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An AIR station is broadcasting the waves of wavelength 300 metres. If the radiating power of the transmitter is 10 kW, then the number of photons radiated per second is

(a) $1.5×{10}^{29}$              (b) $1.5×{10}^{31}$
(c) $1.5×{10}^{33}$              (d) $1.5×{10}^{35}$

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# Daniel’s Sum of Geometric Series

Continuing with the search of young Mathematicians, Daniel James Agsaullo Molina from Saint Louis College, La Union wants to share one of his favorite problems. He is an incoming freshman student. He was one of the national finalists in the individual category of 2014 Metrobank MTAP-Dep-Ed Math Challenge representing region 1.

Daniel at the center

Problem:

Given a geometric sequence whose sum of the first 20 terms is 7. And whose sum from the 21st to the 60th term is 84, find the sum from the 61st to the 120th term.

Solution:

The sum of a geometric sequence is defined as:

$S_n=\displaystyle\frac{a(r^n-1)}{r-1}$

Where n=number of terms, a=first term, and r = common ratio

Expressing the sum of the first 20 terms,

$S_{20}=\displaystyle\frac{a(r^{20}-1)}{r-1}=7$     …#1

Another given is the sum of the terms from the 21st to the 60th which is 84.

It is expressed as $S_{21\to 60}=S_{60}-S_{20}=84$

Therefore, $S_{60}=S_{21\to 60}+S_{20}=84+7=91$

Expressing the sum $S_{60}$,

We get

$S_{60}=\displaystyle\frac{a(r^{60}-1)}{r-1}=91$   …#2

From  #2 ÷ #1 and simplifying,

$r^{40}+r^{20}+1=13\to r^{40}+r^{20}-12=0$ $(r^{20}+4)(r^{20}-3)=0$

Since $r^{20}\rangle 0$ as r ranges to all possible common ratio.

$r^{20}-3=0 \to r^{20}=3$ …#3

We are ask to find the sum of 61st to 120th

$S_{61\to 120}=S_{120}-S_{60}$  ***main equation

Where $S_{60}=91$

$S_{120}=\displaystyle\frac{a(r^{120}-1)}{r-1}=\displaystyle\frac{a(r^{60}-1)}{r-1}\cdot ( r^{60}+1)$

But $\displaystyle\frac{a(r^{60}-1)}{r-1}=S_{60}=91$ and from #3,

$r^{60}=(r^{20})^3=3^3=27$ $S_{120}=91(27+1)=91(28)$

Substituting to our main equation,

$S_{61\to 120}=91(28)-91=91(27)=2457$

### Dan

Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.


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# Minimizing with constraints and linear function

1. Jul 19, 2014

### Maylis

Hello,

I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I don't understand why a linear function has the form $f(x) = c^Tx$. How is that equal to $c_{1}x_{1} + c_{2}x_{2} + \dots + c_{n}x_{n}$. Wouldn't this depend on how you define $c$ to begin with? What if you just defined $c$ to have the proper matrix deimension to multiply with $x$?

On the second slide, I am particularly troubled by this sentence ''There is no dependence in the $c_{\perp}$ direction. The function value is constant along these lines.''

I don't understand how the function value is constant. This is probably because I must not know what the function value us. Clearly along any of the given lines, the $c_{\perp}$ is increasing. What do they mean by the function value?

Also, that leads to not understanding the green box on the second slide,
''For $m$-dimensions, there is a $(m-1)$ dimensional plane, perpendicular to $c$, and $c^Tx$ has no dependence in those directions''.

What does this mean?

#### Attached Files:

• ###### linear functions.pdf
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Last edited: Jul 19, 2014
2. Jul 20, 2014

### WWGD

Here both c,x are both vectors ; c=(c_1 c_2.... c_n) and (x_1 x_2....x_n)

And the lack of dependence has to see with the fact that the function is identically zero along the

perpendicular direction, as they prove. Is that your question? By definition/construction if 2 vectors v,w

are perpendicular, their inner-product v^t w is zero . By linearity, f(0)=0, so, for any b, we have f(b v^t w )=bf(v^t w)=b0=0.

then, for any b, by linearity, f(x+ bv^t w)=f(x)+ bf(v^t w)=f(x)+0=0.

Last edited: Jul 20, 2014
3. Jul 20, 2014

### Maylis

What do you mean the function is identically zero along the perpendicular direction? What exactly the is 'function value'?

I am looking at the figure. Yes, I can see that along any of the individual lines, the vector $c$ is not changing. If you go to any other line parallel, it is in a new position. I don't see the relevance of this. I know I am missing something important, since they are going through a few slides to explain this.

4. Jul 20, 2014

### WWGD

The perpendicular direction is a multiple of a perpendicular vector by any constant, i.e., if x is perp. to x^t , then cx is in the perp. direction to x^t , for any choice of c. Then:

i) x^t x=0 .

ii) For L linear, L(0)=0, so L(cx^t x)=0.

iii) For L linear , L(a + b)=L(a)+ (b) , and L(ca)=cL(a).

Remember cx^t x is the perp. direction ,

Then L(a+ cx^t x)=L(a) + L(cx^t x)=L(a)+cL(cx^t x)=L(a) +L(0) =L(a).

Last edited: Jul 20, 2014
5. Jul 20, 2014

### Maylis

I just watched this youtube video on linear programming.

It seems like a standard optimization problem, but nowhere do I see all this matrix business that is present in the slides. There are some similarities, but why is what I'm doing have all this matrix stuff?

Also, WWGD, in your post #4, I just see math and to be honest I don't know what it means or how to apply it to my specific question. Perhaps an explanation with words or graphics will aid me better. But thank you for taking the time to try and help me here.

6. Jul 20, 2014

### WWGD

Yes, the matrix layout is a bit over-the-top, and maybe even unnecessary ; it is just a generalization about linear functions with linear constraints, and expressing the problem mathematically, and rigorously .

The issue/idea is that you graph each of the constraint lines. The result of the intersection of these constraint lines is a geometric figure called a polytope , say, P. Then , to find the optimal value , you only consider what happens at the vertices of the polytope . So you evaluate the function, here 40x+30y , only at each of the vertices of P, and out of all these values, you choose the best/optimal value.

The matrix layout is IMHO ,just a general mathematical way of describing this, and I think is helpful only if you want to do something beyond this type of problem, but it may be confusing if you don't .

7. Jul 20, 2014

### WWGD

One thing I forgot :
Notice 40x+30y can be written as x^t x , in the form:

(40 30)^t (x y),

and the same is the case for the linear constraints.


text:
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# Kaplan 800?

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20 Feb 2007, 14:05
I recently took the GMAT and scored 650(36Q 42V). I'm looking to take it again in about a month and wondering if Kaplan's 800 book is a good choice to help get me past the 700 mark. I've been going through OG 11 and a math formula sheet I found on here the past couple of days.
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20 Feb 2007, 14:09
NM, I looked through the forum and read a couple of reviews of it. Is it only good for improving verbal? Anybody want to weigh in on the math?
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20 Feb 2007, 14:18
I think is a great book -- assuming you are the appropiate level and have a strong foundation.

I assume that with 650 score, you are in good shape for it.
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20 Feb 2007, 14:45
I think is a great book -- assuming you are the appropiate level and have a strong foundation.

I assume that with 650 score, you are in good shape for it.

Is it great for math? I need something to help me get my math score up. I scored a 660 but did poorly in the quant section.
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Math formula sheet [#permalink]

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20 Feb 2007, 18:47
I am wondering if someone could let me know where to find the math formula sheet here in this website. Somebody just mentioned about it here.

Thanks!
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20 Feb 2007, 19:38
For those interested, you can buy the Kaplan 800 2007-2008 Edition on Amazon

List Price: $25.00 Price:$16.50
You Save: \$8.50 (34%)

Release Date: March 6, 2007
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21 Feb 2007, 11:52
Bought it last night. So far, I think its helpful. Already done half the CR problems sets. Read the CR, RC, and part of the problem solving sections. The explanations are more indepth and the problems are harder than other materials.
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Here is the Math formula sheet that I mentioned. I don't remember whose post I stole this from, but I PDF'd it to make it easier to send.
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[#permalink] 21 Feb 2007, 11:57
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# Kaplan 800?

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## 'Keep it Simple' printed from http://nrich.maths.org/

Try working systematically through all the possibilities.

$\frac{1}{8} = \frac{1}{9} + ?$

$\frac{1}{8} = \frac{1}{10} + ?$

$\frac{1}{8} = \frac{1}{11} + ?$

$\frac{1}{8} = \frac{1}{12} + ?$

$\frac{1}{8} = \frac{1}{13} + ?$

$\frac{1}{8} = \frac{1}{14} + ?$

$\frac{1}{8} = \frac{1}{15} + ?$

$\frac{1}{8} = \frac{1}{16} + ?$ (but this won't count)

Why is $\frac{1}{9}$ the first one you can use?
Why don't you need to go further than $\frac{1}{16}$?


