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+0

-5
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+1015

What is the value of the expression shown below?

7 + (10 − 4)2 ÷ 4 × 1/2    2       2 is a Numerical Expressions

I am trying to make after 4 times 1/2 with a 3 sort of above but in Numerical Expressions form.

This is Numerical Expressions

Mar 13, 2019

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Your question does not make sense Nickolas.

Perhaps you can fix it?

Mar 13, 2019
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I see what he measn I'll just edited my answer the first two towards the end is meaning that he wants 1/2 to the second power you could say or squared and the two at the end is just saying to show that the two next to the 1/2 is a numerical expression so mathmatically that two is just for an example in his case he forgot to add an equals sign

But here's my work along with it

In previous problems I have explainded before I have stated the operations of pemdas

1.Exponets

2. Parenthasess

3. Mutiplication

4. Division

6. Subtraction

7 + (10 − 4)2 ÷ 4 × 1/2    2  so we first take care of the parenthasses.

7 + 6(2) ÷ 4 × 1/2    2   The next sep is multiplication

7 + 12 ÷  1                   Now when you multipply the fraction and every thing said and done you get 4/4's and I am going to treat this as 1

Then we divide which = 19 and when we divide by 1 we still get 19

Now if I were to kept the four It would have been 4.75

#3
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Nicholas, you need to learn to express yourself properly.

7 + (10 − 4)2 ÷ 4 × 1/2    2       2 is a Numerical Expressions

The black numbers are fine and so is the writing at the end BUT  what  are the two red 2s supposed to mean?

I honestly do not understand.

Mar 13, 2019
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I was saying two is the numerical expression but I did not put two in words..

The 1st 2 is a numerical expression

1/2 WITH A 2 ALITTLE OBOVE IT....

Numerical Expressions

Nickolas  Mar 13, 2019
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I still don't understand

Is one of these what you want?

$$7+(10-4)^2\div 4\times 1/2^2\\ or\;\;maybe\\ 7+(10-4)^2\div 4\times( \frac{1}{2})^2\\$$

Are either of those right?  If not can you try to explain what is different.

Melody  Mar 13, 2019
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The bottom one is right

Nickolas  Mar 13, 2019
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Melody, thank you for clarifying the question.

$$7 + (10-4)^2\div 4 \times \left(\dfrac{1}{2}\right)^2\\ =7+36\div 4 \div 4\\ =7+\dfrac{9}{4}\\ =\dfrac{37}{4}$$

.
Mar 13, 2019
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Now i'm confused how did the second division symbol get there???

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Multiplying by 1/4 means dividing by 4.

MaxWong  Mar 13, 2019
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Thanks for your answer Max but .........you are talking to a little kid Max  and you have jumped steps

(Sorry Nickolas, but on here you are a little kid. Enjoy the status while you can.)

$$7+(10-4)^2\div 4\times( \frac{1}{2})^2\\$$

Firstly Nickolas you need to learn the correct notation.

If you cannot write in Latex like I have then here are a couple of alternate correct methods.

7 + (10 − 4)to the power of 2      ÷     4 × (1/2)to the power of 2

or

7 + (10 − 4) ^ 2 ÷ 4 × (1/2) ^ 2

or

7+(10-4)^2 / 4*(1/2)^2

See how ^ means 'to the power of'.

and how divide and fractions are really the same thing.  Yea I know it is a bit confusing.

----------------------------------------------

As far as order of operation goes, it is

1) Inside brackets first.

2) powers

3)  Multiplication and division, left to right

4) Addition and Subtraction, left to right.

------------------------------------------------

$$7+(10-4)^2\div 4\times( \frac{1}{2})^2\\ \text{get rid of brackets first}\\ =7+6^2\div 4\times \frac{1^2}{2^2}\\ \text{which means}\\ =7+6^2\div 4\times( \frac{1*1}{2*2})\\ \text{now do the powers}\\ =7+36\div 4\times \frac{1}{4}\\ \text{now multiply and division are equally important so you do them from left to right}\\ =7+9\times \frac{1}{4}\\ \text{mmm tricky, fraction multiplication.}\\ \text{9=9 divided by 1 = 9 over 1, I have to write it like that.}\\ =7+\frac{9}{1}\times \frac{1}{4}\\ =7+\frac{9\times 1}{1\times 4}\\ =7+\frac{9}{4}\\ \text{Note that }\frac{9}{4}\;\;\;\text{is the same as }\;\;9\div 4 \\ =7+2\frac{1}{4}\\ =9\frac{1}{4}\\$$

If you do not full understand some of these steps then you probably need to do a lot of work on basic fractions.

I/we can help if you want us too.

Fractions are hard to understand. There are many concepts with them. And you will not be good at maths unless you master them very soon.

You need to master order of operation too.

Melody  Mar 13, 2019
edited by Melody  Mar 13, 2019
edited by Melody  Mar 13, 2019
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I Honestly urge you not to tell himthat to his face XD

#12
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I know thwe order of operation I get confused with the facts inside I already know the order........):

Nickolas  Mar 14, 2019
#13
+105952
+1

Well that is very good Nickolas :)

Melody  Mar 14, 2019

format: plain


text:
# How Can One Legitimately Use the Rules of Substitution and Repalcement in a Non-Mechanical Fashion?

Charles Stewart said I might ask the following as a question here.

If an author doesn't use parentheses for logical expressions like x->y, say in propositional calculus, I don't see how the introduction of parentheses comes as justified when using the rule of uniform substitution, or the rule of replacement on those expression. In other words, when taking unparenthesized expressions like x->y, parenthesizing them, and uniformly substituting or replacing the parenthesized expression for a variable or expression respectively, I don't see how one could do this without implicitly referring to the meaning of the unparenthesized expression like x->y. How is the unparenthesized statement of the same category as the parenthesized statement, especially if the unparenthesized statement is not a wff, while the parenthesized statement is a wff? If we insert parentheses when replacing a statement p by statement q, how is the parenthesized statement q' equiform with q? Doesn't the rule of replacement, to get used correctly, require mechanical replacement? Doesn't the rule of uniform substitution also require mechanical substitution?

"Equiformity" just means "equal in terms of form". This includes the order of the symbols in the string, and we can't rotate, twist, reflect, etc. or change the symbols... "p" is not equiform with "q" even though one is a reflection of the other. Only "p" is equiform with "p", though that isn't quite precise, since other "p"s exist equiform.

The rule of substitution basically says (this might not quite work as a precise definition) that if, for any thesis of the logical system with variable "x", we uniformly substitute all instances of "x" by any wff, then we may infer the resulting expression also as a thesis of the system. For example, if (q&(p*q)) is a thesis of some logical system, and also if (p!q) is a wff, then we may infer ((p!q)&(p*(p!q)) as a thesis of the logical system, since if one starts with "(q&(p*q))" and we substitute each instance of q with (p!q), one obtains ((p!q)&(p*(p!q)). The removed wff need not come as logically equivalent to the inserted wff.

The rule of replacement more-or-less says that we may replace any given wff x with any other logically equivalent wff y freely, as opposed to uniformly, within any wff z whatsoever without changing z in any "significant" way (this is not a formal definition, this gets tricky to make precise). In other words, if we apply the rule of replacement, it will simply not happen that "z" changes from a theorem to a contradiction, a contradiction to a theorem, a contingency to a theorem, a theorem to a contingency, a contradiction to a contingency, or a contingency to a contradiction. So, if we replace an instance of x with y within z obtain z', and if we have z as a theorem, we may infer z' as a theorem also (except "theorem" could get uniformly substituted by "contingency" or "contradiction"). For example, if we have ((p^q)&r)==((p@q)!s), and we have ((r@((p^q)&r))@((p^q)&r)) as either a theorem, or a contingency, or a contradiction, then we may infer ((r@((p@q)!s))@((p^q)&r)) as a theorem, contingency, or contradiction respectively. In contradistinction to the example above, the left instance of ((p^q)&r) has gotten replaced by ((p@q)!s), while the right instance has not.

By theorem I mean a formally provable wff.

By contradiction I mean that the negation of the contradiction comes as a theorem.

By contingency I mean a wff which for which the wff can't get proven, nor can its negation get proven. I hope the explanations help.

-
Would you please define (or at least explain) the terms rule of substitution, rule of replacement, category, and equiuniform, so I can understand the question? –  Quinn Culver Aug 29 '11 at 14:49
Perhaps the parentheses are never part of the formulas themselves, and are just written in the presentation of results to help clarify what formula is being written. Each book will have a particular definition of formulas, which determines once and for all where the parentheses go, if anywhere. –  Carl Mummert Aug 29 '11 at 15:23
You have a great skill in setting storms in teacups! –  Mariano Suárez-Alvarez Aug 29 '11 at 16:12
Once again you are confusing syntax and semantics. Substitution and replacement rules don't apply to unparsed strings but, rather, to terms parsed into some (equational) language. So the rules may be interpreted as rewriting not strings but trees (representing parsed well-formed algebraic expressions). –  Bill Dubuque Aug 29 '11 at 16:13
@Doug Of course you can attempt to "simulate" this in some lower-level string language. But you have to do it faithfully - which you are not. Your problems occur only because your are not faithfully preserving the higher-level structure when you represent it in your string language. –  Bill Dubuque Aug 29 '11 at 16:46

We commonly drop parentheses in the natural-language presentations about formal logic. So, assuming that your formal definition of well formed formulas includes parentheses, the first thing you have to do when reading a natural-language presentation is to determine which well formed formula the authors refer to when they write something like "$x \to y$".
For example, an author might write something like "the result of substituting $y$ with $y \to x$ in $x \to y$ is $x \to (y \to x)$." Even if none of the expressions inside the quotes is actually a well-formed formula, it is still completely clear what they mean. We just have to look up the formal definition of a well-formed formula and then translate the natural-language text using that definition.
The avoidance of parentheses is made easier by conventions that give some operations precedence over others. For example $\lnot A \to B$ means $(\lnot A) \to B$.
Humans read proofs in natural language, and we do a good job at checking them (in my opinion). If someone wants to run a proof through a formal proof checker, that's a different matter - the proofs in math textbooks are not intended to be formally verified, they are intended for humans. Most authors assume that if they say "Replace all the 5s in the number $17^8$ with 6s", the reader will not respond that "$17^8$ does not have any 5s in it". The same goes for formulas in logic. –  Carl Mummert Aug 29 '11 at 23:02


text:
Non-open subgroups of finite index in the idele class group of a number field

Let $K$ be a number field and $C_K$ be its idele class group. Exercise 5.11 in Milne's notes asks me to show that there is a finite-index subgroup $H$ of $C_K$ which is not open. I haven't found an example, and am having trouble believing it for the following reason:

If $K=\mathbb{Q}$, there is an isomorphism of topological groups

$C_\mathbb{Q} \cong \mathbb{R}^\times_{>0} \times \hat{\mathbb{Z}}^\times$.

