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Dear Uncle Colin, I'm told that the graphs of the functions $f(x) = x^3 + (a+b)x^2 + 3x - 4$ and $g(x) = (x-3)^3 + 1$ touch, and I have to determine $a$ in terms of $b$. Where would I even start? - Touching A New Graph Except Numerically TroublingRead More →
Some while ago, I showed a slightly dicey proof of the Basel ... |
Suppose the application is a Lamport signature scheme.
Is the following a secure hash $\{0,1\}^n \rightarrow \{0,1\}^n$? $$ H(x) = x \oplus P(x) $$ where $P$ is a public permutation that permutes an input of length $n$.
Cryptography Stack Exchange is a question and answer site for software developers, mathematicians an... |
Is it possible to solve Killing equations in
Mathematica for a general vector?
I am looking for a way to create Killing equations and then find what the vectors are, but I have a problem with this.
Introduction
First of all what they are. Without going in to the all gory details of general relativity, in short, Killing... |
Neil Sloan's On-Line Encyclopedia of Integer Sequences, which everyone who works seriously (or recreationally) with integer sequences regards as the ultimate authority, lists the triangular numbers as sequence A000217, and unambiguously includes 0 as a triangular number:
It was brought to my attention that all the refe... |
Prove that the number of subgroups in $D_n = \tau (n) + \sigma (n)$ where $\tau (n)$ represents number of divisors of $n$ and $\sigma (n)$ represnts the sum of divisors of $n$.
Attempt: $D_n = \{e,r,r^2, \cdot \cdot \cdot, r^{n-1},s,rs,r^2s, \cdot \cdot \cdot, r^{n-1}s \}$
Then, $\{e,r,r^2, \cdot \cdot \cdot, r^{n-1}\}... |
Welcome to our 100% community authored science and math blog. All of our blog authors are experts in their respective STEM fields. You’ll find high quality, engaging and interesting math and science articles (physics, mathematics, engineering, chemistry, biology, technology…). Even better we have science and math tutor... |
I am studying the deformation theory of associative algebras (and Poisson algebras) and came across a question for which I cannot find an answer:
Let $(A,\mu)$ be a commutative associative algebra over a field $\mathbb{F}$. The first order deformations of $\mu$ are classified up to equivalence by the second Hochschild ... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
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Let f:C→Cf : \mathbb{C} \to \mathbb{C}f:C→C be holomorphic on C\mathbb{C}C. Also, suppose the following holds: ∣f(z)∣→+∞ as ∣z∣→+∞.\big|f(z)\big| \to +\infty \text{ as } |z| \to +\infty.∣∣f(z)∣∣→+∞ as ∣z∣→+∞.
Then which of the following necessarily holds?
Details... |
\[\]
\defl{Hypergeometric distribution has the following properties:}
When units are selected from a finite population without replacement and the population consists of successes and failures. The major difference between the Hypergeometric distribution and the Binomial distribution is that the probability of selectin... |
LaTeX is a great tool for printable professional-looking documents, but can be also used to generate PDF files with excellent navigation tools. This article describes how to create hyperlinks in your document, and how to set up LaTeX documents to be viewed with a PDF-reader.
Contents
Let's start with a minimal working ... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Spanish.
Contents
Spanish language has some special characters, such as the
ñ and some accentuated words. For this reason the preamble of your document must... |
For those interested, here is a slightly more rigorous proof that the construction exists using measure theory.
We will define a function $H$ which is continuous from the left at ever $x \in [0,1]$ but is only continuous from the right at the irrationals. To build such a function we need the folliowing scaffolding.
