FC) protocol and designed for use in a ... All Rights Reserved, Otherwise, the output is "false.". Das will ich haben! But in practice, there is a limit to the number of gates that can be packed into a given physical space.

Microsoft word xnor symbol There is a rupee symbol on the keyboard of dell inspiron laptop.

If the input is 1, then the output is 0. both represent the XNOR gate with inputs A and B. What does tm symbol on top of a word indicate? Most logic gates take an input of two binary values, and output a single value of a 1 or 0. random letters: ozzmrlroaxqh?

Please paste the youtube video url in the field below: This site is best viewed while logged in. What does the numeric symbol mean when it is typed before a word? when i try to install it it says "updatetool.exe" cannot find or called different?

What does the numeric symbol mean when it is typed before a word? Otherwise, the output is "true. mother in law is panicking..this is a new thing/problem. S Like the and, the Insert Symbol tool lets you insert single characters into a document so you can change 'P implies Q' to the logical formulation P ⊃ Q or P → Q depending on your symbolism (and you can also switch between 'P and Q,' P & Q or P ∧ Q). How to type a cross symbol on your computer keyboard? There are two ways that can enable you to. If ALT+X is converting the wrong character code, you may select the correct character code before pressing ALT+X, or you can precede the code with the letters 'U+'. Another way of looking at this circuit is to observe that the output is 1 if the inputs are different, but 0 if the inputs are the same. ⋅ .

Hello:) i want to try and make a guitar symbol or some kind of rockstar symbol with the keyboard..do you know how to do that and help? Please note that there are no 7 basic gates but there are ONLY and ONLY 2 basic gates that are AND and OR and an INVERTER with using AND, OR and INVERTOR you can create any type of gate, perhaps author was confused with 7 colors of white lights, but digital binary world is a way different than the Analog business. B provide an explanation f... 4 pic 1 word 6 letter word. If the four NOR gates are replaced by NAND gates, this results in an XOR gate, which can be converted to an XNOR gate by inverting the output or one of the inputs (e.g. ¯ CMOS, or Complementary Metal-Oxide-Silicon, ICs are constructed from MOSFET or JFET type Field Effect Transistors.

Click the character that you want to insert, and then click Insert. {\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)} ) Insert a special character. How to change voice and video symbol in gmail chat to original symbol? = Like us to stay up to date However, this approach requires five gates of three different kinds. How to make an illuminati symbol on word? )
For 2-input gate, it can be interpreted as when both of the inputs are same, then the output is High state and when the inputs are different , then the output is Low state “ 0 ”.

Use this list to choose from an extended list of language characters, including Greek and Russian (Cyrillic), if available. TTL, or Transistor-Transistor Logic, ICs will use NPN and PNP type Bipolar Junction Transistors. when both of p and q are false.In grammar, nor is a coordinating conjunction..

I cant get the watsapp icon symbol whn msgg arives i only get notify sound not symbol on my picrmax canvas 4 destop will u guys plz help meee? Otherwise, the output is "false." im now using a different computer but cant get into facebook a lock symbol appears near the f icon for faceboo... How to type rupee symbol from hp keyboard in windows 7 desktop? U+2299 ⊙ CIRCLED DOT OPERATOR the sign for the XNOR operator (negation of exclusive disjunction).

An alternative arrangement is of five NAND gates in a topology that emphasizes the construction of the function from In a Boolean comparison, the Xor operator always evaluates both expressions, which could include making procedure calls.

In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately five volts positive (+5 V).

What does the symol "hide im" on the skype bar code under the face symbol means.

