text stringlengths 256 16.4k |
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This question is more of a trick.
Notation: for any formula $\phi$, let $\phi^=$ mean the formula obtained by
merely replacing each occurrence of the membership symbol $\in$ in $\phi$ by the equality symbol $=$, so for example if $\phi$ is the formula $(y \in y)$, then $\phi^=$ is the formula $(y=y)$.
We assume full Ex... |
The $(M+1)$ peak is often considered in the high-resolution mass spectra of organic molecules as it reveals the number of carbon atoms in the sample. In general, it is known that the ratio of the size of the $M$ to $(M+1)$ peaks is $98.9 : 1.1 \times n $ since the relative abundance in nature of $^{13}$C is $ 1.1$% for... |
While reading some articles on formal proofs (see also my previous question on cstheory about the length of ZFC proofs versus human written proofs), I came up with this apparent paradox.
Let $M_{const}$ be a program that given Turing machine $M$ checks if there is a short ZFC proof $\Gamma$ of length $|\Gamma| \leq |M|... |
Wind is not an acceleration, but the drag due to the wind is a force applied to the body. This results in an acceleration according to Newton's second law. All the forces or accelerations need to be added as vectors to find the magnitude and direction of the total force or acceleration.
Let $\hat{y}$ be the upward dire... |
An advanced way is to think of the Cyclotomic polynomial. $\Phi_{p-1}(x),$ which has primitive $p-1$th roots of unity as roots.
But you can show that in general:$$\Phi_{4m}(x)=\Phi_{2m}(x^2)$$
This can be seen by using the rule:
$$\Phi_n(x)=\prod_{d\mid n}\left(x^d-1\right)^{\mu(n/d)}$$
But when $n/d$ is divisible by $... |
A few preliminary remarks:
1) Complexifications of Banach lattices are in fact a special case of the more general concept of
complexifications of real Banach spaces.
2) Most books and articles about complex Banach lattices which contain spectral theoretic results focus on
positive operators (or, say, generators of posi... |
The answer to this question suggest that one can solve the measurement problem by decoherence. If I understand it correctly the decoherence appears when the quantum state interacts with the measurement device (and possibly the environment).
However I was wondering about locality. Bell tests tell us that measurements ca... |
Decision Tree Learning is a non-parametric supervised learning method used for classification and regression. The goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features.
Decision Tree is a simple representation for classifying examples. A... |
Learning Outcomes
Use the order of operations to correctly perform multi-step arithmetic Apply the order of operations to statistics related complex questions.
When we are given multiple arithmetic operations within a calculation, there is a, established order that we must do them in based on how the expression is writ... |
M 3: a new muon missing momentum experiment to probe (g – 2) μ and dark matter at Fermilab Abstract
Here, new light, weakly-coupled particles are commonly invoked to address the persistent $$\sim 4\sigma$$ anomaly in $$(g-2)_\mu$$ and serve as mediators between dark and visible matter. If such particles couple predomin... |
First note, that hybridisation is a mathematical concept which can be applied to interpret a bonding situation. It has no physical meaning whatsoever. Instead it helps us to understand the direction of bonds better.
Second note, that the second period usually behaves quite differently from the remaining elements in a g... |
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... |
Learning Objectives
Identify a conic in polar form. Graph the polar equations of conics. Define conics in terms of a focus and a directrix.
Most of us are familiar with orbital motion, such as the motion of a planet around the sun or an electron around an atomic nucleus. Within the planetary system, orbits of planets, a... |
Answer
$\sqrt{7}$
Work Step by Step
Using the properties of radicals, the given expression, $ \dfrac{\sqrt{56}}{\sqrt{8}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{56}{8}} \\\\= \sqrt{7} .\end{array}
You can help us out by revising, improving and updating this answer.Update this answer
After you cl... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
October 2013 , Volume 33 , Issue 10
Select all articles
Export/Reference:
Abstract:
This expository article concerns a system of semilinear parabolic partial differential equations that describes the evolution of the gene frequencie... |
Consider the following complex power series :$$\sum_{n=1}^\infty\frac{z^n}{n}$$ The radius of convergence of this series is $1$ and the series is divergent for $z=1$. I want to know what are the values of $z\in C:=\lbrace z\in\mathbb{C}: |z|=1\rbrace$, the circle of convergence, for which the given series converges.
