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Difference between revisions of "Weeks-Chandler-Andersen perturbation theory"
(New page: The '''Weeks-Chandler-Anderson perturbation theory''' is based on the following decomposition of the intermolecular pair potential (in particular, the [[Lennard-Jones model | Lennard-J...)
m (Moved colloids to a new page)
(6 interm... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
Following Gather (the volatility surface, chapter 2) we assume the following process:
$$ dS_t = S_t(\mu_t dt+\sqrt{\nu_t}dZ^1_t)$$ $$ d\nu_t= -\lambda(\nu_t-\bar{\nu})dt+\eta\sqrt{\nu_t}dZ^2_t$$
where $Z^1,Z^2$ are two brownian mortion such that $d\langle Z^1,Z^2\rangle_t= \rho dt$. Using the general valuation pde for ... |
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math.CO
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Combinatorics Title: Simple expressions for the long walk distance
(Submitted on 1 Dec 2011 (v1), last revised 23 Jul 2012 (this version, v4))
Abstract: The walk distances in graphs are defined as the resul... |
Julia set
Julia set, set of values in range of holomorphism of function, but out of holomorphism of some its integer iteration.
Julia set is often defined with symbol \(J\) or \(\mathbb J\). The name of the function can be indicated either as the subscript or in the parenthesis immediately after this symbol.
Let \(f\) ... |
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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... |
Consider an Ornstein-Uhlenbeck position process:
$dV_t=dB_t-\lambda V_tdt$
$dX_t=V_tdt$
where $B_t,V_t,X_t$ are all in $R^d$ with $d\geq 3$. Let $X_0\neq0$, $V_0=0$ .
Let $r>0$ and $S_r$ be the sphere with centre $0$ and radius $r$. Let $H(r)$ be the probability that $X_t$ ever hits $H(r)$. The problem is to find $\lim... |
Where did you come up with interpolating the "error"? (And how do you measure the error?)
On the first visit to a finer grid, the entire solution $u$ must be interpolated, ideally using a higher order operator (e.g., postprocessed/reconstructed solution for FEM). This FMG interpolation is $u^h \gets \mathbb{I}_H^h u^H$... |
i need some help on this question
Let $\Omega$ be an open subset of $\mathbb{R}^{2}$ (say a square) with $\partial{\Omega} =\Gamma_{1} \cup \Gamma_{2} \cup\Gamma_{3} \cup\Gamma_{4}$. A structure ocupying this surface is subject to :
1) A weight force F, i am given the explicit expression at each point of $\Omega$ . 2) ... |
It is impossible to construct an explicit example of a non-Borel-measurable subset of $ \mathbb{R} $ as any proof of the existence of such a subset must require the Axiom of Choice ($ \mathsf{AC} $). As you may already know, any construction that relies on $ \mathsf{AC} $ is never explicit — $ \mathsf{AC} $ yields only... |
Show that $X$ is countably compact if and only if every nested sequence $C_1 \supset C_2 \supset ...$ of closed nonempty sets of $X$ has a nonempty intersection.