B My iphone 4s wont come on its just stuck on a itunes symbol and a charger import symbol any ideas how to get my phone back on? i see nba players doit after a three point shot.. i see it done by a street gang called the b. Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.
Couple Handprint Painting Tiktok, Bluetooth Jammer Diy, Leisure Travel Unity Murphy Bed For Sale, Dog Chew Treats, Masterminds Show Gsn, Gelati Vs Gelato Strain, Pat Priest Lds, Johnny Gargano New Theme Song, Sous Vide Woodcock, Xm42 Backpack For Sale, St Louis County Police Blotter, Serveur Ark Gratuit, Huffy Torex Utv Parts, Edam Entertainment Website, Sons Of Guns Game, Agathe Cléry Film Complet, The Theme Best Expressed In Both Excerpts Is, Rever D'une Star Islam, F2 Boiling Point, How Old Is Vikas Vasu, Best Frozen Food At Safeway, Quinn Bradlee Net Worth, Epic Mickey Nintendo Switch, Alex Scott Parents, Victoria 2 Hpm Formable Nations, Virginia Slaghekke Wikipedia, " />

# xnor symbol in word

A logic gate is a building block of a digital circuit. key "4" has three symbols. There are seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR, and XNOR. Getting a red cross symbol in the tray icon on battery symbol?

See an introductory tutorial on logic gates: NetOps, also referred to as NetOps 2.0, is a networking approach that encompasses the use of DevOps tools, methods and techniques to create an agile, scalable and programmable infrastructure capable of delivering business-critical applications and services rapidly and efficiently. The output is "false" if both inputs are "false" or if both inputs are "true."

{\displaystyle (A\cdot B)+({\overline {A}}\cdot {\overline {B}})}

An XNOR gate is also called exclusive NOR gate or EXNOR gate.In a two input XNOR gate, the output is high (logic 1 or true) when two inputs are same.

If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. 4 pictures 1 word 4 desserts 2 on a plate 2 in a cone 6 letter word? On the app 4 pics 1 word, what is the answer to the one with the presidental mic.

it is not..? (

Or if you're especially insane, you can develop your own logic symbol keyboard utility. .

If the Subset box is available, click a character subset. Word | Zeichen darstellen.

( How do i type Boolean algebra symbols in word? A

Graphical characteristics:Symmetric, Closed shape, Monochrome, Contains both straight and curved lines, Has crossing lines. Click Close. Note: If you are using an expanded font, such as Arial or Times New Roman, the Subset list appears. where is the magnifier glass symbol in word?

Four pics one word game whats the word, music symbol, chello, chello case and a plate with 3 fish on it?

The Private Use set-up undoubtedly prevents a lot older documents from breaking. The NAND gate operates as an AND gate followed by a NOT gate. ( A A logical inverter, sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. Instead, you can type '1U+B5' and press ALT+X, or you can type '1B5', select 'B5', and press ALT+X. with a fifth NAND gate).

( ¯ How can i insert a computer power symbol into ms word? how to make a pentagram symbol on the keyboard If both inputs are "false," then the output is "false." + Please paste the youtube video url in the field below: This site is best viewed while logged in. +

( you can normally type 4, yo How to type a cross symbol on your computer keyboard? My i phone shows a plug symbol instead of a bolt symbol when charging, what does that mean? [11.06] a cone has a base area of 45 inÂ² and a lateral area which is 2.2 times bigger than the base area.

Cloud disaster recovery (cloud DR) is a combination of strategies and services intended to back up data, applications and other ... A storage area network (SAN) is a dedicated high-speed network or subnetwork that interconnects and presents shared pools of ... FCoE (Fibre Channel over Ethernet) is a storage protocol that enable Fibre Channel (FC) communications to run directly over ... A Fibre Channel switch is a networking device that is compatible with the Fibre Channel (FC) protocol and designed for use in a ... All Rights Reserved, Otherwise, the output is "false.". Das will ich haben! But in practice, there is a limit to the number of gates that can be packed into a given physical space.

Microsoft word xnor symbol There is a rupee symbol on the keyboard of dell inspiron laptop.

If the input is 1, then the output is 0. both represent the XNOR gate with inputs A and B. What does tm symbol on top of a word indicate? Most logic gates take an input of two binary values, and output a single value of a 1 or 0. random letters: ozzmrlroaxqh?