Since $\mathbb{R}^\times_{>0}$ has no nontrivial finite-index subgroups, $H$ must contain it, so $H \mathbin/ \mathbb{R}^\times_{>0}$ is a finite-index subgroup of $\hat{\mathbb{Z}}^\times$. However, finite-index implies open for the latter.

What am I missing?

Contrary to the statement in the OP, the profinite group $\widehat{\mathbb Z}^{\times}$ admits non-open finite index subgroups.
For example, it admits a surjection onto $\prod_{n = 1}^{\infty} \mathbb Z/2\mathbb Z$, and this product has non-open finite index subgroups. (They correspond to non-principal ultrafilters on $\mathbb N$.)
• Sorry, but how this surjection onto $\prod\limits_{n=1}^{\infty}\mathbb Z/2\mathbb Z$ looks like? – Anna Abasheva Jan 5 '18 at 10:28
• For $p > 2$, consider the reduction map $\mathbf{Z}_p^\times \rightarrow \mathbf{F}_p^\times \simeq \mathbf{Z}/(p-1) \mathbf{Z}$ Since $p - 1$ is even, this surjects onto $\mathbf{Z}/2\mathbf{Z}$. Since we can do this for each prime $p > 2$, projecting on each component (and sending $\mathbf{Z}_2$ to $1$) gives the desired surjection. – Dorebell Feb 14 '18 at 7:14


text:
# Disprove : $\varnothing$ from a non-empty set to a non-empty set is a function

Counter-example : Take $A=\{1\}$ and $B=\{2\}.$ Then under $\varnothing$, the element $1$ of $A$ does not have an image in $B$. Thus $\varnothing : A \to B$ is not a function.

I seek feedback about my approach whether it is right or wrong.

I know that $\varnothing$ is a function when $A$ is empty. Otherwise it is not. I have gone through this and this, it helped me to understand the cases when $A$ is empty and when $B$ is empty but $A$ is non-empty.

EDIT : The definition of function that I am using is as follows,

A relation $F$ from a set $A$ to set $B$ is said to be a function if and only if-

1. For every $x \in A$, $\exists y \in B$ such that $(x,y) \in F$,

2. If $(x,y) \in F$ and $(x,z) \in F$, then $y=z$.

• I see no problem here. – smb3 Aug 1 '17 at 4:42

The title can be read two ways. One is that $\emptyset: A \to B$ is not always a function when $A,B$ are non-empty. Your example proves that. Another is that $\emptyset: A \to B$ is never a function when $A,B$ are non-empty. One example cannot prove that. You would then have to argue along the lines of "Take $a \in A$, which we can do because $A$ is non-empty. There is no ordered pair in $F$ with $a$ as a first element, so it fails criterion $1$."
• Yes yes. I actually was also thinking now that I just disproved that "$\varnothing : A \to B$ is a function" by taking counter-example. Thanks. – Error 404 Aug 1 '17 at 5:09


text:
## Calculus 8th Edition

$[-1,1/2]$
Simplify the expression on one side $2x^2+x-1\leq0$ Identify key numbers by equating to zero $x=-1$ $x=1/2$ Assign a test value $[-1,1/2]$


text:
# Getting Sentimental: Conference Call Sentiment and Stock Returns

#### January 26, 2017

Robert A. Gillam, Chief Investment Officer McKinley Capital Management, LLC
John B. Guerard Jr., Director of Quantitative Research McKinley Capital Management, LLC

Rochester H. Cahan, U.S. Portfolio Strategist Empirical Research Partners

Quantitative investing is, as the name suggests, all about numbers. Successful quantitative strategies have always had a voracious appetite for numerical data, happily devouring terabytes of ones and zeros without breaking a sweat. But there is a limit to how much of the world’s information is naturally encoded in numbers. After all, most of human experience is expressed in written and spoken language, not sterile numbers. For a long time this imprecise world of emotions was off-limits to quantitative investors. But now advances in natural language processing and machine learning have given quants the tools they need to extract information from unstructured, text-based data sets.

In this research we study whether the sentiment expressed in company conference calls, like the now-ubiquitous quarterly earnings call, can predict the cross-section of future stock returns. Conference calls are a direct interface between the C-suite of a listed company, its shareholders, and the sell-side analysts covering the company. As such, conference calls present a unique opportunity to put context around the cold, hard numbers presented in a company’s financial statements. Our basic question is whether there is useful information in the language used in conference calls that goes above and beyond what one can glean from the numbers alone.

## Listen Up: Extracting Sentiment from Conference Calls

The data set for our study is a large archive of conference call transcripts collected by FactSet, a data vendor. The database includes the transcribed proceedings of over 50,000 conference calls for global companies, beginning at the start of 2010 and finishing at the end of June 2016. Around 85% of the calls are quarterly or semiannual earnings calls. An unique feature of the database is that the transcripts are in XML format, which makes it possible to separate out different parts of the call. For example, it is possible to extract the prepared remarks by the company’s CEO from the analyst Q&A session that usually follows.

Exhibit 1 shows the share of stocks in the McKinley Capital global stock universe that have conference call data over time, as well as the coverage by country. About 60% of companies in the universe have conference call data and, as we would expect, the coverage is skewed toward companies domiciled in English-speaking locales.

### Exhibit 1: Conference Call Transcript Coverage of the McKinley Capital Global Stock Universe

The first question is how to quantify the information contained in each call. One plausible approach is to try to measure the sentiment expressed unconsciously by each speaker on the call. To do that we deploy the dictionary developed in Loughran and McDonald [2011]. In their research the authors classified words in the English language in those with positive, negative, and neutral connotations. An important feature of their dictionary is that the classifications are based on a financial context, for example the word “restatement” is generally more negative when used in finance-speak than when used in general English. Following their lead, we define the sentiment for a body of text to be the count of positive words less the count of negative words scaled by the total number of words.

Armed with this metric we can compute the aggregate sentiment of all the conference calls over time and also the sentiment of the management discussion and analyst Q&A sections separately, see Exhibit 2.

There are two noteworthy results. First, aggregate conference call sentiment tends to track the MSCI World Index, a promising result because it suggests a link between the tone used by participants on the conference calls and market sentiment. Second, the prepared remarks by company managers are consistently more positive than the analyst Q&A that follows, a result that will not come as a huge surprise to anyone who has listened to the carefully-vetted opening monologues that companies prepare these days.

### Exhibit 2: Aggregate Conference Call Sentiment

Source: McKinley Capital, FactSet Research Systems

## Unstructured Alpha

To test whether conference call sentiment predicts future stock returns we first aggregate sentiment at the company level. To do that for a given company at a given point in time we collect all the conference call transcripts for that firm over the prior 12 months and compute the average sentiment across all the calls for the management discussion sections and analyst Q&A sessions separately. We also compute a difference-in-sentiment factor, which is the sentiment in the analyst Q&A session less that of the management discussion.

Exhibit 3 shows the time-series of the monthly rank information coefficients (IC) over time and also the average over the whole sample. An information coefficient is a simple way to measure the predictive power of a stock-selection factor and is defined as the cross-sectional correlation between stocks ranked on the factor at time t and the ranking of stocks by their subsequent return from time t to t+1. A positive correlation indicates that stocks which scored highly on the factor, in this case stocks with highly positive conference call sentiment, went on to deliver the largest returns in the following month.

### Exhibit 3: Information Coefficients for Conference Call Sentiment Factors

Source: McKinley Capital, FactSet Research Systems

Based on the simple IC metric, sentiment derived from the analyst Q&A session of the calls has the strongest predictive power for month-ahead stock returns: the time-series is consistently positive and the average IC over the sample is around +4.5%, a high number by the standards of ICs. The IC for management discussion sentiment is lower but still positive, a finding that is somewhat intuitive given CEOs rarely depart from their attorney-vetted remarks these days. Interestingly the difference in sentiment seems to have little predictive power. Our hypothesis was that a big divergence in sentiment between the company’s management and the analysts covering it might tell us something, but that was not borne our in the data.