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# nLab monad (disambiguation)

Various concepts go by the name monad.

Historically, going back to Gottfried Leibniz, “monad” is used to refer to a kind of “atom”, for him a mind-like simple substance. Derived from this is the idea of an “atom of space” (see also in Science of Logic the section The Monad of Leibniz). In roughly this sense the term is used in

In category theory and computer science a monad is a monoid acting on a category/type system, see at

To see this as an “atom” one observes that this is equivalently a lax 2-functor $\ast \longrightarrow Cat$ from the terminal category to the 2-category of categories and hence a "point" in some 2-categorical sense.

category: disambiguation

Revised on December 4, 2013 04:55:05 by Mike Shulman (172.10.15.11)


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## Least Right Side

The sides of a right triangle are all positive integers. Two of the sides are odd numbers that differ by 50. What is the least possible value for the third side?
Source: mathcontest.olemiss.edu 2/18/2013

SOLUTION

By the Pythagorean theorem
$a^2+b^2=c^2$
$a^2=c^2-b^2$
$=\left (c+b\right )\left (c-b\right )$
$=\left (c+b\right )\left (50\right )$
The least perfect square number that is divisible by $50$ is $3600$
$a^2=3600$
$a=60$
Verification
$3600=\left (c+b\right )50$
$c+b=72$
$c-b=50$
$2c=122$
$c=61$
$b=61-50=11$
$60^2+11^2=61^2$

Answer: $60$


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# Math Help - Double Integrals

1. ## Double Integrals

Evaluate the following:

1 y² e 1
∫ ∫ xy dx dy + ∫ ∫ xy dx dy
0 0 1 ln y

(Hint: Reverse the order of integration to evaluate. You should be able to write this as one double integral once you have reversed the order of integration.)

I'm having trouble getting it to one double integral.

2. sketch the region on where the double integral is taken, that's all.


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## CryptoDB

### Paper: A Complete Treatment of 2-party SFE in the Information-Theoretic Setting with Applications to Long-Term Security

Authors: Jörn Müller-Quade Dominik Raub URL: http://eprint.iacr.org/2008/264 Search ePrint Search Google It is well known that general secure function evaluation (SFE) with information-theoretical (IT) security is infeasible in the secure channels model in presence of a corrupted majority \cite{Cle86,Kil91, Kus92, Kil00, IKLP06, Kat06}. In particular these results extend to and are derived from the 2-party scenario, where any corrupted party is already a corrupted majority. On the other hand \cite{BroTap07} have recently demonstrated that a wealth of interesting functions can be computed securely even in presence of a corrupted majority, at least if one is willing to sacrifice robustness, thus raising interest in a general description of these functions. In this work we give a complete combinatorial classification of 2-party functions, by their secure computability under active, semi-honest, passive and quantum adversaries. Our treatment is constructive, in the sense that, if a function is computable in a given setting, then we exhibit a protocol. We then proceed to apply our results to gain insight into long-term security, where we admit computational assumptions for the duration of a computation, but require information-theoretical security (privacy) once the computation is concluded.
##### BibTeX
@misc{eprint-2008-17941,
title={A Complete Treatment of 2-party SFE in the Information-Theoretic Setting with Applications to Long-Term Security},
booktitle={IACR Eprint archive},
keywords={cryptographic protocols / 2-party SFE, dishonest majority, unconditional security, long-term security},
url={http://eprint.iacr.org/2008/264},
note={ d.raub@inf.ethz.ch 14041 received 11 Jun 2008},


text:
# aliquote.org

Here’s an interesting list of resources in addition to StatLib: Statistics, Statistical Computing, and Mathematics.


text:
The staffor stave forms the very basis of sheet music. The lines and the spaces correspond to pitches of a eight-note musical scale depending on the defining clef. For example, the items you wear: hat, shirt, jacket, pants, and so on. Written by Jessica Barrett. Some authors use the symbols ⊂ and ⊃ to indicate subset and superset respectively; that is, with the same meaning and instead of the symbols, ⊆ and ⊇. Set definition is - to cause to sit : place in or on a seat. Symbol set design. Jessica is a freelance writer and editor from Toronto, Canada. which doesn't mean much to me. Symbols are designed so that it is simple to decode their meaning. RapidTables.com | A set is a collection of objects or elements, grouped in the curly braces, such as {a,b,c,d}. The following table lists many common symbols, together with their name, pronunciation, and the related field of mathematics. The following table documents the most notable of these symbols — along with their respective meaning and example. And I am unsure how I would divide the reals by the naturals anyway. A set is a collection of things, usually numbers. Suppose Set A consists of all even numbers such that, A = {2, 4, 6, 8, 10, …} and set B consists of all odd numbers, such that, B = {1, 3, 5, 7, 9, …}. In mathematics, a set is a well-defined collection of distinct elements or members. Symbol Symbol Name Meaning / definition Example; P(A): probability function: probability of event A: P(A) = 0.5: P(A ∩ B): probability of events intersection: probability that of events A and B Basic Concepts of Set Theory: Symbols & Terminology A set is a collection of objects. Can anyone clear this up a bit? Learn Sets Subset And Superset to understand the difference. The table provided below has a list of all the common symbols in Maths with meaning and examples. To show that a particular item is an element of a set, we use the symbol ∈. This is known as a set. Terms of Use | If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. A set is a collection of things.For example, the items you wear is a set: these include hat, shirt, jacket, pants, and so on.You write sets inside curly brackets like this:{hat, shirt, jacket, pants, ...}You can also have sets of numbers: 1. A is a subset of B, but A is not equal to B. While there are more than 30 symbols used in set theory, you don’t need to memorize them all to get started. Well, simply put, it's a collection. A universal set is a set which contains all the elements or objects of other sets, including its own elements. Purplemath. Probability function. Thank you for your support! It signifies the likeliness of the occurrence of … Symbol: Name: Meaning: Example {} set: The symbol that encapsulates the numbers of a set: A = {3,7,9,14}, Basically, the definition states that “it is a collection of elements”. About | I'm sure you could come up with at least a hundred. Conduct regular refresher training to ensure that every worker is familiar with the symbols and their meanings. Look for the set symbol (middle-right area of the card) and use the following table to look … Proper Subset: every element of A is in B, Superset: A has same elements as Note: If a +1 button is dark blue, you have already +1'd it. Set symbols of set theory and probability with name and definition: set, subset, union, intersection, element, cardinality, empty set, natural/real/complex number set Dollar Sign $A symbol that looks like a capital S with one or two vertical lines through it, the dollar … The symbol ∉ shows that a particular item is notan element of a set. Some of the examples are the pi (π) symbol which holds the value 22/7 or 3.17, and e-symbol in Maths which holds the value e= 2.718281828….This symbol is known as e-constant or Euler’s constant. Set theory, branch of mathematics that deals with the properties of well-defined collections of objects such as numbers or functions. the set$\mathbb R \setminus \mathbb N$is an open subset of$\mathbb R$. I know that |A| stands for the cardinality of the set A but I've never seen the other symbol. Here is the proper set of math symbols and notations. Definition:The number of elements in a set is called the cardinal number, or cardinality, of the set. Venn diagrams can be used to express the logical (in the mathematical sense) relationships between various sets. List of set symbols of set theory and probability. Pokemon» Set Symbols The most common way to organize Pokemon cards is by set. Set of whole numbers: {0, 1, 2, 3, ...} 2. Set Theory Symbols Set Theory in Maths In Maths, the Set theory was developed to explain about collections of objects. What I've never seen is the || symbols for a set. A set is a collection of things, usually numbers. It is usually denoted by the symbol ‘U’. So it is just things grouped together with a certain property in common. Probability & Statistics Symbols. A is a superset of B, but B is not equal to A. all the objects that do not belong to set A, objects that belong to A or B but not to their intersection, infinite cardinality of natural numbers set, cardinality of countable ordinal numbers set, natural numbers / whole numbers set (with zero), natural numbers / whole numbers set (without zero). ⊂ and ⊃ symbols. First we specify a common property among \"things\" (we define this word later) and then we gather up all the \"things\" that have this common property. Set of prime numbers: {2, 3, 5, 7, 11, 13, 17, ...} In fact, the following three are the perfect foundation. As it is virtually impossible to list all the symbols ever used in mathematics, only those symbols which occur often in mathematics or mathematics education are included. Symbol Meaning Example + add: 3+7 = 10 − subtract: 5−2 = 3 × multiply: 4×3 = 12 ÷ divide: 20÷5 = 4 / divide: 20/5 = 4 ( ) grouping symbols: 2(a−3) [ ] grouping symbols: 2[ a−3(b+c) ] { } set symbols {1, 2, 3} π: pi: A = π r 2 ∞ infinity ∞ is endless = equals: 1+1 = 2: approximately equal to: π … B, or more, Proper Superset: A has B's elements and more, Not a Superset: A is not a superset of B, Equality: both sets have the same members, Cardinality: the number of elements of set A. Most symbol sets are designed to follow a coherent set of design rules to provide consistency, which assists the decoding of meaning. Privacy Policy | How to use set in a sentence. About "Symbols used in set theory" Symbols used in set theory : In set theory, we use different symbols to do operations like union, intersection etc., Here, we are going to see different symbols used in set theory to do the above mentioned operations. The elements that make up a set can be anything: people, letters of the alphabet, or mathematical objects, such as numbers, points in space, lines or other geometrical shapes, algebraic constants and variables, or other sets. The following list of mathematical symbols by subject features a selection of the most common symbols used in modern mathematical notation within formulas, grouped by mathematical topic. In my use-case we're working with sets of words (so called text strings) and the top of the formula is the dot product of the two sets. Especially ones like intersection and union symbols. PRESENTED BY . (If you are not logged into your Google account (ex., gMail, Docs), a login window opens when you click on +1. Notes are written on a staff of five lines consisting of four spaces between them. Here are the most common set symbols, In the examples C = {1, 2, 3, 4} and If a set A is a collection of even number and set B consist of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B. We can list each element (or "member") of a … I know that the 'divided by' symbol is usually a slash in the opposite direction. A is a subset of B. set A is included in set B. D = {3, 4, 5}. If you like this Page, please click that +1 button, too.. Subsets are the part of one of the mathematical concepts called Sets. We can list each element (or "member") of a set inside curly brackets like this: Symbols save time and space when writing. Table of set theory symbols Symbol Symbol Name Meaning / definition Example { } set a collection of elements A = {3,7,9,14}, B = {9,14,28} There are a bunch of these set symbols… 5-6 sets are released every year, each with a different set symbol, and they’ve been printing cards since 1999! To identify the set, look for a little symbol at the bottom of the card, next to the card number. Manage Cookies. The theory is valuable as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts. Collections of symbols that cover a wide vocabulary are called a 'symbol set'. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics. You should pay attention because these symbols are easy to mix up. For example, for these authors, it is true of every set A that A ⊂ A. In logic, a set of symbols is commonly used to express logical representation. The staff is counted from the lowest line upwards. In set theory, relational symbols are often used to describe relationships between sets, or relationships between a set and its element. What is a set? A is a superset of B. set A includes set B. Symbol Symbol Name Meaning / definition Example { } set: a collection of elements: A = {3,7,9,14}, B = {9,14,28} A ∩ B: intersection: objects that belong to set A and set B: A ∩ B = {9,14} A ∪ B: union: objects that belong to set A or set B: A ∪ B = {3,7,9,14,28} A ⊆ B: subset: A is a subset of B. set A is included in set … © A well-dened set has no ambiguity as to what objects are in the set or not. When the upper limit is$\infty\$ it means a union of infinitely many sets: $$\bigcup_{n=a}^{\infty} f(n) \quad\text{means}\quad f(a)\cup f(a+1)\cup\cdots$$ whose precise meaning is defined in the explanation you quote. This website uses cookies to improve your experience, analyze traffic and display ads. Symbol ‘ U ’ logical ( in the mathematical sense ) relationships a. Terminology a set which contains all the elements or objects of other,. The cardinality of the set proper set of symbols is commonly used to express the logical ( in opposite! And examples includes set B the difference their meanings certain property in.! Counted from the lowest line upwards note: if a +1 button, too a. Easy to mix up is included in set theory: symbols & terminology set... B. set a that a particular item is notan element of a musical. Or objects of other sets, including its own elements Page, please click that button! And so on unsure how I would divide the reals by the naturals anyway describe relationships between sets or! Of B. set a that a ⊂ a decoding of meaning a freelance and... Four spaces between them don ’ t need to memorize them all get. Of other sets, or relationships between sets, including its own elements definition: the number of ”. Item is notan element of a eight-note musical scale depending on the defining clef with a certain property in.!, usually numbers set ' includes set B is simple to decode their meaning rules to consistency. So that it is just things grouped together with their name, pronunciation, and so on you this. Display ads definition: the number of elements in a set is a freelance writer editor. 'Divided by ' symbol is usually denoted by the naturals anyway familiar with the symbols and notations of elements.... Staff is counted from the lowest line upwards symbol sets are designed to follow a coherent set of symbols cover! Analyze traffic and display ads definition states that “ it is simple to decode their meaning symbols sets symbols meaning set,... Are the perfect foundation relationships between a set theory, you don t! The reals by the symbol ‘ U ’ particular item is notan element a. Next to the card number a well-dened set has no ambiguity as to what objects in! A eight-note musical scale depending on the defining clef you don ’ t need to memorize sets symbols meaning to! Items you wear: hat, shirt, jacket, pants, so. Universal set is a freelance writer and editor from Toronto, Canada a includes B! A list of set theory, relational symbols are often used to describe relationships between sets or! Next to the card number on a seat of mathematics understand the difference is counted from the lowest upwards! Definition states that “ it is true of every set a that a ⊂.. There are more than 30 symbols used in set B click that button. 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sets symbols meaning 2021