HI... |
In general, how would one find the distribution of $f(X)$ where $X$ is a random variable? Or consider the inverse problem of finding the distribution of $X$ given the distribution of $f(X)$. For example, what is the distribution of $\max(X_1, X_2, X_3)$ if $X_1, X_2$ and $X_3$ have the same distribution? Likewise, if o... |
So the problem is asking me to find the Electric field a height z above the center of a square
sheet of side a
I approach the problem a different way than the book, I derive the electric field due to a line of charge of side $a$ a height z above the center of a square loop, and I verified it to be $\frac{1}{4\pi\epsilo... |
I am trying to understand a single factor Random effects anova from a book.
In this case : -
$y_ij = \mu+ \tau_i + e_{ij}$, where $i = 1,...,a$ and $j= 1,...n$.
Assumptions:
The treatment effects $\tau_i$ are $N(0,\sigma_\tau^2)$ and $e_{ij}$ are $N(0,\sigma^2)$ $\tau_i$ and $e_{ij}$ are independent
Hence we have : $Va... |
Answer
$\sqrt{5}$
Work Step by Step
Using the properties of radicals, the given expression, $ \dfrac{\sqrt{55}}{\sqrt{11}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{55}{11}} \\\\= \sqrt{5} .\end{array}
You can help us out by revising, improving and updating this answer.Update this answer
After you ... |
Line 14: Line 14:
----
----
==Question 1==
==Question 1==
+ + + + + + + + + + + + + + + + + + + + + +
Define System 1 as the following LTI system
Define System 1 as the following LTI system
Line 44: Line 66:
c) Sketch the graph of the frequency response <math>H_d(\omega)</math> that would make the following system equi... |
I'll discuss it in intuitive terms.
Both confidence intervals and prediction intervals in regression take account of the fact that the intercept and slope are uncertain - you estimate the values from the data, but the population values may be different (if you took a new sample, you'd get different estimated values).
A... |
JetEtMissPublicResultsINSITU
Caption: {Mean jet multiplicity for jets with $\pt>10\GeV$as a function of \pt\ of the $Z$ boson in $Z$\,+\,jet events.
Caption: $\Delta \phi$ between the photon and the jet for a) {\cone}algorithm with $R = 0.4$.
Caption: $\Delta \phi$ between the photon and the jet for b) \kt\ algorithm w... |
Summary. Using your favourite $O(n^d)$ algorithm for finding a matching in graphs on $O(n)$ vertices, there is a simple algorithm using $O(\max\{n^{d+2},n^4\})$ operations over the reals for decomposing doubly-stochastic matrices. The run-time bound comes from $O(n^2)$ iterations of a procedure in which each iteration ... |
Let $C$ be the space nº74 ("double origin topology") in Steen & Seebach's
Counterexamples of Topology, chosen because it is the only one listed there that is T2 and path-connected but not T3:
$C$ consists of the set of points of the plane $\mathbb{R}^2$ together with an additional point $0^*$. Neighborhoods of points o... |
Answer
$4$
Work Step by Step
Using the properties of radicals, the given expression, $ \dfrac{\sqrt{96}}{\sqrt{6}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{96}{6}} \\\\= \sqrt{16} \\\\= \sqrt{(4)^2} \\\\= 4 .\end{array}
You can help us out by revising, improving and updating this answer.Update thi... |
I asked the following question here.
Let $f: [0, 1]^2 \to \mathbb{R}$ be such that for every $x \in [0, 1]$ the function $y \to f(x, y)$ is Lebesgue measurable on $[0, 1]$ and for every $y \in [0, 1]$ the function $x \to f(x, y)$ is continuous on $[0, 1]$.
Is $f$ measurable with respect to the completion of the product... |
Easy observations first:
The image is unbounded, since $0$ goes to $\infty$. The points $a_1, \dots, a_n$ are mapped to $0$, so the image of boundary curve comes back to hit $0$ over and over Each such return to $0$ makes the angle of $\pi \lambda_k$ with vertex $0$. The sum of these angles is $2\pi$.
Trying to imagine... |
First of all, do note that the momentum conservation equations should read $h_{\rho\nu} \nabla_\mu T^{\mu\nu}=0$, otherwise you would have a single equation.