Please paste the youtube video url in the field below: This site is best viewed while logged in. What does the numeric symbol mean when it is typed before a word? when i try to install it it says "updatetool.exe" cannot find or called different?

What does the numeric symbol mean when it is typed before a word? Otherwise, the output is "true. mother in law is panicking..this is a new thing/problem. S Like the and, the Insert Symbol tool lets you insert single characters into a document so you can change 'P implies Q' to the logical formulation P ⊃ Q or P → Q depending on your symbolism (and you can also switch between 'P and Q,' P & Q or P ∧ Q). How to type a cross symbol on your computer keyboard? There are two ways that can enable you to. If ALT+X is converting the wrong character code, you may select the correct character code before pressing ALT+X, or you can precede the code with the letters 'U+'. Another way of looking at this circuit is to observe that the output is 1 if the inputs are different, but 0 if the inputs are the same. ⋅ .

Hello:) i want to try and make a guitar symbol or some kind of rockstar symbol with the keyboard..do you know how to do that and help? Please note that there are no 7 basic gates but there are ONLY and ONLY 2 basic gates that are AND and OR and an INVERTER with using AND, OR and INVERTOR you can create any type of gate, perhaps author was confused with 7 colors of white lights, but digital binary world is a way different than the Analog business. B provide an explanation f... 4 pic 1 word 6 letter word. If the four NOR gates are replaced by NAND gates, this results in an XOR gate, which can be converted to an XNOR gate by inverting the output or one of the inputs (e.g. ¯ CMOS, or Complementary Metal-Oxide-Silicon, ICs are constructed from MOSFET or JFET type Field Effect Transistors.

Click the character that you want to insert, and then click Insert. {\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)} ) Insert a special character. How to change voice and video symbol in gmail chat to original symbol? = Like us to stay up to date However, this approach requires five gates of three different kinds. How to make an illuminati symbol on word? )
For 2-input gate, it can be interpreted as when both of the inputs are same, then the output is High state and when the inputs are different , then the output is Low state “ 0 ”.

Use this list to choose from an extended list of language characters, including Greek and Russian (Cyrillic), if available. TTL, or Transistor-Transistor Logic, ICs will use NPN and PNP type Bipolar Junction Transistors. when both of p and q are false.In grammar, nor is a coordinating conjunction..

I cant get the watsapp icon symbol whn msgg arives i only get notify sound not symbol on my picrmax canvas 4 destop will u guys plz help meee? Otherwise, the output is "false." im now using a different computer but cant get into facebook a lock symbol appears near the f icon for faceboo... How to type rupee symbol from hp keyboard in windows 7 desktop? U+2299 ⊙ CIRCLED DOT OPERATOR the sign for the XNOR operator (negation of exclusive disjunction).

An alternative arrangement is of five NAND gates in a topology that emphasizes the construction of the function from In a Boolean comparison, the Xor operator always evaluates both expressions, which could include making procedure calls.

In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately five volts positive (+5 V).

What does the symol "hide im" on the skype bar code under the face symbol means.

B My iphone 4s wont come on its just stuck on a itunes symbol and a charger import symbol any ideas how to get my phone back on? i see nba players doit after a three point shot.. i see it done by a street gang called the b. Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.

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Chiudi


text:
### Tony Phillips' Take Blog on Math Blogs

 Mail to a friend · Print this article · Previous Columns Tony Phillips' Take on Math in the Media A monthly survey of math news

# This month's topics:

## Leonardo, Michelangelo and the elevated dodecahedron

The lantern atop the dome of the Sagrestia Nuova (San Lorenzo, Florence; in March 2010, before the restoration of the coronamento; the polyhedral structure of the "sphere," legible in this enlargement, is almost imperceptible from the street). The Sagrestia Nuova, essentially a mausoleum for Lorenzo and Giuliano de' Medici and two of their kinsmen, was built by Michelangelo between 1520 and 1534. The architecture, the interior decoration and the sculpture are considered among his greatest masterpieces. Photo: Tony Phillips.