Suppose that $X$ is not countably compact. Then there exists a countable open cover $\{U_n\}$ of $X$ that has no finite subcover. Consider the collection of c... |
(Log-)convex functions do not need to be twice differentiable, so any proof through $\frac{d^2}{dx^2}$ lacks generality. On the other hand $e^x$ is both a convex and log-convex function, and we may wonder when the composition of two convex functions is convex. Assume that $f(x)$ is convex . Then $g(x)=e^{f(x)}$ is conv... |
The governing equations are listed here of my notes on page 4. It's a reproduction of other's paper which solves the equations with COMSOL. The problems arise when I want to solve for the consistent initial condition of the algebraic components, $\phi_1$ and $\phi_2$. They consist of a kinetic reaction term for five re... |
I'm trying to solve this advection-diffusion equation (ADE):
$$\frac{\partial \phi}{\partial t} + \nabla \cdot (-D \nabla \phi + \mathbf{u} \phi) = 0$$
In fact, this ADE framework is coupled to a Navier-Stokes (NS) solver and I get velocity field ($\mathbf{u}$) from NS solver. My question is about ADE boundary conditio... |
Nadeem Ur Rehman
Articles written in Proceedings – Mathematical Sciences
Volume 124 Issue 4 November 2014 pp 497-500
The main purpose of this paper is to prove the following result: Let $n \gt 1$ be a fixed integer, let 𝑅 be a $n!$-torsion free semiprime ring, and let $f : R \to R$ be an additive mapping satisfying th... |
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Now showing items 1-10 of 26
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... |
2019-09-20 08:41
Search for the $^{73}\mathrm{Ga}$ ground-state doublet splitting in the $\beta$ decay of $^{73}\mathrm{Zn}$ / Vedia, V (UCM, Madrid, Dept. Phys.) ; Paziy, V (UCM, Madrid, Dept. Phys.) ; Fraile, L M (UCM, Madrid, Dept. Phys.) ; Mach, H (UCM, Madrid, Dept. Phys. ; NCBJ, Swierk) ; Walters, W B (Maryland U... |
The Challenge
Write a program or function that takes no input and outputs a vector of length \$1\$ in a
theoretically uniform random direction.
This is equivalent to a random point on the sphere described by $$x^2+y^2+z^2=1$$
resulting in a distribution like such
Output
Three floats from a theoretically uniform random ... |
The Annals of Statistics Ann. Statist. Volume 45, Number 5 (2017), 2151-2189. Phase transitions for high dimensional clustering and related problems Abstract
Consider a two-class clustering problem where we observe $X_{i}=\ell_{i}\mu+Z_{i}$, $Z_{i}\stackrel{\mathit{i.i.d.}}{\sim}N(0,I_{p})$, $1\leq i\leq n$. The featur... |
I am trying to derive Galerkin type weak formulation for the Stokes equations. I'm having a bit of a problem reconciling the notation in the integration by parts. I know that the answer I'm looking for is: $ \int_\Omega \Delta\mathbf{u}\cdot\mathbf{v}d\Omega = \int_\Gamma (\mathbf{n}\cdot\nabla\mathbf{u})\cdot\mathbf{v... |
Summary: it is cheapest and most accurate to use
sqrt(fma(c, c, 1)) if you have FMA, and
sqrt(1+c*c) otherwise. In my testing, though, the difference is extremely marginal: of the 1065353216 32-bit floating point numbers $0\leq c\leq 1$, the first formula is better 532509 times (0.05%), and worse 382159 times (0.035%),... |
I have before me a copy of "The Indian Mathematician Ramanujan", by G. H. Hardy (not actually related to me, as far as I know), which appeared in volume 44, number 3 (March 1937) of
The American Mathematical Monthly, on pages 137‒155.
One of the theorems of Ramanujan stated there is this:
If $\displaystyle F(k) = 1 + \... |
I understand that the usual way of deriving the Boltzmann distribution involves considering a small system of energy $\epsilon$ embedded in a much larger heat bath of energy $E - \epsilon$ and the total system energy is $E$.
Given that the bath has accessible microstates $\Omega_b(E - \epsilon)$ and the system has micr... |
I have four partial differential equations representing mass conservation of two compressible fluid phases (marked by subscripts $p1$ and $p2$) in two different continuum media (marked by subscripts $c1$ and $c2$) and they are coupled together by the term $T_{c1c2}$ as shown below.
Continuum 1:$$\begin{align}\text{Phas... |
So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$?
Diagram of system:
[m]-////-[m]
Now the real problem I'm having is trying to decide what the forces are acting on the system i... |
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Can you help me with this mechanics problem?
Note by Kyle Finch 4 years, 6 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solutio... |
Inverse problem of finding the coefficient of u in a parabolic equation on the basis of a nonlocal observation condition 66 Downloads Citations Abstract
We consider the problem of reconstructing the coefficient
c( x) multiplying u( x, t) in a parabolic equation. To find it, in addition to initial and boundary condition... |
I have a 2D triangle which deforms with each vertex moving by some small ($\sin(x) \approx \tan(x) \approx x$) displacement vector. The displacement of any point in the triangle is linearly interpolated from the displacements at the vertices.