Because ICs are a very crude measure of predictive power, we also studied the performance of realistic, optimized portfolios based on the sentiment factors. The mean-variance (MV) portfolio construction can be summarized as:

$$minimize\;\mathcal w^TC\mathcal w\;-\;\lambda\mu^T\mathcal w$$
(1)

where μ is the expected return vector, $$C$$ is the variance-covariance matrix, w is the portfolios weights, and λ is the risk-return tradeoff parameter. The estimation of $$C$$ is usually done by a multifactor model, in which the individual stock return Rj of security j, at time t, dropping the subscript t for time, may be written like this:

$$R_j={\textstyle\sum_{k=1}^K}\beta_{jk}\widetilde{f}_k+\widetilde{e}_J$$
(2)

The non-factor, or asset-specific return on security j, ej is the residual risk of the security after removing the estimated impacts of the K factors. The term ƒk is the rate of return on factor k. The factor model simplifies the $$C$$ as the sum of systematic risk covariance and diagonal specific variances,

$$C\;\;=\beta C_{f,f}\;\beta’\;+\;\sum$$
(3)

The portfolio risk is accordingly decomposed into systematic risk and specific risk

$$\begin{array}{l}\sigma_p^2=w’\beta C_{f,f}\beta’w+w'{\textstyle\sum_{}}w\\\;\;\;\;\;=\sigma_{\beta p}^2+\sigma_{SP}^2\end{array}$$
(4)

If the investor is more concerned about tracking a particular benchmark, mean-variance optimization (1) can be reformulated as mean-variance tracking error at risk (MVTaR) optimization:

$$minimize(w-w_b)^TC(w-w_b)-\lambda\mu^T(w-w_b)$$
(5)

### Exhibit 4: Real-World Portfolio Performance for Conference Call Sentiment Factors

Source: McKinley Capital, Zephyr StyleADVISOR, and FactSet Research Systems

where wb is the weight vector of benchmark. One can also add equal active weighting constraints (EAW):

$$\left|w_j-w_{(b)j}\right|\leq x,for\;all\;j$$
(6)

The MVTaR with constraints (6) will be noted as EAWTaR. The total tracking error can be decomposed into systematic tracking error and specific tracking error:

$$\sigma_{pTE}^2=(w-w_b)’\beta C_{f,f}\beta'(w-w_b)+(w-w_b)'{\textstyle\sum}(w-w_b)$$

$$=\sigma_{\beta PTE}^2+\sigma_{SPTE}^2$$

(7)

Guerard, Markowitz, and Xu [2015] tested several optimization techniques: (1) total risk minimization with no reference to systematic risk, denoted MVM59, which uses mean-variance analysis with a fixed maximum weight (4%) with the same optimization conditions; (2) mean-variance analysis with tracking error at risk, denoted MVTaR; and (3) an equal active weighting tracking error at risk with a maximum deviation of two percent, denoted EAW2TaR. The EAW2TaR optimization technique weights the systematic risk at three times the importance of specific risk and EAW2TaR where x in constraints equation (7) is set to be 2. MVM59, MVTaR, and EAW2TaR have proved to be effective techniques in real-world portfolio construction and management. We seek to maximize the geometric mean of the portfolios, consistent with Latane [1959] and Markowitz [1959]1. We refer to the creation of portfolios with a multifactor model and the generation of the efficient frontier as a Level II test of portfolio construction.

Exhibit 4 shows the results for the sentiment factors using the EAW2TaR methodology. The risk model deployed was the Axioma Statistical Risk Model, composed of 15 factors from a Principal Components Analysis (PCA) estimation, see Guerard, Markowitz, and Xu [2015] for more details. The portfolios delivered excess returns over the MSCI All Country World Index of +2-3% per annum. The information ratios for the signals both have a value 0.4. Both numbers are economically significant in a real-world active management setting.

We conducted attribution analysis on the optimized portfolios to assess the contributions made by stock-selection and factor exposures to active risk and returns. Exhibit 5 shows the results for the Analyst Q&A factor, based on a mean-variance optimization. The left-hand chart decomposes the active return into the specific portion, due to stock-selection ability, and the portion due to factor and style exposures. The specific return is positive and significant at the 5% level while all other contributions are insignificant. That suggests most of the observed alpha in the signal is being produced by picking the right stocks, and not as the byproduct of embedded factor exposures. The right-hand chart shows the same decomposition for the active risk of the portfolio.

## Contains MSG: Sentiment as a Flavor-Enhancer

The evidence so far suggests that conference call sentiment, particularly when derived from the analyst Q&A session, has some predictive power for future stock returns. In this section we study the interaction between conference call sentiment and a proprietary earnings forecasting factor called CTEFROIC that is deployed at McKinley Capital. CTEFROIC combines forecast earnings yield, one-month earnings revisions, breadth, and direction of revisions into a single factor that has delivered strong alpha as a stock-selection signal in live, out-of-sample performance (see Guerard et al. [1997] for more details). Thus a factor that can enhance CTEFROIC has cleared a high hurdle rate.

### Exhibit 5: Attribution Analysis for Real-World Portfolios Based on Difference in Sentiment Factor

Source: McKinley Capital, Axioma

The left hand side of Exhibit 6 shows there is a low correlation of ICs between CTEFROIC and the two conference call sentiment factors. That suggests it may be possible to glean some diversification benefit by combining signals. Indeed that proved to be the case. The right-hand side of Exhibit 6 shows the time-series of monthly ICs for CTEFROIC as a stand-alone signal as well as 50/50 combinations of CTEFROIC with each sentiment factor. Over time the combination of CTEFROIC and the analyst Q&A sentiment factor is consistently better than CTEFROIC on its own.

### Exhibit 6: Analysis of Sentiment Combined with CTEFROIC

CTEFROIC Analyst Q&A Sentiment Management Discussion Sentiment
CTEFROIC 100%
Analyst Q&A Sentiment 6 100%
Management Discussion Sentiment 7 83 100%

Source: Compustat, DataExplorers, Russell, Thomson Reuters, Deutsche Bank.

Source: Compustat, DataExplorers, Russell, Thomson Reuters, Deutsche Bank

The improvement in predictive power over the whole sample is depicted in Exhibit 7 (over). The left-hand chart shows the average IC for CTEFROIC increases by +35-45% when combined with the sentiment signals in a 50/50 blend. Note that in this analysis stocks that do not have a sentiment score (around 40% of the sample, as per Exhibit 1) are omitted. This potentially makes the comparison between CTEFROIC and the sentiment factors unfair, since the performance of the latter is measured over a smaller universe. Therefore we repeated the same exercise in the right-hand chart, except this time we gave any stock with missing sentiment data the median score of the universe. The result is qualitatively the same, but the improvement in average IC does come down to about +25%.

### Exhibit 7: Enhancement in CTEFROIC Information Coefficient with Sentiment

Source: McKinley Capital, FactSet Research Systems

## The Rise of the Machines: Sentiment and Machine Learning Models

The fact conference call sentiment can enhance CTEFROIC is promising, because that factor has been powerful in live performance. However, an even higher hurdle is to benchmark the sentiment factors against a broad universe of factors known to predict future stock returns. To that end we collected 41 different factors, representing a comprehensive survey of the factors used by practitioners. Included are all the usual suspects like price momentum, earnings revisions, valuation ratios, earnings quality metrics, along with a number of proprietary factors developed at McKinley Capital. The first chart in Exhibit 8 shows the top ten factors over the sample period, when ranked by average IC. It turns out the analyst Q&A sentiment factor finishes third out of the pool of 41 factors.

### Exhibit 8: Sentiment Factors Benchmarked Against a Broad Universe of Factors

Source: McKinley Capital, FactSet Research Systems

That is a promising start, but to harvest that alpha we would have had to know ex-ante that analyst Q&A sentiment would end up being a good factor, i.e., back in 2010 we would have had to somehow know that we should bet on that factor instead of the 41 other factors. Thus an even stricter test is whether a factor-selection algorithm would have identified the sentiment factor as useful back at each point in time, knowing only what one knew back then. The right-hand chart in Exhibit 8 uses the AdaBoost machine learning algorithm as a factor-selection tool.

At each point in time the model is trained on the prior 12 months of factor performance. The idea is the machine should “learn” which factors are useful, based only on the information known at the time. If there was enough information back through time to suggest the sentiment factor would be a useful factor going forward, then the machine would select it and use it to improve performance.
The white bars in the chart show that when the AdaBoost model was allowed to draw from a pool of factors that included sentiment, it did indeed use it to further enhance performance. In other words, the analyst Q&A sentiment factor showed enough performance even early in the sample to convince a machine learning algorithm that it should use the factor going forward.

## Conclusion: A Promising New Alpha Source

Unstructured, text-based data from conference call transcripts appears to contain useful information for forecasting the future returns of global stocks. Specifically, sentiment extracted from the language used in the analyst Q&A session that usually concludes an earnings call has positive predictive power for month-ahead stock returns. In addition to stand-alone alpha, we found evidence that conference call sentiment can be used to enhance a proprietary earnings forecasting factor. Furthermore the factor’s performance consistency was high enough to allow a machine learning model to identify the factor’s potential ex-ante.

Please refer to the full McKinley Capital Disclosure at the end of this article. The information contained herein does not constitute the provision of investment, legal, or tax advice by any of the authors. Any views expressed reflect the current views of the authors which may change without notice.

Mr. Cahan’s contribution and comments do not necessarily correspond to the opinions of Empirical Research Partners or its affiliates. Opinions expressed may differ from views set out in other documents, including separate research published by Empirical Research Partners. Information is provided for informational purposes only and without any obligation, whether contractual or otherwise. No warranty or representation is made as to the correctness, completeness and accuracy of the information given of the assessments made.

1 Guerard, Markowitz, and Xu [2015] referred to the creation of portfolios with a multifactor model and the generation of the efficient frontier as a Level II test of portfolio construction.

