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Papadopoulos, P., Matiadou, N., Pappas, A. (2015). Global existence, stability results and compact invariant sets for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$. International Journal of Nonlinear Analysis and Applications, 6(1), 85-95. doi: 10.22075/ijnaa.2015.220
P. Papadopoulos; N.L. Matiadou; A. Pappas... |
Doping methods available in QuantumATK¶
The effect of electrostatic doping is generally modelled by either increasing (n-doping) or decreasing (p-doping) the number of electrons of the system with respect to the neutral case. QuantumATK offers two general methods to introduce electrostatic doping. Both lead to the same... |
The population Variance Formula in mathematics is sigma squared equals the sum of x minus the mean squared divided by n.
\[\ \huge \sigma^{2}=\frac{\sum\left(x-\overline{x}\right)^{2}}{n}\]
The variance of a sample is defined by slightly different formula:
\[\ \huge S^{2}=\frac{\sum\left(x-\overline{x}\right)^{2}}{n-1}... |
LHCb Collaboration; Aaij, R; Adeva, B; Adinolfi, M; Anderson, J; Bernet, R; Bowen, E; Bursche, A; Chiapolini, N; Chrzaszcz, M; Dey, B; Elsasser, C; Graverini, E; Lionetto, F; Lowdon, P; Mauri, A; Müller, K; Serra, N; Steinkamp, O; Storaci, B; Straumann, U; Tresch, M; Vollhardt, A; Weiden, A; et al (2015).
Measurement o... |
A conformal transformation is one which alters the metric up to a factor, i.e.
$$g_{\mu\nu}(x)\to\Omega^2(x)g_{\mu\nu}(x)$$
A field theory described by a Lagrangian invariant up to a total derivative under a conformal transformation is said to be a
conformal field theory. These transformations include Scaling or dilati... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
This problem is taken from Linear Algebra by Fueng Zhang. R is real numbers, C is complex numbers and Q is rational numbers.
Let $V = \{(x,y) \mid x,y \in \mathbb{C}\}$. Under the standard addition and scalar multiplication for ordered pairs of complex numbers, is $V$ a vector space over $\mathbb{C}$? Over $\mathbb{R}$... |
A conformal transformation is one which alters the metric up to a factor, i.e.
$$g_{\mu\nu}(x)\to\Omega^2(x)g_{\mu\nu}(x)$$
A field theory described by a Lagrangian invariant up to a total derivative under a conformal transformation is said to be a
conformal field theory. These transformations include Scaling or dilati... |
calculateLCAOBasisSpilling¶
calculateLCAOBasisSpilling(
configuration, k_point_sampling=None, basis=None, bands_above_fermi_level=<class 'NL.ComputerScienceUtilities.NLFlag._NLFlag.All'>, processes_per_kpoint=None)¶
Method for calculating the spilling factors per band (and spin) for a given configuration with an attach... |
Few weeks ago, a Reddit user
xieta posted really neat results of flow past a cylinder to
/r/CFD. These results were computed using the
vorticity – stream function method. My background in CFD is quite limited, and to be honest, this was the first time I’ve heard of this method. Turns out it’s a rather popular method fo... |
A
set is one of the simplest structures we can define in math. One may intuitively think of a set as a collection of objects (there are formal definitions that are used to define this more rigorously). With only this structure, we can do some things, but not much. If we have two sets, we may consider maps between them.... |
Let $R$ be an integral domain, and $A , B$ be non trivial ideals of $R$. Then prove that $|A \cap B|>1$.
Let $0 \ne a \in A$, $0 \ne b \in B$; we know such $a, b$ exist by virtue of the assumption that $A$ and $B$ are nontrivial. Then since $A$ and $B$ are ideals of the integral domain $R$, we have $0 \ne ab \in A$ and... |
(38.) $\mathbb{Z} \rightarrow S_3$?
Let $φ(n) = \begin{cases} \mathrm{id} \in S_3 &, \text{for all $n$ even,} \\ \mathrm{transposition} (1,2) &, \text{for all $n$ odd integers.} \end{cases}$
Note that (1, 2) is of order 2, isomorphic to Z2.
(41.) $D_4 \rightarrow S_3$?