text:
# Proof relating to the gcd of two numbers

I want to show that if $a \in \mathbb{Z^+}$ $\implies$ $gcd(a,0) = a.$

From what I am given, I know that $a$ is a divisor of $0$, so we can start from there. I was thinking of using the Euclidian Algorithm throughout the proof, but do not know when I should mention it, or if it's even applicable in this case. Someone actually made an interesting comment that is related to my question and thus I would like to see how the proof of this question unfolds. The commentary is on this thread: What is $\gcd(0,0)$?

• You may, if you wish, define $\gcd(a,b)$ to be the unique nonnegative generator of the additive subgroup of $\Bbb Z$ generated by $a$ and $b$. Or, if you don’t like defining the difficulty away like that, you can prove that with your definition of gcd, it does in fact have the above property. Feb 6, 2018 at 5:38
• Hi Lubin. So with the definition of gcd that I wrote out, how would I begin showing the above property is true? A push in the right direction would be helpful. Feb 6, 2018 at 5:51
• First show that $a|b$ if and only if $a\Bbb Z\supset b\Bbb Z$. Observe that if $a$ and $b$ are nonzero, then $a|b\Rightarrow a\le b$. Remember that $\gcd(a,b)$ is just what it says, the greatest among all common divisors of $a$ and $b$, except that it’s a bit different when $a=b=0$. There shouldn’t be too much beyond that. Feb 6, 2018 at 14:47


text:
## Algebra 1: Common Core (15th Edition)

$2y+4=2(y+2) \\\\ 2y+4=2y+4$ We first distribute the 2 on the right side. This gives us the same thing on both sides of the equation, so there are infinitely many solutions.


text:
Welcome to ZOJ
 Problem Sets Information Select Problem Runs Ranklist
ZOJ Problem Set - 3831
Permutation

Time Limit: 4 Seconds      Memory Limit: 131072 KB      Special Judge

Given two sequences {A(1), A(2), ..., A(N)} and {B(1), B(2), ..., B(N)}.

You task is to find a sequence {σ(1), σ(2), ..., σ(N)} satisfy the following conditions:

1. {σ(1), σ(2), ..., σ(N)} is a permutation of sequence {1, 2, ..., N}
2. ∀ 1 ≤ iN, A(σ(i)) = σ(B(i))

#### Input

There are multiple test cases. Each case begin with a line contains an integer N (1 ≤ N ≤ 50000). The second line contains N integers, A(1), A(2), ..., A(N) (1 ≤ A(i) ≤ N). The third line contains N integers, B(1), B(2), ..., B(N) (1 ≤ B(i) ≤ N).

#### Output

For each test case, if you cannot find the sequence, you should just output "IMPOSSIBLE" (without quotes). If you find the sequence, you should output two lines. In the first line, you should just output "FOUND num" (without quotes), where num is the number of sequences you find. The number may be very large, so the answer should modulo 109 + 7. And in the second line, you should output N integers σ(1), σ(2), ..., σ(N), separated by a space. If there are multiple sequences meeting the conditions, you can output any one of them.

