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Sukalpa Biswas
☆
India,
2019-08-06 09:15
(edited by Sukalpa Biswas on 2019-08-07 09:07)
Posting: # 20475
Views: 631
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... |
7th SSC CGL Tier II level Question Set, topic Trigonometry 1
This is the 7th question set of 10 practice problem exercise for SSC CGL Tier II level exam and 1st on topic Trigonometry.
We repeat the method of taking the test. It is important to follow result bearing methods even in practice test environment.
Method of t... |
I have a nonlinear inequality constrained optimization problem of the form $$\begin{array}{cc} \min & f(x) \\ \textrm{s.t.} & g(x) \ge 0 \end{array}$$ where $x \in \mathbb{R}^n$, $f : \mathbb{R}^n \to \mathbb{R}$, $g : \mathbb{R}^n \to \mathbb{R}^m$. I am currently solving this system with pseudotransient continuation ... |
GR8677 #20
Problem
Special Relativity}Rest Energy
If one remembers the formulae from special relativity, arithmetic would be the hardest part of the problem.
The problem is to solve , where and .
The rest-mass of both the kaon and the proton are given in the problem. Thus, the equation reduces to .
Now, because the ran... |
This is our first contributed gemstone! Submitted by user Anon1.
In the following, $p$ denotes a prime. We wish to prove that, for all positive integers $n$, there is a finite field of order $p^{n}$.
Step 1. Restating the problem. Claim: It suffices to show that, for some power of $p$ (call it $q$), there exists a fini... |
GR8677 #22
Problem
Electromagnetism}Lorentz Transformation
When an electric field is Lorentz-transformed, afterwards, there might be both a magnetic and electric field (in transverse components). Or, more rigorously, one has,
for motion in the direction.
(A) Obviously not. Suppose initially, one has just , afterwards, ... |
News
Recent result from PandaX-II was published on Physical Review Letter (Phys. Rev. Lett. 119, 181302, "Editor's Suggestion") on October 30, 2017, back-to-back with the first result from XENON1T experiment. The papers are highlighted by a Physics "Viewpoint" commentary by Dan Hooper from FNAL and Univ. of Chicago, co... |
It is true that K-means clustering and PCA appear to have very different goals and at first sight do not seem to be related. However, as explained in the Ding & He 2004 paper K-means Clustering via Principal Component Analysis, there is a deep connection between them.
The intuition is that PCA seeks to represent all $n... |
I decided to translate a book but I have hard time to design my own LaTeX template for the book
Quantum Mechanics by Leonard Susskind & Art Friedman Below is showing one page: I wonder what kind of LaTeX book class the author uses?
I decided to translate a book but I have hard time to design my own LaTeX template for t... |
GR8677 #23
Problem
Advanced Topics}Solid State
Actually, one can figure this one out with only knowledge of lower div baby physics.
(A) Electrical conductivities for conductors, semiconductors, and insulators go (in general), like this . Thus, copper should be more conductive than silicon. This is true (but one is tryi... |
Per the title, other than using a general purpose LP solver, is there an approach for solving systems of inequalities over variables $x_i, \ldots, x_k$ where inequalities have the form $\sum_{i \in I} x_i < \sum_{j \in J} x_j$? What about the special case of inequalities that form a total order over the sums of the mem... |
Let $\mu^\star$ be a real-valued function defined on the power set of the positive integers $\mathbf{N}^+$ such that for all $X,Y\subseteq \mathbf{N}^+$ the following axioms hold:
(F1) $\mu^\star(\mathbf{N}^+)=1$;
(F2) $\mu^\star(X) \le \mu^\star(Y)$ if $X\subseteq Y$;
(F3) $\mu^\star(X\cup Y) \le \mu^\star(X)+\mu^\sta... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
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We've seen that classical logic is closely connected to the logic of subsets. For any set \( X \) we get a poset \( P(X) \), the
power set of \(X\), whose elements are subsets of \(X\), with the partial order being \( \subseteq \). ... |
EMP models are defined by both the usual content of a GAMS model and annotations found in a simple text file named
emp.info (aka the EMP info file). It is often most convenient to create this file via the GAMS put writing facility. The annotations primarily serve to
define the model (e.g. to specify that a variable
u i... |
GR8677 #27
Problem
Quantum Mechanics}Spin
Spin explains a lot of things.