View D4 as a group of permutations. Same answer as... |
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Now showing items 1-10 of 33
Reaction dynamics of excited states of helium and magneto-optical trapping of helium metastable atoms
(1993)
The temperature dependence of conversion of $\rm He(2\sp3S\sb1)$ metastable atoms to $\rm He\sb2(a\sp3\Sigma\sbsp{u}{+})$ metastable molecules in the three-body reaction $\rm ... |
Degenerate elliptic equation
$ \newcommand{\abs}[1]{\left|#1\right|} $
A partial differential equation \begin{equation} \label{eq1} F(x,Du) = 0 \end{equation} where the real-valued function $F(x,q)$ satisfies the condition \begin{equation} \label{eq2} \sum_{\abs{\alpha} = m} \frac{\partial F(x,Du)}{\partial q_\alpha} \... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Integration or Integral Calculus is usually passed as the Integral calculus and defined as the reverse operation of the differential calculus. It is true in certain cases but does not capture the true essence of it. Integration is an important part of mathematics that was introduced earlier to differentiation.
\[\large... |
Triangular summation method
$$A=\| a_{nk}\|,\quad n,k=1,2,\ldots,$$
that is, by a matrix for which $a_{nk}=0$ for $k>n$. A triangulation summation method is a special case of a row-finite summation method. A triangular matrix $A$ is called normal if $a_{nn}\neq0$ for all $n$. The transformation
$$\sigma_n=\sum_{k=1}^na... |
Here is a well-known interview/code golf question: a knight is placed on a chess board. The knight chooses from its 8 possible moves uniformly at random. When it steps off the board it doesn’t move anymore. What is the probability that the knight is still on the board after \( n \) steps?
We could calculate this direct... |
Let $A$ and $B$ be two real $n\times n$ matrices, and let $C(x)=B(I-xB)^{-1}$, where $I$ is the identity matrix of order $n$, for any real scalar $x$ such that $I-xB$ is invertible. Denote by $\mathrm{tr}$ the trace operator.
Is it possible to get a closed form solution for
$$\int{\mathrm{tr}}\left( {AC(x)}\right) {\,d... |
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1. Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8... |
There are 3 units that are used to express charge.
This is most commonly used in macroscopic situations.
1 coulomb of charge is that which, if placed at a separation of 1 metre from another charge of magnitude 1 coulomb, experiences a force of $8.99\times 10^9$N along the line joining the charges.
This definition resul... |
Let's say you have a number $x$, and a priori, you know that $x \in [0, 1)$ (each value from 0 to 1 is equally likely.) Then a wizard comes and tells you that $x \in [a, b) \subseteq [0, 1)$. How much information does this give you?
It would seem to be $-\log_2(b-a)$ bits, but I don't know how to prove this, since both... |
Can you express the fraction $\frac{1949}{1999}$ in the form $\frac 1a+\frac 1b$? Give reasons supporting your answer.
I think the only way to do this is keep trying numbers but then I will never get the answer. I cry every time.
Mathematics Stack Exchange is a question and answer site for people studying math at any l... |
Learning Objectives
Create and interpret graphs of potential energy Explain the connection between stability and potential energy
Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, calle... |
This is a theoretical computer science question, regarding the proof of whether or not context-free languages are closed under an operation. This means basically that any context-free language which undergoes this operation would still be context-free.
For a language $A$ which is a subset $\Sigma^*$, define the languag... |
I'm trying understand where electricians came to agreement that Ie = Ib + Ic. I know that the base of a NPN transistor is very thin, allowing electrons to flow through to the collector which explains why $I_{c} = \beta I_{b}$. Mathematically, I can also see that when we have $\alpha = \frac{I_{c}}{I_{e}} = \frac{\beta}... |
If Einstein traveled 99.99999999% the speed of light, and shined a flashlight backwards, he would see photons moving at the speed of light. A stationary observer would also see photons moving at the speed of light. This is one of the fundamental principles of Special Relativity:
The speed of light is the same in all re... |
Motivation:
It is a well known fact that the gravitational field (in General Relativity and direct generalizations of it) has no local energy-momentum density.
Usually there are two reasons stated, one is heuristic, one is mathematical.
Heuristic reasoning:The gravitational field can be "turned off" at any one $x\in M$... |
Let's say I have a gas of Li atoms in the $1s^2 2s^1$ ground state configuration and I want to excite the $2s \to 3s$ transition of the outermost electron with a laser pulse on resonance. (That is the mean photon energy is equal to the energy difference of the two levels.)