## References

Gillam, R.G., Guerard, J.B., Jr., and R. Cahan, 2015. “News Volume Information: Beyond Earnings Forecasting in a Global Stock Selection Model”, International Journal of Forecasting, Vol. 31, pp. 575-581.

Guerard, J.B., Jr., Gultekin, M., and B.K. Stone, 1997. “The Role of Fundamental Data and Analysts’ Earnings Breadth, Forecasts, and Revisions in the Creation of Efficient Portfolios.” In Research and Finance 15, Edited by A. Chen.

Guerard, J.B., Jr., R.T. Rachev, and B. Shao, 2013. “Efficient Global Portfolios: Big Data and Investment Universes”, IBM Journal of Research and Development 57, No. 5, Paper 11, 1-11.

Guerard, J.B., Jr., H.M. Markowitz, and G. Xu, 2015. “Earnings Forecasting in a Global Stock Selection Model and Efficient Portfolio Construction and Management”, International Journal of Forecasting, Vol. 31, pp. 550-560.

Loughran, T., and B. McDonald, 2011. “When is a Liability not a Liability? Textual Analysis, Dictionaries, and 10-Ks.” Journal of Finance, Vol. 66, pp. 35-65.

## Disclosure

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text:
Citation

Naimi, Ashley Isaac; Cole, Stephen R.; Westreich, Daniel J.; & Richardson, David B. (2011). A Comparison of Methods to Estimate the Hazard Ratio under Conditions of Time-Varying Confounding and Nonpositivity. Epidemiology, 22(5), 718-723. PMCID: PMC3155387

Abstract

In occupational epidemiologic studies, the healthy worker survivor effect refers to a process that leads to bias in the estimates of an association between cumulative exposure and a health outcome. In these settings, work status acts both as an intermediate and confounding variable and may violate the positivity assumption (the presence of exposed and unexposed observations in all strata of the confounder). Using Monte Carlo simulation, we assessed the degree to which crude, work-status adjusted, and weighted (marginal structural) Cox proportional hazards models are biased in the presence of time-varying confounding and nonpositivity. We simulated the data representing time-varying occupational exposure, work status, and mortality. Bias, coverage, and root mean squared error (MSE) were calculated relative to the true marginal exposure effect in a range of scenarios. For a base-case scenario, using crude, adjusted, and weighted Cox models, respectively, the hazard ratio was biased downward 19%, 9%, and 6%; 95% confidence interval coverage was 48%, 85%, and 91%; and root MSE was 0.20, 0.13, and 0.11. Although marginal structural models were less biased in most scenarios studied, neither standard nor marginal structural Cox proportional hazards models fully resolve the bias encountered under conditions of time-varying confounding and nonpositivity.

URL

http://dx.doi.org/10.1097/EDE.0b013e31822549e8

Journal Article

2011

Epidemiology

Author(s)

Naimi, Ashley Isaac
Cole, Stephen R.
Westreich, Daniel J.
Richardson, David B.

PMC3155387


text:
### Effective dimension

#### (Feb 19, 2014)

Actuaries often need to smooth mortality rates.  Gompertz (1825) smoothed mortality rates by age and his famous law was a landmark in this area.  Figure 1 shows the Gompertz model fitted to CMI assured lives data for ages 20-90 in the year 2002. The Gompertz Law usually breaks down below about age 40 and a more general smooth curve would be appropriate.  However, a more general smooth curve would obviously require more parameters than the two for the simple Gompertz model.

Figure 1.  Crude mortality rates (black dots) with fitted Gompertz line (solid red) on a logarithmic scale.

When we switch to a forecasting scenario, Figure 2 shows both a straight line and a parabola fitted to years 1947-2002 for age 70.  Clearly,…


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help with time series analysis
1
0
Entering edit mode
11 months ago

Hello,

I have readcount data from my metagenome experiment. My metagenome experiment looks like this:

control T0   T1   T2   T3   T4
case    T0   T1   T2   T3   T4

I have two conditions (case and control) and five time points. I have readcounts data from each control and case samples across these 5 time points. I want to conduct analysis as below:

1. Calculate abundance differences within each condition i.e. control and for example, T0 vs T4, T1 vs T4, T2 vs T4 and T3 vs T4). Like which taxa is significantly different at different time point compared to baseline (T4).

2. Measure differences between control and cases on each time point i.e case vs control @ T0, case vs control @ T1, case vs control @ T2, case vs control @ T3, case vs control @ T4.

I know I should be doing time series analysis but I don't know how to perform this complex longitudinal analysis.

I would really appreciate if you someone could help me in deciding where to start? Or direct me to any tutorial where I could learn and apply the same on my data.

time-series readcount time series RNAseq • 708 views
0
Entering edit mode

This seems a good one and may serve my purpose. So, I tried it but I get the error when I run the following:

variance_per_genes = apply(data, 1, mad)

I get the following error:

Error in x - center : non-numeric argument to binary operator

I looked at the shoemaker data too and it contain all the values greater than 0 whereas my data contains 0 as well. Also, shoemaker data has equal replications (1,2,3) whereas i have different replication number for some samples. Could that be the reason? Any thoughts?

0
Entering edit mode

This issue seems to be related to the file format. When I loaded the shoemaker2015 data directly from the package, I can run rest of the all steps without any error. However, when I first saved the "data" and "meta" on my computer in .txt/.csv format then loaded it from my computer, it gives me the following error:

Code:

moanin_model = create_moanin_model(data=data, meta=meta,  degrees_of_freedom=6)

Error:

Error in contrasts<-(*tmp*, value = contr.funs[1 + isOF[nn]]) : contrasts can be applied only to factors with 2 or more levels

Any ideas in which format the shoemaker2015 data is?

0
Entering edit mode
11 months ago
Chris Dean ▴ 280

There are a couple of options, depending on which analysis you would like to do.

If you would like to proceed with a longitudinal differential abundance analysis, you can use the fitTimeSeries function in the metagenomeSeq package. If you would like to proceed with a differential abundance analysis between your grouping variables, you can use ANCOM, ALDEx2, and others.

I suggested ANCOM and ALDEx2 because these have become increasingly popular in the microbiome literature.

I hope this helps!


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• Corpus ID: 118920677

# Modification in Silling's Peridynamic Formulation of Elasticity Theory for Discontinuities and Long-Range Forces

@article{Pandya2012ModificationIS,
title={Modification in Silling's Peridynamic Formulation of Elasticity Theory for Discontinuities and Long-Range Forces},
author={R. Vikram Raj Pandya},
journal={arXiv: Mathematical Physics},
year={2012}
}
• R. Pandya
• Published 3 April 2012
• Physics
• arXiv: Mathematical Physics
We suggest modified version of Silling's peridynamic equation of motion within the framework of Silling's peridynamics formulation (J. Mech. Phys. Solids {\bf 48}, pp.175-209, 2000) of elasticity theory. The modified equation contains an additional damping force term. This term can eliminate artificial oscillations in displacement field at large values of time as predicted by Silling's peridynamic equation.


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Goto Chapter: Top 1 2 3 4 Bib Ind

FactInt

Advanced Methods for Factoring Integers

1.6.2

18 February 2018

Stefan Kohl
Email: stefan@gap-system.org
Homepage: https://stefan-kohl.github.io/

Alexander Konovalov
Email: alexander.konovalov@st-andrews.ac.uk
Homepage: https://alexk.host.cs.st-andrews.ac.uk
Address:
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh,
St Andrews, Fife, KY16 9SX, Scotland

Abstract

This package for GAP 4 provides a general-purpose integer factorization routine, which makes use of a combination of factoring methods. In particular it contains implementations of the following algorithms:

• Pollard's p-1

• Williams' p+1

• Elliptic Curves Method (ECM)

• Continued Fraction Algorithm (CFRAC)

• Multiple Polynomial Quadratic Sieve (MPQS)

It also contains code by Frank Lübeck for making use of Richard P. Brent's tables of factors of integers of the form b^k ± 1. FactInt is completely written in the GAP language and contains / requires no external binaries. It needs GAPDoc 1.6 [LN17] or higher. FactInt must be installed in the pkg subdirectory of the GAP distribution.

Copyright

© 1999 - 2017 by Stefan Kohl.

FactInt is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

FactInt is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

For a copy of the GNU General Public License, see the file GPL in the etc directory of the GAP distribution or see http://www.gnu.org/licenses/gpl.html.

Acknowledgements

I would like to thank Bettina Eick and Steve Linton for their support and many interesting discussions.

Goto Chapter: Top 1 2 3 4 Bib Ind

generated by GAPDoc2HTML


text:
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# Showing that a function is of class $C^{\infty}$

I would like to show that the following function $h:(-\pi/2,\pi/2) \rightarrow [0,\infty)$,

$$h(x) = \begin{cases} e^{-(1/x)} \sec{x} & \text{for} \quad x \in (0,\pi/2) \\ 0 & \text{for} \quad x \leq 0, \end{cases}$$

is $C^{\infty}$ on $(-\pi/2,\pi/2)$. Now by definition a function is $C^{\infty}$ at a point if it is $C^k$ for all $k \geq 0$ at that point.

Now I think it is plain that if $x \leq 0$ then $h(x)$ is $C^k$ for all $k \geq 0$. This is because the only cause for concern is that the $kth$ derivative at $0$ may fail to be continuous, but using the leibniz rule

$$h^{(k)} (0) = \sum_{k=0}^{n}f^{(k)}(0)g^{(n-k)}(0), \qquad\text{where } f(x) = e^{-1/x}\text{ and }g(x) = \sec{x},$$

we see that $h^{(k)} (0) = 0$ as $f^{(k)} (0) = 0$ for all $k \geq 0$.

