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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
It is.
Prior to continuity, which is a property of the preference relation, the preference relation $\succsim$ itself has been defined to be a binary relation that is characterized by transitivity, and, to begin with, by completeness. Then if $S_1\cup S_2 \neq [0,1]$, it means that there exist some values of $\alpha$ s... |
Liouville's Theorem (Complex Analysis) Theorem Then $f$ is constant. Proof
By assumption, there is $M \ge 0$ such that $\cmod {\map f z} \le M$ for all $z \in \C$.
For any $R \in \R: R > 0$, consider the function:
$\map {f_R} z := \map f {R z}$
Using the Cauchy Integral Formula, we see that:
$\displaystyle \cmod {\map ... |
I built a Precision Full Wave Rectifier Circuit, like in the following figure( with better amplifiers) to rectify a sine wave of 1kHz. As expected i got a rectified wave with 2kHz but doing its FFT analysis i noticed that the biggest frequency component is at DC(0) can anyone explain me why? Also, I'm sampling this sig... |
Snell's Law, Frequency, Speed and Wavelength
\[n= \frac{sin \theta_1}{\sin \theta_2}\].
In fact
\[n=\frac{v_1}{v_2}= \frac{\lambda_1}{\lambda_2}\].
These relationships mean that as waves pass from medium to medium, the sin of the angle between the wave and the normal, the speed and the wavelength all change in proporti... |
Definition of a Vector
Just being able to put numbers on physical quantities is not sufficient for describing nature. Very often physical quantities have directions. For example, a description of something’s motion is incomplete if you merely state how fast it is going. [
Okay, so an asteroid is moving at 35,000 miles ... |
Last week we saw that the best strategy for
Wythoff’s game is to always move to one of the blue squares in the diagram below (if you can). We found the locations of the blue squares with an iterative algorithm that builds outward from (0,0), but we haven’t yet discovered the underlying pattern in how these blue cells a... |
Quadratic Formula – Solution of quadratic equation using factorization
A quadratic equation is of the form of \( ax^2~+~bx~+~c~=~0, a~≠~0, a,b, ~and~ c\) are real numbers.
Consider the
quadratic equation \( x^2~-~3x~+~2\) = 0; substituting x=1 in LHS of the equation gives,
\(1^2~-~3~+~2\) = 0 which is equal to RHS of t... |
What is Curie-Weiss temperature? What is the difference between Curie-Weiss temperature and Curie temperature?
The Curie temperature or Curie point is the temperature at which a ferromagnetic or a ferri-magnetic material becomes paramagnetic when heated. The effect is reversible.
On the other hand,the Curie-Weiss tempe... |
Difference between revisions of "User:Nikita2/sandbox"
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====$\mathcal N$-property of a function $f$, continuous on an interval $[a,b]$====
====$\mathcal N$-property of a function $f$, continuous on an interval $[a,b]$====
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For any set
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For any set of measure =0, the image of this set, , also has meas... |
I have a function $g(x)$ that looks like this:
ListPlot[Table[{x, g[0.5, x, 3, 1]}, {x, -15, 15, 0.1}], Joined -> True, ImageSize -> Large, InterpolationOrder -> 2, PlotRange -> All] // AbsoluteTiming
I am trying to calculate the following integral:
$$\int_{-\infty}^{\infty} \cos (5.5x) g(x) \,dx \tag{1}$$
Naturally, t... |
№ 9
All Issues Volume 55, № 3, 2003 Algorithms for the Best Simultaneous Uniform Approximation of a Family of Functions Continuous on a Compact Set by a Chebyshev Subspace
Ukr. Mat. Zh. - 2003. - 55, № 3. - pp. 291-306
We generalize the cutting-plane method and the Remez method to the case of the problem of the best si... |
In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, etc.
The concept appears in ergodic theory—the study of stochastic processes and measure-preserving dynamical systems. Seve... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
January 2011 , Volume 29 , Issue 1
Select all articles
Export/Reference:
Abstract:
Non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations (VE
k), are applied to pr... |
If we solve the heat equation $u_t=u_{xx}$ by separation of variables, we assume that $u(x,t)=f(x)g(t)$, and solving 2 ordinary differential equations we can derive that $u(x,t)=e^{\omega^2t}(b\cdot \sin(\omega x)+ a\cdot \cos(\omega x))$ for some $a,b$, is a solution.
