text stringlengths 256 16.4k |
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Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
It will be shown how to compute the density matrix for the harmonic oscillator:
\[ H = {P^2 \over 2m} + {1 \over 2}m\omega^2 X^2\]
using the functional integral representation. The density matrix is given by
\[ \rho(x,x';\beta) = \int_{x(0)=x}^{x(\beta\hbar)=x'}{\cal D} x (\tau ) exp \left [ - {1 \over \hbar } \int _0^... |
How to solve that eqation?
$\displaystyle 3^x=4y+5$
Follow Math Help Forum on Facebook and Google+
$\displaystyle 3^x\equiv 5=1 \ \mbox{(mod 4)}$
Ok, but what it is. How can I do i to my equation.
What happens when x = 2? How about x = 4? ....
Can you solve me a complete this equation, Step by step?
I pretty much solve... |
Homoclinic solutions of discrete $ \phi $-Laplacian equations with mixed nonlinearities
School of Mathematics and Information Science, Guangzhou University, Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
By using critical point theory, we obtain some new sufficient conditions on the exist... |
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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 ... |
Wednesday, March 4, 2015
Since Github Pages is way nicer than Blogger, I'm writing over there at http://davidchudzicki.com now. To keep old posts alive, these pages at http://blog.davidchudzicki.com will remain as is.
Tuesday, January 21, 2014 Saturday, October 26, 2013
Then I learned that GIFs can only use 256 colors ... |
In the days before email, mathematicians relied upon pen, paper and the postman to share ideas and communicate fiendish numerical taunts. An excited Dirichlet wrote to Kronecker in 1858:
… that sum, which I could only describe up to an error of order $\sqrt{x}$ at the time of my last letter, I’ve now managed to home in... |
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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... |
Solving Nonlinear Static Finite Element Problems
Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. This information is presented in the context of a very simple 1D finite element problem, and builds upon our previous entry on Solving Linear Static Finite Element Mod... |
L-function
Calculates an estimate of the \(L\)-function (Besag's transformation of Ripley's \(K\)-function) for a spatial point pattern.
Usage
Lest(X, ...)
Arguments Details
This command computes an estimate of the \(L\)-function for the spatial point pattern
X. The \(L\)-function is a transformation of Ripley's \(K\)-... |
Again, let \(x_i\) and \(x_j\) be specific components of the phase space vector \(x = (p_1,\cdots ,p_{3N},q_1,\cdots,q_{3N})\). Consider the canonical average
\[ \langle x_i \frac {\partial H}{\partial x_j} \rangle \]
given by
\( \langle x_i \frac {\partial H}{\partial x_j} \rangle \)
\(\frac {1}{Q} C_N \int dx x_i \fr... |
Given an single vector field $A_\mu(x)$ is it possible to make a diffeomorphism invariant action in 4 dimensions? In the same way that General Relativity is diffeomorphism invariant?
My first guess would be:
$$ S = \int \left( \det_{ij}(\partial_i A_j(x))\right)^{1/2} dx^4 $$
or the same question with a single scalar f... |
FARADAY MAGNETO OPTICAL (MCD) ACTIVITY IN CUBIC COMPLEXES Issue Date:1970 MetadataShow full item record Publisher:Ohio State University Abstract:
Magneto-optical rotational strengths of d-d and charge-transfer electronic transitions were measured using MCD spectroscopy. Magnetic fields ranging from 25 000 gauss to 45 0... |
AliPhysics b76e98e (b76e98e)
#include <AliFMDCorrNoiseGain.h>
AliFMDCorrNoiseGain () AliFMDCorrNoiseGain (const AliFMDFloatMap &map) Float_t Get (UShort_t d, Char_t r, UShort_t s, UShort_t t) const void Set (UShort_t d, Char_t r, UShort_t s, UShort_t t, Float_t x) const AliFMDFloatMap & Values ()
AliFMDFloatMap fValues... |
I haven't checked the details of this myself, so I can't tell you the correct answers to your questions, but I would suggest that you try to apply the adjoint functor theorem of category theory:
http://en.wikipedia.org/wiki/Adjoint_functors#General_existence_theorem
To translate the problem into categorical language, l... |
I have just been to Perimeter Institute, by generous invitation of Thomas Galley. I gave a talk there about my recent-ish paper, Probability in two deterministic universes. Since I have already blogged about it here, I’m not writing about it again, but rather what I discussed with Thomas about his derivations of the Bo... |
I promised I'd come back to this one because it merits special discussion. Now it's time to do exactly that, as this one (as well as its many variations) has piqued my ire every time I've seen it.
