text stringlengths 256 16.4k |
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One quick way to think about it is that
you're transposing the entire problem. Imagine placing the primal coefficients in a matrix, with the objective at the bottom. This gives $P = \begin{bmatrix} 1 & -6 & 2 \\ 5 & 7 & -4 \\ 8 & 3 & \end{bmatrix}$. Transposing yields $P^T = D = \begin{bmatrix} 1 & 5 & 8 \\ -6 & 7 & 3 ... |
410 0 [SOLVED] Baker, Campbell, Hausdorff and all that
I'm posting this here because, although it is a mathematics problem, it is related to perturbation theory and is the kind of problem physicists might be more skilled at answering.
Does anyone know an elegant proof of
[tex]e^{A+B} = \int_0^1 d\alpha_1 \,\delta(1-\al... |
Category:Dark Energy
The observed accelerated expansion of the Universe requires either modification of General Relativity or existence within the framework of the latter of a smooth energy component with negative pressure, called the
dark energy. This component is usually described with the help of the state equation ... |
I will just expand a little on what doraemonpaul posted, as I do think that post is useful for most real-world reasons to ask this type of question.
Write
$$f(x) = \sum_{j=0}^{\infty} f_j x^j$$
(and similarly$g(x) = \sum_{j=0}^{\infty} g_j x^j$).
Then we know that
$$f'(x) = \sum_{j=0}^{\infty} (j+1) f_{j+1} x^j$$
$$(f'... |
Geometric Mean
Here we will learn all the
Geometric Mean Formula With Example. The Geometric Mean is n th root of the product of n quantities of the series. It is observed by multiplying the values of items together and extracting the root of the product corresponding to the number of items. Thus, the square root of th... |
Let $u$ be a continuous utility function on $\mathbb R^2_+\setminus\{0\}$. Consider the following three conditions:
Local non satiationsays that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) < U(y)$. Local non satiation* says that for any $x \in X$ and $\epsilon > ... |
Let $\phi: R \to R'$ be a ring isomorphism and $I$ an ideal of $R$. Define $\phi(I)=\{\phi(i): i \in I\}$.
Show that $\frac RI \cong \frac {R'}{\phi(I)}$.
To use the first isomorphism theorem, I was trying to show that the kernel of $\pi \circ \phi$ was $I$, where $\pi: R'\to \frac {R'}{\phi(I)}$. It seems to me this f... |
The two questions are as follow and the image attached shows all my steps towards attempting to solve them:
a) $1+ \log y = \log (y+3)$: I am missing something since my steps do not make sense. IF I collect the $\log y$ terms, they cancel each other out when I bring it to the other side to isolate for $y$.
b)$\log_2 (x... |
I have the following problems on my Statistics course (using Casella and Berger's book) problem set:
1) Let $Y_{i} = X_{i}'\theta + U_{i}$ where $\theta \in \mathbb{R}^k$ and $U_{i}$ are iid $N(0, \sigma^2)$ random variables and $X_{i}$ is a fixed vector for each $i$. Find the minimal sufficient statistic when $\sigma^... |
Current browse context:
physics.soc-ph
Change to browse by: References & Citations Bookmark(what is this?) Physics > Physics and Society Title: The role of voting intention in public opinion polarization
(Submitted on 16 Sep 2019)
Abstract: We introduce and study a simple model for the dynamics of voting intention in a... |
Abbreviation:
ComBCK
A
is a structure $\mathbf{A}=\langle A,\cdot ,0\rangle$ of type $\langle 2,0\rangle$ such that commutative BCK-algebra
(1): $((x\cdot y)\cdot (x\cdot z))\cdot (z\cdot y) = 0$
(2): $x\cdot 0 = x$
(3): $0\cdot x = 0$
(4): $x\cdot y=y\cdot x= 0 \Longrightarrow x=y$
(5): $x\cdot (x\cdot y) = y\cdot (y\... |
All quantum operators must be unitary. Unitary means the conjugate-transpose of the operator is its inverse. In your case:
