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Introduction
In some of the technical articles, the converter operation is studied in ideal conditions. An ideal condition is when there is no interruptions, disturbances and errors that cause the operation to deviate from its normal condition. These inevitable interruptions from normal condi... |
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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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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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Now showing items 1-1 of 1
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... |
L # 1
Show that
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
Offline
Last edited by krassi_holmz (2006-03-09 02:44:53)
IPBLE: Increasing Performance By Low... |
Averaged and Integral Characteristics
These characteristics can be monitor in the course of
design process.
It is possible to monitor minimum and maximum values as well.
Example. As an example, a 6-layer metal-dielectric coating was designed. The corresponding design bar is shown on the bottom of the Evaluation window ... |
Let $H(s)$ be a transfer function of the form$$H(s) = \frac{1}{s-p}$$where $p$, which is a pole of $H(s)$, can be written as a complex number $a+jb$. Taking the inverse Laplace transform of $H(s)$ gives the corresponding impulse response $h(t)$ (that is, the output of your system when given $\delta(t)$ as input). Notin... |
Update: An idea very similar to this one is described in "Digital Access to Comparison-Based Tree Data Structures and Algorithms".
Here's an idea for a structure that might meet these bounds.It uses an balanced binary search tree where each node is annotated with a pair of integers in $[-1,k-1]$ to indicate how much of... |
If you want to multiply two matrices $A$ and $B$ then observe that$$\begin{pmatrix}I_n&A&\\&I_n&B\\&&I_n\end{pmatrix}^{-1}=\begin{pmatrix}I_n&-A&AB\\&I_n&-B\\&&I_n\end{pmatrix}$$which gives you $AB$ in the top-right block.It follows that inversion is at least hard as multiplication.
EDIT: I had misread the question, th... |
The kinetic energy of the bullet is $\frac12 mv^2 \approx 1$ kilojoule.
If the deceleration is continuous over $x=1$ meter, energy conservation gives us an acceleration $a = v_\text{initial}^2/2x \approx 65,000\,\mathrm{m/s^2} \approx 6600\,g$, and the stopping time is $t = v_\text{initial}/a \approx 5.6$ milliseconds.... |
The General Curl The Theory
The image you posted above is trace visualization for what is known as a divergence free vector field. To understand what that means, consider particles that move along the lines you see above (the field represents their instantaneous velocity), if the field is indeed divergence free, those ... |
First principle of stationary action
Consider a real Klein-Gordon scalar field $\phi$ living in a $D$ dimensional flat spacetime. The field is considered
off shell (the on shell condition is defined below). Suppose for simplicity that its action on an arbitrary region of spacetime $\Omega$ is \begin{equation}\tag{1} S ... |
Base: \(a\)
Legs: \(b\) Base angle: \(\beta\) Vertex angle: \(\alpha\)
Legs: \(b\)
Base angle: \(\beta\)
Vertex angle: \(\alpha\)
Altitude to the base: \(h\)
Perimeter of an isosceles triangle: \(P\) Area of an isosceles triangle: \(S\)
Perimeter of an isosceles triangle: \(P\)
Area of an isosceles triangle: \(S\)
An i... |
A generalized sequential machine (GSM) is a generalization of a Mealy machine where on each transition one input symbol is read and 0 or more output symbols are written. As in a Mealy machine, we assume that there are no final states, i.e. a GSM operates on infinite input/output words. A GSM has finitely many states.
A... |
I'm reading Altland & Simons' Condensed Matter Field Theory, and when presenting the t-J model, $$ H = -t \sum_{<mn>}P_s a^{\dagger}_{m\sigma} a_{n\sigma} P_s + J \sum_{<mn>} S_m \cdot S_n $$ they say that Nagaoka's theorem asserts that, in the $U=\infty\ (J=0)$ limit, when we remove one electron from the half-filled H... |
Tagged: conjugate Problem 209
Let $G$ be a group. We fix an element $x$ of $G$ and define a map
\[ \Psi_x: G\to G\] by mapping $g\in G$ to $xgx^{-1} \in G$. Then prove the followings. (a) The map $\Psi_x$ is a group homomorphism. (b) The map $\Psi_x=\id$ if and only if $x\in Z(G)$, where $Z(G)$ is the center of the gro... |
Consider the language
$$L = \{1^i 0^j 1^k \mid i + j = 2k, k ≥ 1\}\,,$$
and let $x_n$ be the canonical $n$'th word in $L$. My problem involves proving that the Kolmogorov complexity of $x_n$ can be bounded by
$$K(x_n) \leq c + 2\log_2 |x_n|$$
for some constant $c$.