Fir... |
For one of my applications it is necessary to know the geopotential at each model level of the ERA5 data. Since ERA5 and ERAI only store the geopotential at the surface, it may not be immediately obvious how to arrive at the remaining values. This post deals with how to achieve this. While shown for ERA5, the procedure... |
To show that the series $\sum_{k=1}^{\infty} {{1}\over {k}}$ diverges ; I have to prove that $${\sum_{k=1}^{n}}{{1}\over{k}} \ge {\log n}$$ The given hint is that $${{1}\over {k}}\ge \int_k^{k+1} {1\over x} dx$$
Now,evaluating the RHS, say $$L=\int_k^{k+1} {1\over x} dx\\=\log(k+1)-\log\ k\\=\log(1+{1\over k})\\={1\ove... |
School, from our house as the crow flies, is 5.73 km. If we neglect air resistance and deal strictly with ballistic flight then we can materialize a wonderful fantasy. Starting in the backyard, extending over the top of the house, is a
launch-o-rocket, a rail-like launcher that accelerates the school-bound student unti... |
We are challenged to determine "how fast MMa can get" and, in so doing, to suggest rules "to choose different programming styles." The original solution takes 116 seconds (on my machine). At the time the question was posted, the solution time had been reduced by a factor of 1000 (10 doublings of speed) to 0.124 seconds... |
I wanted to read a bit about modular forms of half integral weight. There is the notion of a 'factor of automorphy' (as for example, R.Rankin uses it in the book 'Modular Forms and Functions'). Now I am confused about the following: In modern literature, people seem to follow Shimura, i.e. they define modular forms of ... |
The Annals of Probability Ann. Probab. Volume 20, Number 2 (1992), 681-695. The A.S. Behavior of the Weighted Empirical Process and the LIL for the Weighted Tail Empirical Process Abstract
The tail empirical process is defined to be for each $n \in \mathbb{N}, w_n(t) = (n/k_n)^{1/2}\alpha_n(tk_n/n), 0 \leq t \leq 1$, w... |
June 5th, 2017, 09:00 AM
# 1
Newbie
Joined: Jun 2017
From: Bucharest
Posts: 5
Thanks: 0
Impossible limit!
Sorry for the title. There is a limit that's giving me hell. I cannot solve it, but I know the answer is 0.
lim x->0 with x<0 from f(x)=(e^(1/x))/(x^2)
I sure know the limit is 0, but I don't know why. It is a vert... |
Hi Oz./.. just wanted to clarify some things:
Originally Posted by
oz93666
I find it hard to read such articles .. I have problems with nearly every line , just take the first line ...
"The stars still have their secrets. We know why they shine .We know why they trinkle . But we ...."
Well no , I don't believe establis... |
What's the effective key length of Two-Key Triple-DES, for some (possibly several) reasonably well-defined and sensible definitions of
effective key length, say assuming attack using ample chosen plaintext?
A sensible definition of effective key length (in bits) of a block cipher under some attack assumptions could be:... |
The mapping class group of the closed unit disk $D_n\subset\mathbb{C}$ with $n$ equally spaced points $P$ on the x-axis (0,1) removed is defined as the set of isotopy classes of self-homeomorphisms $D_n\rightarrow D_n$ which fix the boundary: $\phi\partial D_n=\partial D_n$, and permute the distinguished points: $\phi ... |
I'm trying to find the maximum of a function $f = a^T\mu$ where a is a vector when we have a constraint of the form:
$$g(\mu) = n\mu^T S^{-1}\mu - C = 0$$
where C is a fixed constant, $S^{-1}$ is a fixed matrix , $n$ is a number and $\mu$ is a vector of variables. In fact, my goal is to find a $\mu$ that satisfies $g(\... |
So, since $V\in\mathbb R^{m\times n}$ has full column rank $n$, implying also $m\geq n$, we might obtain the pseudoinverse using$$V^+=(V^TV)^{-1}V^T$$since $V^TV$ is invertible and $V^*=V^T$ in $\mathbb R$.
Now, let's denote by $i$ the index of the row which is scaled and by $d_i$ - the scaling factor.Thus, a perturbed... |
Evan Schwab
1, Rene Vidal 2, and Nicolas Charon 3
1Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, United States, 2Biomedical Engineering, Johns Hopkins University, Baltimore, MD, United States, 3Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, United States
Syn... |
What can be said about $\sigma(T_1 \otimes T_2)$ and $\sigma(T_1) \otimes \sigma(T_2)$, when $T_i$ are topologies that aren't necessary second countable, and $\otimes$ denotes, at the left, the product topology, and at the right, the product $\sigma$-algebra ?
Do you know examples where neither of these is included in ... |
This post contains several code blocks, you can copy them easily with the help of
importCode.
Analytic Solution
The analytic solution can be obtained with
LaplaceTransform and
FourierSinCoefficient. First, make a Laplace transform on the equation and b.c.s and plug in the i.c.s:
Clear[f];
f[x_] = x (1 - x);
eqn = D[u[t... |
Multicollinearity Harsha Achyuthuni December 23, 2018
I want to go thru some basic statistical concepts before continuing with the EDA and in-time problem. I want to explain what is multicollinearity and how and when to tackle it.