$UU^{\dagger} = \begin{bmatrix}1 & 0 & 0 & 0\\0 & 1 & 1 & 0\\0 & 0 & 0 & 0\\0 & 0 & 0 & 0\end{bmatrix}\begin{bmatrix}1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 0 & 0\end{bmatrix} =\begin{... |
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Now showing items 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
Abbreviation:
CRPoMon
A
is a residuated partially ordered monoid $\mathbf{A}=\langle A, \cdot, 1, \to, \le\rangle$ such that commutative residuated partially ordered monoid
$\cdot$ is
: $xy=yx$ commutative
Remark: This is a template. If you know something about this class, click on the ``Edit text of this page'' link a... |
Brezis Pseudomonotonicity is Strictly Weaker than Ky–Fan Hemicontinuity 528 Downloads Abstract
In 1968, H. Brezis introduced a notion of operator pseudomonotonicity which provides a unified approach to monotone and nonmonotone variational inequalities. A closely related notion is that of Ky–Fan hemicontinuity, a contin... |
Abbreviation:
Gph
A
is a structure $\mathbf{G}=\langle G, E\rangle$ such that graph
$G$ is a set,
$E$ is a binary relation on $G$: $E\subseteq G\times G$, and
$E$ is symmetric: $xEy\Longrightarrow yEx$
Remark: This is a template. If you know something about this class, click on the 'Edit text of this page' link at the ... |
Suppose that $L$ is a regular language and $0<\alpha<1$ and $\alpha \in Q$. Define $L_\alpha$ as
$$L_\alpha = \{\omega \in \Sigma^* \mid \exists \omega_1 \in \Sigma^* .\omega\omega_1 \in L,\frac{|\omega|}{|\omega\omega_1|}=\alpha\}$$
How do I prove that $L_\alpha$ is regular?
Here is my attempt. If we assume that $D$ i... |
If $x>0$, find the set of all values of $x$ such that series is convergent$$\sum_{n=1}^{\infty} x^{\ln{n}}$$
My attempt:- I used Ratio test for finding the set of all values of $x$ such that series is convergent.
$$\lim_{x\to\infty}\frac{x^{\ln{n+1}}}{x^{\ln{n}}}$$
$$=\lim_{x\to\infty}x^{\ln\frac{n+1}{n}}$$ This quanti... |
How would you go about solving integral of a floor? The particular problem I have is:
$$\int \,\left\lfloor\frac{1}{x}\right\rfloor\, dx$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join... |
I am reading Sec. 1.12 of the Cosmology book by Weinberg.
In this section he explains the very simple model of quintessence which attempts to provide a dynamical explanation of the smallness of the cosmological constant today.
He considers an example of a time-dependent but space-independent scalar field in a space wit... |
Initial problem solving strategy formulation and strategy review midway are the key steps
Some problems look difficult, but if you have a clear strategy of dealing with this type of problems, and is ready to change track by reevaluating the strategy midway, chances are high that you will reach the efficient solution in... |
The intrinsic parameters of a camera allow us to map a point in the 3D scene, as measured relative to the camera (in the camera coordinate system), to the 2D location of the pixel it activates on the camera image plane. You can go the other way too, i.e. use the intrinsic parameters to get the 3D coordinates of a point... |
Let $Y_1,Y_2,...,$ be independent $C(0,1)$ random variables, determine the limit distribution of :
$Z_n = \dfrac{1}{n} \cdot max\{Y_1, Y_2,..Y_n \} $ as $n \rightarrow \infty $,
Here is my approach:
$F_{Z_n} (x) = \mathbb{P}(Z_n \leq x) = \mathbb{P}(\dfrac{1}{n} max\{ Y_1,Y_2,...Y_n \} \leq x ) = \mathbb{P}( Y_1 \leq x... |
Most tutorials about digital currencies (like BitCoin) say that a hash function is a cryptographic function that takes an input and always return a binary string of length $256$ such that a small change in the input would result in a totally different hash.