My ideas :
(please note that I'm not writing this in a... |
I essentially agree with Martin's comment, I can elaborate on that to make a tentative answer, knowing that there is no general formal definition of
calculus or abstract machine and that what I am going to describe cannot possibly cover the meaning of all instances of these two words found in the literature.
In brief: ... |
dyld: Library not loaded: /sw/lib/libpng12.0.dylib Referenced from: /sw/bin/latex Reason: Incompatible library version: latex requires version 30.0.0 or later, but libpng12.0.dylib provides version 26.0.0 sh: line 1: 81964 Trace/BPT trap latex -output-directory=/var/folders/71/71wgK3o7FtGClPSEzjU3v++++TM/-Tmp-/inkscape... |
The heart is the muscular organ responsible to pump blood in order to supply the body with oxygen and nutrients. The heart consist of four chambers, namely the left and right atria and the left and right ventricles.
What is modeling?
Before talking about cardiac modeling, it make sense to first define what we mean by m... |
I came across an identity involving binomial coefficients. I'm not sure if I'm looking at the identity the wrong way but I am not aware if this identity is known and if there is an (easy) proof for it.
Take a nonnegative integer $n$ and form two $k$-tuples consisting of integers at most $n$, say, $(a_1,a_2,\ldots,a_k)$... |
I have 2 questions - the first is what the title refers to, and the second is something I want a reference on (I thought I'd include them in one post since they are very strongly related). Sorry this post is a bit long, I tried to put as much as detail as I could ..
$1$-st question: I'm interested only in the group $GL... |
Definition of Exact Equation
A differential equation of type
\[{P\left( {x,y} \right)dx + Q\left( {x,y} \right)dy }={ 0}\]
is called an exact differential equation if there exists a function of two variables \(u\left( {x,y} \right)\) with continuous partial derivatives such that
\[{du\left( {x,y} \right) \text{ = }}\ke... |
3.1
Show that, if you ignore drag, a projectile fired at an initial velocity \(v_0\) and angle \(\theta\) has a range R given by A target is situated 1.5 km away from a cannon across a flat field. Will the target be hit if the firing angle is \(42^{\circ}\) and the cannonball is fired at an initial velocity of 121 m/s?... |
Difference between revisions of "State Feedback"
(→Textbook Contents)
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{{chheader|Linear Systems|State Feedback|Output Feedback}}
{{chheader|Linear Systems|State Feedback|Output Feedback}}
−
This chapter describes how feedback can be used shape the l... |
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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... |
$\DeclareMathOperator{\PGL}{PGL} \DeclareMathOperator{\GL}{GL} \newcommand{\F}{\mathbb{F}} \newcommand{\p}{\mathfrak{p}} \DeclareMathOperator{\Sym}{Sym}$ Let $F$ be a number field, and let $\Gamma$ be a congruence subgroup of $\PGL_2(\mathbb{Z}_F)$ with level supported at some finite set of primes $S$. To a Hecke-eigen... |
My query is regarding following question:-
Let $\mathcal Q$ denote the additive group of rational numbers, i.e. the structure $\langle Q ; +; 0\rangle$. Let $\mathcal L$ be the language of $\mathcal Q$ and let $\mathcal T$ be the complete theory of $\mathcal Q$.
(i) By considering automophisms of $\mathcal Q$ prove tha... |
Difference between revisions of "stat946w18/Rethinking the Smaller-Norm-Less-Informative Assumption in Channel Pruning of Convolutional Layers"
m (→Image Foreground-Background Segmentation Experiment)
(→Results)
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== Results ==
== Results ==
− +
=== CIFAR-10 Experiment ===
=== CIFAR-10 Experiment ===
Re... |
A bit of pedanticism first. Some of your terminology usage is inaccurate, I'd just like to take the opportunity to clear some of it up.
Nuclear spins do not "undergo a FID", they undergo
free precession. The free induction decay (FID) is the signal that is measured when spins undergo free precession.