How can I find the rotation angle of any point in the triangle?
I want the ro... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
If you have the wavefunctions you automatically have the eigenvalues since $$-(1/2) \psi''[x] + (1/2) x^2 \psi[x] = \epsilon \psi[x] \tag{1}$$ will converge
only when $\epsilon$ is an eigenenergy.
If you do not have $\epsilon_n$, there are several methods available, but all are ultimately based on the observation that ... |
80 1
Hello Everybody,
Instead of solving the geodesic equations for the Schwarzschild metric, in many books (nearly in all books that I consulted), conserved quantities are looked at instead.
So take for eg. Carroll, he looks at the killing equation and extracts the equation
[tex] K_\mu \frac{dx^\mu}{d \lambda}= consta... |
Despite being able to simply provide a link to wikipedia's already excellent article on Linear Programming, I wanted to provide a short introduction in order to present what I am doing exactly on my thesis in a future article.
Linear Programming is best described as a technique, in which we want to maximize or minimize... |
Why do we care about eigenvalues, eigenvectors, and singular values? Intuitively, what do they tell us about a matrix? When I first studied eigenvalues in college, I regarded it as yet another theoretical math trick that is hardly applicable to my life. Once I passed the final exam, I shelved all my eigen-knowledge to ... |
Yes: for white noise perturbations of the 1D dynamical system $\dot{x}=b(x)$, the action functional is $S(\phi)=\frac{1}{2} \int_0^T |b(\phi(s))-\dot{\phi}(s)|^2 ds$ for $\phi \in H^1$ and otherwise infinity. The LDP says that $\sigma^2 \log(P(X_\cdot \in A))$ is asymptotically between $-\inf_{f \in \mathrm{Int}(A)} S(... |
I was playing with N-body simulations of a game called Kerbal Space Program, which itself uses the patched conics approximation. I have read that for long term stability it is best to use symplectic integrators and one of the simplest would be Störmer-Verlet method: $$ \ddot{\vec{x}}_n = F(\vec{x}_n) $$ $$ \vec{x}_{n+1... |
31 3
I’m trying to derive the infinitesimal volume element in spherical coordinates. Obviously there are several ways to do this. The way I was attempting it was to start with the cartesian volume element, dxdydz, and transform it using
$$dxdydz = \left (\frac{\partial x}{\partial r}dr + \frac{\partial x}{\partial \the... |
Voltage-controlled oscillations in neurons
Frank Hoppensteadt (2006), Scholarpedia, 1(11):1599. doi:10.4249/scholarpedia.1599 revision #129939 [link to/cite this article] VCON is an acronym for the voltage controlled oscillator neuronmodel. It has the form\[\tau\ddot\theta + F(\dot\theta) + A \sin\theta = \omega \]wher... |
Wave Electricity Mathematics News | Published September 14, 2019
Electronic two poles named say employees tend to be utilized for correct engineering programs, and so are worked on some study tools such as the Aqua Alta wind generator tower in the Adriatic Marine, just offshore of Venice. Storm surf start off while eno... |
Images are essential elements in most of the scientific documents. LaTeX provides several options to handle images and make them look exactly what you need. In this article is explained how to include images in the most common formats, how to shrink, enlarge and rotate them, and how to reference them within your docume... |
How is the induced drag calculated for a wing with elliptical planform ? Is this wing shape the most efficient ?
Induced drag is caused by the downward deflection of the air streaming around the wing. The resulting aerodynamic force is tilted backwards by half the deflection angle, and the air flows off the wing with a... |
Baudhayana, (fl. c. 800 BCE)[1] was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sutra—appendices to the Vedas giving rules for the construction of altars—called the Baudhayana Sulbasûtra, which contained several important mathematical results. He is older ... |
To send content items to your account,please confirm that you agree to abide by our usage policies.If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.Find out more about sending content to .