Now, if we assume the boundary conditions $u(0,t)=... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
AI News, Deep Learning: Regularization Notes Deep Learning: Regularization Notes
In previous article (long ago, now I am back!!) I talked about overfitting and the problems faced due to overfitting.
Many regularization approaches are based on limiting the capacity of models, such as neural networks, linear regression, ... |
Can anyone state the difference between frequency response and impulse response in simple English?
The impulse response and frequency response are two attributes that are useful for characterizing linear time-invariant (LTI) systems. They provide two different ways of calculating what an LTI system's output will be for... |
A thermal process of pasteurization is an operation that aims to reduce the initial number $N_0$ of microbial pathogens that are in a state of vegetative cells. The reduction of the number of microorganisms can be represented by the following equation:$$ N_0 \to N $$
Where $N_0$ is the initial number of microorganisms ... |
Circuit requirements:
DC voltage gain: 50dB Unity gain bandwidth: 50MHz Phase margin: 45 deg(60 deg is recommended).
The circuit is completely symmetric, so M1=M2, M3=M4, and M5=M6. Therefore the DC gain of the first stage without the buffer is
\$A_{V_o}=-g_{m_1}R_{out}, \ R_{out}=\frac{1}{1/r_{o_1}+1/r_{o_3}+1/r_{o_5}... |
I am trying to figure out the details on how to implement the 3D structure tensor in C/C++ in an easy but efficient way and need some advice!
For a discrete function $ I(x_i,y_j,z_k)$ the 3D structure tensor is given by: $$ S=\begin{pmatrix} W \ast I_x^2 & W \ast (I_xI_y) & W \ast (I_xI_z)\\ W \ast (I_xI_y) & W \ast I_... |
Permanent link: https://www.ias.ac.in/article/fulltext/pram/073/06/0961-0968
We propose to substitute Newton’s constant $G_{N}$ for another constant $G_{2}$, as if the gravitational force would fall off with the $1/r$ law, instead of the $1/r^{2}$; so we describe a system of natural units with $G_{2} , c$ and $\hbar$. ... |
Consider the following series:
$$\sigma (\text{x$\_$})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the series tends to $0$ with a very low slope as $n$ approaches $+\infty$, this is the case in the article that I'm studying
... |
Consider the log likelihood of a mixture of Gaussians:
$$l(S_n; \theta) = \sum^n_{t=1}\log f(x^{(t)}|\theta) = \sum^n_{t=1}\log\left\{\sum^k_{i=1}p_i f(x^{(t)}|\mu^{(i)}, \sigma^2_i)\right\}$$
I was wondering why it was computationally hard to maximize that equation directly? I was looking for either a clear solid intu... |
My question is about
6.C.4. of Mas-Colell et.al.'s Microeconomic Theory book.
We have N risky assets with returns $z_n, n = (1,...,N)$ per dollar invested which are distributed over $F(z_1,...,z_n).$ All returns are non-negative with probability one. For an individual with a continuous, increasing, and concave Bernoull... |
1) Let's imagine we have a string of length $L$ that is fixed at both ends. When we refer to harmonics we are talking about standing waves. Since we are talking about standing waves, we are limited on the allowed wavelengths our standing waves can have. (See picture below)
As you can see, the first harmonic has wavelen... |
I use the poweRlaw package in R to fit a power law to my data. I am trying to figure out what is the value of the Pareto exponent.
Assume the probability mass function is defined by:
$$ p(x) = \frac{\alpha-1}{x_{min}} \left(\frac{x}{x_{min}} \right)^{-\alpha} $$
and the complementary cumulative density function is defi... |
and I need to determine inductance of the filtering chokes. I have deduced following formula $$L=\frac{V_{dc}\cdot(1-d)}{f_s\cdot\Delta i_L}$$ (based on \$v=L\frac{di}{dt}\$), where \$V_{dc}\$ is dc link voltage, \$f_s\$ is switching frequency (=12 kHz), \$\Delta i_L\$ is desired current ripple and \$d\$ is duty ratio ... |
Let’s say I have a content type article with a field “taxonomy”.