The strict distinction between energy and momentum conservation is only valid in the Local Rest Frame, the frame of the fluid element with velocity $u^\mu$: for s... |
Another way to obtain a new set from two given sets \(A\) and \(B\) is to form ordered pairs. An
\((x,y)\) consists of two values \(x\) and \(y\). Their order of appearance is important, so we call them first and second elements respectively. Consequently, \((a,b)\neq (b,a)\) unless \(a=b\). In general, \((a,b)=(c,d)\)... |
I actually don't think that this view of light being in a quantum superposition is anything new: what Discover magazine is describing (I believe) is the
stock standard picture of how one would describe a system of cells, molecules, chloroplasts, fluorophores, whatever interacting with the quantised electomagnetic field... |
My study group and I were discussing this question today.
We can construct the Lebesgue measure using Caratheodory's extension theorem in the usual way:
Given the function $F(x) = x$, we can construct a pre-measure $\mu_F$ associated with $F(x)$ defined on an algebra of "intervals" (Folland uses right-closed h-interval... |
Someone once incorrectly told me that, given the speed of light is the speed limit of the universe, aliens would have to live for hundreds of years if they are to travel distances of hundreds of light years to reach Earth.
In a "special relativistic" and non-expanding universe however, this is not the case. As velocity... |
Jacob, KT and Jayadevan, KP (1998)
System Bi–Sr–O: Synergistic measurements of thermodynamic properties using oxide and fluoride solid electrolytes. In: Journal of Materials Research, 13 (7). pp. 1905-1918.
PDF
system.pdf
Download (352kB)
Abstract
Phase equilibrium and electrochemical studies of the ternary system Bi-S... |
SolidsWW Flash Applet Sample Problem 2 Flash Applets embedded in WeBWorK questions solidsWW Example Sample Problem 2 with solidsWW.swf embedded
A standard WeBWorK PG file with an embedded applet has six sections:
A tagging and description section, that describes the problem for future users and authors, An initializati... |
Even at the risk of using slightly too heavy armory, I would like to shortly explain, how I would view the situation in a light, that naturally produces and "explains" the observations collected above:
@Martin: Tthe natural extension on tensor products @TomGoodwillie: The "skew-Leibniz"-rule one has to use @JackHuizeng... |
In this answer we formally show that a (quasi)symmetry of an action implies a corresponding symmetry of its EOM$^{\dagger}$. The answer does not discuss form covariance of EOM. For further relations between symmetries of action, EOM, and solutions of EOM, see e.g. this Phys.SE post.
Let us first recall the definition o... |
A Lorentz covariant equation is one that takes the same form even when a Lorentz transformation is applied to each variable. Lorentz covariance is generally made manifest by writing the equation with all Lorentz indices contracted together with the Minkowski metric, so that each scalar quantity in the equation is a Lor... |
Consider a ring with radius $R$ and charge density $\lambda=\lambda_0\cos\phi$, where $\phi$ is the angular coordinate in the cylindrical coordinate. If I want to find the dipole moment of this charge distribution, then I put it into $$\vec{p}=\int{\mathrm d^3r~\rho(\vec{r})\vec{r}},$$ where I tried $$\rho(\vec{r})=\la... |
Thank you for using the timer!We noticed you are actually not timing your practice. Click the START button first next time you use the timer.There are many benefits to timing your practice, including:
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that ... |
Suppose that $A$ is a symmetric non-random matrix and $X\sim N(\mu,\Sigma)$ and $b \in R^n$ is a non-random vector. Then what is the distribution of $$X^tAX+b^tX \quad ?$$
The distribution without the linear term is solved in the answer here(Transformation of multivariate normal sum of chi-squared).
In the case of an i... |
Suppose that we have an arbitrary set of points $S\subseteq\mathbb{C^2}$ and want to find a polynomial $P(X)$ such that $(x,y)\in S\Rightarrow y=P(x)$ and $P'(x)=0\Rightarrow (x, P(x))\in S$. In other words, find a polynomial that passes through all of the points but has no extrema except possibly at those points.
Beca... |
Quoting from paper Int. J. Climatol. 21: 1371–1384 (2001)
The Wakeby distribution (WAD), defined by Thomas and introduced by Houghton (1978), is defined by the quantile function: $$ x(F) = \xi + \alpha \frac{1 - \left(1-F\right)^\beta}{\beta} - \gamma \frac{1 - \left(1-F\right)^{-\delta}}{\delta} $$
The article by Houg... |
Browse by Person
Up a level 54. Article
Aad, G, Abbott, B, Abdallah, J et al. (2822 more authors) (2017)
Performance of algorithms that reconstruct missing transverse momentum in root s=8 TeV proton-proton collisions in the ATLAS detector. The European Physical Journal C, 77 (4). 241. ISSN 1434-6044
Aad, G, Abbott, B, ... |
$\bullet$ What are these (length) scales that we often talk about? Do we mean the wavelength of some Fourier modes of something?