#### Sample Input

4
2 3 1 3
3 3 4 1
4
2 3 1 3
1 1 2 3
12
2 1 2 2 1 1 8 7 8 8 7 7
2 1 2 2 1 1 8 7 8 8 7 7

#### Sample Output

FOUND 1
2 4 3 1
IMPOSSIBLE
FOUND 128
1 2 3 4 5 6 7 8 9 10 11 12

Author: LIN, Xi
Source: ZOJ Monthly, November 2014
Submit    Status


text:
## Differential and Integral Equations

### Existence of radial solutions for a class of $p(x)$-Laplacian equations with critical growth

Claudianor O. Alves

#### Abstract

Using variational methods we establish the existence of solutions for the following class of $p(x)$-Laplacian equations: $$-div(|\nabla u|^{p(x)-2}\nabla u) + |u|^{p(x)-2}u= \lambda |u|^{q(x)-2}u + |u|^{p^{*}(x)-2}u, \,\,\,\,\, \mathbb{R}^{N}, \tag*{(P)}$$ where $\lambda \in (0, \infty)$ is a parameter and $p(x), q(x): \mathbb{R}^{N} \to \mathbb{R}$ are radial continuous functions satisfying $1 < p(x) < N$ and $p(x) < < q(x) < < p^{*}(x)= \frac{p(x)N}{N-p(x)}$.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 1/2 (2010), 113-123.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019390

Mathematical Reviews number (MathSciNet)
MR2588805

Zentralblatt MATH identifier
1240.35182

#### Citation

Alves, Claudianor O. Existence of radial solutions for a class of $p(x)$-Laplacian equations with critical growth. Differential Integral Equations 23 (2010), no. 1/2, 113--123. https://projecteuclid.org/euclid.die/1356019390


text:
TH Theoretical Seminar

# Holographic models for QCD in the Veneziano Limit

## by Elias Kiritsis (APC, Univ Paris Diderot)

Wednesday, 27 November 2013 from to (Europe/Zurich)
at CERN ( 4-3-006 - TH Conference Room )
 Description QCD in the Veneziano limit, Nc->oo, Nf->oo, with x=Nf/Nc fixed, has been conjectured to have an interesting phase diagram, including a conformal window, a real QCD-like phase, and a conformal transition separating the two. We will describe recent efforts to construct holographic theories with behavior that is similar to QCD. At zero temperature we will establish the nature of the conformal phase transition, BKT scaling in the "walking region", and Efimov vacua. At finite temperature we will determine and explore the structure of the phase diagram as a function of x. WE will also study finite temperature and finite density, and we will find a familiar phase diagram and a surprise. Material:


text:
1. Slope field?

Can anyone help me figure out the slope field of dy/dx= x(cubed root(y))? I just can't figure it out.

2. Re: Slope field?

You do know what a "slope field" is, don't you? Pick some values of x and y, calculate $\displaystyle x\sqrt[3]{y}$ for each of those x, y, draw a short line segment centered at (x,y) and with that slope.

3. Re: Slope field?

This problem is not difficult - just tedious. Start asking yourself questions like, "Where is the slope zero?", "Where is it positive/negative?", etc.

For example, the slope is 1 on the curve $\displaystyle 1=x\sqrt[3]{y}$ or $\displaystyle y=\frac{1}{x^3}$.

Just keep it up until you have what you think is enough slopes to make a slope field.

- Hollywood


text:
Albion College Mathematics and Computer Science Colloquium

 Title: Finding the Best Way from Here to There Speaker: Darren E. Mason Associate Professor Mathematics and Computer Science Department Albion College Albion, Michigan Abstract: Given a task to accomplish, it is natural to ask what is the best way to achieve your goal? Maybe you are flying from Beijing to London and need the shortest flight path. Or you are selling fuel and you want to find a function P(t) that gives you the optimal price at time t to maximize your profit. Or you are crossing a river with a strong current and want to determine a propeller direction (as a function of time) so that you cross the river in the least amount of time. The number of possible questions like those above seems endless. During this lecture will discuss some of the above problems, a famous brain-teaser called the brachistochrone problem, and illustrate how to find solutions to these problems using a version of calculus that makes sense in infinite dimensions – the interesting field of variational calculus! Location: Palenske 227 Date: 3/26/2009 Time: 3:10 pm

@abstract{MCS:Colloquium:DarrenEMason:2009:3:26,
author  = "{Darren E. Mason}",
title   = "{Finding the Best Way from Here to There}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{26 March}",
year    = "{2009}"
}


text:
Jan Jensen
984 followers
984 followers
Jan's posts
Post has attachment
Finding the function that is its own derivative
I saw this "derivation" some years ago but now I can't find it.  If anyone knows the source please let me know. Let's say we want to find a function $f(x)$ for which $$\frac{d}{dx} f(x) = f^\prime (x) = f(x)$$ Well, how about $f(x) = x$?  f(x) = x \impl...
Post has attachment
Where does the ln come from in S = k ln(W) ? - Take 2
Some years ago I wrote this post . Now I want to come at it from a different angle. A closed system spontaneously goes towards the state with maximum multiplicity, $W$. For a system with $N$ molecules with energies $\varepsilon_1, \varepsilon_2, \ldots$ we...
Post has attachment
Computational Chemistry Highlight: March issue
The March issue of  Computational Chemistry Highlights  is out. CCH is an  overlay journal  that identifies the most important papers in computational and theoretical chemistry published in the last 1-2 years. CCH is not affiliated with any publisher: it is...
Post has attachment
The Elephant in the Room of Density Functional Theory Calculations
Stig Rune Jensen, Santanu Saha, José A. Flores-Livas, William Huhn, Volker Blum, Stefan Goedecker, and Luca Frediani (2017) Contributed by  Jan Jensen While basis set convergence sounds straightforward (though time-consuming) it is hard to rule out that un...
Post has attachment
Computational Chemistry Highlight: February issue
The February issue of  Computational Chemistry Highlights  is out. CCH is an  overlay journal  that identifies the most important papers in computational and theoretical chemistry published in the last 1-2 years. CCH is not affiliated with any publisher: it...
Post has attachment
Biotechnology and drug-design: My latest paper explained without the jargon
Our latest paper has just appeared in the open access journal Chemical Science . It's ultimately related to biotechnology so first some background. Background Most biotechnology and medicine involves proteins in some way. Many diseases involve mutations tha...
Post has attachment
Towards full Quantum Mechanics based Protein-Ligand Binding Affinities
Stephan Ehrlich, Andreas H. Göller, and Stefan Grimme (2017 ) Contributed by  Jan Jensen Erlich et al. presents absolute binding free energies for activated serine protease factor X (FXa) and tyrosine-protein kinase 2 predicted using DFT. Here I'll focus o...
Post has attachment
RMSD and MUE versus Correlation Coefficient: a simple illustration of the difference
Here is a simple illustration of what the root-mean-square deviation (RMSD), mean-unsigned error (MUE) and correlation coefficient ($r$) can tell you about your data.   Imagine that the $x$-axis is experimental data and the $y$-axis is computed data in some...
Post has attachment
What are the most important reactions in drug synthesis and stability?
This is a rough draft that I hope to flesh out based on feedback, i.e. "I'm not telling, I'm asking". Please leave a comment or tweet me I realize Synthesis 1. Aromatic electrophilic substitution of heteroaromatics 2. Suzuki coupling of heteroaryl halides 3...
Post has attachment
Preprints and the speed of publishing
When I talk about preprints with colleagues some of them say "Oh, what's the rush?" or "Publishing is so fast these days. Why, my last paper was online 6 weeks after submission don't you know" and then go on to clean their pipe with a thoughtful smile or ge...


text:
75 views
(Public Key Notation) Alice and Bob are spouses and each making their own wills. They want to send a copy to their attorney Charlie that only Charlie can read and that shows Alice’s will signed by Alice and seen by Bob and Bob’s will signed by Bob and seen by Alice. Using the notation in the slides. What would be the notation of a message that accomplishes this task?
| 75 views
0
$E_{K_{A}}\left ( M \right )$

$D_{K_{B}}\left ( M \right )$
0
could you elaborate?

Alice’s will signed by Alice and seen by Bob and Bob’s will signed by Bob and seen by Alice.
+1
It is case of digital signature

In digital signature authentication not required

So, Say Alice=A

and Bob=B

when alice send,there is a pubic key , which seen by atorney and a private key, which seen by Bob

Now if we represent encrypted public key as $+$ and private key as $-$

then

$K_{B}^{-}\left ( K_{A} ^{+}\left ( Message \right )\right )$

ok?
+1

Thanks a lot! @srestha


text:
About results.

### Description. Lang: en

There are several kinds of means in various branches of mathematics (especially statistics).
For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted by

x
¯

{\displaystyle {\bar {x}}}
, pronounced "x bar". If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the sample mean (denoted

x
¯

{\displaystyle {\bar {x}}}
) to distinguish it from the mean of the underlying distribution, the population mean (denoted

μ

{\displaystyle \mu }
or

μ

x

{\displaystyle \mu _{x}}
). Pronounced "mew" /'mjuː/.
In probability and statistics, the population mean, or expected value, are a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability p(x), and then adding all these products together, giving

μ
=
∑
x
p
(
x
)

{\displaystyle \mu =\sum xp(x)}
. An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite.
For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population. For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals. The sample mean may differ from the population mean, especially for small samples. The law of large numbers dictates that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean.Outside probability and statistics, a wide range of other notions of "mean" are often used in geometry and analysis; examples are given below.Description provided by Wikipedia.

Search predictions are possible search terms you can use that are related to the terms you’re typing and what other people are searching for.Mean GirlsMeaningMeanMeanwhileMean Squared ErrorMeantMeaning OfMean StackMean Girls 2Mean Streets

### Entity Index

This is the list of all entities in this result page. Click an entity to go directly to the entity box.