"Noise" in spectro... |
Difference between revisions of "stat946w18/Rethinking the Smaller-Norm-Less-Informative Assumption in Channel Pruning of Convolutional Layers"
(→Results)
(→Results)
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== Results ==
== Results ==
− +
=== CIFAR-10 Experiment ===
=== CIFAR-10 Experiment ===
Latest revision as of 00:18, 21 April 2018 Conte... |
The Effect of Symmetry Even-function symmetry Odd-function symmetry Half-wave symmetry Quarter-wave symmetry Even-Function Symmetry
A function is defined to be even if and only if
f( t) = f(- t) 1.1
If a function satisfies Eq. 1.1, then it is said to be even because polynomial functions with only
even exponents have th... |
Category: Group Theory
Group Theory Problems and Solutions.
Popular posts in Group Theory are:
Problem 625
Let $G$ be a group and let $H_1, H_2$ be subgroups of $G$ such that $H_1 \not \subset H_2$ and $H_2 \not \subset H_1$.
(a) Prove that the union $H_1 \cup H_2$ is never a subgroup in $G$.
Add to solve later
(b) Pro... |
Answer
Express $\cos(180^\circ-\theta)$ as a function of $\theta$ alone. $$\cos(180^\circ-\theta)=-\cos\theta$$
Work Step by Step
$$\cos(180^\circ-\theta)$$ To be expressed as a function of $\theta$ alone, we need here the identity for difference of cosines: $$\cos(A-B)=\cos A\cos B+\sin A\sin B$$ Apply it to $\cos(180... |
CryptoDB Mark Zhandry Affiliation: Princeton University, USA Publications Year Venue Title
2019
EUROCRYPT
On ELFs, Deterministic Encryption, and Correlated-Input Security 📺
We construct deterministic public key encryption secure for any constant number of arbitrarily correlated computationally unpredictable messages. ... |
It is my understanding that upthrust from a liquid on a body is due to pressure difference on the top of the body and the bottom of the body. How, then, is this fact used in order to derive/work out that the upthrust on a body is equal to the weight of fluid displaced? (For example, if a ball bearing is dropped through... |
I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better.
As an exercise in stenography I wrote down the Chern Simons action:
$$ S = \frac{k}{4\pi} \int_{M_3} (A \wedge dA + \frac{... |
Nuclei Radioactivity α-decay can be written as, ZP A→ Z−2D A− 4+ 2He 4 Ex: 92U 238→ 90Th 234+ 2He 4 β – decay can be written in the form, ZP A→ Z+1D A+ −1e 0 Ex: 90Th 234→ 91Pa 234+ −1e 0 The emission of γ-rays from the nucleus does not alter either atomic number Z or mass number A. The wave lengths of γ-rays is less t... |
This is a bad metaphor for rubes, as you say. The axle gives a conserved quantity across the transition for a wagon, the distance between the wheels is constant as the transition is happening. So the bending goes to 90 degrees when the boundary becomes parallel to the direction of cart propagation. This is not what hap... |
Differential and Integral Equations Differential Integral Equations Volume 22, Number 5/6 (2009), 575-585. On pairs of positive solutions for a class of quasilinear elliptic problems Abstract
We prove, by using bifurcation theory, the existence of at least two positive solutions for the quasilinear problem $-\Delta_p u... |
I have a problem writing an equation in
eqnarray environment, where I split a single line into two lines. The first line starting with
\left[ and the second line ending with
\right], but I could not compile it using latex.