Most people who have had at least a basic prealgebra class tend to agree that the \(1+2\) in parentheses should be evaluate... |
I am learning qiskit software and this term keeps popping up and I am unable to get a grasp on the technical definition given by wikipedia. For example, the functions state fidelity and process fidelity.
Simply it is the distance (similarity measure) between two quantum states, for example the fidelity between $|0\rang... |
I am going through the derivation of CMS convexity from the notes of Lesniewski
There is a transformation from $T_p$ forward measure to annuity measure $Q$ as
$$ P(0,T_p)E^{Q_{T_p}}\left[S(T_0,T)\right]=A(0,T_0,T_n)E^Q\left[S(T_0,T)\frac{P(T_0,T_p)}{A(t,T_0,T_n)}\right] $$
where $A(t,T_0,T)=\sum_{1\le j \le n} \alpha_i... |
Century
First, you'd have to watch through a night to see if Polaris wobbles - currently, the radius is about 1° I think, but that changes with precession (and nutation, but that's small enough to ignore).
Once you know that, you can try to find a point in the sky that stays still all the time (like Polaris nearly does... |
Existence of Solutions of Some Nonlinear φ-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions
Existence of Solutions of Some Nonlinear φ-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions
Abstract
We study the existence of solutions of the quasilinear equation $$(D(u(t))\phi(u'(t... |
I thought I was done writing about this topic, but it just keeps coming back. The internet just cannot seem to leave this sort of problem alone:
I don't know what it is about expressions of the form \(a\div b(c+d)\) that fascinates us as a species, but fascinate it does. I've written about this before (as well as why "... |
LombScargle¶ class
astropy.timeseries.
LombScargle(
t, y, dy=None, fit_mean=True, center_data=True, nterms=1, normalization='standard')¶
Compute the Lomb-Scargle Periodogram.
This implementations here are based on code presented in [R14388b5a5a57-1] and [R14388b5a5a57-2]; if you use this functionality in an academic ap... |
Definition:Restriction/Operation Definition
Let $\left({S, \circ}\right)$ be an algebraic structure, and let $T \subseteq S$.
The restriction of $\circ$ to $T \times T$ is denoted $\circ {\restriction_T}$, and is defined as: $\forall t_1, t_2 \in T: t_1 \mathbin{\circ {\restriction_T}} t_2 = t_1 \circ t_2$ The notation... |
Definition:Trigonometric Function Contents 1 Definition 2 Sine 3 Cosine 4 Tangent 5 Cotangent 6 Secant 7 Cosecant 8 Also known as 9 Sources Definition
In the above right triangle, we are concerned about the angle $\theta$.
The
sine of $\angle \theta$ is defined as being $\dfrac {\text{Opposite}} {\text{Hypotenuse}}$. T... |
On the geometry of the
p-Laplacian operator
1.
Mathematisches Institut, Universität zu Köln, 50923 Köln, Germany
2.
Fakultät Maschinenbau, TH Ingolstadt, Postfach 21 04 54,85019 Ingolstadt, Germany
$p$
$\Delta_pu={\rm div }\left(|\nabla u|^{p-2}\nabla u\right)$
$p\in(1,2)\cup(2,\infty)$
$p\to \infty$
$p\to 1$
$p$
$p\to... |
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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... |
Stoyan's Rule of Thumb for Bandwidth Selection
Computes a rough estimate of the appropriate bandwidth for kernel smoothing estimators of the pair correlation function and other quantities.
Usage
bw.stoyan(X, co=0.15)
Arguments X
A point pattern (object of class
"ppp").
co
Coefficient appearing in the rule of thumb. See... |
K-Means, coverings, and Voronoi diagrams This is the 4th of a series of posts on cluster-algorithms and ideas in data analysis.
The $k$-Means algorithm computes a Voronoi partition of the data set such that each landmark is given by the centroid of the corresponding cell. Let me quickly quote Wikipedia on the history o... |
Peter Saveliev
Hello! My name is Peter Saveliev. I am a professor of mathematics at Marshall University, Huntington WV, USA.