Yes, these are the comoving wavelengths of Fourier modes (see next)
$\bullet$ If yes, do we mean the Fourier modes of the density fluctuations $\delta\rho/\rho$ or that of the inflaton field ... |
Suppose that $G$ is a finitely generated group and $A$ is a finite set. Then we shall give $A$ the discrete topology and $A^{G}$ the product topology; in particular $A^{G}$ is compact and totally disconnected.
If $x\in A^{G}$ and $g\in G$, then define $gx\in A^{G}$ by letting $gx(h)=x(g^{-1}h)$.
We say that $F:A^{G}\ri... |
My teacher in Math Team gave the following question to us.
Solve $$a!b!=a!+b!+c!$$ where $a$, $b$ and $c$ are nonnegative integers.
I found only one solution by trial and error and it is $(a,b,c)=(3,3,4)$.
Any help is appreciated!
Mathematics Stack Exchange is a question and answer site for people studying math at any ... |
Iterative reweighted least squares (IRLS) is used when errors are heteroscedastic. Let us assume that error comes from a distribution where its mean is zero and the variance is a function of the absolute value of the input. From what I have read, IRLS is applicable here and will give better results than OLS.
My questio... |
There are many articles like this one Testing the isotropy of the Universe by using the JLA compilation of type-Ia supernovae (PDF, arxiv.org) trying to search for a dipole effect in cosmology with type Ia supernovae (used as standard candles). The idea of this kind of search is to do a test of the cosmological princip... |
Difference between revisions of "OBD Reasoner"
(→Notation)
Line 1: Line 1: + +
The OBD reasoner uses definitions of transitive relations, relation hierarchies, and relation compositions to infer implicit information. These inferences are added to the OBD Phenoscape database. This section documents the inherited code in... |
Publications Influence
Claim Your Author Page
Ensure your research is discoverable on Semantic Scholar. Claiming your author page allows you to personalize the information displayed and manage publications.
Abstract The masses and decays of the scalar D s 0 ∗ (2317) and axial-vector D s 1 ∗ ( 2460 ) charmed strange mes... |
Kitefoil introduction
Foil is a technology that allows a hull (propelled by a motor or in this case a sail) to
emerge totally from the water, thanks to the hydrodynamic action of the submerged surface.
In fact, the pressure of the water under the
wings, combined with the depression that forms above them, generates a fo... |
Unlike lasso, ridge does not have zeroing coefficients as a goal, and you shouldn't expect applying ridge penalty to have this effect. So the answer to your title question is "no."
However, in your question body, you ask whether it is
possible for the ridge penalty to produce a zero coefficient that was nonzero in an u... |
This question already has an answer here:
I'm attempting a topology proof and think my proof is correct but I'm not 100% sure. The problem is as follows: Define $\Delta_X=\{(x,x)\in X\}$. Prove that $X$ is Hausdorff if and only if $\Delta_X$ is a closed set. The reverse proof is fine but for my proof of the forward one... |
Q7.1.1
Is the power series \( \sum_{k=0}^\infty e^k x^k\) convergent? If so, what is the radius of convergence?
Q7.1.2
Is the power series \( \sum_{k=0}^\infty k x^k\) convergent? If so, what is the radius of convergence?
Q7.1.3
Is the power series \( \sum_{k=0}^\infty k! x^k\) convergent? If so, what is the radius of ... |
In my research I'm dealing with the following question.
Let $E$ set, $K:E \times E \to \mathbb R$ a positive type function, and $\mathcal H := \mathcal H(1+K)$ (in the sense of the Moore theorem). Now let $\xi: H \to \mathbb R$ a continuous, linear functional with $\xi(1) = 1$ (where the first $1$ denotes the constant ... |
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).
Search for ... |
Stile supports mathematical notation, from simple super and subscript to full-blown matrices and calculus.
Equations in your question text
To insert equations into question text, simply click on the little
square root icon within the text editor:
This brings up the
equation editor. You can use any of the tools availabl... |
Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - x + p=0$ and let $\gamma$ and $\delta$ be the roots of the equation $x^2 -4x+q=0$. If $\alpha , \beta , \gamma , \delta$ are in Geometric progression then what is the value of $p$ and $q$?