(A) Remember orbitals? Whether a shell is full or not determines the properties of each column of the periodic table. A full shell has all electron spins paired together, while a partially filled or empty shell doesn't have that. So, spin is defin... |
Journal of Operator Theory
Volume 46, Issue 3, Supplementary 2001 pp. 605-618.Composition operators between Nevanlinna classes and Bergman spaces with weights
Authors: Hans Jarchow (1), and Jie Xiao (2) Author institution:(1) Institut f\"ur Mathematik, Universit\"at Z\"urich, CH-8057 Z\"urich, Switzerland
(2) Departmen... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Let $G$ be a finite group. Consider the set $$X = \bigcup_{H \le G} G/H$$ which is a disjoint union of left cosets of subgroups $H$ of $G$. Then $G$ acts on $X$ by left multiplication, and the number $|X/G|$ of orbits is the number of subgroups of $G$. I want to apply Burnsides Lemma in this situation $$|X/G| = \frac{1... |
1d diffusion equation
Integrating the diffusion equation,
$$ \frac{\partial u}{\partial t} = D \frac{\partial^2 u}{\partial x^2}, $$
with a constant diffusion coefficient D using forward Euler for time and the finite difference approximation for space,
$$ u_i^{t+1} = u_i^t + D\frac{\Delta t}{\Delta x^2} ( u_{i+1}^{t} +... |
By Joannes Vermorel, February 2012
More accurate demand forecasts generate savings as far inventory is concerned. This article quantifies savings for
inventories with turnovers lower than 15
. We adopt a viewpoint where the extra accuracy is entirely invested in lowering inventory levels while keeping stockout rates un... |
The Concurrency of the Altitudes in a Triangle A Trigonometric Proof Dušan Vallo February 2012
Let \(ABC\) be a triangle. Using the standard notations, we denote the altitudes \(h_a = AH_a\), \(h_b = BH_b\), \(h_c = CH_c\).
Theorem
The three altitudes of a triangle are concurrent.
Proof
First observe that in a right-an... |
Write the Taylor series of $\text{Log}(1+w)$ with center at $w=0$ on $|w|<1$;
check that if $|z-2|<1$, then $|z|>1$. (If you have difficulties in checking this formally, try to draw a picture of the situation). Use these facts to compute
$$ \int_C \text{Log}\left(1+\frac{1}{z}\right)dz\, $$ $$ C:w(\theta) = 2 + (1/2)e^... |
Let $f$ be a map whose domain is $X$. If $f$ satisfies the property that for all $x\in X$, $$f(f(x))=f(x)\text{,}$$ is there any standard name for such a function? Not sure if "projection" is the answer.
This is called an idempotent map. More generally, one can talk about idempotent elements: given a set $S$ with a bin... |
Abstract
A comprehensive design of wavefront-splitting interferometers (WSIs) is introduced for integration into wafer light circuits and optical fiber systems. The WSI detects the coherent interference of two wavefronts after being equally split by a single buried resonator and collected into a single mode waveguide. ... |
Motivation:
There is a persistent belief among evolutionary biologists that chance played a significant role in biological evolution. This would imply that life and its building blocks could have been significantly different. In particular, some protein scientists suspect that evolution could have used as few as 10 ami... |
Is there a formula to calculate the distribution of the mean waiting time for a server which processes a workload of $N$ jobs, which behaves like a M/G/1 queue?