My current projects are these two books:
In part, the latter book is about
Discrete Calculus, which is based on a simple idea:$$\lim_{\Delta x\to 0}\left( \begin{array}{cc}\text{ discrete }\\ \te... |
The qualifier "natural" is meant to exclude examples like "PA + P=NP" or "PA + True $\Pi_1$".
For concreteness, let's say that "natural" = sound, computably enumerable, with a feasible proof-checker. Context of the question.
A naive way to approach the P vs NP problem, from the logical point of view, could go like this... |
What is Perceptron?
Perceptron is one of the simplest types of artificial neural network and invented by Frank Rosenblatt in 1957. A single layer Perceptron is typically used for binary classification problems (1 or 0, Yes or No). The goal of Perceptron is to estimate the parameters that best predict the outcome, given... |
I suppose the right way to do C (charge), T (time reversal), P(parity) transformation on the state $\hat{O}| v \rangle$ with operators $\hat{O}$ is that:
$$C(\hat{O}| v \rangle)=(C\hat{O}C^{-1})(C| v \rangle)\\P(\hat{O}| v \rangle)=(P\hat{O}P^{-1})(P| v \rangle)\\T(\hat{O}| v \rangle)=(T\hat{O}T^{-1})(T| v \rangle)$$
T... |
Hananish Joy G. Odarve and Majvell Kay G. Odarve
The wavefunction, or quantum state, is a complete description that can be given into a physical system. The Schrodinger equation can describe how the wavefunction changes as time propagates.
A particle state, for example, can be determined by solving the Schrodinger equa... |
Definition:Jump Discontinuity Definition
Let $X$ be an open subset of $\R$.
Let $f: X \to Y$ be a real function.
Let $f$ be discontinuous at some point $c \in X$.
Then $c$ is called a jump discontinuity of $f$ if and only if: $\displaystyle \lim_{x \mathop \to c^-} \map f x$ and $\displaystyle \lim_{x \mathop \to c^+} ... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
March 2007 , Volume 19 , Issue 1
Select all articles
Export/Reference:
Abstract:
We are interested in a remarkable property of certain nonlinear diffusion equations, which we call
blow-downor delayed regularization. The following ha... |
Is there a group $G$ with the property that $G$ is a smooth manifold, the multiplication map of $G$ is smooth, but the inversion map of $G$ is not smooth?
Robert L. Bryant "An Introduction to Lie Groups and Symplectic Geometry" requires in the definition of a Lie group only that the multiplication map be smooth, and th... |
Surds are less common in MBA entrance tests, including CAT. However, the concept of surds is quite simple and could be applied in other calculations. Note that we may not have direct questions, but these concepts might have to be applied while solving other algebraic questions.
Questions on Indices are quite common in ... |
I have a Hamiltonian and I want to know the corresponding density matrix. The matrix I'm interested in is the one in this question.
There's many different density matrices that can correspond to a given Hamiltonian.
For the 8x8 matrix in your question, there's 8 different "eigenstate" density matrices that can be obtai... |
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Now showing items 1-1 of 1
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
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 ... |
It's misleading. It's unnecessary.
Let's start with the "P" (Parentheses). People claim that PEMDAS
is"the order of operations." This is already problematic because parentheses aren't really a mathematical operation.** Operations dothings. Parentheses don't actually doanything - they just group things together. This di... |
OpenCV 4.1.0
Open Source Computer Vision
void cv::accumulate (InputArray src, InputOutputArray dst, InputArray mask=noArray()) Adds an image to the accumulator image. More... void cv::accumulateProduct (InputArray src1, InputArray src2, InputOutputArray dst, InputArray mask=noArray()) Adds the per-element product of tw... |
I have a sequence of positive terms $(a_n)$, for which $\sum_{n=1}^\infty a_n = A <\infty$, and wish to take a psuedo-random sample from the discrete probability distribution
\begin{equation} \mathbf{P}[ X = n] = \frac{a_n}{A}. \end{equation}
The standard approach to sampling $X$ is to first sample a (continuous) unifo... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
I never learned stochastic differential equations, and so am trying to do some self study. I've arrive at this question: $tB_t\sim N(0,t^3)$? $B_t$ is standard brownian motion. $B_t\sim N(0,t)$, so just applying standard probability, we get the $t^3$. Is that ok?