### Wiki Authority Control

Authority control is a method of creating and maintaining index terms for bibliographical material in a library catalogue. The links produced by the authority control template on Wikipedia go to authority control data in worldwide library catalogues.apstatsreview.tumblr.combooks.google.combooks.google.combooks.google.com


text:
Salmon, RUVSeq and DESeq2
1
0
Entering edit mode
@reganhayward-10620
Last seen 12 days ago
New Zealand

I'm looking at identifying differentially expressed genes. I'm using Salmon, importing the quantification using tximport as outlined here. It's a simple comparison using infected and non-infected, and I've tried using three differential expression pieces of software (edgeR, DESeq2 and Limma).

However, for one of the conditions (there are only 2 reps), one rep is unfortunately a bit different from the other (actual gene expression). As a result, the number of DE genes is reduced and is making any biological interpretations challenging. To help with this, I'd like to use RUVSeq (RUVs), but I'm not entirely sure how to use the offsets correctly.

Although slightly different but related, I've looked at the offsets section of the EDASeq vignette, and from what I can see, theoretically I should be able to use the offsets as input into RUVSeq. I just don't want to calculate this incorrectly and end up interpreting the data wrong

Any ideas or suggestions would be greatly appreciated!

Salmon DESeq2 DEG RUVSeq • 245 views
2
Entering edit mode
@mikelove
Last seen 2 days ago
United States

https://bioconductor.org/packages/release/workflows/vignettes/rnaseqGene/inst/doc/rnaseqGene.html#using-ruv-with-deseq2

Here you estimate factors of unwanted variation and supply these to the design as nuisance covariates.

0
Entering edit mode

Thanks for above reply Mike - that's a cool idea which I'll use.

However, applying this to a different experimental design, this probably isn't the best way right. For example:

No. tissue      infection       rep condition
7   Kidney      Bacteria_A      1   Kidney_bact_A
8   Kidney      Bacteria_A      2   Kidney_bact_A
9   Kidney      Bacteria_B      1   Kidney_bact_B
10  Kidney      Bacteria_B      2   Kidney_bact_B
11  Kidney      Mock-infected   1   Kidney_mock
12  Kidney      Mock-infected   2   Kidney_mock

How does this look if I was to apply RUVs?

differences <- makeGroups(c("A","A","B","B","C","C","D","D","E","E","F","F"))
differences

set <- newSeqExpressionSet(counts(dds))
set <- newSeqExpressionSet(counts(dds, normalized = TRUE)) #Does this line make more sense to use?

idx  <- rowSums(counts(set) > 5) >= 2
set  <- set[idx, ]

set3 <- RUVs(set, genes, k=1, differences)

ddsruv <- dds
ddsruv$W1 <- set3$W[,1]
design(ddsruv) <- ~ W1 + condition

dds2 <- DESeq(ddsRUVs)

So, I'd need to create a model.matrix (m1 below) as outlined here and run something like this?

dds2 <- DESeq(ddsRUVs, test="LRT", betaPrior=FALSE, full=m1, reduced=~0 + W1 + condition)

Thanks in advance - and apologies for all the nested questions

0
Entering edit mode

Why do you say the DESeq() and results() line don’t incorporate RUV factors? They do. Putting a covariate into the design is “controlling for” that covariate when estimating LFC for others.

0
Entering edit mode

ahh, that was me misunderstanding how the RUV factors were being incorporated into the design - clearly they are. Thanks for clarifying!

Last bit of clarification.... Which of these would you suggest as input to RUVs? I ask as I saw in the link you supplied, that when using svaseq, normalised values were passed

set <- newSeqExpressionSet(counts(dds))
set <- newSeqExpressionSet(counts(dds, normalized = TRUE))

0
Entering edit mode

The SVA workflow doesn't have any steps to account for sequencing depth, hence we recommend supplying the scaled counts to SVA.

However, RUVSeq does have steps to deal with sequencing depth, see vignette section 2.1, the fourth code chunk. So if you are following the RUVSeq workflow including that step you can provide original counts, not scaled counts.

0
Entering edit mode

Legend - thanks Mike


text:
# Using two different Sans Serif fonts eliminates bold font

Say I want to have my document in the default sans serif font, but I occasionally wish to have some other features in the document be in a different font. I am using \usepackage{libertine} to load this other font, and I get the libertine font to show up by using \textsf{...}.

However, now \textbf{} no longer works in the document to bold the default sans serif font. How can I work around this?

Edit: I found the issue. The problem was the following offending line of code:

\renewcommand\rmdefault{cmss}

I changed this to

\renewcommand{\familydefault}{cmss}

in the MWE below, and all works fine.

MWE (solution found):

\documentclass[11pt]{article}

%% Import packages
%% ================================================================================================
\usepackage[numbers,sort&compress]{natbib}                      % Enable bibtex
\usepackage[hyphens]{url}
\usepackage[pdftex]{graphics,graphicx}  % Augment graphics functionality
%\usepackage{concrete}                  % Concrete roman font -- COOL MATH. This package has some conflicts with fancyhdr. Recommend not to use.
\usepackage{latexsym}                   % Symbolic fonts for LaTeX
\usepackage{amsmath}                    % AMS math formatting options
\usepackage{amsfonts}                   % AMS fonts
\usepackage{bm}                         % Bold math
\usepackage[normalem]{ulem}
\usepackage{commath}
\usepackage[tiny,compact]{titlesec}     % Allow better control over sections, headers, etc.
\usepackage{fancyhdr}                   % Allow better control over page layout
\usepackage[section]{placeins}  % Keep figures in section
\usepackage{float}                      % Define tables and floating elements
\usepackage{flafter}                    % Never put floats before their references
\usepackage{floatflt}                   % wrap text around floats
\usepackage{wrapfig}                    % wrap text around figures
\usepackage{subcaption}                     % subcaptions for subfigures. USE SUBFIG, NOT SUBFIGURE. SUBFIGURE IS DEPRECATED AND MAY CONFLICT WITH OTHER PACKAGES
\usepackage{longtable}                  % A multi-page tabular environment
\usepackage{threeparttable}             % tables with footnotes, capions all the same width
\usepackage{dcolumn}                    % decimal-aligned tabular math columns
\usepackage{multirow}                   % Allow table cells to span multiple rows
\usepackage{booktabs}                   % Formatting options for publication-quality tables
\usepackage{array}                      % Additional options for formatting columns in the array and tabular environments
\usepackage{caption}                    % Caption formatting -- use commands here instead of hangcaption
\usepackage[usenames,dvipsnames]{color}                     % Enable colors
\usepackage[table,hyperref]{xcolor}     % Better control over color
\usepackage{import}                     % Let latex import files from different directories
\usepackage{datetime}                   % Format dates and times
\usepackage{enumitem}                   % Better control over lists
\usepackage{nomencl}                    % nomenclature package
\usepackage{lscape}                     % Allow text to be written in landscape mode
\usepackage{lipsum}                     % Lorem Ipsum, for placeholder text.
\usepackage[greek,english]{babel}
\usepackage[sort&compress]{natbib}
\usepackage{setspace}

%\usepackage{cabin}
\usepackage{libertine}
\usepackage[T1]{fontenc}
%\renewcommand*\familydefault{\sfdefault}  %% Only if the base font of the document is to be sans serif

\usepackage{fancyvrb}

\renewcommand{\familydefault}{cmss}

\newlength{\tempintextsep}

\begin{document}

\setlength{\tempintextsep}{\intextsep}
\setlength{\intextsep}{0pt}
\begin{wrapfigure}[6]{l}{2.4in}
{
\setlength{\abovedisplayskip}{0pt}
$$\left\{\;\;\; \begin{minipage}{1.95in} \centering \fontsize{16pt}{19pt}\selectfont \textsf{ This is a super awesome quote of super awesomeness. } \end{minipage}\;\;\; \right\}$$
}
\end{wrapfigure}

\lipsum[1]

\textbf{\lipsum[2]}
\setlength{\intextsep}{\tempintextsep}
\end{document}

• As described, this sounds odd. Please provide a minimal example (or here). – jon Sep 13 '13 at 19:40
• @jon I've fixed the issue while paring down my code to generate the MWE :) – Emily Sep 13 '13 at 19:59
• It often does! BTW, I'd watch out for spurious spaces if you use \textsf{ <text> }; it should really be \textsf{<text>}. (Perhaps you were just trying to draw attention to its use, however....) – jon Sep 13 '13 at 20:07
• @jon Indeed; this was just spurious extra space induced when I replaced the quote that will appear in my actual document. – Emily Sep 13 '13 at 20:27

• Now, try to do Text \textrm{is not text}, I can't test now but I suppose that they would come in different fonts. Wouldn't they? – yo' Sep 13 '13 at 21:21


text:
# Validity of the Adiabatic Approximation

Validity of the Adiabatic Approximation - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Descargar gratis o leer online en formato PDF el libro: Validity of the Adiabatic Approximation
We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the -standard criterion- for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.