To send content items to your Kindle, first ensure no-rep... |
I am working on zero-inflated count data models using the
pscl package. I am just wondering why there is no development of models for one-inflated count data models! Also why there is no development of bimodal, say zero-and-2-inflated, count data models! Once I generated one-inflated Poisson data and found that neither... |
Suppose that we use the Schwinger-fermion ($\mathbf{S_i}=\frac{1}{2}f_i^\dagger\mathbf{\sigma}f_i$) mean-field theory to study the Heisenberg model on 2D lattices, and now we arrive at the mean-field Hamiltonian of the form $H_{MF}=\sum_{<ij>}(\psi_i^\dagger u_{ij}\psi_j+H.c.)$ with $u_{ij}=t\sigma_z$($t>0$), where $\p... |
$\newcommand{\M}{\mathcal{M}}$
Suppose I have a monoidal simplicial model category in which every object is cofibrant $(\M,\otimes,\mathbb{1})$ and I want to look at its underlying monoidal quasicategory, which I'll write as $N(\M)$, the simplicial nerve of $\M$. One way to do this is the following construction (follow... |
I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia.
If the ball has mass $m$ and is going around in a circle with velocity $v_0$ then I can determine it's angular momentum.
$\vec{L}=m(r_0\times v_0)$
Now suppose someone pulls on the string ... |
Jansen, Maurice ; Qiao, Youming ; Sarma M.N., Jayalal
Deterministic Black-Box Identity Testing $pi$-Ordered Algebraic Branching Programs
AbstractIn this paper we study algebraic branching programs (ABPs) with restrictions on the order and the number of reads of variables in the program. An ABP is given by a layered dir... |
Does increase in the thickness of a camber airfoil mean more drag will be produced? Why do slow flying planes have thick airfoils when it will just slow them down even more?
There are several reasons for using thick$^*$ airfoils.
Slow planes need high lift coefficients in order to fly slow. The increased drag coefficie... |
The Busemann-Petty problem (posed in 1956) has an interesting history. It asks the following question: if $K$ and $L$ are two origin-symmetric convex bodies in $\mathbb{R}^n$ such that the volume of each central hyperplane section of $K$ is less than the volume of the corresponding section of $L$:$$\operatorname{Vol}_{... |
I've seem sometimes a construction being carried out
specificaly in Minkowski spacetime: One picks the standard metric tensor $$g = -dt^2 + dr^2 + r^2 d\Omega^2$$ an introduces two new coordinate functions $T,R$ defined by $$T=\arctan(t-r)+\arctan(t+r),\quad R=\arctan(t+r)-\arctan(t-r)$$ these coordinates have finite r... |
I have the series:
$$\sum_{n=1}^{\infty}\frac {1}{25n^2 + 5n - 6}$$ and I am supposed to prove that the series converges and then find its sum. I have to do multiple problems like this. Can I get an example of how to solve problems like these? You don't have to solve this problem in particular if you don't want. I feel... |
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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... |
Difference between revisions of "Probability Seminar"
(→Thursday, April 23, Hoi Nguyen, Ohio State University)
(→Thursday, April 16, TBA)
Line 158: Line 158: −
== Thursday, April 16,
+
== Thursday, April 16, ==
−
Title:
+
Title:
−
Abstract:
+
Abstract:
== Thursday, April 23, [http://people.math.osu.edu/nguyen.1261/ Hoi... |
> Input
> Input
>> 1²
>> (3]
>> 1%L
>> L=2
>> Each 5 4
>> Each 6 7
>> L⋅R
>> Each 9 4 8
> {0}
>> {10}
>> 12∖11
>> Output 13
Try it online!
Returns a set of all possible solutions, and the empty set (i.e. \$\emptyset\$) when no solution exists.