But I have derived the formula: $tB_t=\int_0^t sdB_s+\in... |
Smoothing Estimate of Intensity as Function of a Covariate
Computes a smoothing estimate of the intensity of a point process, as a function of a (continuous) spatial covariate.
Usage
rhohat(object, covariate, ...)
# S3 method for ppprhohat(object, covariate, ..., baseline=NULL, weights=NULL, method=c("ratio", "reweight... |
Two common analytical problems are: (1) matrix components that interfere with an analyte’s analysis; and (2) an analyte with a concentration that is too small to analyze accurately. We have seen that we can use a separation to solve the first problem. Interestingly, we often can use a separation to solve the second pro... |
January 11 Matt Papanikolas (Brown University) Periods of Drinfeldmodules with complex multiplication
We investigatetranscendence properties of periods of Drinfeld modules withcomplex multiplication. In particular we show that if suchDrinfeld modules have different CM fields then their fundamentalperiods are algebraica... |
I am working with functions like
f[z_] = Hypergeometric2F1[4, 4, 8, z]
Here is a plot of this function over the interval $z \in [0,1]$:
Plot[f[z], {z, 0, 1}]
As you can see, Mathematica has difficulties evaluating it in the region $z \approx 0$. This is surprising, because the hypergeometric function admits by definiti... |
№ 9
All Issues Chaichenko S. O.
↓ Abstract
Ukr. Mat. Zh. - 2019. - 71, № 4. - pp. 516-542
We compute the exact values of the exact upper bounds on the classes of bounded holomorphic and harmonic functions in a unit disk for the remainders in a Voronovskaya-type formula in the case of approximation by Fej´er means. We a... |
JET-COOLED DIODE LASER SPECTRUM OF THE $\nu_{3}$ BAND OF $N_{2}O_{3}$ AT $1304 CM^{-1}$ Issue Date:1993 MetadataShow full item record Publisher:Ohio State University Abstract:
The jet-cooled spectrum of the $\nu_{3}$ (symmetric $NO_{2}$ stretch) band of $N_{2}O_{3} (NO_{2}$-NO mixed dimer) at $1304 cm^{-1}$ has been ob... |
Use Case
Mathematica evaluate the partial derivative as:
$$\frac{\partial}{\partial A_{abc}}\sum _{j=1}^J \sum _{k=1}^K \log \left(\sum _{l=1}^L A_{jkl} B_{jkl}\right) = \sum _{j=1}^J \sum _{k=1}^K \frac{\sum _{l=1}^L\delta _{aj} \delta _{bk} \delta _{cl} B_{jkl}}{\sum _{l=1}^L A_{jkl}B_{jkl}}$$
Instead of
$$\frac{B_{a... |
I found that some theories about quantum theory is similar to Fourier transform theory. For instance, it says "A finite-time light's frequency can't be a certain value", which is similar to "A finite signal has infinite frequency spectrum" in Fourier analysis theory. I think that a continuous frequency spectrum cannot ... |
Some weeks ago, Robert Kucharczyk and Peter Scholze found a topological realisation of the ‘hopeless’ part of the absolute Galois group $\mathbf{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$. That is, they constructed a compact connected space $M_{cyc}$ such that etale covers of it correspond to Galois extensions of the cycl... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Once we have ascertained that our Euler diagram fits well, we can turn to visualizing the solution. For this purpose,
eulerr relies on the grid graphics system (R Core Team 2017) and offers intuitive and granular control over the output.
Plotting the ellipses is straightforward using the parametrization of a rotated el... |
Consider two canonical systems, 1 and 2, with particle numbers \(N_1\) and \(N_2\), volumes \(V_1\) and \(V_2\) and at temperature \(T\). The systems are in chemical contact, meaning that they can exchange particles. Furthermore, we assume that \(N_2 \gg N_1 \) and \(V_2 \gg V_1 \) so that system 2 is a particle reserv... |
You may as well assume that $U=N$, otherwise restrict to $U$.