I would like to be able to answer the following: what is the chance that for a workload of $N$ items, the mean waiting time is above X. If taking the distribut... |
Degree $n$ : $39$ Transitive number $t$ : $21$ Group : $C_{13}\times C_{13}:C_3$ Parity: $1$ Primitive: No Nilpotency class: $-1$ (not nilpotent) Generators: (1,28,22,11,35,20,9,31,24,2,38,19,13,39,25,10,37,23,12,33,16,7,32,18,4,30,21,5,34,15,8,36,14,3,29,26,6,27,17), (1,21,27,8,23,34,7,24,33,13,17,38,11,15,28,3,16,36,... |
You could accomplish this using a secret sharing scheme, which doesn't require any public key cryptography. An $(n,k)$ secret sharing scheme allows a secret to be divided up into $n$ shares such that the secret can be recovered from any $k$ shares. However, if you only have $k - 1$ shares you cannot recover any informa... |
Another great feature of SDC Verifier is described here. Connections made with bolts according to
EN 1993-1-8 (2005) Chapter 3 can now be checked with SDC Verifier directly within your standard FEA program. For the EN 1993-1-8 bolt check the following checks can be performed:
Shear connection
A.bearing type; B.slip-res... |
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J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: vi... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{17})\). We also show the integral \(q\)-expansion of the trace form.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded ... |
Good day, I am attempting an optional exercise and I am finding it hard to interpret the problem in terms of matrices and vectors.
Coin 1 has probability 0.4 of coming up heads, and coin 2 has probability 0.8 of coming up heads. The coin to be flipped initially is equally likely to be coin 1 or coin 2. Thereafter, if t... |
Let $\ \mathbf N = \{1\ 2\ \ldots\}\ $ be the set of natural numbers. Let $\ f : \mathbf N\rightarrow\mathbf N\ $ be an arbitrary function, and $\ \forall_{n\in\mathbf N}\, F(n)\ :=\ \max_{k = 1\ldots n}\, f(k)$.
Let's assume that, with respect to a fixed universal Turing machine, there exists at least one algorithm wh... |
Definition:Boolean Algebra/Definition 1 Contents Definition
Furthermore, these operations are required to satisfy the following axioms:
\((BA_1 \ 0)\) $:$ $S$ is closed under $\vee$, $\wedge$ and $\neg$ \((BA_1 \ 1)\) $:$ Both $\vee$ and $\wedge$ are commutative \((BA_1 \ 2)\) $:$ Both $\vee$ and $\wedge$ distribute ov... |
In Fig. 7, two equal circles, with centres O and O?, touch each other at X. OO? produced meets the circle with centre O? at A. AC is tangent to the circle with centre O, at the point C. O'D is perpendicular AC. Find the value of \[\frac{DO'}{CO}\] . Answer:
Given, AC is tangent to the circle with centre O and O'D is pe... |
I have $k$ distinct prime numbers $\ell_1 < \dots <\ell_k$, and for each $i=1,\dots,k$, a subset $A_i$ of $\mathbb Z / \ell_i \mathbb Z$. Let $L=\ell_1 \dots \ell_k$. Now using the chinese reminder theorem, $\mathbb Z/ L \mathbb Z = \prod_{i=1}^k \mathbb Z /\ell_i \mathbb Z$, hence the subset $\prod_{i=1}^k {A_i}$ of t... |
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How many ordered pairs of real numbers (x,y) (x,y) (x,y) are there such that
{x2−y2+πx+ϕyx2+y2=2,2xy+ϕx−πyx2+y2=0. \begin{cases} x^2 - y^2 & + \frac{\pi x+\phi y}{x^2+y^2} & = \sqrt{2}, \\2xy & + \frac{ \phi x-\pi y}{x^2 + y^2} & = 0. \\ \end{cases} {x2−y22xy+x2+... |
45 1 Summary Clarifying the concept of RKHS
I have been reading a lot about Reproducing Kernel Hilbert Spaces mainly because of their application in machine learning. I do not have a formal background in topology, took linear algebra as an undergrad but mainly have encountered things such as, inner product, norm, vecto... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
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Now showing items 1-2 of 2
Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
GR9677 #74
Alternate Solutions
asdfman 2009-11-05 00:11:38 Used POE.
Expect there to be a change in entropy - E is out.
Know the typical integral to find S will involve a - A is out.
Expect the entropy to increase for the system - D is out.