How it works
Unsurprisingly, it works almost identically to most other answe... |
To evaluate detection performance, we plot the
miss-rate $mr(c) = \frac{fn(c)}{tp(c) + fn(c)}$ against the number of false positives per image $fppi(c)=\frac{fp(c)}{\text{#img}}$ in log-log plots. $tp(c)$ is the number of true positives, $fp(c)$ is the number of false positives, and $fn(c)$ is the number of false negat... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
I want to implement a Bilinear Finite Volume discretisation of the anisotropic diffusion problem:
$$\frac{du}{dt} = \nabla \cdot (\textbf{D} \nabla u)$$
Both my degrees of freedom as well as the Diffusion Tensors are given on the vertices of my quadrilateral grid. I can, therefore, use bilinear test/trialfunctions on e... |
I am trying to use Newtons algorithm for polynomial interpolation. The original polynomial is $p(x) = 3x^2+4x+7$ and the Points from which I am trying to interpolate the polynomial are $p(1) = 14$, $p(6) = 139$ and $p(7) = 182$.
Now as far as I know the formula for the interpolated polynomial should be $r(x) = a_0+a_1(... |
light diffraction grating
Grating applications. Light incident on a diffraction grating is dispersed away from the grating surface at an angle dependent on its wavelength, allowing a grating to be used to select a narrow spectral band from a much wider band. This ability of a grating is particularly useful for laser tu... |
The SciPy tutorial explicitly states
Note that ARPACK is generally better at finding extremal eigenvalues: that is, eigenvalues with large magnitudes. In particular, using
which = 'SM' may lead to slow execution time and/or anomalous results. A better approach is to use shift-invert mode.
and goes on to describe that. ... |
Linear algebra¶ Vector spaces¶
The
VectorSpace command creates a vector space class, from whichone can create a subspace. Note the basis computed by Sage is“row reduced”.
sage: V = VectorSpace(GF(2),8)sage: S = V.subspace([V([1,1,0,0,0,0,0,0]),V([1,0,0,0,0,1,1,0])])sage: S.basis()[(1, 0, 0, 0, 0, 1, 1, 0),(0, 1, 0, 0, ... |
If someone falls from a sixth storey building, with what force will he land? By this I mean to say that if he weighs 50 kg and was initially at rest before falling, which implies it was a free fall. We can easily calculate the velocity and momentum as we know the acceleration due to gravity... but with what force he wi... |
This regime is very unintuitive and it is indeed seen very rarely in physics, though some superconducting circuits do follow a similar equation. It is complicated to deal with mathematically, as taking the limit of $m\to0$ changes the character of the ODE, but it can be done if you're careful about it. This limit is mo... |
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Why can fire be not considered a living thing??It possesses all the features that a living being does.Please someone guide me...
Note by Jahnvi Verma 4 years, 6 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the m... |
FINAL EDIT: There is one main question left: According to the answer, we have choosen $\theta=1$ , where we could choose $0<\theta<\infty$ as we like. His this sufficient, if we regarde the convergence to $\theta$ as a finite positive random variable?
This post seems long, but its almost everything proofed except the l... |
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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 ... |
A co-$A_n$ space is a based space $Y$ equipped with a co-action by the Stasheff associahedron operad $K_\bullet$. This means that $Y$ is comes with certain maps $c_n: Y \times K_n \to Y^{\vee n}$, $n = 2,3,\dots$ that are inductively described (the definition of $c_n$ uses $c_{n-1}$ as input; the map $c_2$ is a co-$H$ ... |
I am looking at the following image (from http://www.schoolphysics.co.uk/age16-19/Atomic%20physics/X%20rays/text/X_ray_spectra/index.html):
and I want to know, of the two curves, which one represents the element with the higher atomic number. That is, I understand that X-rays are scattered and that the peaks are charac... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
Recently my work has led me to consider octonion algebras. Not having much of a background with non-associative anything, I decided to check out a basic text on the subject, R.D. Schafer's
Introduction to Nonassociative Algebras.
I was reading it happily for a good while, until I got to the discussion of alternative al... |
Simple question about rent split
If the rent for a house is £895 per month and is being rented by 2 people. One is accepted to pay £20 more per week, what is going to be monthly payment for each of those people?
Is it going to be £407.50 for one and £487.50 for the other OR £367.50 and £527.50 for the other?
I'm pretty... |
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Now showing items 1-10 of 26
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... |
Modular construction of special mixed quantum states 31 Downloads Abstract.