Collinearity
Collinearity is a linear association between two variables. Two variables ar... |
Electronic Journal of Probability Electron. J. Probab. Volume 17 (2012), paper no. 5, 27 pp. Novel characteristics of split trees by use of renewal theory Abstract
We investigate characteristics of random split trees introduced by Devroye [SIAM J Comput 28, 409-432, 1998]; split trees include e.g., binary search trees,... |
Longitudinal relaxation times of
13 Macromolecular (MM) resonances are reported for a gray matter rich voxel at
9.4 T for the first time. In addition, a
sequence was optimized based on calculated magnetizations from Bloch
simulations for combinations of inversion times using a DIR MC-semiLASER. The
results from this wo... |
Understanding and Specifying LIDT of Laser Components
This is
Section 3.1 of the Laser Optics Resource Guide.
Laser Induced Damage Threshold (LIDT) is defined within ISO 21254 as the “highest quantity of laser radiation incident upon the optical component for which the extrapolated probability of damage is zero”.
1 The... |
AliPhysics 6f1d526 (6f1d526)
Scripts used in the analysis Algorithms Corrections Monte-carlo code Mid-rapidity tracklet code for dN/deta Tasks Topical
file AliAODForwardMult.h Per-event \( N_{ch}\) per \((\eta,\varphi)\) bin. file AliFMDEventPlaneFinder.h file AliForwardUtil.h Various utilities used in PWGLF/FORWARD. f... |
Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions -- and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.
Dear Uncle Colin,
Is there an easy way to write series in sum notation? I h... |
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... |
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... |
For multi-rail shots, just expand the solution of Alex, above. Reflect the pool table left and right, above and below the original pool table. Include reflections of reflections. It might help to color the original four sides in four different colors, to keep track of which side is which in the reflected pool tables. B... |
I have some basic questions around the theorem giving quantum error correction conditions that give necessary & sufficient conditions to have an error correcting operation.
The theorem is stated this way (page 436 of Nielsen & Chuang)
Let C be a quantum code, and let P be the projector onto C.
Suppose $E$ is a quantum ... |
Suppose I have a number $x$ represented in a residue number system, so $x = (x_1, \ldots, x_m)$, where $x_i \equiv x \pmod{p_i}$, and the $p_i$'s are all relatively prime (they can be distinct primes if it helps).
I would like to compute $x \bmod{p^*}$ for some $p^* \not\in \{p_1, \ldots, p_m\}$, but with low space.
Of... |
The domain of a function $f:X\to Y$ is normally defined as $\operatorname{dom}f\equiv X$, but I would like the
domain-function $\operatorname{dom}$ to be a funtion itself, i.e. I would like to define the function $\operatorname{Dom}$ defined by:
$$\forall X\,\forall Y\,\forall f\,(f:X\to Y\Rightarrow\operatorname{Dom} ... |
Well $e^i = \cos 1 + i \sin 1$ soo $e^{e^i} = e^{\cos 1 + i \sin 1} = e^{\cos 1}[\cos (\sin 1) + i \sin(\sin 1)] \approx e^{0.54030230586813971740093660744298}(\cos 0.8414709848078965066525023216303 + i \sin 0.8414709848078965066525023216303) = 1.7165256995489035179801866917897(0.66636674539288052633780454726237 +i0.55... |
Iosif Pinelis has given an answer to question 1 and partial answers to 2 and 3. Since he advised me to turn my comments into an answer, here it is.
I will deal with the case where the axiom of choice holds, and mention the case where it does not only at the end.
I will start with some definitions. A measure $\mu$ on $(... |
Current Transformer Current Transformers or CT's are Instrument Transformers that convert a generally high primary current I p to a k-times lower secondary current Ithat can be connected to standard measuring or protection devices. The primary and secondary windings are galvanically separated and can be on a different ... |
№ 9
All Issues $G$-convergence of periodic parabolic operators with a small parameter by the time derivative Abstract
In this paper, we consider a sequence $\mathcal{P}^k$ of divergent parabolic operators of the second order, which are periodic in time with period $T = \text{const}$, and a sequence $\mathcal{P}^k_{\psi... |
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A free-floating planet candidate from the OGLE and KMTNet surveys
(2017)
Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (bel... |
I want to solve following system of ODEs:
$ \Bigg\{ \begin{array}{} \frac{\partial C}{\partial t}=\frac{2W_b}{Rsin(\theta)}(1-\frac{C}{\gamma})+\frac{\nu}{\pi R^2}\frac{\partial C}{\partial Z} \\ \frac{\partial R}{\partial t}=\frac{W_b}{\gamma sin(\theta)} \end{array} $
Where $W_b=k_bC_h(1-\frac{C}{C_h})^{\frac{4}{3}}$... |
[K] refers to Kontsevich's paper "Deformation quantization of Poisson manifolds, I".
