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Third post of our series on classification from scratch, following the previous post introducing smoothing techniques, with (b)-splines. Consider here kernel based techniques. Note that here, we do not use the “logistic” model… it is purely non-parametric.
kernel based estimated, from scratch
I like kernels because the... |
I wanted to check following possibility .
I have $$ A=\left [\begin{matrix} a & b \\ c & d\\ \end{matrix} \right] $$ Now I wanted to find Polynomial such that $$ f(A)=\left [\begin{matrix} 0 & -1 \\ 1 & 0\\ \end{matrix} \right] $$. Is this always possible? I had done some calculatution but I did not get. Any Help will ... |
I am working on 2D Liouville field theory and trying to follow mostly Harold Erbin's note on 2d quantum gravity and Liouville theory.
I have a really simple question:
One consider the Euclidean Liouville action which is given by
$S_L = \frac{1}{4\pi}\int d^2\sigma\sqrt{h}\left(h^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}... |
Suppose $a,b \in GL(n,\mathbb{C})$, and $\langle a,b\rangle$ is a free group of rank $2$.
Is there a way to choose a $c$ to guarantee that $\langle a,b,c\rangle$ is a free group of rank $3$?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related field... |
Let $B \subset \mathbb R^2$ be the unit ball and $T>0.$ Let $u \in W^{2,1}_p(B \times [0,T]),$ that is $u \in L^p(B \times [0,T])$ and we also have, $$ \partial_t u, \nabla u, \nabla^2 u \in L^p(B \times [0,T]). $$ Here $\nabla$ denotes differentiation in the spacial direction only.
I am looking for a proof of the foll... |
I want to calculate the activity coefficients of mixed solvent salt solutions. I am seeing very strange behavior when I try calculating the activity coefficient of salts in non-polar solvents using Debye-Huckel theory though and its messing up my down-stream calculations.
In a simple example, let's compare the activity... |
Personally I think the problem is interesting, so let me extend my comments to an answer. First of all,
DSolve can solve OP's problem straightforwardly (in
Mathematica 10.3 or higher, if I remember correctly):
With[{u = u[t, x]},
eq = D[u, t] == k D[u, x, x];
ic = u == Piecewise[{{1, 0 < x < 2}}] /. t -> 0;
bc = D[u, x... |
Arkiv för Matematik Ark. Mat. Volume 40, Number 1 (2002), 89-104. The harmonic Bergman kernel and the Friedrichs operator Abstract
The harmonic Bergman kernel
Q Ω for a simply, connected planar domain Ω can be expanded in terms of powers of the Friedrichs operator F Ω ║ F Ω║<1 in operator norm. Suppose that Ω is the im... |
In my last post I solved a problem from chapter 2 of M.G. Bulmer’s Principles of Statistics. In this post I work through a problem in chapter 11 that is basically a continuation of the chapter 2 problem. If you take a look at the previous post, you’ll notice we were asked to find probability in terms of theta. I did it... |
I think something crucial here is the distinction between the
pre-existence of an inner product on our space.How can you speak about choosing an 'orthornormal basis' if there is no notion of an inner product?
In this answer, we will therefore consider $\langle \cdot ,\cdot \rangle$ to be an inner product on some $N$-di... |
On p. 76 of the 1996 edition of Serre's
A Course in Arithmetic, one reads the following (inline) remark:
One can prove that, if $A$ has natural density $k$, the analytic density of $A$ exists and is equal to $k$.
Here, $A$ is a subset of $\bf P$ (the set of all positive rational primes), and the natural density of $A$ ... |
I (accidentally) stumbled upon the following statement in Atkins' "Elements of Physical Chemistry" (p378):
We represent dipole moments by an arrow with a length proportional to $\pmb{\mu}$ and pointing from the negative charge to the positive charge (
1). (Be careful with this convention: for historical reasons the opp... |
We went over a lemma in class leading up to a larger theorem. The Lemma states:
Let $\succeq$ be a rational preference relation on $\mathscr{L}$ and let $\succeq$ admit utility representation under Von-Neumann-Morgenstern expectations. Then
$U(\sum_{k=1}^{K} \alpha_k L_k) = \sum_{k=1}^{K} \alpha_k \ U(L_k)$ $\succeq$ s... |
I am solving a non-linear second order system of PDEs in two variables. The equations are too complicated to write out here, but an essential feature is that there is a propagating wave which then bounces on a boundary.