Based on the numbers, expect there to be a ratio as an argument of the - C is t... |
Difference between revisions of "Moser-lower.tex"
Line 207: Line 207: −
Actually it is possible to improve upon these bounds by a slight amount. Observe that if $B$ is a maximiser for the right-hand side of \eqref{cn3} (subject to $B$ not containing isosceles triangles), then any triple $(a,b,c)$ not in $B$ must be the... |
Let us reformulate OP's question as follows:
Give a proof that a local coordinate transformation $x^{\mu} \to y^{\rho}=y^{\rho}(x)$ between two local coordinate systems (on a 3+1 dimensional Lorentzian manifold) must be affine if the metric $g_{\mu\nu}$ in both coordinate systems happen to be on constant flat Minkowski... |
Let us take as a vocabulary the $\in$ relation (is an element of), and a single unary predicate $C$, where $Cx$ is read "$x$ is constructible" or "$x$ is a constructible set" (I'm making this up, but the term seems appropriate). We may then write down an alterative set theory with three intuitive axioms (one of them an... |
Let $\Omega$ = closed ball $B_1(0)$ in $\mathbb{R}^n$ with metric d induced by the Euclidean norm. Suppose the mapping $T: \Omega \to \Omega$ satisfies
$d(Tx,Ty) \leq d(x,y)$ for all $x,y \in \Omega$
Prove that there exists at least on fixed point of T. Hint consider the map $T_k = (1-\frac{1}{k})T$
So I first start of... |
Left Distributive and Commutative implies Distributive
Jump to navigation Jump to search
Theorem
Let $\struct {S, \circ, *}$ be an algebraic structure.
Let $\circ$ be commutative.
Then $\circ$ is distributive over $*$. Proof
Let $a, b, c \in S$.
Then
\(\displaystyle \paren {a * b} \circ c\) \(=\) \(\displaystyle c \cir... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
This is a nice question, as it confronts a very replicable and common experience with a well established yet seemingly contradictory fact. As you expected, the smell of metal has nothing to do with the metal actually getting into your nose, as most metals have far too low of a vapor pressure at ordinary temperatures to... |
Welcome in part 4 of this AR series. In the previous chapter, you could see how homography makes possible to draw into a projected planar surface. This chapter will extend the previously calculated homography into form, which allows drawing 3D objects into the scene.
The program related to this chapter is CameraPoseVid... |
There is a widely accepted opinion that the Axiom of Countable Choice (further,
ACC)
$$ \forall n\in \mathbb{N} . \exists x \in X . \varphi [n, x] \implies \exists f: \mathbb{N} \longrightarrow X . \forall n \in \mathbb{N} . \varphi [n, f(n)] $$
is justified constructively due to certain interpretations of intuitionist... |
Difference between revisions of "Timeline of prime gap bounds"
Line 893: Line 893:
[http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi600d7m5_3473955908.mpl 3,473,955,908]? [m=5]* ([http://terrytao.wordpress.com/2014/04/14/polymath8b-x-writing-the-paper-and-chasing-down-loose-ends/#comment-302031 xfxie])
[htt... |
GTU First Year Engineering (Semester 2)
Vector Calculus and Linear Algebra June 2014
Vector Calculus and Linear Algebra
June 2014
Total marks: --
Total time: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons (2) Marks are given to the right of every question (3) Draw neat diagrams wherev... |
As every MO user knows, and can easily prove, the inverse of the matrix $\begin{pmatrix} a & b \\\ c & d \end{pmatrix}$ is $\frac{1}{ad - bc} \begin{pmatrix} d & -b \\\ -c & a \end{pmatrix}$. This can be proved, for example, by writing the inverse as $ \begin{pmatrix} r & s \\\ t & u \end{pmatrix}$ and solving the resu... |
Note that the value of the series
$$\sum_{n=1}^{\infty}B_n\sin(nx)\tag{1}$$