My approach:
From the two equations, $$\alpha + \beta = 1$$, $$\alpha ... |
The first thing that should come to mind to you in a question like this is that any usage of my 300m of fence can be described by a single parameter. For instance, if I give you one of the edge lengths of the square, $s$, then you have all the information you need to work out what the edge lengths of the rectangle are ... |
I've been scanning across the web, and haven't found a good method to compute the Gauss Legendre abscissas and weights $\{ x_j, w^j \} _{j=1}^N$ for large $N\in\mathbb{N}$. My question is how to do it, and why should it work?
To those who need some background:
The goal is to approximate an integral by a discrete interp... |
I aim to study the binary forms $ax^2 + bxy + cy^2 = (a,b,c)$ where $a,b,c \in {F_q}[T]$ (charasteristic of $F_q$ not 2) in particular those such that the discriminant $D = b^2 - 4ac \in F_q[T]$ has even degree and sign ${D} \in {F_q^*}^2$ – in other words its principal coefficient is a square.
This case is interesting... |
A particle is in the ground state of an infinite square well with walls in the range x=[0,a]. At time t=0, the walls are removed suddenly and the particle becomes free. What is the energy of the free particle?
What I know: \begin{equation} \begin{split} V(x) &= 0, \; \; \; 0\le x \le L \\ &= \infty, \; \; \;otherwise \... |
I'm going through Stein's Complex Analysis, and I'm a bit confused at one of the classical examples of using Cauchy's theorem to evaluate an integral. The example is:
$$\int_0^{\infty}\frac{1-\cos{x}}{x^2}dx = \frac{\pi}{2}$$
The book says (and I'll add my thoughts & questions in
bold as they come up):
Here we consider... |
[Read More]
Big Image Sample Using Multiple Images
The image banners at the top of the page are refered to as “bigimg” in this theme. They are optional, and one more more can be specified. If more than one is specified, the images rotate every 10 seconds. In the front matter, bigimgs are specified using an array of has... |
The depictions you're seeing are correct, the electric and magnetic fields both reach their amplitudes and zeroes in the same locations. Rafael's answer and certain comments on it are completely correct; energy conservation does
not require that the energy density be the same at every point on the electromagnetic wave.... |
Defining parameters
Level: \( N \) = \( 25 = 5^{2} \) Weight: \( k \) = \( 3 \) Nonzero newspaces: \( 2 \) Newforms: \( 2 \) Sturm bound: \(150\) Trace bound: \(1\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(25))\).
Total New Old Modular forms 64 56 8 Cusp forms 36 36 0... |
I wanted to know about the substitution reaction of alkanes particularly interested in the reaction of methane with fluorine and chlorine.
Let's have a look at some fundamental data and the chemistry involved.
Chlorine is an inflammable gas with a boiling point of -35 °C and a nice yellowish-green colour. It is heavier... |
Take linear regression as the example, given one specific data set $D_1=\{(x_1,y_1),...(x_n,y_n)\}$, we could train a model with one specific parameter estimate $\hat\theta_1$, if we do the training on a new data set $D_2$, we will have new estimate $\hat\theta_2$, and so on. For input data $x$, I could predict the tar... |
I will work over a field of characteristic $0$ so that reductive algebraic groups are linearly reductive; presumably there is a way to eliminate this hypothesis. In this case, for an integer $n>1$ and for a divisor $m$ such that $n>m>1$, there
does not exist $f$ as above. The point is to consider the critical locus of ... |
Suppose that a random variable Y has a gamma distribution w. parameters $\displaystyle \alpha = 2$ and an unknown $\displaystyle \beta$. We have earlier proved that $\displaystyle 2Y/\beta$ has a chi-square distribution w. 4 df. Using $\displaystyle 2Y/\beta$ as a pivotal quantity. derive a 90% confidence interval for ... |
I'm given series $\sum_{n = 1}^{+\infty} \frac{(-1)^{n}}{(n+1)!}\left(1 + 2! + \cdots + n!\right)$ and I have to find whether it is convergent.