The problem I have is that the numerics breaks down at the boundary, when the wave reaches this poin... |
A gaseous sample of a compound has a density of $\pu{0.977 g/L}$ at $\pu{710.0 torr}$ and $\pu{100.00 ^\circ C}$. What is the molar mass of this compound?
When I worked the problem I got $\pu{29.9 g/mol}$ is that right?
Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and stud... |
In a series of posts, I wanted to get into details of the history and foundations of econometric and machine learning models. It will be some sort of online version of our joint paper with Emmanuel Flachaire and Antoine Ly, Econometrics and Machine Learning (initially writen in French), that will actually appear soon i... |
I'll reword your question a bit. Let me know if I have not framed it properly.
Say we have a collection of $r$ unique elements each of which occurs in multiple copies. Namely, our collection has $n_1$ identical copies of $X_1$, $n_2$
identical copies of $X_2$, $\ldots$, and $n_r$ identical copies of
$X_r$.
How many way... |
hot!", referring of course to negative absolute temperatures.
But why are they hot? Well, a common explanation is that it's not really the temperature $T$ that is the fundamental quantity, but rather the statistical beta, or "coldness" $\beta=1/T$. So negative temperatures have
negativecoldness, which is hotter than an... |
I have a electrochemical reactor assumed isothermal and isobaric with 4 reactions and I am trying to calculate the "ideal chemical work' exerted by each reaction using the extent of reactions for each reaction (which I have already calculated).
I am calculating the 'chemical work' $w$ by multiplying the extent of react... |
...of two propositions, that produces a value of ''true'' if and only if both of its operands are true.The [[truth table]] of <math>p ~\operatorname{AND}~ q,</math> also written <math>p \land q\!</math
5 KB (658 words) - 02:02, 31 October 2015
A '''logical graph''' is a graph-theoretic structure in one of the systems o... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
The AUC score is a popular summary statistic that is often used to communicate the performance of a classifier. However, we illustrate here that this score depends not only on the quality of the model in question, but also on the difficulty of the test set considered: If samples are added to a test set that are easily ... |
For my system I can write down the Hamiltonian in this form:
$$ H = \begin{pmatrix} \epsilon_{1\downarrow}-\mu_{B}B & 0 & 0 & 0 \\ 0 & \epsilon_{2\uparrow}+\mu_{B}B & 0 & 0 \\ 0 & 0 & \epsilon_{1\uparrow}+\mu_{B}B & 0 \\ 0 & 0 & 0 & \epsilon_{2\downarrow}-\mu_{B}B \end{pmatrix} $$
where $\mu_{B}B$ are the Zeeman split.... |
Turritopsis dohrnii"the immortal jellyfish" are biologically immortal. This means that they do not die due to biological reasons -- however, they obviously may die due to other physical reasons, like getting smashed with a hammer. If I asked you to calculate what the probability of a biologically immortal species being... |
Why does the pH rapidly increase near the equivalence point during--why does the slope of the graph of a pH curve sharply increase around this area?
I'll try to answer your question firstly qualitatively, then quantitatively (using mathematical equation):
Let's consider the case of the titration of strong acid (volume ... |
Motivation
Here I've asked how to derive coefficients of numerical approximation of the linear transport equation $$ u_t + u_x = 0, \tag{1} $$ on a fixed 3-point stencil automatically and here I've asked about automatical derivation on general m-point stencil as well.
In the present question I would like to ask about a... |
Difference between revisions of "Reflecting"
(→$\Sigma_2$ correct cardinals: more information)
(One intermediate revision by the same user not shown) Line 17: Line 17:
For any class $\Gamma$ of formulas, an inaccessible cardinal $\kappa$ is ''$\Gamma$-reflecting'' if and only if $H_\kappa\prec_\Gamma V$, meaning that f... |
In the above example, how is it that $f^{-1}((1,3)) = (2,3]$ ? Here is my understanding, kindly correct the misconceptions. The inverse for $(2,4]$ is not defined. The inverse is as below. $$f^{-1}(y)=\begin{cases} y+1 & \text { if } y \le 2\\ 2y-5 & \text{ if } y \gt 4\\ \end{cases}$$ So, if I have to find out for exa... |
Suppose $A\subseteq X$. Prove that the boundary $\partial A$ of $A$ is closed in $X$.