"When Michelangelo 'copied' Leonardo" was the headline in La Repubblica, January 17, 2013. The gilded bronze coronamento of the lantern above the dome of the Sagrestia Nuova had been removed, restored and replaced by a copy; the original was now on display in the crypt of the Medici chapels. As Laura Larcan tells the story (article, slide show) Florentines for the first time realized that the spherical element in the spire was actually an elevated dodecahedron. To make one you replace each face of a dodecahedron with a pyramid of equilateral triangles. It is combinatorially the same as the stellated dodecahedron (there was one on the pavement of Saint Mark's in Venice, perhaps due to Paolo Uccello when he worked there in 1425) except for the shape of the triangles; and in fact for San Lorenzo the triangles have been additionally flattened to make the solid more spherical (see below). Leonardo comes into the story because he had drawn an elevated dodecahedron as one of his illustrations for Luca Pacioli's De Divina Proportione (1496-1498, published in Venice, 1509); he may well have invented this object.

Hollow Elevated Dedocahedron, woodcut after a design by Leonardo da Vinci, from a copy of De Divina Proportione sold at auction for £110,000 on May 27, 2010. Image courtesy of liveauctioneers.com and Bloomsbury Auctions.

Larcan quotes Vincenzo Vaccaro of the Soprintendenza per i Beni Architettonici di Firenze on the symbolism of this polyhedron. Leonardo's picture represents "the force inherent in the ether, in that space of which the dodecahedron is the symbol, that tries to expand, to emerge in every direction. But this image is too far from the familiar and reassuring sphere, all-comprehensive and all-inclusive. Michelangelo borrows the image of force and expansion from the original design of Leonardo, but hides it using isosceles triangles which give the pentagonal pyramids a lesser height and make the polyhedron resemble a crystal that amplifies and decomposes light." [My translations -TP]

## New prime in the news

On February 5, 2013 Jacob Aron, writing on New Scientist, picked up a press release from the Great International Mersenne Prime Search (GIMPS): a new Mersenne prime had been identified by GIMPS volunteer Curtis Cooper (University of Central Missouri). As Aron put it: "The largest known prime number has just shot up to $2^{57,885,161}-1$, breaking a four-year dry spell in the search for new, ever-larger primes." Aron describes GIMPS as a "distributed computing project designed to hunt for a particular kind of prime number first identified in the 17th century." These are the Mersenne primes, of the form $2^p-1$, where $p$ is itself a prime. "The new prime, which has over 17 million digits, is only the 48th Mersenne prime ever found and the 14th discovered by GIMPS." What is the point? Aron quotes Chris Caldwell (Tennessee): "It's sort of like finding a diamond. For some reason people decide they like diamonds and so they have a value. People like these large primes and so they also have a value." But Aron adds: "Prime-hunting isn't a completely esoteric pastime though, as these numbers underpin the cryptographic techniques used to make online transactions secure."

The discovery was also reported on Fox News, CNN ("You know you're a geek if you felt all warm and fuzzy inside when you read that headline"), the BBC ("'No practical use' for 17-million digit prime number") and CBS News, who quote George Woltman, the creator of GIMPS: "It's analogous to climbing Mt. Everest. People enjoy it for the challenge of the discovery of finding something that's never been known before."


text:
# Effects of meson mixing on dilepton spectra

@article{Teodorescu2001EffectsOM,
title={Effects of meson mixing on dilepton spectra},
author={O. Teodorescu and A. K. Dutt-mazumder and Charles Gale},
journal={Physical Review C},
year={2001},
volume={63},
pages={034903}
}
• Published 3 August 2000
• Physics
• Physical Review C
The effect of scalar and vector meson mixing on the dilepton radiation from hot and dense hadronic matter is estimated in different isospin channels. In particular, we study the effect of $\sigma$-$\omega$ and $\rho-a_0$ mixing and calculate the corresponding rates. Effects are found to be significant compared to standard $\pi$-$\pi$ and $K$-${\bar K}$ annihilations. While the mixing in the isoscalar channel mostly gives a contribution in the invariant mass range between the two-pion threshold…
14 Citations