for $x=0$ is always zero, regardless of the coefficients $B_n$ (assuming convergence). Furthermore, since the functions $\sin(nx)$ are odd, (1) can only represent odd functions. So you cannot represent general functions with the series (1). Thi... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
Abstract:
The main contribution of this article is to show that within the context of adaptive agents the Causal Path Entropy and Empowerment are equivalent only in deterministic environments. In non-deterministic environments, it is shown that the Causal Path Entropy generally under-estimates the number of intrinsic o... |
Inspired by the ancient Greek mythological creature Chimera (χίμαιρα) which had a lion’s head, a goat’s body and a serpent’s tail, Abrams and Strogatz [1] coined the term “chimera states” for the counterintuitive self-organized phenomenon in which
synchronous and desynchronous oscillatory behavior coexist in the same s... |
Note first that the first $=$ (equals) in $\frac{dl(\theta)}{d\theta} = 0 = −\frac{1}{2\sigma^2}(0−2X^TY + X^TX \theta)$ should be interpreted as a "is set to", that is, we set $\frac{dl(\theta)}{d\theta} = 0$. Given that (apparently) $\frac{dl(\theta)}{d\theta} = −\frac{1}{2\sigma^2}(0−2X^TY + X^TX \theta)$, $\frac{dl... |
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We've seen that classical logic is closely connected to the logic of subsets. For any set \( X \) we get a poset \( P(X) \), the
power set of \(X\), whose elements are subsets of \(X\), with the partial order being \( \subseteq \). ... |
I'm following the derivation from Finite Element Method using Matlab 2nd Edition, pg 311-315, which derives of the local stiffness matrix for planar isotropic linear elasticity as follows:
Force Balance Equations
$\frac{\partial\sigma_x}{\partial x}+\frac{\tau_{xy}}{\partial y} + f_x=0$ $\frac{\partial\tau_{xy}}{\parti... |
Difference between revisions of "Main Page"
(→IP-Szemeredi (a weaker problem than DHJ))
(Highlighting headings)
Line 71: Line 71: −
High-dimensional Sperner
+
High-dimensional Sperner
Kalai.29: There is an analogous for Sperner but with high dimensional combinatorial spaces instead of "lines" but I do not remember the ... |
20 July 2017:
1) The paper Blake and I wrote on [A compositional framework for reaction networks](https://arxiv.org/abs/1704.02051) has been accepted by _Reviews in Mathematical Physics_. The best part: it seems no corrections were demanded!
2) More news from Daniel, who is at the big annual category theory conference:... |
Diophantine approximation, metric theory of
The branch in number theory whose subject is the study of metric properties of numbers with special approximation properties (cf. Diophantine approximations; Metric theory of numbers). One of the first theorems of the theory was Khinchin's theorem [1], [2] which, in its moder... |
uses two $3\times 3$ matrices $A$ and $B$ and calculates difference between $A$and $B$. It is an online math tool specially programmed to perform matrix subtraction between the two $3\times 3$ matrices $A$ and $B$. 3x3 matrix subtraction calculator
Matrices are a powerful tool in mathematics, science and life. Matrices... |
Question #2f185 2 Answers Answer:
Any body may be acted upon by a number of forces in different directions. Forces add up or cancel each other either fully or partially. The net force is the amount of force that is effective on the body. The net force is not the actual amount of force acting on it. It is the sum of the... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Revista Matemática Iberoamericana
Full-Text PDF (270 KB) | Metadata | Table of Contents | RMI summary
Volume 27, Issue 1, 2011, pp. 93–122 DOI: 10.4171/RMI/631
Published online: 2011-04-30
Isoperimetry for spherically symmetric log-concave probability measuresNolwen Huet
[1](1) Université de Toulouse, France
We prove a... |
EDIT: As pointed out in the comments, the following proof is found in Knuth’s book, The Art of Computer Programming, Vol. 3, and is attributed to MacMahon.