Background
Let $X$ be a smooth affine variety (over $\mathbb{C}$ or maybe a field of characteristic zero) or resp. a smooth (compact?) real manifold. Let $A = \Gamma(X; \mathcal{O}_X)$ or resp. $C^\infty(X)$.
Denote the dg
Lie algebra ... |
I wonder
1 whether there is a known relativization barrier against proving $L\neq NP$. Hence I'm looking for a language $A$ for which $L^A=NP^A$.
My first idea was to try $A:=SAT$, but then I thought that $L^A\subset P^A = \Delta_2^P$ and $NP^A=\Sigma_2^P$. This seems to disqualify not only $A:=SAT$, but any complete p... |
We use numbers all the time but rarely stop to think how they work. In this section we will consider decimal, binary and hexadecimal numbers, we will look at exponential numbers to see how the exponents work under different operations and we will look at scientific and engineering notation (also known as standard form ... |
Question
Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $$\frac{X}{1296}.$$ What is the value of $X$?
My Approach
I simplified it to the equation of the form:
$x_{1}+x_{2}+x_{3}+x_{4}=22, 1\,\,\leq x_{i} \,\,\leq 6,\,\,1\,\,\leq i \,\,\leq 4 $
Solving this equation result... |
Algebra is a way of generalising arithmetic by replacing numbers with letters. There are no rules about which letters to use but you will often find numbers replaced with $ a, b $ and $ c $ and variables represented by $ x, y $ and $ z $.
A term is a mathematical quantity that consists of a coefficient, a variable and ... |
Resonance Contents Classical Derivations Series Resonance
The classical circuit to demonstrate series resonance is the RLC circuit shown in the figure right, which shows a voltage source connected to R, L and C impedances in series. Given a fixed ac voltage source U operating at angular frequency [math] \omega [/math],... |
I'm reading Anton's Elementary Linear Algebra. I have come upon the rotation matrix.
$\begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$
They start the discussion with the fact that $T(e_1) = T(1,0) = (\cos \theta, \sin \theta)$ and $T(e_2) = T(0,1) = (-\sin \theta, \cos \theta)$.
Th... |
The ideal encryption scheme $E$ would be one that, for every ciphertext $C=E(K, M)$, if the key remains secret for the adversary, the probability of identifying $M$ is
negligible. Since that is not possible in practice, the second most reasonable approach is to define constraints strong enough to satisfy some definitio... |
I am looking for a counter example to the fact that a faithfully flat morphism isan effective descent morphism for the category of quasi-coherent sheaveswhen one forgets the quasi-compact hypothesis. If possible, I'd like a counter-exampleon the
descent of morphism aspects. In other words, I am looking fora morphism of... |
Reading a paper about eta invariants I came across a zeta-like function.
I'm looking for the analytic continuation of $$\sum_{k=1}^\infty k(k+a)^{-s}$$ at $s=0$, where $a$ is positive.
In the paper he just says "The [...] term causes no problem and at $s=0$ has the value $\left[\frac{(4a^2-1)}{12}\right]$." Unfortunate... |
Given a positive integer $n$ which is not a perfect square, it is well-known that Pell's equation $a^2 - nb^2 = 1$ is always solvable in non-zero integers $a$ and $b$.
Question:Let $n$ be a positive integer which is not a perfect square. Is there always a polynomial $D \in \mathbb{Z}[x]$ of degree $2$, an integer $k$ a... |
Figure 7.1 shows a triangle with sides a, b and c and angles subtending the sides A, B and C respectively.
Figure 7.1: Triangle with side lengths a, b and c.
For the triangle in Figure 7.1 we can write
$\dfrac{a}{sin(A)}=\dfrac{b}{sin(B)}=\dfrac{c}{sin(C)}$
These equations are called the sine rule.