My knowledge:
$A^{\circ}$ is the interior $A^{\circ}\subseteq A \subseteq \overline{A}\subseteq X$
My proof was as follows:
To show $\partial A = \overline{A} \setminus A^{\circ}$ is closed, we have to show that the complement $( \par... |
I want to know if there is a way to find for example $\ln(2)$, without using the calculator ?
Thanks
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 this community
And let's not forget t... |
Calculate (via two methods) the flux integral $$\int_S (\nabla \times \vec{F}) \cdot \vec{n} dS$$ where $\vec{F} = (y,z,x^2y^2)$ and $S$ is the surface given by $z = x^2 +y^2$ and $0 \leq z \leq 4$, oriented so that $\vec{n}$ points downwards.
I have applied Stokes' Theorem and resulted with $$\oint_{\partial S} \vec{F... |
I don't have much experience with solving equations using mathematica. I have the following equation:
$$A=u\cdot f^{-1}(u)-\int_a^{f^{-1}(u)}f(x)dx$$ For some given constant $A>0$ and $a\in[0,1]$, and given function $f$, with the following properties:
$f(x)\geq 0$. $f(x)=0$ on $x\in[0,a]$ $f^{-1}(u)\in [a,1]$ I know th... |
Lebesgue Measurable But Not Borel The Basic Idea
Our goal for today is to construct a Lebesgue measurable set which is
not a Borel set. Such a set exists because the Lebesgue measure is the completion of the Borel measure. (The collection $\mathscr{B}$ of Borel sets is generated by the open sets, whereas the set of Leb... |
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I would like to know what is the selection criteria for a problem to get reshared by the best ofsIs it the number of people who reshare it or solve it or it must have a solution or what???
Note by Milun Moghe 5 years, 7 months ago
Easy Math Editor
This discussion... |
This morning I saw a tweet mentioning an article with the exciting title:
Counterintuitive problem: Everyone in a room keeps giving dollars to random others. You’ll never guess what happens next
So naturally, I was quite excited and wanted to see what happens next! The problem under consideration is:
Imagine a room ful... |
Is it possible to provide an explanation to the observations of the Stern Gerlach Experiment using the classical theories?
Some Considerations:
We consider the standard set-up for the Stern-Gerlach experiment. The predominant component of $\vec{B}$ is $B_{z}$ Again $B_{z}$ varies most strongly with changes in z
$$\vec{... |
Eigenvalues are properly one of the most important metrics which can be extracted from matrices. Together with their corresponding eigenvector, they form the fundamental basis for many applications. Calculating eigenvalues from a given matrix is straightforward and implementations exist in many libraries. But sometimes... |
There is a good Planet Money episode on ticket scalping; I recommend it.The reason for banning ticket scalping has nothing to do with economic harm, and everything to do with making the arts (or sports, whatever) accessible to people of more-modest means. Consider the fact that artists could, if they wanted, just aucti... |
pre-calculus-trigonometric-identity-calculator
verificar \frac{\sin(3x)+\sin(7x)}{\cos(3x)-\cos(7x)}=\cot(2x)
en
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An inequation is an algebraic expression formed by numbers, a variable that we will call $$x$$ and a symbol of inequality.
Examples of inequations would be:
$$x < 2$$
$$4x+2\geqslant -1$$
$$-x > -3+2x$$
In these cases, we would say that the inequation 1 would already be solved, because if $$x$$ takes values less than $... |
A simple control problem on a system usually involves a variable $x(t)$ that denotes the state of the system over time, and a variable $u(t)$ that denotes the input into the system over time. Linear constraints are used to capture the evolution of the system over time:$$x(t) = Ax(t - 1) + Bu(t), \ \mbox{for} \ t = 1,\l... |
apex.normalization.fused_layer_norm¶ class
apex.normalization.
FusedLayerNorm(
normalized_shape, eps=1e-05, elementwise_affine=True)¶
Applies Layer Normalization over a mini-batch of inputs as described in the paper Layer Normalization .
Currently only runs on cuda() tensors.\[y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathr... |
We defined in the class branched covering as follows.