There are some things I don't understand about... |
Revised Answer
(I have again misinterpreted your question, which is simpler than I had anticipated.)
This question is Problem 3.44 in Griffiths' "Introduction to Electrodynamics". A solution is given as Exercise 2 in Physics Pages using
Green's Reciprocity Theorem, but it is not easy to understand.
In the simplified pr... |
I want to evaluate the integral:
$$I=\int_{-\infty}^{\infty}dx_1 \int_{-\infty}^{\infty}dx_2 \ \Theta(x_1-x_2) \ e^{i(ax_1+bx_2)}$$ where $\Theta(x)$ is the Heaviside function.
What I was doing now was taking the relation for $\Theta$: $\Theta (x)=-\frac{1}{2\pi i}\int_{-\infty}^{\infty}d\tau \frac{1}{\tau + i\epsilon}... |
The electrostatic force between the electron and the proton (in classical terms) varies as $1/r^2$ so when the electron and proton are separated by a large distance the force goes to 0 therefore at large distance the electron and proton become free particles. Note that when the electron and proton are very close the fo... |
I've solved this circuit but i got some issues about the alternatives.
English question at this picture:
Switch \$S_1\$ had been closed for long time and after that \$S_2\$ was opened. Therefore, at \$t=0\$, the switch \$S_2\$ has closed.
The current \$i_1(t)\$ is equal for \$t\geq 0\$
My attempt:
\$L\frac{di_1(t)}{dt}... |
The Eulerian Number $A(n,k)$ is the number of permutations of $1$ to $n$ with exactly $k$ rises (or ascents, i.e., positions $i$ such that $x_i<x_{i+1}$).
The article The Boundary of the Eulerian Number Triangle by Alexander Gnedin and Grigori Olshanski, presents the following asymptotic relation (Remark 12):
$$\lim_{n... |
My textbook asked me to evaluate the integral $\int_1^5\left(\frac{x}{\sqrt{2x-1}}\right)$ using u-substitution. I rewrote the integrand as $x*(2x-1)^{-\frac{1}{2}}$, but I soon became stuck because I couldn't settle on what was $g'(x), g(x),$ or $F(x)$ (I didn't know how to define u or du). I checked the book (this wa... |
Maybe a little bit obvious but what I would do is the following:
$\textrm{Let:}$
$$\omega + \phi + \psi = \pi$$
Then take the tangent function to both sides.
$$\tan \left ( \omega + \phi + \psi \right) = \tan \left ( \pi \right)$$
Since $\tan \pi = 0$, then:
$$\tan \left ( \omega + \phi + \psi \right) = \tan \left ( \p... |
78Skills to Develop
Calculate position vectors in a multidimensional displacement problem. Solve for the displacement in two or three dimensions. Calculate the velocity vector given the position vector as a function of time. Calculate the average velocity in multiple dimensions.
Displacement and velocity in two or thre... |
In ASK, a carrier is multiplied by a set of discrete amplitudes, depending on the information bits. In practice, binary ASP (BASK) is often used, where one of the amplitudes is zero, i.e. for a digital \$0\$, the modulated signal is zero, and for a digital \$1\$ the modulated signal is the carrier multiplied with some ... |
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Now showing items 11-20 of 51
Multiplicity dependence of jet-like two-particle correlations in pp collisions at $\sqrt s$ =7 and 13 TeV with ALICE
(Elsevier, 2017-11)
Two-particle correlations in relative azimuthal angle (Δ ϕ ) and pseudorapidity (Δ η ) have been used to study heavy-ion collision dynamics, inclu... |
Consider the functional $$J(y)=y^2(1)+\int_0^1y'^2(x)\,dx$$ with $y(0)=1$ , where $y\in C^2[0,1]$. If $y$ extremizes $J$ then find the value of $y(x)$.