Obviously, in the simplest interpretation, the hash function m... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
Prove: If $|x+y|<|x|+|y|$, then $x<0$ or $y<0$
This looks as though it's true from the start. Take $x=-4, y=4$.
$|-4+4|<|-4|+|4|$
$0<8$ is true.
The question is asking for a proof by contradiction or contrapositive. Which means I am going to negate some part of the ending in order to find a contradiction in the hypothe... |
DEFINITION - EXPONENTS
Exponents and Roots: Tips and hints
Exponents are a "shortcut" method of showing a number that was multiplied by itself several times. For instance, number \(a\) multiplied \(n\) times can be written as \(a^n\), where \(a\) represents the base, the number that is multiplied by itself \(n\) times ... |
I made a cardinal property as follows
Let $\kappa$ be $\lambda$-Monotonous iff: $$\forall S\in\mathcal{P}_{=\lambda}(\mathrm{V})\forall T\in\mathcal{P}_{=\kappa}(\mathrm{V})(S\subseteq T\rightarrow (S,\in)\prec (T,\in))$$ The intuition behind this is that many $S$ of cardinality $\lambda$ are too similar to tell apart ... |
I would like to show Pillai's lower bound. Here we use $ \varphi^*(n) $ to denote $ \Phi(n) $ because of the famous log-star function ($ \log^* $) in complexity.
To get started, we need a special variety of Euler's totient function $ \hat\varphi $, which is $\varphi$ without considering 2, namely $ \hat \varphi(x):=\be... |
Global Modeling of a Non-Maxwellian Discharge in COMSOL®
Global modeling of plasmas is a powerful approach to study large chemistry sets. In these models, the reactions are represented by rate coefficients. In particular, the rate coefficients of electron impact collisions depend on the electron energy distribution fun... |
Congruence Modulo 3 of Power of 2 Theorem
Let $n \in \Z_{\ge 0}$ be a positive integer.
Then:
$2^n \equiv \paren {-1}^n \pmod 3$
That is:
$\exists q \in \Z: 2^n = 3 q + \paren {-1}^n$ Proof
The proof proceeds by induction.
For all $n \in \Z_{\ge 0}$, let $\map P n$ be the proposition:
$2^n \equiv \paren {-1}^n \pmod 3$... |
Abbreviation:
MA
A
is a structure $\mathbf{A}=\langle A,\vee,0,\wedge,1,\neg,\diamond\rangle$ such that modal algebra
$\langle A,\vee,0, \wedge,1,\neg\rangle $ is a Boolean algebras
$\diamond$ is
: $\diamond(x\vee y)=\diamond x\vee \diamond y$ join-preserving
$\diamond$ is
: $\diamond 0=0$ normal
Remark: Modal algebras... |
Natural number The numbers which are generally used in our day to day life for counting are termed as natural numbers. They are also referred to as "counting" numbers , N = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 {\displaystyle \mathbb {N} =0,1,2,3,4,5,6,7,8,9} Even number Number divides by 2 without remainder . Even num... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (22) (remove)
301
We extend the methods of geometric invariant theory to actions of non reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non recutive. Given a linearization of the na... |
The classic middle-thirds Cantor set can be generalized to a middle-$\alpha$-th Cantor set, for $0<\alpha<1$. It can be formed by removing the open middle $\alpha$-th from the unit interval, and continuing to remove the middle $\alpha$-th from each of the remaining intervals ad infinitum.
It can be shown by induction t... |
Abbreviation:
ApGrp
An
is a $p$-group $\mathbf{A}=\langle A, +, -, 0\rangle$ such that Abelian $p$-group
$\cdot$ is
: $x+y=y+x$ commutative
Remark: This is a template. If you know something about this class, click on the 'Edit text of this page' link at the bottom and fill out this page.
It is not unusual to give sever... |
Please read this introduction first before looking through the solutions. Here’s a quick index to all the problems in this section.