Now for $x > 0$, it is plain that I can keep differentiating the function $h(x)$. So if I can differentiate it $k$ times then I know that its $k-1$ derivatives are all continuous. However is this sufficient to conclude that $h(x)$ is $C^{\infty}$ for every real $x$?

Thanks.

-
Hint: $\sec(x)$ is $C^{\infty}$ on the interval, so since the product of two $C^{\infty}$ functions is $C^{\infty}$, it suffices to prove the result where $\sec(x)$ is removed (i.e. replaced by 1). This can be done inductively, and the major issue is showing it at $x = 0$ where you have to actually look at difference quotients. –  Zarrax Jun 27 '11 at 14:00
@Zarrax I think i've shown that already as I stated above that $f^{(k)}(0)=0$ for all $k \geq 0$. So you mean that as both $f,g$ are $C^{\infty}$ then their product is as well? –  user38268 Jun 28 '11 at 1:35
@D Lim Yes that is true, the product of two $C^{\infty}$ functions is always $C^{\infty}$. This is easily provable by repeatedly differentiating the product of the two functions and then using the product and sum rules for derivatives. –  Zarrax Jun 29 '11 at 20:03

If $a<c<b \in \Bbb{R}$ and $f: (a,b) \to \Bbb{R}$ by $$f(x)=\begin{cases}g(x), & x \in (a,c] \\ h(x), & x \in (c,b)\end{cases},$$
continuous, with $g,h$ derivable functions on $(a,c)$ and $(c,b)$, respectively, then for $f$ to be derivable on $(a,b)$ it is enough to prove that $$\lim_{x \to c, x<c} g'(x)=\lim_{x \to c,x>c} h'(x).$$
Now, I think this is enough to prove that your function is differentiable, since from what you've shown, the value of the derivative in $0$ on one side is equal to the derivative in $0$ in the other side, for all orders of derivation.


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Crazy results
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Alex didn't understand a word the man said but definitely knew that he would be taken care if the mans expression was anything to go by. this was further proven when the man took alex out of the basket and read the letter in it. "hmm , alexander drake huh , what an odd name." the man said before laying alex down in a crib with a baby girl. alex was very uncomfortable since the girl seemed to treat alex as a stuffed animal and latched unto him. alex had only woken up again not long ago so he wasn't tired yet.

NAME: Alexander drake                                                                                RACE: human                                                                                AGE: n/a                                                                                TITLE: none                                                                                Feats: aspirant                                                                                Solar points:20,000                                                                                Weapon: none                                                                                Armor: none                                                                                Accessories: none , none                                                                                Physique: celestial body{draws in the energy of the sun and moon passively strengthening the body over time with no limit.}                                                                                Affinities: fire , yang , lightning                                                                                Kekkai genkai: celestial release{fire , lightning and yang fusion mutated from solar release and far more powerful.}                                                                                Dojutsu: none                                                                                Chakra control: awakened (0%)

To pass the time alex checked his status and noticed that it had changed greatly compared to before. for a start he now had four new tabs that each listed the various things that those with chakra had access to.

Alex noticed that he had a single kekkai genkai that used all three of his affinities that must have been the one the rob had said he would have. alex wasn't that surprised when he saw the description of the celestial body since he had long known about the relationship between the sun and moon. the biggest problem alex found was his lack of knowledge regarding what even kekkai genkai and dojutsu were. this system of power seemed far different than the aura he was familiar with as he couldn't just will things to happen , he tried.

Alex could feel the warm current of energy traveling through his body from his stomach since it felt vastly different than aura but he had no clue how to control it. it moved under his will but it was wild and didn't flow evenly so he was at a loss as to really use it. after thirty minutes of continuous failures alex gave up for the night and went back to sleep. alex officially met his new family the next morning as apparently his new parents also woke up at dawn.

Alex woke up the instant dawn hit as the energy getting sucked into his body grew many times more potent in an instant. when a slim black haired woman with black eyes came to check on alex and the girl she was surprised to she him already looking at her. the woman held both alex and the girl in one arm each as she bought them into an area with a large table and chairs. the woman set alex down while she tried to figure out the seating arrangement as they only had a single baby seat.

Alex didn't care all that much about the fuss the woman was making as he was far more interested in the strange roll of paper sitting on the coffee table. the man watched as the most strange thing happened when alex played with the scroll. a poof of white smoke replaced the scroll that the man was sure was sealed with the extra kunai's he kept stored in it. this sudden change startled alex who stared at the pile of sharp blades that had seemingly appeared from nowhere. alex's infant body affected him as he giggled in delight at the odd thing that the roll did when he pushed his chakra into it.

The woman scooped up alex before he could grab one of the strange blades and seemed to admonish the man , not that alex understood a word but he had seen his previous dad make the same expression. the woman seemed to forgive the man though when alex giggled at them with a warm smile. the man had brought alex to a hospital after breakfast where several test were run on alex by the staff. alex got several strange stares from his new dad and several of the staff once his results came back but since he didn't understand the language alex had no clue why.

Kaido couldn't believe what the test on the boy he had found on his porch late at night said. apparently the boy not only had an unknown physique that seemed almost on par with a senjus but also seemed to have been born with fully unlocked chakras. what was even more crazy was that the test said it was almost as high as lord fourths son who was the nine tails jinchuriki. this infant boy was also apparently even more special as the blood test said he had an unknown kekkai genkai as well.

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• home
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# ZK Hash Function Cryptanalysis Bounties

## Terms

Task: find $X1,X2,Y1,Y2$ such that $\displaystyle Perm(X1,X2,0)=(Y1,Y2,0)$

where $Perm$ is the inner sponge permutation (bijective mapping) of the hash function the challenge list.

• Solutions should be sent to Dmitry Khovratovich before November 30th 2022.
• First come first win.
• Within 1 month after the submission the authors should provide a technical report with the attack description, which should be released to the public domain at latest December 1st 2022. The code should be also made public before this date.
• Total Bounty Budget: $200,000 USD. • Parameters are fixed on November 23rd 2021. ## Rescue Prime Design spec. • $p=18446744073709551557 \text{\textasciitilde} 2^{64}$ • $m=3$ • $alpha=3$ • Number of rounds: $N$ • Brute force attack complexity: $2^{64}$ We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{1.5s}$ time (function calls) and memory. Reference implementation and bounty instances. CategoryParametersSecurity Level (bits)Bounty Easy$\sout{N=4, m=3}$25$2,000
Easy$N=6, m=2$25$4,000 Medium$N=7, m=2$29$6,000
Hard$N=5, m=3$30$12,000 Hard$N=8, m=2$33$26,000

## Feistel-MIMC

Design spec.

• $p=18446744073709551557 \text{\textasciitilde} 2^{64}$
• $alpha=3$
• Task: find $X,Y$ such that $Feistel\text{\textendash}MiMC(X,0)=(Y,0)$
• Number of rounds: $r$
• Brute force attack complexity: $2^{64}$

We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{2s}$ time (function calls) and memory.

The initial parameters were broken and were replaced.

Reference implementation and bounty instances.

Easy$\sout{N=4, m=3}$25$2,000 Easy$N=6, m=2$25$4,000
Medium$N=7, m=2$29$6,000 Hard$N=5, m=3$30$12,000
Hard$N=8, m=2$33$26,000 ## Poseidon Design spec. • $p=18446744073709551557 \text{\textasciitilde} 2^{64}$ • $d=3$ • $t=3$ • Number of full rounds: $RF=8$ • Number of partial rounds $RP$ varies (see below) • Brute force attack complexity: $2^{64}$ We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{s+37}$ time (function calls) and memory. The initial parameters were broken and were replaced. Reference implementation and bounty instances. CategoryParametersSecurity Level (bits)Bounty Easy$\sout{RP=3}$8$2,000
Easy$\sout{RP=8}$16$4,000 Medium$\sout{RP=13}$24$6,000
Hard$RP=19$32$12,000 Hard$RP=24$40$26,000

## Reinforced Concrete

Design spec.

• Number of layers as in the original design
• Different prime field
• The best attack we have found for these variants is exhaustive search.
• Groebner basis challenges might be declared additionally.

We expect that a variant with $s$ bits of security to withstand attacks of complexity up to $2^{2s}$ time (function calls) and memory.

Decomposition and alpha/beta values.

Reference implementation and bounty instances.

Easy$p=281474976710597$24$4,000 Hard$p=72057594037926839$28$6,000
Hard$p=18446744073709551557$32\$12,000


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# Why doesn't Get work on Image?

Is there another way to get this package to load?

• Why do you believe you need to explicitly load the Image context? It is automatically available when you start Mathematica. Sep 16 '16 at 17:18
• Short answer, because that package isn't on $Path. – Kuba Sep 16 '16 at 17:24 ## 1 Answer These is no such package. Image is a context, not a package. I can see how this is confusing. When we use Get or Needs, we often use a notation which looks like a context. For example, << ErrorBarPlots However, this is not a context. It is a platform independent notation for file paths that Mathematica uses. Mathematica has special rules to resolve the location of the actual file. You can get it using FindFile["ErrorBarPlots"] (* "/Applications/Mathematica 11.app/Contents/AddOns/Packages/ErrorBarPlots/Kernel/init.m" *) When we do load the package, the package symbols will reside in the ErrorBarPlots context. Context[ErrorBarPlot] (* "ErrorBarPlots" *) This is now a context. It is a convention to use a package structure and file organization so that the special file path notation that we can use to load the package will be the same as the name of the package's main context. But this is merely a convention, and nothing is forcing you to write your packages this way. Image is not a package, just a context containing internal symbols. It is always present, it doesn't need to be loaded. Perhaps what you really wanted was to add it to the$ContextPath.