The vocabulary is “fruits”.
The terms are “apple”, “orange”, “bananas”
The article belongs to “orange”.
I can easily print in my twig template the term of the article :
{{ content.field_taxo_fruit }}
Result is “orange”.
But I don’t find an easy way to pri... |
Oh so I've been wondering recently, how exactly does analytic continuation work? I've heard about it all the time as how you extend domains of functions, but like, what's the mechanism by which you do so?
@Daminark You look at the full subdomain $\Omega$ of $\Bbb C$ where $f$ can be analytically continued by paths from... |
Sampling at a higher frequency will give you more effective number of bits (ENOB), up to the limits of the spurious free dynamic range of the Analog to Digital Converter (ADC) you are using (as well as other factors such as the analog input bandwidth of the ADC). However there are some important aspects to understand w... |
Measurements of the QED structure of the photon 38 Downloads Citations Abstract.
The structure of both quasi-real and highly virtual photons is investigated using the reaction \({\rm e^+e^-}\rightarrow{\rm e^+e^-}\mu^+\mu^-\), proceeding via the exchange of two photons. The results are based on the complete OPAL datase... |
DFT Graphical Interpretation: Centroids of Weighted Roots of Unity
Introduction
This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by framing it in a graphical interpretation. The bin calculation formula is shown to be the equivalent of finding the center of mass, or cen... |
Difference between revisions of "Stiffened equation of state"
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It is useful to notice that, given this equation of state, the [[adiabatic]] law is modified from its ideal form:
It is useful to notice that, given this equation ... |
Borel set of ambiguous class $\alpha$
A Borel subset of a metric space, or more generallly, a perfectly-normal topological space, that is at the same time a set of additive class $\alpha$ and of multiplicative class $\alpha$, i.e. belongs to the classes $F_\alpha$ and $G_\alpha$ at the same time. The Borel sets of ambi... |
Difference between revisions of "Convergence of measures"
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In the real-valued case the above definition simplifies as
In the real-valued case the above definition simplifies as
\[
\[
−
\abs{\mu}(B) = \sup_{A\in \mathcal{B}, A\subset B} \left(\abs{\mu (A)} + \abs{\mu (
+
\abs{\mu}(B) = \sup_{A\in \m... |
Difference between revisions of "Talk:Gamma-function"
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\Gamma(z)\Gamma(1-z) = \frac{\pi}{\sin \pi z}.
\Gamma(z)\Gamma(1-z) = \frac{\pi}{\sin \pi z}.
$$
$$
−
In particular, $\
+
In particular, $\(1/2)=\sqrt{\pi}$;
$$
$$
\Gamma(n+1/2) = \frac{1.3\ldots(2n-1)}{2^n}\sqrt{\pi}
\Gamma(n+1... |
A New Contender in the Digital Differentiator Race
This blog proposes a novel differentiator worth your consideration. Although simple, the differentiator provides a fairly wide 'frequency range of linear operation' and can be implemented, if need be, without performing numerical multiplications.
Background
In referenc... |
AliFMDMultCuts () AliFMDMultCuts (EMethod method, Double_t fmd1i, Double_t fmd2i=-1, Double_t fmd2o=-1, Double_t fmd3i=-1, Double_t fmd3o=-1) AliFMDMultCuts (const AliFMDMultCuts &o) AliFMDMultCuts & operator= (const AliFMDMultCuts &o) void Reset () Double_t GetMultCut (UShort_t d, Char_t r, Double_t eta, Bool_t errors... |
Let us now take a closer look at the
hex-fractal we sliced last week. Chopping a level 0, 1, 2, and 3 Menger sponge through our slanted plane gives the following:
This suggests an iterative recipe to generate the hex-fractal. Any time we see a hexagon, chop it into six smaller hexagons and six triangles as illustrated ... |
If we write Schrodinger equation in imaginary time $\tau = it$, then one can easily show that the energy $E(\tau) = \langle \psi(\tau)| \hat{H} |\psi(\tau)\rangle$ is a diminishing quantity, i.e. $$\partial_{\tau} E(\tau) \le 0$$
Imagine that we have a state that depends on variational parameters denoted collectively b... |
The way you pose your question, being so vague, makes it hard to pinpoint exactly things you should avoid, pitfalls you must be aware of, etc, etc, because those things are often related to the context in which you substitute.