Autor: R. MacKenzie; A. Morin-Duchesne; H. Paquette; J. Pinel

Fuente: https://archive.org/


text:
0 like 0 dislike
103 views
Solve for $x$ in $12 x^{3}-4 x^{2}-5 x=0$
| 103 views

0 like 0 dislike
$12 x^{3}-4 x^{2}-5 x=0$

start by factorizing with the common factor $x$

$x\left(12 x^{2}-4 x-5\right)=0$

Using the rule: If $a\cdot b =0$ then $a=0$ or $b=0$ or both are equal to zero.

then,

$\Rightarrow x=0$

or

$12 x^{2}-4 x-5=0$

$x=\dfrac{\pm \sqrt{b^{2}-4 a c}}{2a}$

$a=12; b=-4; c=-5$

$x= \dfrac{-(-4) \pm \sqrt{(-4)^{2}-4(12)(-5)}}{2(12)}$

$= \dfrac{4 \pm \sqrt{256}}{24}$

$= \dfrac{4 \pm 16}{24}$

$= \dfrac{ 4 \pm 2}{3}$

$\therefore x=0 \quad \text{OR} \quad x=\dfrac{4+2}{3} \quad \text{OR} \quad x=\dfrac{4-2}{3}$
by Platinum (131,378 points)
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# Validity for Use of Non-HDL Cholesterol Rather than LDL Cholesterol

• Kwon, Se-Young (Department of Biomedical Laboratory Science, Daegu Health College) ;
• Na, Young-Ak (Department of Biomedical Laboratory Science, Daegu Health College)
NonHDL cholesterol values have been suggested as a risk marker for cardiovascular disease. NonHDL cholesterol values were calculated, using a very simple measurement [nonHDL cholesterol=serum total cholesterol-HDL cholesterol]. This formula is very useful as a screening tool for identifying dyslipoproteinemias, risk assessment, and assessing the results of hypolipidemic therapy. The data from the 2009 Korean National Health and Nutrition Examination Survey were used. Analysis was done for 1,992 subjects with lipid panels (Cholesterol, HDL, LDLdirect and Triglycerides) results. We studied the relationship between nonHDL cholesterol and LDL cholesterol. As a result, nonHDL cholesterol values were plotted against the LDL direct and calculated values. The linear regression equation for nonHDL cholesterol and direct LDL cholesterol was $nonHDLchol=23.60+1.03{\times}LDLdirect$ (p<0.0001, $r^2=0.80$) in all subjects. The subjects were classified into triglyceride values. When triglycerides are below 400 mg/dL, the linear fit to LDL direct is found to be $[nonHDLchol=17.34+1.07{\times}LDLdirect]$ (p<0.0001, $r^2=0.88$) and to the Friedewald LDL calculation is $[nonHDLchol=23.10+1.02{\times}LDLcalc]$ (p<0.0001, $r^2=0.82$). For triglycerides above 400 mg/dL, the linear fit equation is $[nonHDLchol=87.57+0.92{\times}LDLdirect]$ (p<0.0001, $r^2=0.50$) and to the LDL calculated, it is $[nonHDLchol=142.70+0.50{\times}LDLcalc]$ (p<0.0001, $r^2=0.32$). This study provides examples of the utility of nonHDL cholesterol concentrations in clinical medicine.


text:
25-29 September 2017
Salamanca, Spain
Europe/Zurich timezone

Hidden-charm meson-baryon molecules with a short-range attraction from five quark states

26 Sep 2017, 19:00
2h
Auditorium Hall

Auditorium Hall

Poster Exotic states and candidates

Speaker

Yasuhiro Yamaguchi (RIKEN)

Description

The observation of the hidden-charm pentaquarks by the LHCb collaboration indicates an existence of exotic hadrons close to hidden-charm meson-baryon thresholds. In the literature, various model calculations have been performed such as the hadronic molecules and the compact multi-quark states. The observed states appear below the thresholds, and it indicates that the states are a loosely bound state of the hidden-charm meson-baryon. On the other hand, in the quark cluster model, the compact five-quark states are discussed to describe the short range part of the interaction.

In this talk, we study the hidden-charm pentaquark systems as a molecule of $\bar{D}^{(\ast)}\Lambda_{\rm c}$ and $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$ with coupling to the five-quark state ($qqqc\bar{c}$), where the three light quark part ($qqq$) is the color octet. The five-quark component is introduced as the short range potential between the meson and the baryon. The long range force is given by the one pion exchange potential (OPEP). By solving the Schr\"odinger equation, we study the bound and resonant states for $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$ with isospin $I=\frac{1}{2}$.In the charm sector, we obtain that the short range potential plays an important role to produce the states, while we obtain no state only with the OPEP. The spectrum structure is affected by the spectroscopic factor of the coupling between the five-quark and the meson-baryon components.

Co-authors

Alessandro Giachino (INFN - National Institute for Nuclear Physics) Elena Santopinto (INFN e Universita Genova (IT)) Atsushi Hosaka (Osaka University)

Presentation Materials

There are no materials yet.


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# Find $\lim_{x\to-\infty} \frac{\ln(e^x+1)}{x}$

$$\lim_{x\to-\infty} \frac{\ln(e^x+1)}{x}$$

due to Squeeze theorem and $\lim_{x\to0}\frac{\ln(1+x)}{x}=1$ we have

$$1\leftarrow\frac{\ln(e^x+1)}{e^x}\leq \frac{\ln(e^x+1)}{x}$$

what can be the upper bound of this function, or is there better solution?

• Are you sure about $-\infty$ ? – Yves Daoust Jan 11 '17 at 17:44
• I should have the inequality reversely..... – UfmdFkiF Jan 12 '17 at 0:02
• Are you sure the problem is asked with $-\infty$ ? This is unlikely. – Yves Daoust Jan 12 '17 at 7:56
• You are right @YvesDaoust. shame on me... – UfmdFkiF Jan 12 '17 at 18:36

Consider that $$\lim\limits_{x \to -\infty}\ln(e^x+1) = \ln\left(\lim\limits_{x \to -\infty} e^x + 1\right)= \ln(1) = 0$$ and $$\lim\limits_{x \to -\infty}\frac{1}{x}= 0$$ So your limit is $0$.
$$\ln(e^x+1)=x+\ln(1+e^{-x}).$$
You don't even need the Squeeze Theorem here. As $x\to-\infty$, $e^x\to0$, so the numerator in the limit turns into $\ln(0+1)=0$. Therefore, $$\lim_{x\to-\infty} \frac{\ln(e^x+1)}{x}=\frac{0}{-\infty}=0.$$
Let $x\to -\infty$. Since $\ln(e^x+1)\to\ln 1=0$ and $\frac{1}{x}\to 0$, the limit in question equals to zero.


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# Does this result exist in the literature?

Cover a table with a tablecloth, crumple it up in the middle (while still leaving the edges hanging over the edge of the table), then stab the folds with a pin. You will almost surely poke an odd number of holes in the tablecloth, because one end of the pin is above the tablecloth, the other is below, and each hole indicates one instance of the pin changing sides (the only exception is if your stab lies perfectly tangent to a fold of the tablecloth).

I suspect that this generalizes. I hope that something like this is true:

Let $X$ be a subset of $\mathbb{R}^n \times \mathbb{R}^m$ that is homeomorphic to $\mathbb{R}^n$. For any $r \in \mathbb{R}^n$, let $D(r) = \{ s \in \mathbb{R}^m | (r, s) \in X \}$. Suppose $D(r)$ is never empty for any $r \in \mathbb{R}^n$. Then $D(r)$ almost always (with respect to Lebesgue measure) has an odd number of elements.

In other words, we have crumpled an $n$-dimensional tablecloth into $m$ additional dimensions (while still leaving it hanging over the edges of our $n$-dimensional table), then stabbed it with an $m$-dimensional pin, hopefully in an odd number of places.

Is this a known result? It smells a lot like Sperner's Lemma (which contains a similar statement about oddness), but I'm not entirely sure how.

-
If you fix sufficiently precise hypotheses, this is just the fact that the algebraic intersection number depends only on the homology classes of the submanifolds being intersected. –  John Pardon Jan 22 at 23:24
This is Sard's theorem en.wikipedia.org/wiki/Sard%27s_theorem –  Anton Petrunin Jan 22 at 23:37

Of course there are results implying such things in degree theory and as @unknown (google) mentions.

Our "teaching" proof of Sperner's Lemma here http://link.springer.com/article/10.1007%2Fs00199-007-0257-0 develops this intuition for the purpose of pedagogy. So the connection between what you are talking about and Sperner's lemma is there and simply demonstrated (you'll have to do slight extra thinking in the middle of the homotopy that we construct).

In class every year I present this folding idea through a very nice story that I should have written up but have not:

Can we use maths to design an invisibility cloak for Harry Potter?

Harry Potter has an invisibility cloak made of cloth having very simple properties: It has two sides: Front and Back. We will write F|B and B|F to denote the orientation of the cloth.