For a homogeneous quantum network of
N subsystems with n levels each we consider separable generalized Werner states. A generalized Werner state is defined as a mixture of the totally mixed state and an arbitrary pure state \(\vert\psi\rangle\)... |
In a mathematical sense, (differential) topology is imposed on the space-time, it is the "background" of the theory and the metric cannot change the topology of the background manifold. I.e. every metric should come with a "manual of topology" which specifies things such as coordinate ranges and identified coordinate v... |
On the Mathematics of Fast Food
Social media is the worst. Every time I log on to Facebook, I'm inundated with half-baked political arguments and advertising masquerading as memes. The latest one is
totally not an advertisement for McDonald's. It claims that 98% of people cannot solve a certain math problem. Solving th... |
Solving acoustical wave equation:
$$ c_0^2\partial_{xx}p-\partial_{tt}=0 $$
using forward-time centered-space FDM is not very convenient cause of numerical dispersion etc.
What about using a little physics and solve this as a system of first order equations (linearized Euler equations), i.e.:
$$ \nabla p = -\rho_0\part... |
@HarryGindi So the $n$-simplices of $N(D^{op})$ are $Hom_{sCat}(\mathfrak{C}[n],D^{op})$. Are you using the fact that the whole simplicial set is the mapping simplicial object between cosimplicial simplicial categories, and taking the constant cosimplicial simplicial category in the right coordinate?
I guess I'm just v... |
@HarryGindi So the $n$-simplices of $N(D^{op})$ are $Hom_{sCat}(\mathfrak{C}[n],D^{op})$. Are you using the fact that the whole simplicial set is the mapping simplicial object between cosimplicial simplicial categories, and taking the constant cosimplicial simplicial category in the right coordinate?
I guess I'm just v... |
This post tries to be a guide to new members of the (chemical) scientific community for instructions on how to apply the right formatting when writing chemical and mathematical equations.
This answer tries to be a guide to new members of the (chemical) scientific community for instructions on how to apply the right for... |
generation of certain matrices
I'd like to create a list of roughly 100-1000 $2 \times 2$ matrices $[A_1,A_2,...,A_N]$ that have the following properties:
$\det A_j = 1$
The entries of each $A_j$ are in an imaginary quadratic integer ring, such as $\mathbb{Z}[i]$, or $\mathbb{Z}[\sqrt{-2}]$
For example, the matrix $$\b... |
Consider $A =\left( \begin{array}{ccc} -1 & 2 & 2\\ 2 & 2 & -1\\ 2 & -1 & 2\\ \end{array} \right)$. Find the eigenvalues of $A$.
So I know the characteristic polynomial is:
$$f_A(\lambda) = (-\lambda)^n+(trA)(-\lambda)^{n-1}+...+\det A$$
I found the $\det A = 27$, so the characteristic polynomial of $A$ is:
$$-\lambda^... |
A
balanced budget (particularly that of a government) refers to a budget in which revenues are equal to expenditures. Thus, neither a budget deficit nor a budget surplus exists ("the accounts balance"). More generally, it refers to a budget that has no budget deficit, but could possibly have a budget surplus. [1] A cyc... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
TL;DR: The $\ce{O-O}$ and $\ce{S-S}$ bonds, such as those in $\ce{O2^2-}$ and $\ce{S2^2-}$, are derived from $\sigma$-type overlap. However, because the $\pi$ and $\pi^*$ MOs are also filled, the $\pi$-type overlap also affects the strength of the bond, although the bond order is unaffected. Bond strengths normally dec... |
I am trying to compare my finite difference's solution of the scalar (or simple acoustic) wave equation with an analytic solution.
For that purpose I am using the following analytic solution presented in the old paper Accuracy of the finite-difference modeling of the acoustic wave equation - Geophysics 1974 - R. M. Alf... |
Show that L = $\{0^{2^n}| n\geq 0\}$ is not a context free language.
Let string $s = 0^{2^p}$. Then we know we can write $s$ as $s = uvxyz$. I know that |vy| > 0 and $|vxy| \leq p$.