Composing two general euclidean transformations, we get a transformation of the form below. $$\begin{pmatrix} a_{11}b_{11} - a_{12}b_{12}k & a_{12}b_{11}k + a_{11}b_{12} & a_{12}b_{23}k + ... |
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Posets help us talk about resources: the partial ordering \(x \le y\) says when you can use one resource to get another. Monoidal posets let us combine or 'add' two resources \(x\) and \(y\) to get a resource \(x \otimes y\). But cl... |
We consider the inverse problem of finding the volatility σ∈Lρ(0, T) such that \(U_{BS}(X,K,r,t,{{\int }_{0}^{t}}\sigma ^{2}(\tau )d\tau )=u(t)\), 0≤t≤T, where UBS is the Black–Scholes formula and u(t) is the observable fair price of an European call option. The problem is ill-posed. Using the residual method, we shall... |
Let $(X_{n},d_{n})_{n \in \mathbb{N}}$ be a sequence of complete geodesic metric spaces such that:
$X_{n}$ is a regular$^1$ CW-complex of constant local dimension$^3$ $n$, it is of finite type$^4$, boundaryless$^2$, unbounded, uniform$^5$, and it is the $n$-skeleton of $X_{n+1}$, which is n-connected. Moreover, the dis... |
Mapping/Examples/x^2 + y^2 = 1 $R_1 = \set {\tuple {x, y} \in \R \times \R: x^2 + y^2 = 1}$
Then $R_1$ is not a mapping.
Proof
$R_1$ fails to be a mapping for the following reasons:
$(1): \quad$ For $x < -1$ and $x > 1$, there exists no $y \in \R$ such that $x^2 + y^2 = 1$.
Thus $R_1$ fails to be left-total.
$(2): \qua... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
I proved the following sieve result and - since the proof is quite long and I need to use it in a work - I am looking for a reference to it (or at least something from which it could be proved quickly). Thank you in advance for any suggestion.
Lemma. For each prime number $p$, let $\Omega_p \subsetneq \{0,1,\ldots,p-1\... |
Given the comments below, I reformed my questions with more background information and simulation/examples. My question also includes the validity of the method in theory. Please correct me if any statement is not accurate.
Background: 1) For our client (policy makers), it is often interesting for them to check whether... |
Angle Addition Formulas from Euler's Formula
Introduction
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT), but only indirectly. The main intent is to get someone who is uncomfortable with complex numbers a little more used to them and relate them back to already known... |
Four Ways to Compute an Inverse FFT Using the Forward FFT Algorithm
If you need to compute inverse fast Fourier transforms (inverse FFTs) but you only have forward FFT software (or forward FFT FPGA cores) available to you, below are four ways to solve your problem.
$$ Forward \ FFT \rightarrow X(m) = \sum_{n=0}^{N-1} x... |
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Now showing items 1-1 of 1
Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Didn't there used to be a list of said self-complementary rules on the wiki?Apple Bottom wrote:Rules that are their own black/white reversal? According to the wiki, 512.gameoflifemaniac wrote:Related: how many two-state black-white reversal rules are there (rules like Day & Night)?
For general discussion about Conway's... |
I need to design a circuit that implements the following transfer function:
\$G(s)= G\frac{s+z}{s+p}\$
where, G = gain, p = pole and z = zero.
Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. It only takes a minute t... |
Given a probability space $(\Omega, \Sigma, \pi)$, a measurable space $(X, \chi)$ and a measurable function $f : \Omega \rightarrow X$.
We can define a regular conditional probability $v(x, A)$, such that for all $A \in \Sigma$ and all $C \in \chi$,
$\int_C v(x, A) \pi(f^{-1}(dx)) = \pi(A \cap f^{-1}(C))$.
Let $g$ be a... |
I have been asked this question by school kids, colleagues and family (usually less formally):
When ascending a flight of stairs, you exchange mechanical work to attain potential energy ($W_{ascend} = E_{pot} = m \cdot g \cdot h$).
However, when descending, you have to exert an equivalent force to stop yourself from ac... |
Given any solution to PCA, a sign-flipped version of it is an equally valid solution. A numerical solver breaks this symmetry by finding one of these equally valid solutions. Implementation details and initial conditions determine which solution the solver will produce.