I have a problem writing an equation in
Here is an example of using the
\right., and
\left. pair ... |
Word2Vec Algorithm- Skip-gram and Continuous Bag of Words
Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a ve... |
Recall that a family of graphs (indexed by an infinite set, such as the primes, say) is called an
expander family if there is a $\delta>0$ such that, on every graph in the family, the discrete Laplacian (or the adjacency matrix) has spectral gap $|\lambda_0-\lambda_1|\geq \delta$. (Assume all graphs in the family have ... |
One equation to calculate a heat change is $q = c_p \cdot m \cdot\Delta T$. I know that $\Delta T$ can be in either degrees Celsius ($^\circ{}\mathrm{C}$) or kelvin ($\mathrm{K}$). However, one thing that confuses me is how the units cancel if $\Delta T$ is in degrees Celsius, since $c_p$ has units of $\mathrm{J\ g^{-1... |
We define a parabola as the locus of a point that moves such that its distance from a fixed straight line called the
directrix is equal to its distance from a fixed point called the focus. Unlike the ellipse, a parabola has only one focus and one directrix. However, comparison of this definition with the focus - direct... |
Let's examine the one-dimensional three-point stencil case in detail,because I think it's important to be clear just how this behaviourarises, and what it means to set a point to a certain value in afinite-difference grid when the underlying function isdiscontinuous. The equation will be$$ u''(x) = \rho(x). $$Instead o... |
The intuition behing the residual graph in the Maximum flow problem is very well presented in this lecture. The explanation goes as follows.Suppose that we are trying to solve the maximum flow problem for the following network $G$ (where each label $f_e/c_e$ denotes both the flow $f_e$ pushed through an edge $e$ and th... |
This only answers your first question. The groups $(\mathbb Z_2)^k$ have the fastest growing (outer) automorphism groups possible.
We can derive a pretty good upper bound on the size of automorphism groups. In particular, first note that if $G$ is a finite group with $n$ elements, then it has a generating set $S$ of si... |
Newton limit is approximation of GR in weak fields and SMALL velocities.
Small velocities means, that whole 4-velocity of a particle is basically in time component. So you can imagine, that if spacetime is curved same in all directions, than the time component is most significant simply because the particle almost does... |
It may be a pseudo question. But I still decide to ask. Given two $k$-modules $M$ and $N$，it seems to me that in the literature the tensor product $M\bigotimes_kN$ is always defined as the quotient of the free module generated over the set $M\times N$ modulo the ideal generated by the bi-linearity relations. But I am c... |
Let $x$ denote the solution of $Ax=b$ and let $\hat{x}$ denote the computed solution. We cannot hope to do better than $$\hat{x} = \text{fl}(x),$$ i.e., the floating point representation of $x$. In this, the most favorable case, we have $\hat{x}_j = x_j(1+\delta_j)$ where $|\delta_j| \leq u$ and $u$ is the unit roundof... |
Now that we have set our axioms - Newton’s laws of motion and the various force laws - we are ready to start combining them to get useful results, things that we did not put into the axioms in the first place but follow from them. The first thing we can do is write down equations of motion: an equation that describes t... |
This is a picture of a Upsilon system. The thing I'm wondering is that energy width $\Gamma$ for forth one (4S) wave is very different than the first three.
I know there is a formula which explains the relation between cross-section and energy width $\Gamma$ but i don't understand how this graph can be explained using ... |
How do we evaluate the limits: $$ \lim_{x \to 0^{+,-} } \frac{\sin\ 2x}{|\sin\ 2x|}, \lim_{x\to \frac{π}{2}^{+,-} } \frac{\sin\ 2x}{|\sin\ 2x|}$$
if we have absolute value at the denominator?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fiel... |
I am struggling with this question:
Prove or give a counterexample: If $f : X \to Y$ is a continuous mapping from a compact metric space $X$, then $f$ is uniformly continuous on $X$.
Thanks for your help in advance.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and profe... |
While studying a certain Diophantine equation in the integer $k \ge 2$, I believe I have proven the necessary restriction
$$2^{k-1} \equiv 1\!\!\pmod{k^2}. \qquad(\star)$$
Based on what I read about Wieferich primes on Wikipedia (http://en.wikipedia.org/wiki/Wieferich_prime), if $k$ is a prime, it must be a Wieferich p... |
The Hong–Ou–Mandel effect can be described like this: Two photons enter a particular type of beamsplitter, one from each side. If the two photons are "identical" in the sense defined below, then the probability of detecting one photon on each side of the output is zero. Both photons will always be detected on the same ... |
CryptoDB Dongvu Tonien Publications Year Venue Title
2006
EPRINT
An Efficient Single-Key Pirates Tracing Scheme Using Cover-Free Families
A cover-free family is a well-studied combinatorial structure that has many applications in computer science and cryptography. In this paper, we propose a new public key traitor trac... |
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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... |
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If α\alphaα and β\betaβ are the roots of the equation 2x2−5x−1=02x^2-5x-1=02x2−5x−1=0, form equations whose roots are
(a) αβ\frac{\alpha}{\beta}βα, βα\frac{\beta}{\alpha}αβ
(b) α2β\alpha^2\betaα2β, αβ2\alpha\beta^2αβ2
Note by Victor Loh 5 years, 2 months ago
Easy... |
Assume that there is polytime algorithm that given $C(\vec{x}) \in F(\vec{x})$ and $\vec{a}$ computed the result of the multi-linearization of $C$ on $\vec{a}$. (w.l.o.g. I will assume that the output $\vec{b}$ will be a vector of $p$-bit binary numbers $b_i$ is $k$ iff the $b_{i,k}$ is one.)