I tried through Bolza problem. Firstly Euler-Lagrange equation gives , $y''=0$. So general solution is $y(x)=C_1x+C_2$. Now , $y(0)=1$ gives $C_2=1$. Then $y(x)=C_1x+1$... |
One of the first articles on this blog was a sample Particle In Cell code on structured Cartesian mesh. In this article, I will try to outline the steps for developing a PIC code that runs on an unstructured mesh. Although I don’t purposely plan to glance over important details, there is much more math going into devel... |
OpenCV 4.1.2-pre
Open Source Computer Vision
Here, the matter is straight forward. For every pixel, the same threshold value is applied. If the pixel value is smaller than the threshold, it is set to 0, otherwise it is set to a maximum value. The function
cv.threshold is used to apply the thresholding. The first argume... |
$$ \lim_{x \to 0} \frac{\lvert2x-1\rvert - \lvert2x+1\rvert}{x} $$
Defining the function piecewise reveals the limit is in fact, continuous about 0
However when I go to solve it in a normal algebraic manner, the $2x$ terms are canceling, leaving me with an undefined output - 0 in the denominator.
Any hints would be fan... |
(originally a comment, now extended and probably worth being an answer)
The lower right Dini derivate (what you want) would be $-2$ if the function was equal to $2x\sin(1/x)$ for $x>0,$ with $f(0)$ still equal to $0$ (and it doesn't matter what $f(x)$ is for $x < 0).$ See Calculating Dini derivatives for $f(x)=\begin{c... |
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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 ... |
May 19th, 2016, 03:28 AM
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Acceleration components of gravity vector
Hello,
for "fun", I thought I'd have a go at modelling the orbit of planets around the sun in Excel. I'm trying to complete this worksheet I found online:
Building Planetary Orbits
I've stumbled a... |
The niche I have chosen is very competitive…
I can count the keywords on just one hand…
There are tons of irrelevant low comp keywords…
ABC Manuals, ABC Apps, etc…
however, I do not have apps or manuals on my site, so if
i were to target these keywords, then I feel they would not be buyer intent; they are simply lookin... |
Probability -- A Measure Theoretic Approach Probability using Measure Theory
A mathematically rigorous definition of probability, and some examples therein.
The Traditional Definition:
Consider a set \( \Omega \) (called the
sample space), and a function \( X:\Omega\rightarrow\mathbb{R} \) (called a random variable.
If... |
Calmet, Xavier, Fragkakis, Dionysios and Gausmann, Nina (2011)
The flavor of quantum gravity. European Physical Journal C, C71 (11). pp. 1781-1784. ISSN 1434-6044 Abstract
We develop an effective field theory to describe the coupling of non-thermal quantum black holes to particles such as those of the Standard Model. T... |
Note this version of the R package and tutorial addresses two errors in the original paper: 1) The harmonic mean
p-value for set \(\mathcal{R}\) should be compared against a threshold \(\alpha_L\), not \(\alpha_{|\mathcal{R}|}\). 2) The mechanism for calculating asymptotically exact harmonic mean p-values was wrongly s... |
For a differential equation like this with real coefficients: $$\frac{d^2y}{dx^2}+p \frac{dy}{dx}+q y = 0$$ By solving $$\lambda ^2+p\lambda +q = 0$$ we obtain two eigenvalue $\lambda_1 = a+bi$ and $\lambda_2 = a-bi$, if the discriminant $\Delta$ is smaller than 0. then if we want to obtain two real function solutions ... |
Banach Journal of Mathematical Analysis Banach J. Math. Anal. Volume 3, Number 1 (2009), 131-142. A generalization of the weak amenability of Banach algebras Abstract
Let $A$ be a Banach algebra and let $\varphi$ and $\psi$ be continuous homomorphisms on $A$. We consider the following module actions on $A$, $$a\cdot x=... |
Minimum Time to Move Between Fixed Points Through a Point Moving Along x Axis
\[x\]axis between points A and B.Line segments joint to point P to points R and S as shown, and the lines PR and PS make angles
\[\theta\]and
\[\phi\]with the positive and negative
\[y\]axes respectively. How can you find the minimum time to ... |
The Torque Construct: The Rotational Analog to Force
Consider a force
F exerted tangentially on the rim of a wheel or disk. The rim is at a distance r from the axis of rotation. We can formally define torque, represented by the Greek letter \(\tau\) , in terms of the force F and the distance r:
\[ \tau = r_{\perp}F = r... |
In Bohmian mechanics, the initial configurations and the pilot wave determine the future of the system. Given a set of initial positions for particles and a set of arbitrary trajectories, can we define a pilot wave that guides the particles on that trajectories?