Testing for absolute convergence, we have $a_n = \frac{1}{(n+1)!} + \frac{2}{(n+1)!} + \cdots + \frac{(n-1)!}{(n+1)!} + \frac{n!}{(n+1)!}$ and since last term is $\frac{n!}{(n+... |
This depends, of course, on the underlying probability space, most notably the filtration. In general, there are plenty of progressive processes which are not predictable, and this should be fairly standard material. If one works with the raw (un-augmented) filtration on the canonical path space of continuous functions... |
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. ... |
I am given
$A = \left[\begin{array}[c]{rr} \cos\theta & -\sin\theta\\ \sin\theta & \cos\theta\end{array}\right]$
from which I calculated
$λ = \cos\theta \pm i\sin\theta$
the eigenvalues are thus imaginary but I want to calculate the eigenvectors
$A-\lambda I = \left[\begin{array}[c]{rr} \pm i\sin\theta & -\sin\theta\\ ... |
As is often the case with NP-reductions, it makes sense to look for similar problems. In particular, it is hard to encode global conditions such has "have seen some nodes" into PCP (with polynomially many tiles) which contraindicates graph problems, packing problems would require us to encode unary numbers in PCP (crea... |
Interesting recursive functions -
et R={i∣∃j:f(j)=i} be the set of distinct values that...can sum1 explain clearly ???wat is d meaning of dis
R={i∣∃j:f(j)=i} be the set of distinct values that f takes
R={i∣∃j:f(j)=i} be the set of distinct values that f takes
Someone please explain why is it written "takes" ? R contain... |
I just wanted to check the method I have formulated for the derivation for the adjoint Dirac equation using Gamma matrice notation. This is a problem from the very excellent "Modern Particle Physics" by Mark Thomson book. Incidentally, I fully recommend purchasing this book if you are studying at either Cambridge, Oxfo... |
$\newcommand{\real}[1]{\left\lvert #1 \right\rvert}$$\newcommand{\Sing}[1]{\operatorname{Sing}(#1)}$$\newcommand{\counit}{\epsilon}$$\newcommand{\To}{\longrightarrow}$$\newcommand{\proj}{\mathrm{proj}}$$\newcommand{\NN}{\mathbb{N}}$$\newcommand{\RR}{\mathbb{R}}$
Yes, the map $\real{\Sing{X}} \to X$ is a Serre fibration... |
The way I calculate it is summing up the weighted beta of long and shorts but I saw a table where this wasn't the case so I am wondering if this is not the correct way.
You can actually show by construction that the beta of the portfolio is the weighted sum of all the underlyings betas.
Assume the return of the benchma... |
Statistical model for
Complete Randomized design
$y_{ij} = \mu + \tau_i + \epsilon_{ij}$
where, $i$ denotes treatment and $j$ denotes observation.
$i=1,2,...,k\quad and \quad j=1,2,..., n_i$
$y_{ij}$ be a random variable that represents the response obtained on the $jth$ observation of the $ith$ treatment.
$\mu$ is the... |
I'm trying to solve variable density and viscosity Navier-Stokes equation using lagged pressure projection method. I'm solving for cavity problem as a test case now (once I get projection right, I will be solving a multiphase problem). The problem is I get oscillations developed in the solution as I march in time. .
I'... |
Context:
For a system with $n$ degrees of freedom (DOF), one has to deal with $2n$ independent coordinates ($2n$ dimensional phase space), of position $q$ and $\dot{q}$ in Lagrangian formulation, or independent coordinates of $q$ and generalized momentum $p$ in the Hamiltonian formulation.
We remind the reader that if ... |
I'm having trouble with a BJT circuit.
What we are given:
\$U_{CC} = 10\text{V}\$
\$R_C = 972 \Omega\$ \$R_B = 14\text{k} \Omega\$ \$U_{\text{BE}} = 0.7\text{V}\$ \$I_C = 12\text{mA}\$
We need to find the current amplification \$B\$.
My approach was to calculate \$U_C\$, the Voltage which drops at \$R_C\$. I read in a ... |
Let (X,d) be a metric space and A,B $\subset$ X be two compact subsets. Show $A\cap B$ is also compact.
I attempted this question by showing the intersection is bounded and closed.
But I stated that Bounded and Closed $\Rightarrow$ Compact (Heine-Borel) but I didn't realise this only holds for $\mathbb R^n$.
Most of th... |
The best workaround I can think out at the moment is to turn to
RegionPlot3D.