Since $P \subseteq P/poly$... |
Votes cast (165)
all time by type 156 up 57 question 9 down 108 answer
13
How many points are needed to uniquely define an ellipse?
7
Convert infinite 2D plane integer coords to 1D number
5
Calculating the square root of 2
4
Is $\tan^{-1}(-1) = 3\pi /4$ or $=7\pi /4$? I understand they're both valid solutions, but what... |
I am trying to figure out the scattering wave function for the following potential:
$$V(x,x')=-A \phi(x)\phi^*(x')$$ Such that the SE can be written as $$[\frac{\hbar^2\partial^2_x}{2m}-E]\psi = A\phi(x)\int dx'\phi^*(x')\psi(x')$$ This has a solution $$\psi(x)=\alpha e^{ikx}+\beta e^{-ikx}+\lambda[\int dx' K(x,x';E)\p... |
Thank you Kasper. I've build the github version 2.2.7, and soo that you improve my rusty version of the notebooks. Great work!
I'd like to mention that I try the following code:
{M,N,P,Q,J,K,L}::Indices(full, position=independent).
{\mu,\nu,\rho,\sigma,\gamma,\lambda}::Indices(sub,position=independent, parent=full).
e^... |
Learning Objectives
State the forces that act on a simple pendulum Determine the angular frequency, frequency, and period of a simple pendulum in terms of the length of the pendulum and the acceleration due to gravity Define the period for a physical pendulum Define the period for a torsional pendulum
Pendulums are in ... |
Intuitively, shifting then reflecting is not the same as reflecting then shifting. Consider the case of first shifting 1 unit to the right from 0, then reflecting: you end up at $x=-1$. If you reflect first, it does nothing, and then shifting to the right by $1$ means you end up at $x=1$.
The problem is that$$\hat{T}(-... |
Modular forms and the inverse Galois problem for PSL_2( Z /p^n Z )
Adibhatla, Rajender
Presentation (2013, August 28)Detailed reference viewed: 23 (0 UL)
A characterization of ordinary modular eigenforms with CM
Adibhatla, Rajender ; Tsaknias, Panagiotis
in Arithmetic and Geometry (2013, July)Detailed reference viewed:... |
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Finally posted the paper on AoPS here!
It is on a new inequality I discovered while writing a Proofathon problem a while back.
Enjoy, and please give feedback!
Note by Daniel Liu 4 years, 10 months ago
Easy Math Editor
This discussion board is a place to discuss ... |
Let $p:\overline{X}\rightarrow X$ be a simply connected covering of a path connected space $X$ and $A\subset X$ be a path connected set.
Show that the inclusion induced homomorphism $i_{\sharp} : \pi_1(A)\rightarrow \pi_1(X)$ is injective iff each path component of $p^{-1}(A)$ is simply connected.
First of all i do not... |
I'm writing a beamer presentation on basic math type-setting in latex and I've been trying to use verbatim to display how math equations are typed. Using
fragile this works, but I still get several annoying error messages every time I compile, so I'm never sure if I have an actual error or if beamer is just complaining... |
Problem 676
Let $V$ be the vector space of $2 \times 2$ matrices with real entries, and $\mathrm{P}_3$ the vector space of real polynomials of degree 3 or less. Define the linear transformation $T : V \rightarrow \mathrm{P}_3$ by
\[T \left( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \right) = 2a + (b-d)x – (a+c)x^2 +... |
I'm interested in the case where I have received a signal as a composition of three echoes of the transmitted signal $x[n]$ (each echo has its amplitude and time delay). I know that in order to compare the signals I use cross-correlation. My question is if I use $r_{xx}[m] = \delta[m]$, would that make it easier to cal... |
Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$. (a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the multiplicative group $G$. (b) Determine the index $[G : S]$.