There are several nice series expansions involving basic permutation statistics which I’ve been reviewing lately. One of these involves the number of
inversions of ... |
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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 ... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
I'm looking for a formal definition of
Cluster of Solutions. My current understanding is the following. Let $x$ be a boolean assignment on $n$ variables. Let $f: \{ 0,1 \} ^n \to \mathbb{N}$ be a function that, given a boolean assignment $x$ on $n$ variables, just returns the natural number $i \in [0, 2^n-1]$ correspon... |
Beatty Sequences
Let $r$ be a positive irrational number. Set $s = 1/r,$ and define two sequences: $a_{n} = n(r + 1)$ and $b_{n} = n(s + 1)$, $n \gt 0.$
Obviously, all terms of both sequences are irrational. In particular, none of them is integer. A remarkable theorem discovered by Sam Beatty in 1926 states that, for a... |
$\newcommand{\s}{\overset{\text{sgn}}=}\newcommand{\Dx}{\text{Dx}}\newcommand{\logDx}{\text{logDx}}\newcommand{\DlogDx}{\text{DlogDx}}\newcommand{\DDDlogDx}{\text{DDDlogDx}}\newcommand{\DDDDDlogDx}{\text{DDDDDlogDx}}\newcommand{\dif}{\text{dif}}\newcommand{\Ddif}{\text{Ddif}}\newcommand{\R}{\mathbb{R}}$Let us show that... |
uses two $2\times 2$ matrices $A$ and $B$ and calculates both their sum $A+B$ and their difference $A-B$. It is an online math tool specially programmed to perform matrix addition and subtraction between the two $2\times 2$ matrices. 2x2 matrix addition and subtraction calculator
Matrices are a powerful tool in mathema... |
I know implication (—>) is used for conditions like if x is true then b will be true but sometimes implication is used in other than these type of sentences For example : All A's are Bs: ∀X (a(X) ⇒ b(X)) I don't understand why implication is used here? And if implication is necessary to use here then why implication is... |
Motivation:
Rich Sutton’s Bitter Lesson for AI essentially argues that weshould focus on meta-methods that scale well with compute instead of trying to understand the structure and function of biological minds. The latter according to him are
endlessly complex and therefore unlikely to scale. Furthermore, Rich Sutton(w... |
Image Processing
Image editing software like Photoshop provide many image effects like blur, sharpen, and edge detection. These effects are commonly implemented through a kernel, a matrix describing a certain image effect. The kernel is applied to an image through convolution: flipping both the rows and columns of the ... |
The mass of the Moon is 7.342×10
22 kg.One ton is 10 3 kg. How much is thousands of tons? Let's say you have thousands of thousands of tons. That's one million tons, or 10 9 kg. This is still ten thousands times a billion less than the mass of the moon.
(source: Diego Delso)
Just as a comparison, one of the largest min... |
Consider $k$ Hermitian matrices $A_1,\ldots,A_k$ of dimension $d \times d$. Their joint numerical range (JNR) $L(A_1,\ldots,A_k)$ is defined as $$ L(A_1,\ldots,A_k) = \left\{ \left( \Tr \rho A_1,\ldots, \Tr \rho A_k \right): \rho \in \Omega_d \right\}. $$ Due to taking all mixed states the joint numerical range is a co... |
I have exciting news today: The first ever joint paper by Monks, Monks, Monks, and Monks has been accepted for publication in Discrete Mathematics.
These four Monks’s are my two brothers, my father, and myself. We worked together last summer on the notorious $3x+1$ conjecture (also known as the Collatz conjecture), an ... |
Kakeya problem
Define a
Kakeya set to be a subset [math]A[/math] of [math][3]^n\equiv{\mathbb F}_3^n[/math] that contains an algebraic line in every direction; that is, for every [math]d\in{\mathbb F}_3^n[/math], there exists [math]a\in{\mathbb F}_3^n[/math] such that [math]a,a+d,a+2d[/math] all lie in [math]A[/math]. ... |
A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.
A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: vi... |
Using TeX Notation Note: You are currently viewing documentation for Moodle 2.0. Up-to-date documentation for the latest stable version is available here: Using TeX Notation.
While there are quite a few notational systems employed for the purpose of representing Math notation, Moodle core provides a TeX filter that can... |
Union of Right-Total Relations is Right-Total
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Theorem Then $\mathcal R_1 \cup \mathcal R_2$ is right-total. Proof
Define the predicates $L$ and $R$ by:
$\map L X \iff \text {$X$ is left-total}$ $\map R X \iff \text {$X$ is right-total}$
\(\displaystyle \map R {\mathcal R_1} \land \map ... |
Definition:Polynomial Ring Contents 1 One Indeterminate 2 Multiple Indeterminates 3 Terminology 4 Notation 5 Equivalence of definitions 6 Also defined as 7 Also known as 8 Also see One Indeterminate
Let $R$ be a commutative ring with unity.