A funny question which has not really much meaning for ph... |
When I was first learning abstract algebra, the professor gave the usual sequence of results for polynomials over a field: the Division Algorithm, the Remainder Theorem, and the Factor Theorem, followed by the Corollary that if $D$ is an integral domain, and $E$ is any integral domain that contains $D$, then a polynomi... |
Consider the following system consisting of a box sliding down a plane. The coefficient of friction between the plane and the box is $\mu$. A pendulum is attached to the top of the box as shown.
The acceleration of the box+pendulum is $a=g(\sin\theta-\mu\cos\theta)$ I believe.
In a non-inertial frame attached to the bo... |
An important piece of information is:
Theorem: $f$ is not continuous.
Proof: Observe that $f$ is invertible, because
$$f(f(f(f(x)))) = f(f(-x)) = x$$
and so $f \circ f \circ f = f^{-1}$. Any
continuous invertible function on $\mathbb{R}$ is either strictly increasing or strictly decreasing.
If $f$ is strictly increasin... |
Everyone keeps claiming that integer factoring is in $NP$ but I just don't get it... Even with the simplest algorithm (division with all integers up to $\sqrt{n}$) the complexity should be $\sqrt{n}\log(n)$... How is that not in $P$? Is there something I'm missing?
One of the things to remember when dealing with natura... |
where $A,B\in\mathbb{R}^{n\times n}$.
My current solution is that this will only work iff $A$ and $B$ commute. Since:
$(AB)^\top = B^\top A^\top = B A$ $\ $ ($=AB$. iff $A$ and $B$ commute.)
I tried to ...
come up with a counterexample of a product of two symmetric matrices, that does not commute. However, my examples ... |
The Lagrangian of chiral perturbation theory (with two quark flavors) is written using the following matrix $U$
$$U=e^{i\sigma^i\phi_i/f}$$ where $\sigma^i$ are the Pauli matrices, $\phi_i$ are three scalar fields and $f$ is a constant with mass dimension. $U$ is unitary, which makes the $\phi_i$ fields real.
The Lagra... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
Is it possible to solve the linear PDE analytically \begin{equation} \frac{\partial u}{\partial z} + a \frac{\partial u}{\partial t} + \int_{0}^{t} e^{-\beta (t-t')} u(z,t') dt'=f(z,t), \end{equation} subject to the conditions \begin{equation} u(z,0) = 0; \quad u(L,t) = u_0(t), \end{equation} by applying the Laplace tr... |
Take a branch of the function $f(t) = \sqrt{1-t^2}$ on the closed upper-half plane ($\bar{H}$) so that $f(i) = \sqrt{2} > 0$. Then, we can define
$\phi(z) = \int_0^{z} \frac{dt}{f(t)}$, where the path is taken in $\bar{H}$.
This function maps $\bar{H}$ to a half-infinite rectangular strip $[-\pi/2,\pi/2] \times [0,\inf... |
You're doing a titration of the carbonic acid $\ce{H_2CO_3}$ which is the product of the dissolution of $\ce{CO_2}$ in water by a base here the sodium hydroxide. According to wikipedia for carbonic acid, $\ce{pKa_1=3.6}$, $\ce{pKa_2=6.3}$ and $\ce{pKa_3=10.32}$.
When the carbon dioxyde is in water, the solution is acid... |
The below-given problem is in black box setting means input is given by set of generators.
Given an abelian $p$-group $A$ and two matrices $U_1$ and $U_2$ in $R(A)$ such that the order of $U_1$ and $U_2$ are coprime with $p$, output an element $U \in R(A)$ such that $UU_1=U_2U$ if such an element exists.
$R(A)$ denotes... |
I came across this problem
Find the number of solutions of $|\cos(x)|=\cot(x)+\frac{1}{\sin(x)}$ that lie in $[-4\pi,4\pi]$
in a PreCalculus book and I am looking for a simple solution.