One way to think about PCA is that it maximizes t... |
Difference between revisions of "Quantum mechanics"
(Added stuff about probability)
(Adjusted spacing and fixed formula)
Line 35: Line 35:
Collapsing of the wave function is by no means magic. In can be intuitively understood as this: You find a particle at a particular spot; if you look again immediately, it's still i... |
[Image source] kfrom a large dataset of some unknown size n. The hidden assumption here is that nis large enough that the whole dataset does not fit into main memory, whereas the desired sample does.
Let's first review how this problem is tackled in a
sequentialsetting - then we'll proceed with a distributed map-reduce... |
#
1
Problem with understanding the proof of Sauer Lemma
I will replicate the proof here which is from the book "Learning from Data"
Sauer Lemma:
$B(N,K) \leq \sum_{i=0}^{k-1}{n\choose i}$
Proof:
The statement is true whenever k = 1 or N = 1 by inspection. The proof is by induction on N. Assume the statement is true for... |
I am trying to understand singular value decomposition. I get the general definition and how to solve for the singular values of form the SVD of a given matrix however, I came across the following problem and realized that I did not fully understand how SVD works:
Let $0\ne u\in \mathbb{R}^{m}$. Determine an SVD for th... |
Abbreviation:
GEAlg
A
is a separation algebra that is generalized effect algebra : $x\cdot y=e$ implies $x=e=y$. positive
A
is of the form $\langle A,+,0\rangle$ where $+:A^2\to A\cup\{*\}$ is a partial operation such that generalized effect algebra
$+$ is
: $x+y\ne *$ implies $x+y=y+x$ commutative
$+$ is
: $x+y\ne *$ ... |
Abbreviation:
Grp
A
is a structure $\mathbf{G}=\langle G,\cdot,^{-1},e\rangle $, where $\cdot $ is an infix binary operation, calledthe group , $^{-1}$ is a postfix unary operation, called the group product and $e$ is a constant (nullary operation), called the group inverse , such that identity element
$\cdot $ is asso... |
Please read this introduction first before looking through the solutions. Here’s a quick index to all the problems in this section.
1. Prove Theorem 4 by showing that the determination of the required collineation is equivalent to solving a system of 12 homogeneous linear equations in 13 variables when the rank of the ... |
I think this is my first research-level question, so I'm going to ask it here first before going to Math Overflow.
In most tutorial papers like Burges, the Vapnik-Chervonenkis dimension is introduced as a way of bounding the expected error of a learning machine by the sum of its training error and a slightly more compl... |
In many texts, the non-relativistic (Newtonian) kinetic energy formula $$\text{KE}_\text{Newton} =\frac{1}{2}mv^2$$ is referred to as a first order approximation of the relativistic kinetic energy $$\text{KE}_\text{relativistic} = \gamma mc^2 - mc^2$$ The same is also said of the classical momentum formula in relation ... |
I am trying to find the distribution of a random variable that is calculated according to $Y:=\sum_{i=1}^n X_i^2$ where $X_i $ is distributed as $ \mathcal{N}(0,\sigma^2_i)$. Does there exist a particular of calculating this?
Thank you so much!
Cross Validated is a question and answer site for people interested in stat... |
I am trying to solve a real-world problem that I was able to reduce to the problem described below. I would like to know the following things:
Is there literature about this problem? Is the corresponding decision problem NP-complete? Do you know an efficient algorithm to solve the problem? If not, what would be a good ... |
The $\mathbb{Z_5}$-vector space $\mathfrak{B}$ 3 over the field $(\mathbb{Z_5}, +, .)$ $\mathfrak{B}$ 3over the field $(\mathbb{Z_5}, +, .)$ 1. BackgroundThis is a formal introduction to the genetic code $\mathbb{Z_5}$-vector space $\mathfrak{B}^3$ over the field $(\mathbb{Z_5}, +, .)$. This mathematical model is defin... |
It's obvious many times why one prefers an unbiased estimator. But, are there any circumstances under which we might actually prefer a biased estimator over an unbiased one?