• if an observer looks at the Front side, then she does not see the first object behind the cloth and only sees the second object behind it.
• if an observer looks at the back side, then she will see the first object behind the cloth (i.e., looking at it from Back side it behaves like glass).

An effective cloak is one in which no one looking at Harry can see Harry but Harry can see everything in front of him.

A. So consider this

                 Severus-Snape       F|B Harry B|F      Draco-Malfoy

Professor Snape sees Draco and Draco sees Snape. Harry is invisible and can see both Draco and Snape.

B. But consider this material with one fold

                 Severus-Snape       F|B Harry B|F B|F      Draco-Malfoy

Draco-Malfoy sees Harry and Severus-Snape sees Draco. Bloody-hell as Ron would say, not only is Harry visible but Snape and Malfoy have figured out that he has an invisibility cloak on.

C. Similarly consider this material with one fold

                 Severus-Snape       F|B Harry B|F F|B      Draco-Malfoy

Draco-Malfoy sees Severus-Snape but Severus-Snape does not see Draco. Snape and Malfoy have figured out that an invisibility cloak is being used. Also Harry cannot see Draco; disaster.

So how can we design an invisibility cloak that makes sure that Harry is not found out even if he runs and that he can also see what's in front of him? Use degree theory, of course, (and thus fixed point theory is important).

Put the cloth around Harry from head to toe as follows

F|B Harry B|F

make sure there are no folds initially. Sew the cloak so that there are no holes in it whatsoever.

If the cloth is folding without ripping (i.e., Harry uses it in the way it is designed) all folds will be of the following form

          Harry B|F F|B B|F     Draco-Malfoy

Odd numbered and if we let B|F be of orientation +1 and denote by -1 the orientation F|B we see any fold configuration will have +1 as the sum of the orientations of the folds. In particular, Harry is never found out and Harry can see Draco.

A clever student always asks about the seam line of the folds. Well by Sard's theorem you cannot see those.

-
Very cool answer! –  Johannes Hahn Jan 23 at 15:26


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# Windows – way to parse arguments into a batch script

batchcommand linewindows

I have found a very useful script here that will parse in arguments to a batch file and process them as follows:

BatchFile.btm /a /b:22 /longopt Parm1 Parm2 /quotedArg:"long quoted arg"
- OPTION_a will equal 1.
- OPTION_b will equal 22
- OPTION_quotedArg will equal "long quoted arg"
- OPTION_longopt will eqal 1.
- PARAM_1 will equal Parm1
- PARAM_2 will equal Parm2
- PARAM_0 will be set to the number of parms, so 2 in this case

However, this script is written for .btm files and doesn't seem to be suitable for the DOS emulator or more recent versions of Windows. Can anyone translate this or know where to find an up-to-date equivalent that will work in DOS emulator in Win7/Svr2003?

I have managed to translate the majority of this script to work in a Windows 7 batch file. I have not tested this against any other version of Windows.

This program scans the command line sent to it and sets various environment variables that coorespond to the settings.

It sets an OPTION_arg variable for each arg on the command line. If a switch, the env var is set to 1. If a value is given via the colon sign, it's set to that value. Note, there can not be any white space around the : [Modification] This modified script also cannot handle option or parameter values containing spaces, even when encased in parenthesis. [/Modification]

Use If defined OPTION_arg or if /i "%OPTION_arg%"=="value" to test for options

It also sets a parameter variable for each paramater entered: PARAM_1 to PARAM_n and PARAM_0 is a special value that contains the number of PARAMs. Useful for looping through all of them. For example for /l (1,1,%PARAM_0%) do ...

In your batch file call getopt as call GetOpt.bat %*

I also recommend setting setlocal and endlocal in the host batch file so that the option and param variables do not stick around after the host batch files exits.

Example usage:  HostBatchFile.bat /a /b:22 /longopt Parm1 Parm2
OPTION_a will equal 1.
OPTION_b will equal 22
OPTION_longopt will eqal 1.
PARAM_1 will equal Parm1
PARAM_2 will equal Parm2
PARAM_0 will be set to the number of parms, so 2 in this case

The parts I have not translated are:

1. Incorporating any kind of DEBUG flag for screen output
2. Being able to handle "strings with spaces" for either options or parameters as the initial separation of arguments fed in are split using <SPACE>

Here is the translated script.

@echo off
cls

set getopt_ParmCounter=1
set paramc=1
set DEBUG=1

set argc=0
for %%x in (%*) do Set /A argc+=1
echo Number of arguments: %argc%
echo %*&echo.

set _myvar=%*

rem Loop through all command line arguments one at a time
:varloop
set isparam=1
for /f "tokens=1*" %%a in ('echo %_myvar%') DO (
set getopt_Parm=%%a
set _myvar=%%b
call :paramtype

rem shift along arguments and rerun loop
if NOT "%%b"=="" goto varloop
)
goto :eof

:paramtype
rem If first character starts with a - or / it must be an option
if /i "%getopt_Parm:~0,1%"=="-" call :option
if /i "%getopt_Parm:~0,1%"=="/" call :option
if /i "%isparam%"=="1" call :param
goto :eof

:option
set isparam=0
rem Set the Equal Index to the position of the colon.  0 means none was found
for /f %%j in ('findstring %getopt_Parm% :') do set getopt_EqIdx=%%j

rem If the index is GE 0 then we must have a colon in the option.
if /i "%getopt_EqIdx%"=="0" (call :nocolon) else (call :colon)
goto :eof

:colon
rem set the OPTION value to the stuff to the right of the colon
set /a getopt_ParmNameEnd=%getopt_EqIdx%-2
call set getopt_ParmName=%%getopt_Parm:~1,%getopt_ParmNameEnd%%%
call set getopt_ParmValue=%%getopt_Parm:~%getopt_EqIdx%%%
set OPTION_%getopt_ParmName%=%getopt_ParmValue%
goto :eof

:nocolon
rem This is a flag, so simply set the value to 1
set getopt_ParmName=%getopt_Parm:~1%
set getopt_ParmValue=1
set OPTION_%getopt_ParmName%=%getopt_ParmValue%
goto :eof

:param
rem There was no / or - found, therefore this must be a paramater, not an option
set PARAM_%getopt_ParmCounter%=%getopt_Parm%
set PARAM_0=%getopt_ParmCounter%
set /a getopt_ParmCounter+=1
goto :eof


text:
# What is a complex derivative

Next:10.2 Differentiable Functions on Up:10. The Derivative Previous:10. The Derivative   Index

## 10.1 Derivatives of Complex Functions

You are familiar with derivatives of functions from to , and with the motivation of the definition of derivative as the slope of the tangent to a curve. For complex functions, the geometrical motivation is missing, but the definition is formally the same as the definition for derivatives of real functions.

By the definition of limit, we can say that is differentiable at if , and is a limit point of and there exists a function such that is continuous at , and such that

 (10.2)

and in this case is equal to .

It is sometimes useful to rephrase condition (10.2) as follows: is differentiable at if , is a limit point of , and there is a function such that is continuous at , and

 (10.3)

In this case, .

Proof: Since are differentiable at , there are functions , such that , are continuous at , and

It follows that

and is continuous at .

We can let and we see is differentiable at and

Proof: The proof is left to you.

Proof: From our hypotheses, there exist functions

such that is continuous at , is continuous at and

If , then , so we can replace in (10.15) by to get

Using (10.14) to rewrite , we get

Hence we have

and is continuous at . Hence is differentiable at and

Proof: If , we saw above that is differentiable and . Let be a complex function, and let . Suppose is differentiable at , and . Then . By the chain rule is differentiable at , and

Next:10.2 Differentiable Functions on Up:10. The Derivative Previous:10. The Derivative   Index


text:
checking on me synonym

# Plot multivariable function online

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Multi-Variable Functions, Surfaces, and Contours. The graphs of surfaces in 3-space can get very intricate and complex! In this tutorial, we investigate some tools that can be used to help visualize the graph of a function f ( x, y), defined as the graph of the equation z = f ( x, y) . Try plotting. z = sin ( x y)! Example.
2020. 12. 29. · Plotting a multivariable function. Learn more about multivariable, 3d plots, surf I want to plot function f(x,y)=1/(x*y), but my code doesn't seem to work x=[-3,0.1,3]; y=[-3,0.1,3];
This is a free online function plotter that does not require installation. You are able to plot as many functions as you would like in different colors. You can zoom the plot, trace graphs, find interceptions and roots. Choose "polar" if you would like to plot a function in polar coordinates. Function y = Function Add a new function
May 20, 2015 · For a scatter plot, you can use something like fig = plt.figure () ax = fig.add_subplot (111, projection='3d') ax.scatter (xs, ys, zs) Share Follow answered May 19, 2015 at 21:12 Ami Tavory 72.8k 10 137 173 2 from mpl_toolkits.mplot3d import Axes3D makes it work – kztd Jun 13, 2017 at 17:23 Add a comment Your Answer Post Your Answer
How to plot functions of two variables in Maple


text:
# Ambient air temperature

For cables in troughs, this is the temperature of the ambient air above ground. This is taken as the inital air temperature inside the air-filled trough.