Add to solve later
(c) Assume that $-1\notin S$. ... |
This was inspired by many puzzles that use three/four numbers to create other numbers. I chose these numbers in particular because of this post.
Can you find a way to make all the natural numbers from $1$ to $15$ with
all four of just following numbers?
$3,9,9,9$
You are allowed to use
any operation only the following ... |
Hi good people!,
How would I go about finding the modulus, the argument and plotting: \(z=\sqrt2-i\)?
I get this to be in the 4th quadrant, but it seems incorrect?...thanx for the help!..
The modulus is 3, and the angle calculates to 30 or 40 something..cannot remember...anycase the actual question is the quadrant...pl... |
CryptoDB Satrajit Ghosh Affiliation: Aarhus University Publications Year Venue Title
2019
EUROCRYPT
An Algebraic Approach to Maliciously Secure Private Set Intersection 📺
Private set intersection (PSI) is an important area of research and has been the focus of many works over the past decades. It describes the problem... |
Difference between revisions of "NTS ABSTRACTSpring2019"
(→Feb 7)
Line 60: Line 60:
$$trace (\rho(g))/dim (\rho),$$
$$trace (\rho(g))/dim (\rho),$$
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random ... |
Tagged: determinant of a matrix Problem 718
Let
\[ A= \begin{bmatrix} 8 & 1 & 6 \\ 3 & 5 & 7 \\ 4 & 9 & 2 \end{bmatrix} . \] Notice that $A$ contains every integer from $1$ to $9$ and that the sums of each row, column, and diagonal of $A$ are equal. Such a grid is sometimes called a magic square.
Compute the determinan... |
Kinetic Theory of Gas Molecular nature of matter and Behaviour of Gases A gas consisting of large number of identical, tiny spherical, neutral and elastic particles called molecules. In a gas molecules none in all possible directions with all possible speeds. The pressure of gas is due to elastic collisions of the gas ... |
The Danish butcher production and retail chain, MeatMe, is considering whether to start production of dogfood and decides to start a 7 days test production and call the product BargainBone. For the fixating of price, MeatMe wishes to analyze the relation between the produced quantity (in kg.) and the total costs of pro... |
Let $(N \subset M)$ be an irreducible finite index depth $n$ subfactor. Let $P = P(N \subset M)$ its planar algebra.
Let $(B_i)$ be the finite sequence of $N$-$N$-bimodules appearing in the principal graph. Let $2m = n$ if $n$ even, else $2m=n+1$. Let $p_i \in P_{2m,+}$ be the minimal central projection related to the ... |
There is quasi 1-D C-D nozzle test case for compressible flow codes, like that "is there any 1-D test case for incompressible flow codes?"
To build on Bill Barth's commment, there really isn't any depth here. The equations you're trying to solve are: \begin{align} u_t + uu_x &= - \frac{1}{\rho}p_x + \nu u_{xx} \\ u_x &... |
I am reading some old papers regarding Learning With Malicious Noise. In one of them,
Learning in the presence of Malicious Errors, by Kearns and Li $[1]$ (https://www.cis.upenn.edu/~mkearns/papers/malicious.pdf), it is proved that in the case that an adversary may choose a fraction $\beta \in [0, \frac{1}{2})$ of the ... |
I am trying to implement an algorithm in real-time on a Fixed point DSP (The Blackfin from Analog Devices). The algorithm does a lot of stuff, but in the middle it performs an algorithm called "Fast Data Projection Method" (FDPM), which goes something like this:
Let $\mathbf{x}_{k} = [x_{1}, x_{2},\dotsb,x_{M}]^{T}$ be... |
Does 1 kHz sine tone means $\sin(2(1000)\pi t)$ or $\sin(2(500)\pi t)$?
The trigonometric functions "do not know" what a Hertz is and they do not care either. The only thing they know is that a full circle is $2 \pi$ radians. Whether this circle concludes in days, hours, picoseconds or a slice of it represents the angl... |
Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$. (a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the multiplicative group $G$. (b) Determine the index $[G : S]$.