Thus the question is, given a manifold $N$, and a distribution $\Delta$ such that $\Delta_q= \newcommand\Span{\operatorname{Span}}\Span(X_{1,q},\ldots,X_{i,q},\ldots)$ for $X_i$ global vector fields on $N$, then for any $X\in \Delta$, do there exist locally ... |
Over the last days I’ve been staring at the Bost-Connes algebra to find a ringtheoretic way into it. Ive had some chats about it with the resident graded-guru but all we came up with so far is that it seems to be an extension of Fred’s definition of a ‘crystalline’ graded algebra. Knowing that several excellent ringthe... |
The Compton effect concerns the inelastic scattering of x‑rays by electrons. Scattering means dispersing in different directions, and inelastic means that energy is lost by the scattered object in the process. The intensity of the scattered x‑ray is measured as a function of the wavelength shift \(\Delta \lambda\), whe... |
Steiner Quadruple Systems¶
A Steiner Quadruple System on \(n\) points is a family \(SQS_n \subset \binom {[n]} 4\) of \(4\)-sets, such that any set \(S\subset [n]\) of size three is a subset of exactly one member of \(SQS_n\).
This module implements Haim Hanani’s constructive proof that a Steiner Quadruple System exist... |
This is mostly a recap of the observations made in the comments, plus some more analysis, because I think it's a nice problem to analyse.
First, both the functional form of the system and the reflection symmetry (see also the phase plane) suggest it's a good idea to introduce $x = \alpha+\beta$, $y = \alpha-\beta$, to ... |
To address your questions 1 and 2: this graph shows the real part of $\Psi{(\vec r, t)}=A e^{i(\vec k \cdot \vec r-\omega t)} $ in blue and the real part of $\Psi{(\vec r, t)}=A e^{i(\phi + \vec k \cdot \vec r-\omega t)} $ in purple. Obviously $\Psi$ is a function of two variables, so you can regard the graph either as... |
Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum
School of Mathematics, South China University of Technology, Guangzhou 510641, China
In this paper we consider the non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid, assuming th... |
Say $f:X\rightarrow Y$ and $g:Y\rightarrow X$ are functions where $g\circ f:X\rightarrow X$ is the identity. Which of $f$ and $g$ is onto, and which is one-to-one?
closed as off-topic by Najib Idrissi, N. F. Taussig, Empty, quid♦, Hagen von Eitzen Oct 25 '15 at 22:42
This question appears to be off-topic. The users who... |
Definition:Strictly Positive/Real Number Definition
The
strictly positive real numbers are the set defined as: $\R_{>0} := \set {x \in \R: x > 0}$
The
strictly positive real numbers, written $R_{>0}$, is the subset of $\R$ that satisfies the following:
\((\R_{>0} 1)\) $:$ Closure under addition \(\displaystyle \forall ... |
When writing a document that contains mathematics, many time the need to add an explanation (e.g. stating the theorem used) is raised. To answer this need I wrote two short LaTeX macros:
\explain and
\explainup.
\newcommand{\explain}[2]{\underset{\mathclap{\overset{\uparrow}{#2}}}{#1}}
\newcommand{\explainup}[2]{\overs... |
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Now showing items 1-10 of 51
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... |
This question came up when I was doing some reading into convolution squares of singular measures. Recall a function $f$ on the torus $T = [-1/2,1/2]$ is said to be $\alpha$-Hölder (for $0 < \alpha < 1$) if $\sup_{t \in \mathbb{T}} \sup_{h \neq 0} |h|^{-\alpha}|f(t+h)-f(t)| < \infty$. In this case, define this value, $... |
Last time we revisited Robin’s theorem saying that 5040 being the largest counterexample to the bound
\[ \frac{\sigma(n)}{n~log(log(n))} < e^{\gamma} = 1.78107... \] is equivalent to the Riemann hypothesis.
\[
\Psi(n) = n \prod_{p | n}(1 + \frac{1}{p}) \]
where $p$ runs over the prime divisors of $n$. It is series A001... |
Yes, your example (pieced together from the original post and the comments) $\begin{bmatrix}F_2&F_2\\0&0\end{bmatrix}$ is a noncommutative rng without identity of order $4$.
Since $\begin{bmatrix}1&0\\0&0\end{bmatrix}$ acts as an identity on the left, it would have to be equal to any candidate two-sided identity, if it... |
Definition:Well-Defined/Mapping Definition
Let $f: S \to T$ be a mapping.
Let $\mathcal R$ be an equivalence relation on $S$.
Let $S / \mathcal R$ be the quotient set determined by $\mathcal R$.