Note: The sine of an... |
As its long ago since Erdős died and mathoverflow is the second best alternative to him (for discussing personal problems), I'd like to start a fruitful discussion about the following problem that I find very interesting.
Let $n \geq 3$ be an integer and let $\alpha(n)$ denote the least integer $k$ such that there exis... |
A sine wave starts at zero when $\theta=0$, rises to its maximum, drops through zero to its minimum and then returns to zero. This cycle is repeated again and again. The vertical distance from zero to the peak value is called the
amplitude. The number of peaks per unit time is called the frequency. Frequency is general... |
It seems that commutative diagrams appeared sometime in the late 1940s -- for example, Eilenberg-McLane (1943) group cohomology paper does not have any, while the 1953 Hochschild-Serre paper does. Does anyone know who started using them (and how they convinced the printers to do this)?
I can muddy the waters...!
In a n... |
15th century printers pioneered the use of movable type printing. Mirror images of each letter were cast in metal. These were arranged, letter by letter, in frames which printed one page at a time. A frame was called a matrix, several frames were called matrices. In mathematics, a matrix is a frame used to hold numbers... |
The Annals of Probability Ann. Probab. Volume 42, Number 1 (2014), 354-397. Explicit rates of approximation in the CLT for quadratic forms Abstract
Let $X,X_{1},X_{2},\ldots$ be i.i.d. ${\mathbb{R}}^{d}$-valued real random vectors. Assume that ${\mathbf{E}X=0}$, $\operatorname{cov} X=\mathbb{C}$, $\mathbf{E}\Vert X\Ver... |
In [20], the existence of Coulomb gauge with respect to a “small” connection on a disk plays an important role in the existence of conservation law. It is quite natural to expect “good estimate” under “good gauge,” and then the existence of conservation law can be obtained from a fixed point argument of systems of elli... |
For simplicity, consider in $\mathbb{R}^3$, and the Fourier transform of the following function $$f=(x_1+x_2+x_3)(1+|x|^2+x_1^2(x_2^2+x_3^2)+x_2^2x_3^2)^{-t+is},~~ \frac12<t<1,~~s\in \mathbb{R}.$$
Note that the function is not in $L^1$, in fact $f$ behaves like $|x|^{-2t+1}$ at $\infty$. So the Fourier transform is tak... |
I put together a series of demos for a group of epidemiology students who are studying causal mediation analysis. Since mediation analysis is not always so clear or intuitive, I thought, of course, that going through some examples of simulating data for this process could clarify things a bit.
Quite often we are intere... |
Carter-Wegman polynomial authenticators
For a given finite field $(\mathbb F,+,\times)$ of $f$ elements, define a Carter-Wegman polynomial authenticator for a message $M=m_1\|m_2\|\dots\|m_l$ of $l$ symbols in $\mathbb F$ as $$H_{(r,s)}(M)=s+\sum_{i=1}^l m_{(l+1-i)}\cdot r^i$$ where $r$ and $s$ are uniformly random ind... |
Quasi-linear Schrödinger–Poisson system under an exponential critical nonlinearity: existence and asymptotic behaviour of solutions
Article
First Online:
74 Downloads Abstract
In this paper we consider the following quasilinear Schrödinger–Poisson system in a bounded domain in \({\mathbb {R}}^{2}\):
depending on the pa... |
We know by the Riemann Existence Theorem that any Riemann surface can arise holmorphically as the branched cover of a sphere:
Therefore, any branched cover of the sphere can be represented by a rational function
polynomial $\frac{p (z)}{q(z)}: X \to \mathbb{C}$.
Given arbitrary polynomial $p$, do there exist ways to co... |
(Reposted from Math StackExchange because this may be more suited for professional mathematicians.)
The Mountain Pass Theorem roughly says the following. Consider a differentiable functional $I: H \rightarrow \mathbb{R}$ from a Hilbert space $H$ to the reals which satisfies an appropriate compactness/properness conditi... |
An autonomous equation is autonomous. Therefore, its solutions are related by time shifts: if $z=f(t)$ is a solution, then so is $z=f(t+C)$ for any constant $C$. In particular, there is nothing special about $x\to 0^+$. If one solution blows up going backwards in time, then they all do, and in exactly the same way, but... |
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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 ... |
R/Normal.R
normal.Rd
The Normal distribution is ubiquituous in statistics, partially because of the central limit theorem, which states that sums of i.i.d. random variables eventually become Normal. Linear transformations of Normal random variables result in new random variables that are also Normal. If you are taking ... |
The writing is certainly less clear than it ought to be.Your instincts are right; they just didn't explain it well.In particular, they're not saying that the term in bracketsonly vanishes for symmetry transformations. It alwaysvanishes for a field obeying the Euler-Lagrange equations.