• Nothing is forcing but there is a message if Package context was not created after calling << Package .
– Kuba
Sep 16 '16 at 17:43


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# Figuring out the solution of the following Integral

## Homework Statement

Hello,I'm having problems figuring out the solution of the following Integral.Any hints would be much appreciated!

There it is:

I= sin(x)/sqrt{4sin(x)^2+cos(x)^2} dx

Last edited:

## Answers and Replies

$$I=\int\frac{sin(x) dx}{\sqrt{4sin^2(x)+cos^2(x)}}$$

O.O wow thats...a toughie, no substitution seems to work...you could try tan(x/2)=y but you'd get a polynomial of degree 4 on the square root...

It would be so much nicer if that 4 was gone...

ok you could try getting rid of those sin^2 x by using those formulas
$$sin^2 (x) = \frac{1-cos 2x}{2}$$
$$cos^2 (x) = \frac{1+cos 2x}{2}$$

that might lead you somewhere decent but you'll have some problems with sin(x) on the top but square root of acos2x + or - something...

Yeah,I've tried everything you've listed above,but had no success lol.
Anyway,thank you !

Gib Z
Homework Helper
Not expressible in elementary functions or in a closed form.

dynamicsolo
Homework Helper

## Homework Statement

Hello,I'm having problems figuring out the solution of the following Integral.Any hints would be much appreciated!

There it is:

I= sin(x)/sqrt{4sin(x)^2+cos(x)^2} dx

It's always a bad sign when it doesn't show up in Gradshteyn & Ryzhik...

Are you sure that you're asked for the indefinite integral? The closest entry I found was [3.676 #1] in G&R, 5th edition:

rewrite $$4sin^2(x)+cos^2(x)$$ as $$1+3sin^2(x)$$ and use

definite integral from 0 to pi/2 of $$\int\frac{sin(x) dx}{\sqrt{1+p^2sin^2(x)}}$$

= (1/p) arctan p , with p^2 = 3 .

It looks like this may be one of those integrals that only has nice solutions for *certain* definite limits, but not in general...

so yea I tried it and my integral has complex numbers, so i'm going to go recheck my work.

HallsofIvy
Homework Helper
$$I=\int\frac{sin(x) dx}{\sqrt{4sin^2(x)+cos^2(x)}}= \int\frac{sin(x)dx}{\sqrt{4- 5cos^2(x)}}$$

Let u= cos(x) so du= sin(x)dx and the integral becomes
$$\int\frac{du}{\sqrt{4- 5u^2}}= \frac{1}{2}\int\frac{du}{\sqrt{1- \frac{5}{4}u^2}}$$
Letting $sin(\theta)= \sqrt{5}/2 u$ should convert it to a rational integral.

Gib Z
Homework Helper
Thats some really nice work there Halls!! I wish i'd seen that =] Just One tiny mistake though, u=cos x so du = - sin x dx, so the actual integral is the one you gave, just with a negative sign stuck out the front.

dynamicsolo
Homework Helper
$$I=\int\frac{sin(x) dx}{\sqrt{4sin^2(x)+cos^2(x)}}= \int\frac{sin(x)dx}{\sqrt{4- 5cos^2(x)}}$$

I am likewise chagrined to have missed that; I was focusing on the sine-squared term, rather than the cosine-squared one.

One other little thing, though: 4 (sin x)^2 + (cos x)^2 =
4 [1 - (cos x)^2] + (cos x)^2 =
4 - 4 (cos x)^2 + (cos x)^ 2 =
4 - 3 (cos x)^2 , no?

HallsofIvy


text:
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## G = C7×S4order 168 = 23·3·7

### Direct product of C7 and S4

Aliases: C7×S4, A4⋊C14, C22⋊(S3×C7), (C7×A4)⋊3C2, (C2×C14)⋊1S3, SmallGroup(168,45)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — A4 — C7×S4
 Chief series C1 — C22 — A4 — C7×A4 — C7×S4
 Lower central A4 — C7×S4
 Upper central C1 — C7

Generators and relations for C7×S4
G = < a,b,c,d,e | a7=b2=c2=d3=e2=1, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=ebe=bc=cb, dcd-1=b, ce=ec, ede=d-1 >

Permutation representations of C7×S4
On 28 points - transitive group 28T31
Generators in S28
(1 2 3 4 5 6 7)(8 9 10 11 12 13 14)(15 16 17 18 19 20 21)(22 23 24 25 26 27 28)
(1 8)(2 9)(3 10)(4 11)(5 12)(6 13)(7 14)(15 26)(16 27)(17 28)(18 22)(19 23)(20 24)(21 25)
(1 24)(2 25)(3 26)(4 27)(5 28)(6 22)(7 23)(8 20)(9 21)(10 15)(11 16)(12 17)(13 18)(14 19)
(8 24 20)(9 25 21)(10 26 15)(11 27 16)(12 28 17)(13 22 18)(14 23 19)
(8 20)(9 21)(10 15)(11 16)(12 17)(13 18)(14 19)

G:=sub<Sym(28)| (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,26)(16,27)(17,28)(18,22)(19,23)(20,24)(21,25), (1,24)(2,25)(3,26)(4,27)(5,28)(6,22)(7,23)(8,20)(9,21)(10,15)(11,16)(12,17)(13,18)(14,19), (8,24,20)(9,25,21)(10,26,15)(11,27,16)(12,28,17)(13,22,18)(14,23,19), (8,20)(9,21)(10,15)(11,16)(12,17)(13,18)(14,19)>;

G:=Group( (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28), (1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)(15,26)(16,27)(17,28)(18,22)(19,23)(20,24)(21,25), (1,24)(2,25)(3,26)(4,27)(5,28)(6,22)(7,23)(8,20)(9,21)(10,15)(11,16)(12,17)(13,18)(14,19), (8,24,20)(9,25,21)(10,26,15)(11,27,16)(12,28,17)(13,22,18)(14,23,19), (8,20)(9,21)(10,15)(11,16)(12,17)(13,18)(14,19) );

G=PermutationGroup([[(1,2,3,4,5,6,7),(8,9,10,11,12,13,14),(15,16,17,18,19,20,21),(22,23,24,25,26,27,28)], [(1,8),(2,9),(3,10),(4,11),(5,12),(6,13),(7,14),(15,26),(16,27),(17,28),(18,22),(19,23),(20,24),(21,25)], [(1,24),(2,25),(3,26),(4,27),(5,28),(6,22),(7,23),(8,20),(9,21),(10,15),(11,16),(12,17),(13,18),(14,19)], [(8,24,20),(9,25,21),(10,26,15),(11,27,16),(12,28,17),(13,22,18),(14,23,19)], [(8,20),(9,21),(10,15),(11,16),(12,17),(13,18),(14,19)]])

G:=TransitiveGroup(28,31);

35 conjugacy classes

 class 1 2A 2B 3 4 7A ··· 7F 14A ··· 14F 14G ··· 14L 21A ··· 21F 28A ··· 28F order 1 2 2 3 4 7 ··· 7 14 ··· 14 14 ··· 14 21 ··· 21 28 ··· 28 size 1 3 6 8 6 1 ··· 1 3 ··· 3 6 ··· 6 8 ··· 8 6 ··· 6

35 irreducible representations

 dim 1 1 1 1 2 2 3 3 type + + + + image C1 C2 C7 C14 S3 S3×C7 S4 C7×S4 kernel C7×S4 C7×A4 S4 A4 C2×C14 C22 C7 C1 # reps 1 1 6 6 1 6 2 12

Matrix representation of C7×S4 in GL3(𝔽337) generated by

 79 0 0 0 79 0 0 0 79
,
 0 0 1 336 336 336 1 0 0
,
 336 336 336 0 0 1 0 1 0
,
 1 0 0 336 336 336 0 1 0
,
 1 0 0 0 0 1 0 1 0
G:=sub<GL(3,GF(337))| [79,0,0,0,79,0,0,0,79],[0,336,1,0,336,0,1,336,0],[336,0,0,336,0,1,336,1,0],[1,336,0,0,336,1,0,336,0],[1,0,0,0,0,1,0,1,0] >;

C7×S4 in GAP, Magma, Sage, TeX

C_7\times S_4
% in TeX

G:=Group("C7xS4");
// GroupNames label

G:=SmallGroup(168,45);
// by ID

G=gap.SmallGroup(168,45);
# by ID

G:=PCGroup([5,-2,-7,-3,-2,2,422,1683,133,1054,239]);
// Polycyclic

G:=Group<a,b,c,d,e|a^7=b^2=c^2=d^3=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,d*b*d^-1=e*b*e=b*c=c*b,d*c*d^-1=b,c*e=e*c,e*d*e=d^-1>;
// generators/relations

Export

׿
×
𝔽


text:
# System Time Discovery

System Time Discovery
Technique
ID T1124
Tactic Discovery
Platform Windows
Permissions Required User
Data Sources Process monitoring, Process command-line parameters, API monitoring

The system time is set and stored by the Windows Time Service within a domain to maintain time synchronization between systems and services in an enterprise network.12

An adversary may gather the system time and/or time zone from a local or remote system. This information may be gathered in a number of ways, such as with Net on Windows by performing net time \\hostname to gather the system time on a remote system. The victim's time zone may also be inferred from the current system time or gathered by using w32tm /tz.2 The information could be useful for performing other techniques, such as executing a file with a Scheduled Task3, or to discover locality information based on time zone to assist in victim targeting.