Let $\Sigma_1, \Sigma_2$ be two surfaces, $f: \Sigma_1 \longrightarrow \Sigma_2$ is a branched covering if $\forall y \in \Sigma_2 $ there exist $V\subset \Sigma_1$ containing y so that $f^{-1}(V)= U_1 \cup U_2 \cup ... \cup U_n $ so that $f: U_j \longrightarrow V$ ... |
The possibility of recursive self-improvement is often brought up as a reason to expect that an intelligence explosion is likely to result in a singleton - a single dominant agent controlling everything. Once a sufficiently general artificial intelligence can make improvements to itself, it begins to acquire a compound... |
Let $M$ be a Riemannian manifold and denote by $\exp_p(v)$ the exponential map at $p \in M$ applied to $v \in T_p M$. Let $q \in M$ be fixed and let $U \subset M$ be a neighborhood of $q$ such that, for each $p \in U$, the map $\exp_p$ is a diffeomorphism in a neighborhood of $exp_p^{-1}(q)$.
Now, the map $V: p \mapsto... |
A simple illustration of the trapezoid rule for definite integration:$$ \int_{a}^{b} f(x)\, dx \approx \frac{1}{2} \sum_{k=1}^{N} \left( x_{k} - x_{k-1} \right) \left( f(x_{k}) + f(x_{k-1}) \right). $$
First, we define a simple function and sample it between 0 and 10 at 200 points
%matplotlib inlineimport numpy as npim... |
$$S = 1 + 2 + 4 + 8 + ...$$
And then apply standard manipulations on it to obtain a bizarrely finite result:
$$\begin{gathered}
\Rightarrow S = 1 + 2(1 + 2 + 4 + ...) \hfill \\
\Rightarrow S = 1 + 2S \hfill \\
\Rightarrow S = - 1 \hfill \\
\end{gathered} $$
How exactly is this result to be interpreted? Surely the defin... |
Is there a possibility to draw large integral signs?
I have found the package
bigints but I have the feeling it is not very professional...
Any better idea?
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.Sign ... |
What is Triangle?
A triangle is a regular polygon, with three sides and the sum of any two sides is always greater than the third side. This is a unique property of a triangle. In other definition, it can be said as any closed figure with three sides with its sum of angles equal to 180.
Being a closed figure, a triangl... |
Learning Objectives
Define the terms wavelength and frequency with respect to wave-form energy. State the relationship between wavelength and frequency with respect to electromagnetic radiation.
During the summer, almost everyone enjoys going to the beach. They can swim, have picnics, and work on their tans. But if you... |
Given real-valued continuous functions $f, g$, is the following (and why?) inequality true?
$$\max \{f + g \} \leq \max f + \max g$$
Can someone give me a proof? I suspect the min is the reverse inequality
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals i... |
I wish to understand the statement in this paper more precisely:
(1). Any 3d Topological quantum field theories(TQFT) associates an inner-product vector space $H_{\Sigma}$ to a Riemann surface $\Sigma$.
-
(2) In the case of abelian Chern-Simons theory $H_{\Sigma}$ is obtained by geometric quantization of the moduli spac... |
Yes, it is the case that $\mu_f' = \mu_v$.
We will use the notation introduced in section "Attempt #2" of the original post. Additionally, we make the following two definitions that will be used throughout the proof:$$\begin{align}Z &:= (a, b] \\\mathcal{J} &:= \left\{(c, d] :\mid c, d\in [a, b] \right\}\end{align}$$
T... |
According to page 53 of Modern Computer Arithmetic (pdf), all of the steps in the Schönhage–Strassen Algorithm cost $O(N \cdot lg(N))$ except for the recursion step which ends up costing $O(N\cdot lg(N) \cdot lg(lg(N)))$.
I don't understand why the same inductive argument used to show the cost of the recursive step doe... |
I saw in a SO thread a suggestion to use
filtfilt which performs backwards/forwards filtering instead of
lfilter.
What is the motivation for using one against the other technique?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processin... |
You shouldn't do a measurement with only one OFDM symbol at first. Instead create some random data, perform QAM modulation, devide QAM symbols array in $N$ OFDM data blocks and make OFDM symbols. Then add CP and paste it together to form a frame. Now you can calculate its power,
$P_{signal} = 1 \div (N \cdot N_{FFT})\s... |
Let $G$ be a finite group and $\Sigma_g$ a closed Riemann surface of genus $g$. Then Mednykh's formula states
$\frac{\left|\mathrm{Hom}(\pi_1(\Sigma_g),G)\right|}{\left|G\right|} = \frac{1}{\left|G\right|^{\chi(\Sigma_g)}}\sum_{V}\left(\dim V\right)^{\chi(\Sigma_g)}$
where the sum on the right is over irreducible compl... |
There is a very simple, direct, and precise mathematical answer to the original question.