What they're really saying is:
A c... |
Deepak Jain
Deen Dayal Upadhyaya College, New Delhi
Model independent constraints on cosmic curvature
We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter (Ω0k) with redshift by using the observations of the Hubble param... |
1,764 69
Hi PF
Given some linear differential operator ##L##, I'm trying to solve the eigenvalue problem ##L(u) = \lambda u##. Given basis functions, call them ##\phi_i##, I use a variational procedure and the Ritz method to approximate ##\lambda## via the associated weak formulation $$\langle L(\phi_i),\phi_j\rangle =... |
I am trying to find a single primitive root modulo $11$. The definition in my textbook says "Let $a$ and $n$ be relatively prime integers with ($a \neq 0$) and $n$ positive. Then the least positive integer $x$ such that $a^x\equiv1\pmod{\! n}$ is called the order of $a$ modulo $n$ and is denoted by $\text{ord}_{n}a$".
... |
I'm trying to solve a system of nonlinear, coupled ODEs, where the governing equation for the $n$-th ODE is of the form:
$$\sum_k^M Q_{nk} \ddot{a}_k -\sum_{\ell}^M\sum_k^M S_n(\ell,k) \dot{a}_{\ell} \dot{a}_k + \frac{1}{2}U_n = 0$$
where
$$Q_{nk}=\frac{1}{2}\sum_{j=1}^MP_{jn}P_{jk},$$
with
$$P_{jn}=\frac{1}{\sqrt{m}n}... |
Need help! I was working on a project when I required to use a projection operator. For an example case, I have the Bell state, $$|\psi\rangle = \frac1{\sqrt2}\left(\color{blue}{|0}0\rangle+|11\rangle\right)$$ which now I want to take to the state, $$|\psi'\rangle = |\color{blue}{0}0\rangle$$ by weeding out the states ... |
The question is: let $X_1, ..., X_n \sim N(\mu, \sigma^2)$. Let $\tau$ be the .95 percentile, i.e. $P(X<\tau)$ = .95. What is the MLE of $\tau$?_
What I have tried:
$P(X<\tau) = P(Z < \frac{\tau - \mu}{\sigma}) = \Phi(\frac{\tau - \mu}{\sigma})$ where Z denotes a Standard Normal random variable, and $\Phi$ is the CDF f... |
Illinois Journal of Mathematics Illinois J. Math. Volume 45, Number 1 (2001), 25-39. Local properties of polynomials on a Banach space Abstract
We introduce the concept of a smooth point of order $n$ of the closed unit ball of a Banach space $E$ and characterize such points for $E = c_0$, $L_p(\mu)$ ($1\leq p \le\infty... |
Anomalous physical transport in complex networks Abstract
The emergence of scaling in transport through interconnected systems is a consequence of the topological structure of the network and the physical mechanisms underlying the transport dynamics. We study here transport by advection and diffusion in scale-free and ... |
Monte Carlo is most useful when you lack analytic tractability or when you have a highly multidimensional problem.For example, even using simple lognormal and poisson models, there exist path-dependent payoffs or multi-asset computations such that no analytic solution exists and such that any PDE finite difference solu... |
Answer
The given models overestimate the total dormitory charge by $2$ .
Work Step by Step
The total dormitory charge for undergraduate education is given by: $\left[ \begin{align} & \left( 4565+5249 \right)+\left( 4824+5413 \right) \\ & +\left( 5046+5629 \right)+\left( 5241+5837 \right) \\ \end{align} \right]=41,804$.... |
Im trying to solve the following Poisson equation:
$$\nabla^2\phi = F(x,y)$$ $$for\ x\in(0,\infty)\ and\ y\in(0,L)$$
$$\frac{\partial\phi(x,0)}{\partial y}=0\ , \ \frac{\partial\phi(x,L)}{\partial y}=0\ , \ \frac{\partial\phi(0,y)}{\partial x}=0$$ $$\phi(x,y)\rightarrow0\ uniformly\ as \ x \rightarrow\infty$$ $$$$
I wa... |
Let $G=\langle x,y,z\mid z^2=1\rangle\cong \mathbb{Z}*\mathbb{Z}*\mathbb{Z}/2$.