## Examples

• BRONZE BUTLER has used net time to check the local time on a target system.4
• Turla surveys a system upon check-in to discover the system time by using the net time command.5
• MoonWind obtains the victim's current time.6
• The net time command can be used in Net to determine the local or remote system time.7
• PowerDuke has commands to get the time the machine was built, the time, and the time zone.8
• RTM can obtain the victim time zone.9
• Shamoon obtains the system time and will only activate if it is greater than a preset date.10
• T9000 gathers and beacons the system time during installation.11

## Mitigation

Benign software uses legitimate processes to gather system time. Efforts should be focused on preventing unwanted or unknown code from executing on a system. Some common tools, such as net.exe, may be blocked by policy to prevent common ways of acquiring remote system time.

Identify unnecessary system utilities or potentially malicious software that may be used to acquire system time information, and audit and/or block them by using whitelisting12 tools, like AppLocker,1314 or Software Restriction Policies15 where appropriate.16

## Detection

Command-line interface monitoring may be useful to detect instances of net.exe or other command-line utilities being used to gather system time or time zone. Methods of detecting API use for gathering this information are likely less useful due to how often they may be used by legitimate software.


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# Two Parameters¶

Why is Cosmology Dedicated to Finding Two Parameters Before 90’s

Basically, the cosmology before the 90’s have only two tasks. The first one is to find out the Hubble constant, while the second one is looking for the deceleration parameter.

We don’t rush to define what Hubble constant and deceleration parameter are, but have a look at what observations do at that time.

## Observations¶

Astronomers are really good at measuring distances. They have infinite tricky ways to find out some distance.

### Luminosity Distance¶

#### Luminosity Distance from Observation¶

We can find out how bright a star is by observation. One way to represent the brightness is to use the energy crossed per unit area per unit time at the observer, because this is what our eyes do.

This quantity is related to how much energy was emitted at the star, how far we are from the star. The more energy the star emitted, the brighter it look like. The nearer the star is, the brighter it is. Just like what we feel like with a candle.

This schematic picture shows that energy spread out on a surface because the total energy is conserved. Isotropic energy flux through the same solid angle at different radius must be the same.

Through a very simple calculation, it is as simple as

$L_0 = \frac{ L }{ 4\pi r^2 } .$

We are dealing with Cosmology now. The space-time manifold should be a great concern. The luminosity turns out to be

$L_0 = \frac{L_\mathrm{abs} }{4\pi d^2} \frac{1}{1+z} \frac{1}{1+z} .$

Here d is the physical distance between the star and the observer. L is the absolute luminosity of the star, which stands for the power of the star. z is the redshift of the star.

The first $$\frac{1}{1+z}$$ term comes from the fact that the energy of each photon decrease due to expansion of the universe, while the second is the result that the rate of photons arrived at the observer is less.

We are happy to define

$d_L = d (1+z) ,$

then the luminosity becomes simpler,

$L_0 = \frac{L_{\mathrm {abs}}}{4\pi d_L^2} .$

Now we come back to have a look at this luminosity.

• We can measure how much energy is passing through a unit area at a unit time, which means we can determine this luminosity directly from observations.
• We can predict the absolute luminosity from a star evolution model.
• The $$d_L = d (1+z)$$ is only valid for a flat universe, with curvature term $$K=0$$ in Friedmann equation.

Then we can find out this so called luminosity distance

$d_L = \frac{ L_{\mathrm {abs}} }{ 4\pi L_0 }$

from some data.

#### Luminosity Distance from Theory¶

We don’t just do the observation for the luminosity distance itself. We observe to test theories.

What is this distance in theory?

$d_L = d (1+z)$

Wait, didn’t we just mention that this is only valid for a flat universe? So we just do some extension.

$d_L = R(d) (1+z)$

where R(d) is a function of d and can be determined through geometry,

• Spherical: $$4\pi \sin^2 d$$ ,
• Flat: $$4\pi d$$ ,
• Hyperbolic: $$4\pi \sinh^2 d$$ .

#### Nearby Objects¶

For nearby objects, we can always use flat geometry and use Taylor expansion at current time for a(t).

Luminosity distance is

$d_L = d (1+z) = r a(t) (1+z) ,$

where r is the comoving distance and a(t) is the scale factor at time t.

We know

$r = \int_t^{t_0} \frac{1}{a(t')} \mathrm d t' .$

So we are happy to use Taylor expansion around $$t_0$$ for $$a(t)$$, and keep only up to the second order of time. And do some substitution with

\begin{align}\begin{aligned}H_0 = \dot a(t_0)/a(t_0)\\q_0=\ddot a (t_0) / a(t_0)\end{aligned}\end{align}

We then do the same thing on redshift

$z=a(t_0)/a(t) - 1 .$

Finally, we can find out the relation $$r(z)$$, which leads us to the result we need, $$d_L(z) = H_0^{-1} (z - \frac12 (1+q_0) z^2)$$.

• For very near objects (not as near as our sun of course),

$d_L = H_0^{-1}z .$

This is a model independent observation and derivation. We can draw a line to represent the case when deceleration parameter is zero, lines higher than this stands for a accelerating universe while lower region show a decelerating universe.

We can show that for a vacuum energy dominated universe, the line would go up and for a matter dominated universe, it would below the zero deceleration line.

#### Comment¶

In this model independent method, the only two parameters occur are Hubble constant $$H_0$$ and deceleration parameter $$q_0$$ .

### Angular Diameter Distance¶

#### Observation¶

Angular diameter distance is really useful if we have some standard ruler. Now assume we have a ruler d, we can find out the angle between the two ends of the ruler, by some kind of measurement.

At the same time, we can use magic of math

$\theta = d/D .$

Now as we already find out what $$\theta$$ is by a measurement, and we said about the d is a standard ruler, which means we know the length of it very well. Then we can find out the distance $$D$$, which is the distance between us and the standard ruler.

#### Theory¶

We can find out this kind of distance, which we will denote it as $$d_A$$ from now on. What is it for?

A angular diameter distance is the physical distance between us and the standard ruler,

$d_A = a(t)r .$

We can use the same trick we used in luminosity distance calculations, and it is easy to find that

$d_A = H_0^{-1} (z - \frac{1}{2} (3 + q_0)z^2 ) .$

Again, the observation is related to only two parameters, Hubble constant $$H_0$$ and deceleration parameter $$q_0$$.

#### Standard Rulers¶

It is hard to imagine that we really have some standard rulers. In fact, we do. They are

### Galaxy Number Count¶

Now we can see anything that is only (simply) related to physical or comoving distance can be determined by this trick. The result is that only two cosmological parameters would come in our equation as long as we keep only upper to order two of redshift.

Here another example is the galaxy number count.

$\frac{\mathrm d N_g}{\mathrm d z \mathrm d\Omega} = z^2 \frac{n_0}{H_0^3} (1-2(1+q_0) z) .$

© 2017, Lei Ma. | Created with Sphinx and . | | | |


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# Mapping a free variable of type A to a cartesian closed category

In From Lambda Calculus to Cartesian Closed Categories, the author explains the interpretation of lambda calculus in cartesian closed category and at one point he explains how a term representing a free variable of type A is mapped to the cartesian closed category as follow:

 [Γ x:A :- x:A] = π2 : ([Γ ] × [A]) → [A]

(A term which is a free
variable of type A is an arrow from the product of Γ and the type object A to A;
That is, an unknown value of type A is some arrow whose start point will be
inferred by the continued interpretation of gamma, and which ends at A.
So this is going to be an arrow from either unit or a parameter type to A -
which is a statement that this expression evaluates to a value of type A.)

I appreciate if someone can elaborate further on what the author means, perhaps with an example, since I am a newbie to category theory.

It's not clear exactly what your confusion is, so I'll try to explain the example more clearly, and you reply in the comments if something's still not apparent.

In the interpretation of the simply-typed $$\lambda$$-calculus in a cartesian-closed category, contexts $$\Gamma$$ and types $$A$$ are interpreted as objects $$⟦\Gamma⟧$$ and $$⟦A⟧$$ (types being equivalent to one-variable contexts), while a term $$\Gamma \vdash t : A$$ is interpreted as a morphism $$⟦t⟧ : ⟦\Gamma⟧ \to ⟦A⟧$$.

Context extension is represented by taking the product in the cartesian-closed category, that is: $$⟦\Gamma, x : A⟧ = ⟦\Gamma⟧ \times ⟦A⟧$$. We want to form the projection of the variable $$x : A$$, which is represented by a morphism $$⟦x⟧ : ⟦\Gamma, x : A⟧ \to ⟦A⟧$$, which by definition is a morphism $$⟦x⟧ : ⟦\Gamma⟧ \times ⟦A⟧ \to ⟦A⟧$$. There's one obvious choice here: to project the second component of the product. Taking $$⟦x⟧ = \pi_2$$ gives us a term of the correct type and it satisfies the expected properties.

In general, contexts (represented by lists of variables in the type theory) are represented by products of types in the cartesian-closed category, and the term corresponding to the $$i^\text{th}$$ variable is given by the $$i^\text{th}$$ projection from the product, $$\pi_i$$.

It might help to see explicit algorithms to compile the Lambda calculus to Cartesian closed categories.

A simple algorithm threads an environment through and looks up variables using a sequence of fst and snd

1. Start with an expression such as [lam f. lam x. f x] and an empty stack of variables.
2. When you reach a binder turn it into a currying combinator and add the variable to a stack curry [lam x. f x] and [f] and then curry (curry [f x]) and [f, x]
3. Function application is compiled to uncurry f . (fanout id x) so we get curry (curry (uncurry [f] . fanout id [x]))
4. When you reach a variable look it up in the stack. f is the zeroth variable here.
5. Replace the nth variable with a sequence of fst and n snds referring to the variable. So we get curry (curry (uncurry fst . fanout id (fst . snd)))

This works for cs theory but is suboptimal and unreadable.