$S$ is a commutative ring with unity $\iota : R \to S$ is a unital ring homomor... |
A System of Two Equations Replete with Squares Problem
Solution
Let, for simplicity, $a=x^2,\,b=y^2.\,$ The system can be written as
$\displaystyle \left\{\begin{align}&16a+25b=400\\&a+b=\frac{(4a+5b)^2}{400}\end{align}\right.$
The second equation transforms into $400(a+b)=(4a+5b)^2.\,$ Replacing $400\,$ from the first... |
Crane Standard EN 13001-3-1+A2 Limits States and proof competence of steel structure is implemented in
SDC Verifier. The standard is to be used together with EN13001-1 and EN13001-2: EN 13001-3-1 standard deals only with the limit state method. The allowable stress method is reliable in specific cases – for cranes wher... |
GR9277 #71
Alternate Solutions
Herminso 2009-09-22 19:12:05 For , all of the systems are in the lowest energy state (minimum entropy), so the only choice is (B). ramparts 2009-08-15 20:35:32 All the solutions are so complicated! :( Here's a way for us stat mech idiots using boundary conditions:
For (or epsilon=0), this... |
Let $a \in \Bbb{R}$. Let $\Bbb{Z}$ act on $S^1$ via $(n,z) \mapsto ze^{2 \pi i \cdot an}$. Claim: The is action is not free if and only if $a \Bbb{Q}$. Here's an attempt at the forward direction: If the action is not free, there is some nonzero $n$ and $z \in S^1$ such that $ze^{2 \pi i \cdot an} = 1$. Note $z = e^{2 \... |
GR9277 #72
Alternate Solutions
jmason86 2009-09-03 19:19:22 I did this one by limits and general test taking strategy.
Limits: Q --> finite value as T --> . Eliminates (D) and (E)
ETS will generally force you to choose between very similar answers. Eliminates (C)
With only (A) and (B) left, it is a good idea to guess. ... |
Given the work of Turing and Feferman all arithmetical truths can be isolated through a transfinite progression of theories like $T_0=PA$, $T_{\beta+1}=T_β \ plus \ CON(T_\beta)$ and $T\lambda=\cup T\mu(\mu\prec\lambda)$ - when $\lambda$ is a limit ordinal - through all the recursive ordinals. What is the smallest ordi... |
I am given a group $G=\text{Span}(w,x,y,z)$ with relations defined by $$\begin{bmatrix}0&0&1&3\\-2&1&1&3\\-2&4&1&3\\0&-3&1&5\end{bmatrix}\begin{bmatrix}w\\x\\y\\z\end{bmatrix}=0.$$ I was wondering if anyone could give me any hints, or explain a simply way to do this. I have figured out how to solve it, but the method s... |
The Grassmannian
The first thing we need to do to simplify our life is to get out of projective space. Recall that $\newcommand{\PP}{\mathbb{P}}
\newcommand{\CC}{\mathbb{C}} \newcommand{\RR}{\mathbb{R}} \newcommand{\ZZ}{\mathbb{Z}} \DeclareMathOperator{\Gr}{Gr} \DeclareMathOperator{\Fl}{Fl} \DeclareMathOperator{\GL}{GL... |
I read a paper detailing the algebraic process of kernel PCA. I have question though: the paper details the projection of new points onto the new eigenvectors in the feature space, but what if I want eigenvectors themselves? I am performing an analysis that compares eigenvector magnitudes in a Gaussian inner product sp... |
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We've seen that classical logic is closely connected to the logic of subsets. For any set \( X \) we get a poset \( P(X) \), the
power set of \(X\), whose elements are subsets of \(X\), with the partial order being \( \subseteq \). ... |
I have a model whose estimation is a function (finite number of points) over an intervalle. I am looking at the sum of each estimated point of the function : $\hat{\theta} := \sum_{i=0}^k \hat{f}(i)$ which is my parameter of interest.
Now, if I want a $95\%$ CI using resampling, I see two ways to do so:
First, I can do... |
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