I am interested to compute by hand (or by any other means) the quotient groups $\gamma_n/\gamma_{n+1}$ where $\gamma_n$ is the $n$th term of the lower central series. That is $\gamma_1=G$, $\gamma_2=[G,G]$, $\gamma_3=[\gamma_2,G]$, etc.
For... |
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Life is strong but yet fragile. It's a paradox. It's both things, like quantum physics:It's a particle and a wave at the same time!
Note by A Former Brilliant Member 4 years, 3 months ago
Easy Math Editor
This discussion board is a p... |
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Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Probability Title: On non-uniqueness in mean field games
(Submitted on 16 Aug 2019)
Abstract: We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition... |
Epidemiology: The SIR model
Simulation of differential equations with turtle graphics using JSXGraph.
Contents SIR model without vital dynamics
The SIR model measures the number of susceptible, infected, and recovered individuals in a host population. Given a fixed population, let [math]S(t)[/math] be the fraction that... |
From Rogawski ET 2e section 10.7, exercise 4.
Find the Maclaurin series for $f(x) = \dfrac{x^2}{1-8x^8}$.
$$\dfrac{x^2}{1-8x^8} = \sum_{n=0}^{\infty} [\textrm{_______________}]$$
Hi! I am working on some online Calc2 homework problem and I am not quite sure how to go about solving this Taylor series. I know I should su... |
Jeff, your questions were in some sense the motivation for my thesis. Let me say a few things that you probably already know before I try and answer your questions.
The $E_\infty$ algebra structure on integral cochains of a topological space $X$ is a homotopy invariant of $X$. If $X$ is nilpotent and of finite type, th... |
Are you planning to study engineering, physics or another courseinvolving lots of applied mathematics at university?
In your first year you will undoubtedly take maths courses to bringyou up to speed with many of the advanced mathematical techniquesrequired in the serious applications of mathematics to the physicalscie... |
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Change to browse by: References & Citations Bookmark(what is this?) Computer Science > Machine Learning Title: Finite Precision Stochastic Optimization -- Accounting for the Bias
(Submitted on 22 Aug 2019 (v1), last revised 26 Aug 2019 (this version, v2))
Abstract: We consider first order ... |
An Introduction to LaTeX
LaTeX is a way of writing documents that is more like writing a program than using Word. You write the "source code" using a text editor (Notepad or Word will do) then you "compile" it. You can get "front-ends" of various complexity to help you, but I'll concentrate on the basics here without d... |
On any one flip, the probability that all three coins come up the same is $\frac{2}{8}=\frac14$ and the probability that they don't is $\frac34$. Hence, the probability that the three coins come up the same for the first time at exactly the $n$-th flip is ${\left(\frac34\right)}^{n-1}\frac14$.
The expectation is theref... |
I'm working through James Stewart's
Precalculus, and I have some confusion regarding this question: "Find the exact value of the trigonometric function at the given real number: $\cot \frac{25\pi}2$."
So, easy enough... $\frac{25\pi}2$ is simply a multiple of $\pi\over2$. $\cot$ is
undefined at intervals of $n\pi$ wher... |
I am unsure if this is even possible in Mathematica, but my optics professor assigned a project to me on circular apertures and Fourier transforms. I have found plenty on the Airy function, but I am wondering if there is any way to produce an image like the one below in Mathematica:
Physicist chiming in -
Hi!.
I believ... |
This question seems to have been specifically designed to make you realise that the homology groups of a space can sometimes pick out homotopical information about a space which is not contained in the fundamental group alone. In this case, we have $X$ which is homotopy equivalent to $S^2\vee S^1\vee S^1\vee S^1$ (as y... |
I am reading Rudin and I am very confused what a derivative is now. I used to think a derivative was just the process of taking the limit like this $$\lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{(x+h)-x}$$
But between Apostol and Rudin, I am confused in what sense total derivatives are derivatives.
Partial derivatives much... |
Differential and Integral Equations Differential Integral Equations Volume 22, Number 7/8 (2009), 617-636. Exponential stability for the $2$-D defocusing Schrödinger equation with locally distributed damping Abstract
This paper is concerned with the study of the unique continuation property associated with the defocusi... |
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