Add to solve later
(c) Assume that $-1\notin S$. ... |
Wondering if there are any documents, theories, or methodologies for dealing with mutable memory mathematically. Basically a formal algebraic model of how computers manipulate memory. Along the lines of, say I want to model an
add operation at a low level, and it writes its output to a register. Then we can model the c... |
Supposing we have a boolean function from $f:\{0,1\}^n\rightarrow\{0,1\}$. It is clear that a real multivariate polynomial $p(x)$ such that $f(x)=p(x)$ on $x\in\{0,1\}^n$ can be multilinear. What are some interesting classes of boolean functions for which the minimal degree of $p(x)$ is known? Do we have concrete examp... |
The refinement order on partitions of an integer $n$ can be defined as follows: $\lambda=(\lambda_1,\dots,\lambda_k)\leq\mu=(\mu_1,\dots,\mu_\ell)$ if there is a partition of the parts of $\lambda$ into blocks whose sums are the parts of $\mu$.
It is known that the problem of deciding whether $\lambda\leq\mu$ is NP-com... |
If $x(t)$ is an action signal like voltage or current, then the square of $x(t)$ is
to instantaneous power and the constant of proportionality depends on what kinda animal $x(t)$ is and what load $x(t)$ is connected to. proportional
So if $\big|x(t)\big|^2$ is proportional to instantaneous power, so also is the integra... |
Let $k$ be a field. Let $\mathcal{C},\mathcal{D}$ be finitely cocomplete $k$-linear categories, which are essentially small. Then Kelly's tensor product $\mathcal{C} \boxtimes \mathcal{D}$ is a finitely cocomplete $k$-linear category together with an universal functor from $\mathcal{C} \times \mathcal{D}$ which is righ... |
BackgroundI have searched a bit for the definition/constructions on how to "semi-localize" a scheme, but have been unsuccessful in finding a good reference; I apologize in advance if this topic has been covered in detail elsewhere (e.g. in a book or article) and would be happy for a reference!
This question arose from ... |
Neighbourhood density function
Computes the neighbourhood density function, a local version of the \(K\)-function or \(L\)-function, defined by Getis and Franklin (1987).
Usage
localK(X, ..., rmax = NULL, correction = "Ripley", verbose = TRUE, rvalue=NULL) localL(X, ..., rmax = NULL, correction = "Ripley", verbose = TR... |
What is meant by a complete description of a stochastic process? Well, mathematically, a stochastic process is a collection $\{X(t) : t \in {\mathbb T}\}$ of random variables, one for each time instant $t$ in an index set $\mathbb T$, where usually $\mathbb T$ is the entire real line or the positive real line, and a co... |
Current results are able to yield such results. Depending on how generous one is regarding what $X$ is. If it is just the optimal value can be calculated
exactly this will work for many more $k$ and if one is happy with an explicit bound for all $k$.
For example Dusart showed that $$ \frac{x}{\log x - 1} \le \pi(x) \le... |
Home > Semileptonic B-Meson decays at Belle II
BELLE2-CONF-PROC-2018-013
Jo-Frederik Krohn
31 July 2018 Abstract: The Belle II experiment is the upgrade of the Belle experiment, performed at the SuperKEKB asymmetric electron-positron-collider, located in Tsukuba, Japan. With an design instantaneous luminosity of $8\cdo... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (21) (remove) Language English (21) (remove)
293
Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this pap... |
It is not difficult to calculate upper bounds on $s(n)$ from bounds on the prime counting function $\pi(n)$. Just use integration by parts,$$s(n) = \int_0^n x\,d\pi(x) = n\pi(n) - \int_0^n\pi(x)\,dx.$$I'm not sure what the currently best known bounds for $\pi(x)$ are but, checking Wikipedia, gives$$\frac{x}{\log x}\lef... |
In addition to @Nanoputian's excellent description of constructive and destructive interference in the formation of MOs, I want to provide a more mathematical explanation for why the phase of the wavefunction does not matter.
Finding the wavefunction
The time-independent Schrödinger equation, in one dimension, reads:
$... |
Tagged: ideal Problem 624
Let $R$ and $R’$ be commutative rings and let $f:R\to R’$ be a ring homomorphism.
Let $I$ and $I’$ be ideals of $R$ and $R’$, respectively. (a) Prove that $f(\sqrt{I}\,) \subset \sqrt{f(I)}$. (b) Prove that $\sqrt{f^{-1}(I’)}=f^{-1}(\sqrt{I’})$
Add to solve later
(c) Suppose that $f$ is surjec... |
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