More practically one iteratively removes variable bindings without passing through an environment or first compiles to a form intermediate between closed Cartesian categories and the lambda calculus.


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시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 0 0 0 0.000%

문제

“Digital Onion (DO, for short)” consists of parentheses. Null parenthesis (no parentheses) is a DO, and “( )” is also a DO. Then, all DOs can be formally defined recursively as follows:

1. Definition: Null parenthesis is a DO. Especially, we call this the Null DO.
2. Definition: “( )” is a DO. Especially, we call this the primitive DO.
3. Definition: If both A and B are DOs, then the combined form of “( A ) B” is also a DO, where we call A the inside of the DO and B the outside of the DO.

For example, “( ( ) ) ( )” is a DO and “( ( ( ) ) ) ( ( ) ( ) ( ) ) ” is a DO, but “( ) ( ) ) ( ( ” and “( ( ) ) )” cannot be a DO. Let us define the weight of a DO. The weight of a DO is defined as the number of '(' symbols, or equivalently the number of ')' symbols in it. Thus, the weight of the null DO is 0, and the weight of the primitive DO “( )” is 1. Also, it is easy to see that the weight of “( ( ( ) ) ) ( ( ) ( ) ( ) )” is 7.

Also, if X = ( ( ( ) ) ) ( ( ) ( ) ( ) ) , the inside of X is ( ( ) ), and the outside of X is ( ( ) ( ) ( ) ). When X = ( ( ) ( ( ) ) ), the inside DO of X is ( ) ( ( ) ), and the outside DO of X should be the Null DO.

Then, we define the price order of all DO objects. The ordering rules are simple, so we can sort all DOs according to their prices. This means that we can always determine which one is the more expensive between two different DOs given.

[Rule1]: The more weight, the more expensive.
[Rule2]: If the weights of two DOs are equal, then the price depends on the inside DO of the two DOs.
[Rule3]: If the weights of two DOs are the same and the prices of the inside DOs are equal, then the price depends on the outside DO of the two DOs.

Let us explain these rules. There are two DOs, A and B. We denote A < B to show that B is more expensive than A. It is easy to see ( ) < ( ( ) ) and ( ( ) ) ( ) < ( ( ( ) ) ) ( ) by Rule 1, ( ( ) ) ( ( ) ) < ( ( ( ) ) ) ( ) by Rule 2, and ( ( ) ) ( ) ( ) < ( ( ) ) ( ( ) ) by Rule 3.

Given a DO X, your task is to write the “Next More Expensive DO (NMED)” which is a more expensive DO than X, and there is no DO whose price is between NMED and X. That means that NMED is the next rank DO to a given DO when we sort all possible DOs according to their prices.

입력

The input consists of T test cases. The number of test cases (T ) is given in the first line of the input file. Each test case DO is written in a single line. ‘\$’ is placed at the end of each line to denote the end of each input DO representation, and there is at least one blank space to separate ‘(’s and ‘)’s and ‘\$’. Note that the minimum weight of input DO is 1, and the maximum weight is 30.

출력

Print exactly one line for each test case. The line should contain the Next More Expensive DO (NMED) with an ending mark ‘\$’. As was specified in the input format, there is at least one blank space to separate ‘(’s and ‘)’s and ‘\$’.

예제 입력 1

3
( ) $( ) ( )$
( ( ) ( ( ) ) ) ( ( )( ) ) $ 예제 출력 1 ( ) ( )$
( ( ) ) $( ( ) ( ( ) ) ) ( ( ( ) ) )$


text:
Chapter 80

Blunt and penetrating trauma can lead to a myriad of soft tissue injuries. The management of the majority of these injuries is discussed elsewhere in this text. Some soft tissue injuries require detailed explanations for their repair. These injuries are discussed below.

Wounds of unequal thickness are not suited for repair with simple interrupted sutures. Unequal tissue loss on each edge of a wound creates a thick edge–thin edge wound. The depressed edge must be elevated to the level of the nondepressed edge in order to attain proper wound apposition and cosmesis.

There are two techniques to repair wounds with edges of unequal thickness. One technique utilizes a half-buried horizontal mattress suture (Figure 80-1).1 Place the suture through the thick edge of the wound, across the wound and buried into the subcutaneous tissue of the thin edge, and back out the skin of the thick edge (Figure 80-1A). Apply traction to the suture and tie it to approximate the wound (Figure 80-1B). Apply an ointment-based compressive dressing.

Figure 80-1

Closing a wound with edges of unequal thickness using half-buried horizontal mattress sutures.

The second technique requires undermining both wound edges at the same depth in the subcutaneous tissue plane (Figure 80-2).2 Make an incision in the subcutaneous tissues of both wound edges and at the same level (Figure 80-2A). Undermine the area to free the tissue flaps (Figure 80-2B). Grasp the subcutaneous tissue flap from the thicker side and insert it under the thinner side beneath the undermined area (Figures 80-2B and C). Place a buried horizontal mattress suture to maintain the flaps in position. This “flap” elevates the depressed wound edge and facilitates appropriate wound approximation (Figure 80-2).2 Place interrupted sutures to approximate the wound edges (Figure 80-2C).

Figure 80-2

An alternative technique to close a wound with edges of unequal thickness. A. Make an incision in the subcutaneous tissue of both wound edges. B. Undermine the edges. Transpose the subcutaneous tissue of the thicker side into the undermined area of the thinner side (arrow). C. Approximate the wound edges using interrupted sutures.

Tangential flap lacerations over thin skin, such as the dorsum of the hand or the pretibial area, where there is very little subcutaneous tissue can be approximated with a specially placed simple interrupted suture. Insert the needle through the tip of the thin edge, across the wound, into the dermis of the thick edge, and out the skin of the thick edge. Apply traction to the suture to pull the thick edge up to meet the thin edge, producing good ...

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# INFN wiki

### Sidebar

strutture:lnf:da:lego:home

# IRIDE-Interdisciplinary Research Infrastructure based on Dual Electron linac

a multi-purposes high brightness/luminosity linacs for fundamental and applied physics applications

A vigorous development of several initiatives in the international scenario, aiming at producing in the incoming years a new generation of machines, capable to deliver advanced beams of photons and neutrons in the context of integrated facilities for multi-disciplinary research, makes today possible to conceive a rich scenario of new physics to be pursued at a large infrastructure based on advanced Linacs and Lasers, where an evolutionary strategy of development may assure a future of advanced scientific achievements that may span from fundamental and high energy physics to nuclear physics in the era and with the new tools of nuclear photonics, to basic and applied science with a FEL. The backbone of such an evolutionary development of this integrated machine and infrastructure would be an underlying activity of research in advanced acceleration concepts (AAC), spanning from fifth generation synchrotron light sources development, to integration of plasma boosters with RF linacs, to designing and commissioning high luminosity linear colliders at various energy ranges.

The global structure of this project follows

The two superconducting LINACS can operate both with electrons and positrons and in both directions. With the first (rightmost) LINAC one can realize a compton source in association with a LASER, and, with appropriate target and beam line, a neutron source by photo-production. The compton photons are needed for national security and bio-medical applications, while the neutron source is used for material studies, chip irradiation and tomographies. Studies of the neutron properties (e.g. the EDM) could also be considered.

By operating the second LINAC with a different beam of electrons one can have collisions between the electrons and the photons produced by the compton source (e-photon collider) or one can use the additional electron beam to produce photons by compton scattering and have photon-photon collisions for fundamental QED studies.

By operating the second LINAC with positrons, e+e- collisions can be produced, allowing hadronic physics studies at center of mass energies between the phi and the psi. The possibility to tune the center of mass energy to allow muon collider studies is also under investigation.

By operating the second LINAC to further accelerate the electrons passed through the first LINAC and by adding ondulators, a high repetition-rate Free Electron Laser can be obtained. Such a high energy and intensity electron beam can also be exploited for Plasma Wake Field acceleration experiments.

This host of opportunities can be realized in a modular way. The interest (both from the applied and fundamental physics points of view), the feasibility and the cost of each piece is under study. The pages below collect the material produced on each topic.

## Meetings

Brainstorming dec 12th 2012

Presentation in front of the INFN Directorate

Seminario @ "La Sapienza" pdf

Giornate di Studio 14-15 Marzo 2013 Web Site

Video streaming delle Giornate di Studio 14-15 Marzo 2013 streaming live

Riunione conveners 27/4/2013

Presentazione IRIDE a Torvergata 12/6/2013


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# JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Variation of Density with Temperature

Variation of Density with Temperature

Category : JEE Main & Advanced

Most substances (solid and liquid) expand when they are heated, i.e., volume of a given mass of a substance increases on heating, so the density should decrease $\left( \text{as }\rho \propto \frac{1}{V} \right)$.  For a given mass

$\rho \propto \frac{1}{V}$ $\Rightarrow$$\frac{{{\rho }'}}{\rho }=\frac{V}{{{V}'}}=\frac{V}{V+\Delta V}=\frac{V}{V+\gamma V\Delta \theta }=\frac{1}{1+\gamma \,\Delta \theta }$

$\Rightarrow$${\rho }'=\frac{\rho }{1+\gamma \,\Delta \theta }=\rho \,{{(1+\gamma \,\Delta \theta )}^{-1}}=\rho \,(1-\gamma \,\Delta \theta )$

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