The first PC is a linear combination of the original variables $Y_1$, $Y_2$, $\dots$, $Y_p$ that maximizes the total of the $R_i^2$ statistics when predicting the original variables as a regression function of the linear combinati... |
Difference between revisions of "Extendible"
m (→Virtually extendible cardinals: ?)
(→Virtually extendible cardinals: unless...)
Line 131: Line 131:
** $gVP(κ, \mathbf{Σ_{n+1}})$ for a proper class of $κ$
** $gVP(κ, \mathbf{Σ_{n+1}})$ for a proper class of $κ$
** There is a proper class of $n$-remarkable cardinals.
** ... |
I am modeling a stock price that follows Geometric Brownian Motion and have the following:
$E(X)$ = .16 (16%)
$\sigma$ = .24 (24%)
$X_0$ = 95
$T$ = 1 (12 months)
I am trying to find the probability that the price of this stock will be below 93 at the end of this time period. I am calculating this analytically, using th... |
What is an Adjunction? Part 1 (Motivation)
Some time ago, I started a "What is...?" series introducing the basics of category theory:
"What is a category?" "What is a functor?" Part 1 and Part 2 "What is a natural transformation?" Part 1 and Part 2
Today, we'll add adjunctions to the list. An
adjunction is a pair of fu... |
Schelling’s segregation model is a landmark model in sociology. It shows the counter-intuitive phenomenon that residential segregation between individuals of different groups can emerge even when all involved individuals are tolerant. Although the model is widely studied, no pure game-theoretic version where rational a... |
In using the Zorn's lemma to show that every connected graph contains a spanning tree, we let $\{T_{\lambda}: \lambda \in \Lambda \}$ be a family of trees contained in $X$ which is totally ordered by inclusion. But how to show that $\bigcup\limits_{\lambda \in \Lambda} T_\lambda$ is a also a tree in $X$?
Actually, $\bi... |
A. OMAR
Articles written in Journal of Astrophysics and Astronomy
Volume 26 Issue 1 March 2005 pp 1-70
The GMRT
−1. The galaxies are clustered into different sub-groups. The overall population mix of the group is 30% (E + S0) and 70% (Sp + Irr). The observations of 57 Eridanus galaxies were carried out with the GMRT fo... |
What is an Adjunction? Part 2 (Definition)
Last time I shared a light introduction to adjunctions in category theory. As we saw then, an adjunction consists of a pair of opposing functors $F$ and $G$ together with natural transformations $\text{id}\to\ GF$ and $FG\to\text{id}$. We compared this to two stricter scenario... |
What is an Adjunction? Part 3 (Examples)
Welcome to the last installment in our mini-series on adjunctions in category theory. We motivated the discussion in Part 1 and walked through formal definitions in Part 2. Today I'll share some examples. In Mac Lane's well-known words, "adjoint functors arise everywhere," so th... |
From universal law of gravitation, gravitational force exerted on a body of mass m by another body of mass M is $$ \mathbf F = \frac{GMm}{x^2} $$ where x is the distance between the centres of both the objects.