What I can say: let $\displaystyle f(x)=|\cos(x)|$ and $\displaystyle g(x)=\cot(x)+\frac{1}{\sin(x)}$
The functions $f$ and $g$ are $2... |
2019-07-18 17:03
Precision measurement of the $\Lambda_c^+$, $\Xi_c^+$ and $\Xi_c^0$ baryon lifetimes / LHCb Collaboration We report measurements of the lifetimes of the $\Lambda_c^+$, $\Xi_c^+$ and $\Xi_c^0$ charm baryons using proton-proton collision data at center-of-mass energies of 7 and 8 TeV, corresponding to an... |
I'm teaching an applied math class this summer and I want to take a short detour into finance (not my specialty at all); specifically the Black-Scholes model of stock movements. I want my students to be able to simulate stock movements and create some fun graphs. But I still have a couple basic questions about it mysel... |
The main problem lies in the "large logarithms". Indeed, suppose you want to calculate some quantity in Quantum Field Theory, for instance a Green Function. In perturbation theory this is something like:
$$\tilde{G}(p_1,...,p_n)=\sum_k g^k F_k(p_1,...,p_n)$$
for some generic functions $F$ and $g$ is the coupling consta... |
Learning Objectives
Solve for the centripetal acceleration of an object moving on a circular path. Use the equations of circular motion to find the position, velocity, and acceleration of a particle executing circular motion. Explain the differences between centripetal acceleration and tangential acceleration resulting... |
Effective band structure of random alloy InGaAs¶ Version: 2015.1
Random alloys are becoming technologically important materials. For example, SiGe is one of the best known thermoelectric materials, and InGaAs is a prime candidate to substitute or complement silicon in future CMOS devices. Simulations of both thermoelec... |
Let's consider the very basic of a Mean-Variance Portfolio:
$$ \text{max}_{x} (1-\lambda)\sum_i^n\mu_ix_i-\lambda\sum_i^n\sum_j^n x_i Q_{ij}x_j $$ $$\text{ s.t. }\sum_i^nx_i=1 \text{ , } x_i \geq 0 \text{ (No shorting) }$$ where $\lambda, \mu, Q$ is the risk averse parameter, expected return vector and variance-covaria... |
When a ray of light is projected, (say) from the surface of Earth to outside in space. The condition is that, there is no obstruction to it till
infinity(it travels only in vaccum). My question is that how far can that ray of light go?
Also, instead of a
ray of light,if I consider a beam of laserwith same conditions, t... |
I performed an experiment about the RL circuit, with following circuit:
(I used the PASCO RLC circuit lab.)
By Kirchhoff's voltage law, (denoting the emf of the signal generator $\mathscr E$, inductance of the inductor $L$, the resistance of the resistor $R$, and the current of the circuit $i$) $$\mathscr E - iR - L \f... |
Welcome to The Riddler. Every week, I offer up a problem related to the things we hold dear around here: math, logic and probability. These problems, puzzles and riddles come from lots of top-notch puzzle folks around the world — including you! You’ll find this week’s puzzle below.
Mull it over on your commute, dissect... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Given a set of $N$ assets, the amount of strategies proposed in literature to diversify the investors wealth in order to find the 'optimal' portfolio is overwhelming. However, for example DeMiguel et al point out that estimation error is large in general, leading to bad out-of-sample returns for many sophisticated port... |
Keeping Track of Element Order in Multiphysics Models
Whenever you are building a finite element model in COMSOL Multiphysics, you should be aware of the element order that is being used. This is particularly important for multiphysics models as there are some distinct benefits to using different element orders for dif... |
Kasiki's test and the index of coincidence are used to attack a
Vigenère cipher (or other polyalphabetic ciphers with small alphabet and small key size) - they both try to get the length of the keyword.
Kasiki's test gets probable prime factors of the keyword length, while the coincidence index test gets us an estimati... |
I am trying to solve the coupled differential equation numerically with Mathematica. But the range of values are large so mathematica cannot give correct plot. Here is the code:
a = 4.75388*10^26; b = 5.424*10^-3; d = 4.75388*10^20; {X, Y} = {x, y} /. NDSolve[{x'[ z] == -((a/z) (x[z] - b*z^(3/2) E^(-z)) (BesselK[1, z]/... |
I'm following a very good IPython notebook (the whole list can be found here) in which some sampling techniques are explained. However, I don't understand the use of a categorical variable in a change point model.
The posterior distribution for the model is the following:
\begin{aligned} P( \lambda_1, \lambda_2, \tau |... |
There is a one-dimensional diffusion process in which particles start running at $t = 0$ and from $x_o > 0$.
When particles reach x = 0 they are removed from the system, thus the total concentration is not conserved anymore.