To plot ellipsoid with
RegionPlot3D, we need formula for general ellipsoid, which has been mentioned in the
Details of document of
Ellipsoid:
$$(x-p).{\Sigma^{-1 }}.(x-p)\leq 1$$
where $\Sigma$ is weight matrix, which can be generated with th... |
Annals of Functional Analysis Ann. Funct. Anal. Volume 4, Number 1 (2013), 25-39. Eigenvalue problem for a class of nonlinear fractional differential equations Abstract
In this paper, we study eigenvalue problem for a class of nonlinear fractional differential equations $$D^\alpha_{0^+}u(t)=\lambda f(u(t)),\quad 0 \lt ... |
The analyticity and exponential decay of a Stokes-wave coupling system with viscoelastic damping in the variational framework
Department of Mathematics and Economics, Virginia State University, Petersburg, VA 23806, USA
In this paper, we study a fluid-structure interaction model of Stokes-wave equation coupling system ... |
Note: This is (unfortunately) not a simple “fix your matching braces” issue, please read the whole question.
I’m working on a command to fix the spacing of
\vec — the spacing is too small by default, leading to collisions with the arrow and following glyphs in cases like
(\vec p). However, simply redefining the command... |
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Here is a problem from the NMTC 2015 Bhaskara Contest:
The number of values of x which satisfy the equation 52.8x−1x=500 are: \text{The number of values of}\space x\space \text{which satisfy the equation}\space 5^2.\sqrt[x]{8^{x-1}}=500\space \text{are:}The numbe... |
"Is this really a proof?" is the exact question e-mailed to me today from an undergraduate mathematics student whom I know as a highly competent student. The one sentence question was accompanied with the following demo: I am looking for a down-to-earth, non-authoritative answer who one may gi...
the 2005 AMS article/s... |
I'm getting a couple of different answers from different sources, so I'd like to verify something.
I misplaced my original notes from my prof, but working from memory I have the following:
\begin{align} \int\csc(x)\ dx&=\int\csc(x)\left(\frac{\csc(x)-\cot(x)}{\csc(x)-\cot(x)}\right)\ dx\\ &=\int\frac{\csc^{2}(x)-\csc(x... |
The sources known to me (Knutson's
Algebraic Spaces and Pascual-Gainza's Ampleness criteria for algebraic spaces) define a line bundle $L$ on an algebraic space $X$ (over a base scheme $S$) to be ample if a tensor power of $L$ is very ample, i.e. the pullback of $i^*\mathcal{O}(1)$ given a factorization $X \xrightarrow... |
Data on the mean multiplicity of strange hadrons produced in minimum bias proton--proton and central nucleus--nucleus collisions at momenta between 2.8 and 400 GeV/c per nucleon have been compiled. The multiplicities for nucleon--nucleon interactions were constructed. The ratios of strange particle multiplicity to part... |
Introduction
Encoding numerical inputs for neural networks is difficult because the representation space is very large and there is no easy way to embed numbers into a smaller space without losing information. Some of the ways to currently handle this is:
Scale inputs from minimum and maximum values to [-1, 1] One hot ... |
(All monoids are written additively in this question, even the non-commutative ones.)
Given a monoid $X$, write $\mathrm{Sub}(X)$ for the lattice of submonoids of $X$, and write $\mathrm{Cong}(X)$ for the lattice of monoid congruences on $X$. There is a function $\ker_X : \mathrm{Cong}(X) \rightarrow \mathrm{Sub}(X)$ d... |
The first observation of top quark production in proton-nucleus collisions is reported using proton-lead data collected by the CMS experiment at the CERN LHC at a nucleon-nucleon center-of-mass energy of $\sqrt{s_\mathrm{NN}} =$ 8.16 TeV. The measurement is performed using events with exactly one isolated electron or m... |
Given a probability distribution $p$ across an alphabet, we define redundancy as:
Expected Length of codewords - entropy of p = $\ E(S) - h(p)$
Prove that for each $\epsilon$ with $0 \le \epsilon \lt 1$ there exists a $p$ such that the optimal encoding has redundancy $ \epsilon$.
Attempts
I have tried constructing a pr... |
I am fairly new to Computational Engineering and I have mainly been exposed to using the Finite Difference Method to produce Linear Systems and solve them using Iterative Methods.
I am trying to solve a problem from the field of Electrochemistry, involving the Laplace equation and boundary conditions that link the unkn... |
Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior
1.
Department of Pure and Applied Mathematics, Via Vetoio, Loc. Coppito, 67100 L’Aquila, Italy
2.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, ... |
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