Yes. Often it is the case that we are interested in minimizing the mean squared error, which can be decomposed into variance + bias squared. This ... |
Abbreviation:
SchrCat
A
is an enriched category $\mathbf{C}=\langle C,\circ,\text{dom},\text{cod}\rangle$ Schroeder category
in which every hom-set is a Boolean algebras.
Let $\mathbf{C}$ and $\mathbf{D}$ be Schroeder categories. A morphism from $\mathbf{C}$ to $\mathbf{D}$ is a function $h:C\rightarrow D$ that is a
: ... |
> **Conjecture.** Any functor \\( F: \mathbf{Set} \to \mathbf{N}\\) must send every morphism in \\(\textbf{Set}\\) to the identity morphism.
I argue this conjecture is *false*
This might be true for functions in traditional ZF set theory.
However, category theorists define morphisms on \\(\mathbf{Set}\\) a little diffe... |
Abbreviation:
FL$_c$
A
is an FL-algebra $\mathbf{A}=\langle A, \vee, \wedge, \cdot, 1, \backslash, /, 0\rangle$ such that FL$_c$-algebra
$\cdot$ is
: $x\le x\cdot x$ contractive
Remark: This is a template. If you know something about this class, click on the 'Edit text of this page' link at the bottom and fill out this... |
Abbreviation:
OMonZ
An
is of the form $\mathbf{A}=\langle A,\cdot,1,0,\le\rangle$ such that $\mathbf{A}=\langle A,\cdot,1,\le\rangle$ is an ordered monoid and ordered monoid with zero
$0$ is a
: $x\cdot 0 = 0$ and $0\cdot x = 0$ zero
Let $\mathbf{A}$ and $\mathbf{B}$ be ordered monoids. A morphism from $\mathbf{A}$ to ... |
Average of an observable is
where \(\rho\) is the “probability matrix”. In QM, this is
If a system of QM comes to equilibrium, that means
\(\rho = \frac{ e^{-\beta H} }{\mathrm{Tr} e^{-\beta H} }\);
\(\rho\) is diagonal in energy eigen space.
As we already know, from math of classical statistical mechanics, free energy... |
Search for chargino and neutralino production at \(\sqrt{s} = 189\) GeV at LEP 45 Downloads Abstract.
A search for charginos and neutralinos, predicted by supersymmetric theories, is performed using a data sample of 182.1 pb\(^{-1}\) taken at a centre-of-mass energy of 189 GeV with the OPAL detector at LEP. No evidence... |
Category:Dark Energy
The observed accelerated expansion of the Universe requires either modification of General Relativity or existence within the framework of the latter of a smooth energy component with negative pressure, called the
dark energy. This component is usually described with the help of the state equation ... |
I was looking at my teacher's notes and came about the following recurrence equation :
$$T(n) = \begin{cases} 1 &\quad\text{if } n\leq 1\\ 4T\left(\frac{n}{2}\right) + n^3 &\quad\text{if } n\gt1 \\ \end{cases}$$
In order to solve it I proceeded as follows : $$ T(n) = n^3 + 4T\left(\frac{n}{2}\right) = n^3 + 4\big( 4T\l... |
The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically continuing" this result in the number of dimensions $d$. I don't understand how this could possibly work conceptually, because a ... |
I've just learned about the density operator, and it seems like a fantastic way to represent the branching nature of measurement as simple algebraic manipulation. Unfortunately, I can't quite figure out how to do that.