## Figures from this paper

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• Physics
• 2005
Abstract We have studied the π + π − → e + e − process in dense and hot nuclear matter using relativistic non-linear models taking into account all scalar–vector coupling terms up to fourth order in
rho0(770) - f(0)(980) mixing and CPT violation in a non-unitary evolution of pion creation process pi- p ---> pi- pi+ n on polarized target
Unitary evolution from pure initial states to pure final states in pi(-)p-> pi(-)pi(+)n imposes constraints on pion production amplitudes that are violated by CERN data on polarized target at 17.2

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text:
Wrapper functions around options consulted by gargle, which provide:

• A place to hang documentation.

• The mechanism for setting a default.

If the built-in defaults don't suit you, set one or more of these options. Typically, this is done in the .Rprofile startup file, with code along these lines:

options(
gargle_oauth_email = "jane@example.com",
gargle_oauth_cache = "/path/to/folder/that/does/not/sync/to/cloud"
)

## Usage

gargle_oauth_email()

gargle_oob_default()

gargle_oauth_cache()

gargle_verbosity()

local_gargle_verbosity(level, env = parent.frame())

with_gargle_verbosity(level, code)

## Arguments

level

Verbosity level: "debug" > "info" > "silent"

env

The environment to use for scoping

code

Code to execute with specified verbosity level

## gargle_oauth_email

gargle_oauth_email() returns the option named "gargle_oauth_email", which is undefined by default. If set, this option should be one of:

• An actual email address corresponding to your preferred Google identity. Example:janedoe@gmail.com.

• A glob pattern that indicates your preferred Google domain. Example:*@example.com.

• TRUE to allow email and OAuth token auto-discovery, if exactly one suitable token is found in the cache.

• FALSE or NA to force the OAuth dance in the browser.

## gargle_oob_default

gargle_oob_default() returns the option named "gargle_oob_default", falls back to the option named "httr_oob_default", and eventually defaults to FALSE. This controls whether to prefer "out of band" authentication. We also return FALSE unconditionally on RStudio Server or Cloud. This value is ultimately passed to httr::init_oauth2.0() as use_oob. If FALSE (and httpuv is installed), a local webserver is used for the OAuth dance. Otherwise, user gets a URL and prompt for a validation code.

Read more about "out of band" authentication in the vignette Auth when using R in the browser.

## gargle_oauth_cache

gargle_oauth_cache() returns the option named "gargle_oauth_cache", defaulting to NA. If defined, the option must be set to a logical value or a string. TRUE means to cache using the default user-level cache file, ~/.R/gargle/gargle-oauth, FALSE means don't cache, and NA means to guess using some sensible heuristics.

## gargle_verbosity

gargle_verbosity() returns the option named "gargle_verbosity", which determines gargle's verbosity. There are three possible values, inspired by the logging levels of log4j:

• "debug": Fine-grained information helpful when debugging, e.g. figuring out how token_fetch() is working through the registry of credential functions. Previously, this was activated by setting an option named "gargle_quiet" to FALSE.

• "info" (default): High-level information that a typical user needs to see. Since typical gargle usage is always indirect, i.e. gargle is called by another package, gargle itself is very quiet. There are very few messages emitted when gargle_verbosity = "info".

• "silent": No messages at all. However, warnings or errors are still thrown normally.

## Examples

gargle_oauth_email()
#> NULL
gargle_oob_default()
#> [1] FALSE
gargle_oauth_cache()
#> [1] NA
gargle_verbosity()
#> [1] "info"