So how do I show that $uv^2xy^2z$ is not in $L$.
Computer Science Stack Exchange is a question and answer site for students, researchers a... |
The sharp, intense band at 1716 $\mathrm{cm^{-1}}$ is indeed characteristic for a carbonyl group ($\ce{C=O}$ stretch, in this case aldehyde or ketone). The medium and broad bands between 2732-2957 $\mathrm{cm^{-1}}$ suggest that it is more likely an aldehyde. In this case, they would be assigned to the $\ce{=C-H}$ stre... |
2019-10-09 06:01
HiRadMat: A facility beyond the realms of materials testing / Harden, Fiona (CERN) ; Bouvard, Aymeric (CERN) ; Charitonidis, Nikolaos (CERN) ; Kadi, Yacine (CERN)/HiRadMat experiments and facility support teams The ever-expanding requirements of high-power targets and accelerator equipment has highligh... |
There is existing literature on fundamental domains for Hilbert-Blumenthal surfaces, perhaps most noticeably what Siegel did. I am interested in whether such fundamental domains have been approached using Dirichlet domains. More specifically...
I want to know what a Dirichlet domain for a manifold covering a Hilbert mo... |
Technocup 2019 - Elimination Round 1 Finished
Vasya has a sequence $$$a$$$ consisting of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$. Vasya may pefrom the following operation: choose some number from the sequence and swap any pair of bits in its binary representation. For example, Vasya can transform number $$$6$$$ $$$... |
> Input
> Input
>> 1²
>> (3]
>> 1%L
>> L=2
>> Each 5 4
>> Each 6 7
>> L⋅R
>> Each 9 4 8
> {0}
>> {10}
>> 12∖11
>> Output 13
Try it online!
Returns a set of all possible solutions, and the empty set (i.e. \$\emptyset\$) when no solution exists.
How it works
Unsurprisingly, it works almost identically to most other answe... |
Basic Algebra and Calculus¶
Sage can perform various computations related to basic algebra and calculus: for example, finding solutions to equations, differentiation, integration, and Laplace transforms. See the Sage Constructions documentation for more examples.
In all these examples, it is important to note that the ... |
In previous posts I have presented separately the graph coloring problem, as well as its generalization, the partitioned graph coloring problem, and linear programming. It is time to put both of them toghether, by modelling an instance of graph coloring using linear programming.
What we need to model
First we have to d... |
Consider a degree $n$ polynomial $P(x)$ with coefficients $c_i \in \{-1,0,1\}$ chosen uniformly and independently.
What is the probability that $P(x)$ has a root which is a root of unity?
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this c... |
For a University class project we were asked to implement a decision-tree classifier and to use a rule engine in order to develop a recommender system for hands and outcomes in Poker Texas Hold’em matches. An additional challenge to this was to make it in a functional language like Erlang, where no variable state is pe... |
This is a recently developed approach to solve Maxwell’s equations [1] on the surface of nano-structures, based on the idea of principal modes. These generalise the analytical Mie modes of spherical particles to describe arbitrary smooth boundaries and surfaces.
This approach is different from more numerical techniques... |
At first I thought maybe sodium sulphate in contact with water produces sulphuric acid which absorbs water but I do not think it is actually a valid reason.
Sodium sulphate reacts readily with water at room temperature to form hydrates up to sodium sulphate decahydrate, $\ce{NaSO4\cdot10H2O}$. $$\ce{NaSO4 + 10H2O -> Na... |
Faster Force-Directed Graph Drawing with the Well-Separated Pair Decomposition Abstract
The force-directed paradigm is one of the few generic approaches to drawing graphs. Since force-directed algorithms can be extended easily, they are used frequently. Most of these algorithms are, however, quite slow on large graphs ... |
As some people on this site might be aware I don't always take downvotes well. So here's my attempt to provide more context to my answer for whoever decided to downvote.
Note that I will confine my discussion to functions $f: D\subseteq \Bbb R \to \Bbb R$ and to ideas that should be simple enough for anyone who's taken... |
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