Consider a simple example: the state $|+\rangle$, which we will measure in the classical basis (so wi... |
5. Series 30. Year Post deadline: - Upload deadline: -
(3 points)1. space snowman
Consider a snowman consisting of 3 homogeneous spheres of density $ρ$ with centres on a line, floating in free space. The smallest sphere (the head) has radius $r$ and each consecutive sphere has twice the radius of the previous one. Our ... |
Let's suppose t be in the inverval $(-\pi, \pi]$ and that $n$ is a natural number. What is $(\cos t + i\sin t )^{\frac 1n}$? Using Euler's formula would give us the following:
$(\cos t + i\sin t )^{\frac 1n}=$
$(e^{it})^{\frac 1n}=$
$e^{it\times \frac 1n} = $
$e^{\frac{it}{n}} = $
$\cos \frac 1n + i\sin \frac 1n$.
Howe... |
In R, if I write
lm(a ~ b + c + b*c)
would this still be a linear regression?
How to do other kinds of regression in R? I would appreciate any recommendation for textbooks or tutorials?
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and d... |
6. Series 30. Year Post deadline: - Upload deadline: -
(3 points)1. heavy guns
Two machine guns, that are able to shoot bullets of mass $m=25g$ and speed $v_{1}=500\;\mathrm{m}\cdot \mathrm{s}^{-1}$ with at 10 rounds per second, are attached to the front of a car. The car accelerates on a flat surface to a speed $v_{2}... |
For anyone who happens upon this question and doesn't understand, like I did, I would like to elaborate on exactly what
I specifically was missing in my understanding.
When I posted this question, I didn't know what people meant when they said $\sum_{n=1}^\infty n = -1/12$. Now that I'm older and a bit more experienced... |
It is well known that, given a sphere, the maximum number of identical spheres that we can pack around it is exactly 12, corresponding to a face centered cubic or hexagonal close packed lattice.
My question is: given a sphere of radius $R$, how many spheres of radius $r<R$ can we closely pack around it?
With disks, the... |
Let's write your integral as $\DeclareMathOperator{re}{Re}$
$$\int_{-\infty}^{\infty} f(t) e^{kg(t)}\,dt,$$
where
$$f(t) = \frac{1}{1+t^2} \qquad \text{and} \qquad g(t) = \frac{i}{5}t^5 + it.$$
The lay of the land.
The critical points of the exponent function $g$ occur at $t = e^{i\pi (2k+1)/4}$, $k=0,1,2,3$.
Here's a ... |
My answer will be shamelessly Newtonian and Physics 101 in formulation. To start off the assumptions, I'm going to assume the air has no mass. To what extent is this valid? Air has about 1000x the density of other materials like rock and concrete, so we're looking at about that same volume ratio before the air mass bec... |
ISSN:
1930-8337
eISSN:
1930-8345
All Issues
Inverse Problems & Imaging
August 2015 , Volume 9 , Issue 3
Select all articles
Export/Reference:
Abstract:
We present a new qualitative imaging method capable of selecting defects in complex and unknown background from differential measurements of farfield operators: i.e. fa... |
matplotlib.tri¶
Unstructured triangular grid functions.
matplotlib.tri.
Triangulation(
An unstructured triangular grid consisting of npoints points and ntri triangles. The triangles can either be specified by the user or automatically generated using a Delaunay triangulation.
Parameters:
Notes
For a Triangulation to be... |
I'm going through old exams for my Calc III course and came across a problem that I did not know how to do. The problem is:
Find the interval of convergence of the series
$\sum_{n=0}^{\infty}\frac{(x-2)^{n^2}}{2n+1}$
and determine whether the series converges absolutely or conditionally at the endpoints.
I can't think ... |
Question:
An electron and positron are moving in opposite directions, and are in the spin singlet state. Two Stern-Gerlach machines are orientated in some arbitrary direction; one along unit vector $\hat{s}_1$ (which measures the electron's position) and one along unit vector $\hat{s}_2$ (which measure's the positron's... |
Bulletin of the American Physical Society 16th APS Topical Conference on Shock Compression of Condensed Matter Volume 54, Number 8 Sunday–Friday, June 28–July 3 2009; Nashville, Tennessee
Session B5: ID-1: Shock Response of Aluminum Hide Abstracts Chair: Eric Herbold, Georgia Institute of Technology
Room:
Magnolia Ball... |
Does Reed-Muller codes $\mathrm{RM}(r,m)$ exist for $r = 0$ and $m = 0$? Namely, does $\mathrm{RM}(0,0)$ exist? Some books mention that $m$ should be a natural number whereas some books mention that it can be a whole number including $0$, for example Shu Lin and Daniel Costello Error Control Coding book.