So, work done by gravitational force in bringing the object of mass m from infinity to a distance r from the ... |
I'm currently in the process of familiarising myself with some basic concepts of general relativity and have stumbled upon a problem that is probanly quite simple. I'm referring to the book by Hobson, p.541 and 548, where the energy-momentum tensor for a simple matter field action $S$, $$T_{\mu\nu} = \frac{2}{\sqrt{-\d... |
The motivation for studying relativistic dynamics comes from thinking about conservation of the standard forms of energy and momentum with our new relativistic dynamics. It is easy to demonstrate that $mv$ cannot be conserved in all inertial frames of reference in special relativity. Consider two balls of equal mass co... |
$K$, the standard thermodynamic equilibrium constant, is computed from $\Delta G^\circ$, using
$$\Delta G^\circ = -RT\log K \tag1$$
Generally speaking, $K$ in equation (1) is unitless. Its value depends on the specified reference standard states and $T$ (and obviously on the equilibrium activities of reactants and prod... |
@ArunDebray I think that this is a useful subtlety to point out, though. I think the right statement for (1) is a stable trivialization, though I think (1) is true as stated for any bundle of rank 3 (using obstruction theory to see every oriented bundle over a 2-complex is isomorphic to a stabilization of an oriented p... |
The tree diagrams are especially useful to solve problems with compound experiments, that is to say, the ones where we perform more than one random experiment. Some examples of compound experiments are: to throw two coins in the air, and check whether two heads land face up; to say if there are two women out of three s... |
This is the first piece from a series on the conjugate gradient algorithm. It is still very much a work in progress, so please bear with me while it’s under construction. I have split up the content into the following pages:
All of the pages have been compiled into a single pdf document to facilitate offline reading. A... |
Oxides are chemical compounds with one or more oxygen atoms combined with another element (e.g. Li
2O). Oxides are binary compounds of oxygen with another element, e.g., CO 2, SO 2, CaO, CO, ZnO, BaO 2, H 2O, etc. These are termed as oxides because here, oxygen is in combination with only one element. Based on their ac... |
I'd like this question to definitively guide a practitioner to using both $\mathbb{P}$ vs $\mathbb{Q}$ probabilities in trading and research.
Let's take only one fact as given: if I have a risk-neutral probability distribution I can price and hedge any option.
Is the distinction more philosophical or practical? Does it... |
The Word2Vec is a deep learning algorithm that draws context from phrases. Every textual document is represented in the form of a
vector, and that is done through Vector Space Modelling (VSM). We can convert our text using One Hot Encoding. For example, having three words we can make a vector in a three dimentional spa... |
Since you're writing what look to be Riemann integrals, I presume we're keeping to the case where $X$ is a continuous random variable.
If $m$ is a value for which $\int_{-\infty}^m f_X(x)\, dx =\frac12$ then $m$ is a
median of $X$ (if the density is $>0$ in a neighborhood of $m$, then $m$ will be unique; the median).
S... |
In my previous two posts I showed worked solutions to problems 2.5 and 11.7 in Bulmer’s
Principles of Statistics, both of which involve the characteristics of self-fertilizing hybrid sweet peas. It turns out that problem 11.8 also involves this same topic, so why not work it as well for completeness. The problem asks u... |
So I've been puzzled by this problem for some time now: Suppose we have a chocolate bar with dimensions $m*n$ and it is made up out of finite number of $1*k$ chocolates. Proof that for any natural numbers m,n,k, in order for chocolate to be made, k must devide at least one of m,n. Now this solution come so logical to m... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
Can you please help me find this integral?
$$\int \sin(\ln(x)) dx$$
Give me a clue or show step by step solutions please.
Thank you very much.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to ... |
Given $a\in\mathbb{R}^{mn\times n}$, find a $C\in\mathbb{R}^{n}$, $x\in\mathbb{R}^{m\times n}$ such that $$ 0 = f_{k}(\boldsymbol{C}, \boldsymbol{x}):=\sum_{i=1}^{m} C_{i} \left(\prod_{j=1}^{n} a_{kj}^{x_{i,j}} - 1\right) $$ for all $k\in\{1,\dots,mn\}$.
(The rows of $a_{kj}$ are vectors of solutions to a system of dif... |
The electromagnetic spectrum
Electromagnetic radiation, as you may recall from a previous chemistry or physics class, is composed of electrical and magnetic waves which oscillate on perpendicular planes. Visible light is electromagnetic radiation. So are the gamma rays that are emitted by spent nuclear fuel, the x-rays... |
The Annals of Probability Ann. Probab. Volume 12, Number 3 (1984), 760-767. The Hydrodynamical Behavior of the Coupled Branching Process Abstract
The coupled branching process $(\eta^\mu_t)$ is a Markov process on $(\mathbb{N})^S (S = \mathbb{Z}^d)$ with initial distribution $\mu$ and the following time evolution: At r... |
I have an elliptic curve $ y^2=x^3+109x^2+224x$ and a point $P(-100;260)$ on it. And I need to find point $2P$. I took a formulas $$x_2=\left(\frac{ax_1-b}{y_1}\right)^2 -a+x_1$$ and $$y_2=-y_1+\frac{ax_1-b}{y_1}(x_1-x_2)$$ put into this formulas $a=109$, $b=224$, $x_1=-100$, $y_1=260$ and have $2P=(\frac{6850936}{4225... |
This is a delayed answer, but it seems good to clarify what the OP is asking. This kind of statements: "since $f$ is concentrated in such a ball then its Fourier transform is essentially concentrated in such a ball" is quite common in certain fields, but it doesn't mean that the function and its Fourier transform are c... |
What is the process used to distinguish the change in Gross Domestic Product (GDP) due to an increased output of goods and services from the change due to an increased prices? Why do we make it distinction?