Let $\phi: S / \mathcal R \to T$ be a mapping such that: $\map \phi {\eqclass x {\mathcal R} } = \map f x$ Then $\phi: S / \m... |
Ahh, trig identities... a rite of passage for any precalculus student.
This is a huge stumbling block for many students, because up until this point, many have been perfectly successful (or at least have gotten by) in their classes by learning canned formulas and procedures and then doing a bunch of exercises that just... |
Difference between revisions of "Peter Saveliev"
Line 4: Line 4:
My current projects are these two books:
My current projects are these two books:
−
*''[[Topology Illustrated]]'', published 2016
+
*''[[Topology Illustrated]]'', published 2016
−
*''[[Calculus Illustrated]]'',
+
*''[[Calculus Illustrated]]'', 2019
In par... |
Holt-Winters Filtering
Computes Holt-Winters Filtering of a given time series. Unknown parameters are determined by minimizing the squared prediction error.
Keywords ts Usage
HoltWinters(x, alpha = NULL, beta = NULL, gamma = NULL, seasonal = c("additive", "multiplicative"), start.periods = 2, l.start = NULL, b.start = ... |
On a class of nonlinear time optimal control problems
1.
Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma
2.
Dipartimento di Matematica, Università di Roma, Via della Ricerca Scientifica 1, 00133 Roma
$ y'(t)=f(y(t),u(t))\,\quad y(t) \in \mathbb{R}^n,\ ... |
A Belyi-extender (or dessinflateur) is a rational function $q(t) = \frac{f(t)}{g(t)} \in \mathbb{Q}(t)$ that defines a map
\[ q : \mathbb{P}^1_{\mathbb{C}} \rightarrow \mathbb{P}^1_{\mathbb{C}} \] unramified outside $\{ 0,1,\infty \}$, and has the property that $q(\{ 0,1,\infty \}) \subseteq \{ 0,1,\infty \}$.
An examp... |
2017
Was T. S. Eliot's "tantalus Jar" actually a Leyden Jar?, Eric A. Schiff
2014
Electron and hole drift mobility measurements on thin film CdTe solar cells, Qi Long, Steluta A. Dinca, Eric A. Schiff, Ming Yu, and Jeremy Theil
2012
FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact b... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
A Belyi-extender (or dessinflateur) $\beta$ of degree $d$ is a quotient of two polynomials with rational coefficients
\[ \beta(t) = \frac{f(t)}{g(t)} \] with the special properties that for each complex number $c$ the polynomial equation of degree $d$ in $t$ \[ f(t)-c g(t)=0 \] has $d$ distinct solutions, except perhap... |
I want to create a lognormal distribution of future stock prices. Using a monte carlo simulation I came up with the standard deviation as being $\sqrt{(days/252)}$ $*volatility*mean*$ $\log(mean)$. Is this correct?
I'm not sure I understand, but if you want to compute the variance of $exp(X)$, where $X$ is normally dis... |
Suppose we have the following dataset that records individual survival times (dur) and a covariate z:
id| dur | z-------------1 | 1 | -12 | 2 | 13 | 3 | -14 | 4 | 1
I want to model the duration as a function of z. I may specify dur ~ weibull() and parameterize the scale as a function of z. This model can be fitted easi... |
A
tetrahedral snake, sometimes called a Steinhaus snake, is a collection of tetrahedra, linked face to face.
Steinhaus showed in 1956 that the last tetrahedron in the snake can never be a translation of the first one. This is a consequence of the fact that the group generated by the four reflexions in the faces of a te... |
Magnetism results from the circular motion of charged particles. This property is demonstrated on a macroscopic scale by making an electromagnet from a coil of wire and a battery. Electrons moving through the coil produce a magnetic field (Figure \(\PageIndex{1}\)), which can be thought of as originating from a magneti... |
The integrand being a polynomial, I used the binomial formula to separate the monomials:
$$\int_{\frac{1}{4}}^{\frac{3}{4}} x^n(1-x)^n \, dx = \sum_{k = 0}^{n}{ n \choose k}(-1)^{k}\int_{\frac{1}{4}}^{\frac{3}{4}} x^{n+k} \, dx = \sum_{k = 0}^{n}{ n \choose k}(-1)^{k}\left[\frac{(\frac{3}{4})^{n+k+1}-(\frac{1}{4})^{n+k... |
Let $\pi \colon M\to N$ be a smooth map between real smooth manifolds. Then $C^\infty(M)$ forms a module over $C^\infty(N)$ (via pullback). Is this module flat when $\pi$ is a submersion?