The codewords ... |
I have found an example in following book and my answer is a modified version of the Sec 8.4,8.6 of the book in order to make it concise and clear.
Gerber, Hans U. "Life insurance." Life Insurance Mathematics. Springer Berlin Heidelberg, 1990.
$B_1,\cdots B_n$ are arbitrary events. $N$ is a random variable ranging over... |
Answer
The number of different ways to choose and rank the three best movies is 6840.
Work Step by Step
We need to choose 3 movies from a list of 20 movies. The order in which the movies are chosen matters because the movies should be selected according to preference. Therefore, we need to find the number of permutatio... |
Sukalpa Biswas
☆
India,
2019-08-06 09:15
(edited by Sukalpa Biswas on 2019-08-07 09:07)
Posting: # 20475
Views: 632
This is regarding NTI drug Bio equivalence study Statistical approach.
As per regulatory,
Observations during study:
All the above criteria has been met except 90% confidence interval for the test-to-refe... |
Institute of Reproducing Kernels
Kawauchi-cho, 5-1648-16,
Kiryu 376-0041, Japan
February 2, 2018
The Institute of Reproducing Kernels is dealing with the theory of division by zero calculus and declares that the division by zero was discovered as $0/0 =1/0 = z/0 = 0$ in a natural sense on 2014.2.2. The result shows a n... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
I must simplify $\log_4 (9) + \log_2 (3)$. I have tried but I can't get the correct answer $2 \log_2 (3)$. How do I proceed?
The good way is to use calculus's answer.
Another way (I am lazy and I hate bases !) is to convert everything to natural logarithms. So, $$ \log_2 (3)+\log_4 (9) =\frac{\log (3)}{\log (2)}+\frac{... |
This question already has an answer here:
Let $a_{n+1} = \sin{a_n}$ and $a_0 = 1$. Does the series $\displaystyle \sum_{i=0}^\infty a_i$ converge?
Here is my solution.
Let's prove by induction, that $a_n > \frac{1}{n}$.
We see that $\sin{(1)} > \frac{1}{2}$.
Suppose, that $a_n > \frac{1}{n}$. Then:
$$\underbrace{\sin{\... |
I am a newbie on topological space and self-studying general topology when I read this pdf. I find some discrepancy on my proof and the author's proof.
Here is my problem:
If $\{A_i | i \in J\}$, is a collection of connected subspaces of a space X with $\bigcap A_i \neq \emptyset $, then $\bigcup A_i$ is connected.
My ... |
Is there a "simple" mathematical proof that is fully understandable by a 1st year university student that impressed you because it is beautiful?
closed as primarily opinion-based by Daniel W. Farlow, Najib Idrissi, user91500, LutzL, Jonas Meyer Apr 7 '15 at 3:40
Many good questions generate some degree of opinion based... |
I thought that for momentum integrals in Minkowski space, the Wick rotation to Euclidean space $k_0 \to ik_0$ allows one to write (let's say $f$ comes with an $i\epsilon$ prescription):
$$\int_{\mathbb{M}^4} d^4k \ f(k^2) = i \int_{\mathbb{E}^4} d^4k \ f(-k^2) = 2\pi^2i\int_0^\infty dk \ k^3 f(-k^2).$$
Sorry if the not... |
Luzin's theorem says:
(1) Suppose $X$ is a $\sigma$-compact metric space, $\mu$ is a complete Radon measure on $X$, and $f\in\mathcal L_0(X,\mu, E)$. Then for every measurable set $A$ with finite measure and every $\epsilon>0$ there is a compact $K\subset X$ such that $\mu(A\setminus K)<\epsilon$ and $f|_K\in C(K,E)$.
... |
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