Real GDP (RGDP) is a measure of the value of goods and services produced in an economy over a period of time for ... |
Defining parameters
Level: \( N \) = \( 48 = 2^{4} \cdot 3 \) Weight: \( k \) = \( 2 \) Nonzero newspaces: \( 4 \) Newforms: \( 4 \) Sturm bound: \(256\) Trace bound: \(1\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(48))\).
Total New Old Modular forms 92 31 61 Cusp form... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
Tomorrow, for the final lecture of the
Mathematical Statistics course, I will try to illustrate – using Monte Carlo simulations – the difference between classical statistics, and the Bayesien approach.
The (simple) way I see it is the following,
for frequentists, a probability is a measure of the the frequency of repea... |
I have a problem with what seems a very simple functional maximization. Let's define:
$$ J[z]=\int \left( u(z)-\frac{\dot z^2}{2} \right) dt $$
Where $u(z)=-z^2+5$. The problem is to find
$$ \arg\max_z J[z]$$
Said in a colloquial way, to maximize the function $u(z)$ without varying too much $z$ with time. The second va... |
Let $A:=\mathbb{N}\cup\{\infty\}$.
What is a metric on $A$ s.t.
a sequence $(x_n)$ is convergent in a metric space $X\iff$ there exists a continuous map $\phi:A\rightarrow X$ with $\phi(n)=x_n$ for all $n=0,1,2,...$?
What I know: Let $d$ be the metric on $A$ that we are searching $d_X$ the one on $X$. Being convergent ... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
We can start by analyzing equation #15 from the Derivation of Ideal Gas Law below:
\(P=\frac{N}{V}\frac{m\overline{v^2}}{3}=\frac{N}{V}\frac{2E_{kinetic}}{3}=\frac{N}{V}kT=\frac{NkT}{V}\)
Because we want to derive the equation to the speed of gaseous molecules, the most important factor come to mind is the speed v
x. T... |
In a paper I am reading, they are studying states of an harmonic oscillator.
They say that because the coherent states $|\alpha\rangle$ are not orthogonal, we can expand an arbitrary density matrix as a linear combinaison of coherents states :
$$\rho = \int d\alpha ~ w(\alpha) |\alpha\rangle \langle\alpha|$$
I don't un... |
$\bf 2.17\ $
Theorem$\ $ Suppose $X$ is a locally compact, $\sigma$-compact Hausdorff space. If $\frak M$ and $\mu$ are as described in the statement of Theorem $\it 2.14$, then $\frak M$ and $\mu$ have the following properties:
$(a)\ \ $ If $E\in\frak M$ and $\epsilon>0$, there is a closed set $F$ and an open set $V$ ... |
This is essentially an addition to the list of @4tnemele
I'd like to add some earlier work to this list, namely Discrete Gauge Theory.
Discrete gauge theory in 2+1 dimensions arises by breaking a gauge symmetry with gauge group $G$ to some lower
discrete subgroup $H$, via a Higgs mechanism. The force carriers ('photons... |
There's an accepted answer; I don't quite like it, so I'll take a whack.
Suppose that the start, you don't quite know the empty mass of the vehicle, the quantity of fuel in the fuel tanks, the specific impulse, or the mass flow rate. (The empty mass of the vehicle had better be a very good estimate. Otherwise we're toa... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Let $K$ be a field of characteristic $p > 0$. Then it is due to Artin and Schreier that the assignment
$$c \in K \mapsto \text{Splitting field } L_c \text{ of } X^p-X+c$$
induces a bijection between the non-trivial elements in $K/\{a^p-a \mid a \in K\}$ and the $K$-isomorphism classes of Galois extensions of degree $p$... |
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