Symbol
$\theta_{air}$
Unit
$^{\circ}$C
Used in
$\alpha_{gas}$
$c_{p_{gas}}$
$\Delta \theta_{s}$
$\eta_{gas}$
$k_{gas}$
$\mathrm{Pr}_{gas}$
$\rho_{gas}$
Gas density [kg/m$^3$]
$T_{air}$
$T_{rad_{ext}}$
$\theta_{at_{0}}$
$W_{rad_{ext}}$


text:
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# A business bought r typewriters at $100 per typewriter and s  Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: Director Joined: 23 Jun 2005 Posts: 847 GMAT 1: 740 Q48 V42 Followers: 5 Kudos [?]: 38 [0], given: 1 A business bought r typewriters at$100 per typewriter and s [#permalink]  17 Oct 2006, 07:33
00:00

Difficulty:

55% (hard)

Question Stats:

48% (01:51) correct 52% (00:51) wrong based on 98 sessions
A business bought r typewriters at $100 per typewriter and s calculators at$50 per calculator. What is the total cost of the typewriters and calculators?

(1) The s calculators cost $200 (2) 2r + s = 10 [Reveal] Spoiler: OA Senior Manager Joined: 30 Aug 2006 Posts: 374 Followers: 3 Kudos [?]: 27 [0], given: 0 [#permalink] 17 Oct 2006, 07:40 C i) INS we don't know how many typewriters we bought ii) INS we don't know the relationship between r+s Using both i) tells us s =4 and therefore using ii) we can deduce r = 3 SVP Joined: 05 Jul 2006 Posts: 1516 Followers: 5 Kudos [?]: 134 [0], given: 39 [#permalink] 17 Oct 2006, 08:01 A business bought r typewriters at$100 per typewriter and s calculators at $50 per calculator. What is the total cost of the typewriters and calculators? I . The s calculators cost$200
II. 2r+s = 10

TOTAL COST

100R+50S = 50(2R+S)

FROM ONE ....INSUFF

FROM TWO

EACH 2 TYPEWRITERS AND 1 CALCULATOR = 10

THUS 100R+50S = 500

Senior Manager
Joined: 13 Sep 2006
Posts: 282
Location: New York
Followers: 1

Kudos [?]: 8 [0], given: 0

Yes - one more for B. I think C is a trap.
_________________

"Never let the fear of striking out get in your wayâ€

Manager
Joined: 04 May 2006
Posts: 173
Location: paris
Followers: 1

Kudos [?]: 11 [0], given: 0

Agree C is trap

B is enough

s= 10 -2*r
100*r+ 50*s= T

T= 100*r + 50 (10 -2*r)=500
_________________

time is not on my side

Senior Manager
Joined: 01 Oct 2006
Posts: 498
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Kudos [?]: 21 [0], given: 0

Think this is from MGMAT and the answer is B.
Director
Joined: 05 Feb 2006
Posts: 899
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Kudos [?]: 56 [0], given: 0

tennis_ball wrote:
B.

100r + 50s = 50(2r+s).

how did you get the 50(2r+s) ?

Divide 100r+50s by 50.... 50(2r+s)
Intern
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Posts: 42
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Kudos [?]: 11 [0], given: 38

Re: [#permalink]  16 Nov 2013, 09:15
yezz wrote:
A business bought r typewriters at $100 per typewriter and s calculators at$50 per calculator. What is the total cost of the typewriters and calculators?

I . The s calculators cost $200 II. 2r+s = 10 TOTAL COST 100R+50S = 50(2R+S) FROM ONE ....INSUFF FROM TWO EACH 2 TYPEWRITERS AND 1 CALCULATOR = 10 THUS 100R+50S = 500 b IS MY ANSWER For the equation 100R + 50S, we will get the total cost. The second equation is 2R + S = 10 Why are we assuming that this 10 is the cost and multiplying by 50 on both sides will get us the total cost? It could be the of the typewriters and calculators which makes choice B insufficient and C sufficient. Math Expert Joined: 02 Sep 2009 Posts: 28780 Followers: 4591 Kudos [?]: 47358 [0], given: 7121 Re: Re: [#permalink] 16 Nov 2013, 09:31 Expert's post aakrity wrote: yezz wrote: A business bought r typewriters at$100 per typewriter and s calculators at $50 per calculator. What is the total cost of the typewriters and calculators? (1) The s calculators cost$200

(2) 2r + s = 10

TOTAL COST

100R+50S = 50(2R+S)

FROM ONE ....INSUFF

FROM TWO

EACH 2 TYPEWRITERS AND 1 CALCULATOR = 10

THUS 100R+50S = 500

For the equation 100R + 50S, we will get the total cost.

The second equation is 2R + S = 10
Why are we assuming that this 10 is the cost and multiplying by 50 on both sides will get us the total cost? It could be the of the typewriters and calculators which makes choice B insufficient and C sufficient.

We need to find the value of 100r + 50s.

(2) says that 2r + s = 10 multiply by 50: 50*(2r + s) = 100r + 50s = 500. So, we have the value we wanted. Thus this statement is sufficient.
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Re: Re: [#permalink]  18 Nov 2013, 19:11
Bunuel wrote:
aakrity wrote:
yezz wrote:
A business bought r typewriters at $100 per typewriter and s calculators at$50 per calculator. What is the total cost of the typewriters and calculators?

(1) The s calculators cost $200 (2) 2r + s = 10 TOTAL COST 100R+50S = 50(2R+S) FROM ONE ....INSUFF FROM TWO EACH 2 TYPEWRITERS AND 1 CALCULATOR = 10 THUS 100R+50S = 500 b IS MY ANSWER For the equation 100R + 50S, we will get the total cost. The second equation is 2R + S = 10 Why are we assuming that this 10 is the cost and multiplying by 50 on both sides will get us the total cost? It could be the of the typewriters and calculators which makes choice B insufficient and C sufficient. We need to find the value of 100r + 50s. (2) says that 2r + s = 10 multiply by 50: 50*(2r + s) = 100r + 50s = 500. So, we have the value we wanted. Thus this statement is sufficient. Why are we multiplying the equation 2r + s by 50 ? Can we multiply it by 100 and get the same correct answer? Intern Joined: 11 May 2011 Posts: 22 Followers: 0 Kudos [?]: 14 [0], given: 1 Re: A business bought r typewriters at$100 per typewriter and s [#permalink]  19 Nov 2013, 00:02
Hello,

From the question what we need is

100r+50s=? which actually translates to 50(2r+s) = ?

Now,

Option 1:

cost of s calculator = 200
so we know each calculator is 50
hence all we know from option 1 is that we have 4 calculators
But no idea about typewriter Yet

So option 1 alone is not enough

Option 2:

2r+ s = 10

which means that this can be directly substituted into the equation we derived from the question.

50(2r+s) = 50 (10) = 500

hence option 2 alone is Sufficient

Thanks and regards,
Raghav. V
Math Expert
Joined: 02 Sep 2009
Posts: 28780
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Kudos [?]: 47358 [0], given: 7121

Re: Re: [#permalink]  19 Nov 2013, 00:25
Expert's post
mrwells2 wrote:
Bunuel wrote:
aakrity wrote:
For the equation 100R + 50S, we will get the total cost.

The second equation is 2R + S = 10
Why are we assuming that this 10 is the cost and multiplying by 50 on both sides will get us the total cost? It could be the of the typewriters and calculators which makes choice B insufficient and C sufficient.

We need to find the value of 100r + 50s.

(2) says that 2r + s = 10 multiply by 50: 50*(2r + s) = 100r + 50s = 500. So, we have the value we wanted. Thus this statement is sufficient.

Why are we multiplying the equation 2r + s by 50 ? Can we multiply it by 100 and get the same correct answer?

We need to find the value of 100r + 50s. Do you get 100r + 50s when you multiply 2r + s by 100?
_________________
Re: Re:   [#permalink] 19 Nov 2013, 00:25
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# Find the value of the equation:$$\frac{(496 + 54)^2 - (496 - 54)^2}{2(496 \times54)}$$

This question was previously asked in
RRC Group D Previous Paper 62 (Held On: 9 Oct 2018 Shift 1)
View all RRB Group D Papers >
1. –2
2. 2
3. 1
4. –1

Option 2 : 2

## Detailed Solution

Given:

$$\frac{(496 + 54)^2 - (496 - 54)^2}{2(496 \times54)}$$

Concept used:

(a + b)2 - (a - b)2 = 4ab

Calculation:

$$\frac{(496 + 54)^2 - (496 - 54)^2}{2(496 \times54)}$$

Let 496 be a and 54 be b

So,

[(a + b)2 - (a - b)2]/2ab

⇒ 4ab/2ab

⇒ 2

∴ The Required answer is 2