I have to solve the diffusion equation, which is the following partial differential equation:
$... |
The space between the plates of a parallel plates capacitor is filled consecutively with two dielectrics layers $1$ and $2$ having the thickness $d_1$ and $d_2$ respectively and permittivities $\epsilon_1$ and $\epsilon_2$. The area of each plate is equal to $S$ find:
1. The capacitance of the capacitor
2. The density ... |
I am trying to follow the Optimal Kelly derivation on Wikipedia for two continuous assets: one risky and one risk-free.
The derivation begins by assuming that the risky assets follows a GBM (a special type of exponential semi-martingale). It is assumed that we already know the solution for the expected value of $S_t$ (... |
Wooclap allows you to insert mathematical formulas in a question and its possible answers by using the AsciiMath and LaTeX formats.
AsciiMath
Simply surround formulas by backticks ` or by the elements <math> and </math>.
Examples:
<math>1/(x+1)</math>
or `1/(x+1)`
<math>text(N)_2 + 3 text(H)_2 -> 2 text(NH)_3</math>
or... |
Does there exists an uncountable family $\mathcal{A}$ consisting of uncountable compact subsets of $\mathbb{R}$ and pairwise disjoint?
Let $K$ be the set of reals in $[0,1]$ with only $0$s and $1$s in their decimal expansions. For each $x \in K \setminus\{1\}$ the set $2x + K$ is compact, and this family is pairwise di... |
Hybrid Functionals¶
Hybrid functionals are exchange-correlation functionals that take into account exact Fock exchange[Bec93]. There are different approaches as to how to mix in the exact exchange. Themethod we implemented in our
PlaneWaveCalculator code is the HSE functional described in[HSE03].
Background¶
The HSE fu... |
The least count of the watch used for the measurement of time period is $0.01$ s
This information is just telling you to round off to the second decimal place, as you correctly did.
The sample mean is $\mu = 0.56$ and the sample standard deviation is $\sigma = 0.02$. The answer the text is referring to is
$$\frac \sigm... |
Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
1.
Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany
2.
School of Science, Xihua University, Chengdu 610039, China
$\left\{ \begin{align} & {{u}_{t}}=\Delta u-\chi \nabla \... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Gabrišková, Ivana Modelování a odhadování výsledků hokejových utkání
This diploma thesis concerns with modeling and estimating results of hockey matches and use of estimation for betting against bookmakers. The thesis describes models used for estimating winning of home team, a draw or away team win. The thesis deals a... |
In this paper:
in eqns 3,5 the state eqn has the mean removed.
$(z_t-\mu)=A(z_{t-1}-\mu) + \epsilon_t$
$y_t=C z_t + \delta_t$
However I have looked at several implementations of Kalman Filters for state space models I haven't seen this "de-meaned" version any where?
Moreover if you look at implementations such as this ... |
Let $X$ be a random varaible from a distribution with pdf $$ f(x) = \theta x^{\theta-1}, \quad 0< x < 1. $$
a) Name the distribution of $U=-\ln(X)$ by first finding its density
b) Let $X_1, X_2, \ldots,X_n$ be independent and identically distributed random variables with pdf given by earlier with $\theta$= 3. Using the... |
Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Oly... |
The textbook Elements of Information Theory gives us an example:
For example, if we knew the true distribution p of the random
variable, we could construct a code with average description length
H(p). If, instead, we used the code for a distribution q, we would
need H(p) + D(p||q) bits on the average to describe the ra... |
If a linear operator between two Banach spaces is surjective and bounded, can we get any information about a right inverse? For example, is it bounded?
Thanks, trying to understand trace operator stuff on the Sobolev spaces.
Mathematics Stack Exchange is a question and answer site for people studying math at any level ... |
Solve the initial value problem: $y'+2y=e^{-x}$ with $y(0)=4$
Our teacher gave me a mistake / unclear mark at the part which I will mark red here. But I don't understand why and I no longer have the opportunity to ask him.
This is an extract of my solution (it leads to the correct solution):
$$e^{2x} \cdot \frac{dy}{dx... |
Let $k$ be a field and $A=k\times k\times ...$ the product of denumerably many many copies of $k$.
Let $I\subset A$ be the ideal of eventually zero sequences and $\mathfrak m\supset I$ a maximal ideal containing it. Since in $A$ every element $a$ is multiple of $a^2$, we certainly have $\mathfrak m=\mathfrak m^2$ but $... |
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