Recall that the usual definition of flatness is equivalent to the following
equational condition: whenever $ h_1 \ldots h_k\in C^\in... |
EDIT: After mrf's comment below and some discussion with my instructor for the course it was decided that the below was not really an issue. Namely, I went into reading this lecture with the notion that we were going to solve the $\bar{\partial}$ equation--that this was our main goal. In other words, in the below we we... |
I’ve just seen that Open Science, a new journal by the prestigious Royal Society, published the article Quantum correlations are weaved by the spinors of the Euclidean primitives, by Joy Christian. The article, as numerous others by the same author, claims that Bell’s theorem is wrong, and that one can violate Bell ine... |
When I evaluate
Solve[a==Sin[b*c], b] to rearrange the following for $ b $:
$$ a = \sin(bc) $$
I get the following result from Mathematica:
$$\begin{align*} \left\{\left\{b\to \text{ConditionalExpression}\left[\frac{-\sin ^{-1}(a)+2 \pi c_1+\pi }{c},c_1\in \mathbb{Z}\right]\right\},\right.\left.\left\{b\to \text{Condit... |
The Schrödinger equation for one-electron atoms and ions such as H, \(He^+\), \(Li^{2+}\), etc. is constructed using a Coulombic potential energy operator and the three-dimensional kinetic energy operator written in spherical coordinates. Because the radial and angular motions are separable, solutions to the Schrödinge... |
I want to calculate a flux on my fpga using the Euler equations with the finite volume method. Unfortunately the values of the state variables differ a lot. For example the pressure has a value of 100000 and the density 1.16. This makes it complicated to calculate on the FPGA. Now I'm wondering if there is a normalized... |
Model Compensator of K Function
Given a point process model fitted to a point pattern dataset, this function computes the
compensator of the \(K\) function based on the fitted model (as well as the usual nonparametric estimates of \(K\) based on the data alone). Comparison between the nonparametric and model-compensate... |
Is there a decent way to understand coordinate transformations in this representation?
(By the way, the incredible similarity between that equation and Schrodinger's equation is pretty cool. That matrix there behaves a lot like the complex unit $i$ in that it is a rotation by 90 degrees and has eigenvalues $\pm i$.)
If... |
My book is Differential Forms in Algebraic Topology by Loring W. Tu and Raoul Bott of which An Introduction to Manifolds by Loring W. Tu is a prequel.
The characterization of the closed Poincaré dual is given here (the "(5.13)") in Section 5.5. This has $\int_M \omega \wedge \eta_S$, where $\eta_S$ is on the
right rath... |
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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 ... |
i am looking for literature on this kind of problem. $$ \begin{align} \min_x \max_k &\quad \sum_{i,j} x_{ij}c_{ijk}\\ \text{subject to}&\\ &\sum_j x_{ij}=1,&& \forall i\in\mathcal J\\ &x_{ij}\in\{0,1\},&& \forall i\in\mathcal J, j\in\mathcal M \end{align} $$
$\mathcal J$ is a set of Jobs and $\mathcal M$ is a set of Ma... |
I’m trying to get into the latest Manin-Marcolli paper Quantum Statistical Mechanics of the Absolute Galois Group on how to create from Grothendieck’s dessins d’enfant a quantum system, generalising the Bost-Connes system to the non-Abelian part of the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$.
In d... |
You can use the formula for centre-of-mass, CoM, to calculate the location of the "centre", which is the point the total mass "averages down to". Place your coordinate system somewhere and calculate the following x- and y-coordinates:
$$x_{com}=\frac{\sum mx}{\sum m}\quad , \quad y_{com}=\frac{\sum my}{\sum m}\,.$$
Sim... |
Let $\eta(\tau)$ be the
Dedekind eta function. In his Lost Notebook, Ramanujan played around with a related function and came up with some of the nice evaluations,
$$\begin{aligned} \eta(i) &= \frac{1}{2} \frac{\Gamma\big(\tfrac{1}{4}\big)}{\pi^{3/4}}\\ \eta(2i) &= \frac{1}{2^{11/8}} \frac{\Gamma\big(\tfrac{1}{4}\big)}... |
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