It is common to just substitute a big expression that is repeated plenty of times with a simp... |
At zero flow the pressure at the shower head is simply the hydrostatic pressure given by Pascal's law:
$$p=p_0+\rho gy$$Where $p_0$ is the atmospheric pressure, $y$ the height difference between tank meniscus and shower head, $\rho$ the density of water ($g\approx 10$$\:\mathrm{m/s^2}$).
The water pressure coming from ... |
Finite Lexicographic Order on Well-Ordered Sets is Well-Ordering Theorem $\left({x_1, x_2, \ldots, x_n}\right) \prec \left({y_1, y_2, \ldots, y_n}\right)$ if and only if: $\exists k: 1 \le k \le n$ such that $\forall 1 \le j < k: x_j = y_j$ but $x_k \prec y_k$ in $S$. Then for a given $n \in \N_{>0}$, $\preccurlyeq$ is... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Can anyone please help me to prove $ X=M$ using the following set of the equation(first-order logic)in Isabelle/HOL?
$ N>=M$
$ \forall n. 0\leq n<N \rightarrow n<M$
$ X=N$
where $ N, M, X$ are integers constant. $ n$ integer variable.
Can anyone please help me to prove $ X=M$ using the following set of the equation(fir... |
Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length. It should be noted that the arc length is longer than the straigh... |
I'll assume that you want the surface gravity to be the same as earth's.
This means that the average density must be 1/3 that of earth, since for a body, if gs is the surface gravity, $\rho$ the density, and r the radius $$gs=\frac{GM}{r^2} = \frac {GMr}{r^3} = G \rho r$$ and increasing r requires a corresponding decre... |
Traditionally, these filters were implemented as analog filters, and they are different from the usual discrete-time first-order FIR pre-emphasis filter used in speech processing.
The transfer function of such an analog pre-emphasis filter is
$$H(s)=g\frac{1+s\tau_1}{1+s\tau_2},\qquad\tau_1\gt\tau_2,\tag{1}$$
where $g$... |
№ 9
All Issues Volume 57, № 3, 2005
Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 291–304
We obtain exact estimates of the approximation in the metrics $C$ and $L_2$ of functions, that are defined on a sphere, by means of linear methods of summation of the Fourier series in spherical harmonics in the case where differential a... |
Multi-Decimation Stage Filtering for Sigma Delta ADCs: Design and Optimization
During my research on digital FIR decimation filters I have been developing various Matlab scripts and functions. In which I have decided later on to consolidate it in a form of a toolbox. I have developed this toolbox to assist and automate... |
AI News, Speech Processing for Machine Learning: Filter banks, Mel-Frequency Cepstral Coefficients (MFCCs) and What's In-Between On Thursday, October 4, 2018 By Read More Speech Processing for Machine Learning: Filter banks, Mel-Frequency Cepstral Coefficients (MFCCs) and What's In-Between
Speech processing plays an im... |
Faddeeva Package From AbInitio
Revision as of 22:54, 29 October 2012 (edit)
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Line 23: Line 23: :<math>\mathrm{erfcx}(x) = e^{x^2} \mathrm{erfc}(x) = w(ix)</math> (scaled compleme... |
Two-body problem
Set
definiendum $\langle \mathbb R^{2\times 3}, H\rangle \in \mathrm{it} $ … Classical Hamiltonian system postulate $ H({\bf r}_1,{\bf r}_2,{\bf p}_1,{\bf p}_2) = \frac{1}{m_1}\frac{1}{2}{\bf p}_1^2 + \frac{1}{m_2}\frac{1}{2}{\bf p}_2^2 + V(|{\bf r}_1-{\bf r}_2|) $ Discussion
Equations of motion in sui... |
1. Ahmed, Babu, Chitra, David and Eesha each choose a large different number. Ahmed says, “ My number is not the largest and not the smallest”. Babu says, “My number is not the largest and not the smallest”. Chitra says, “My number is the largest”. David says, “ My number is the smallest”. Eesha says, “ My number is no... |
I have a finite harmonic potential where I trap an electron. The confinement length changes in size. Now, I'm interested in the ground state energy, so I have this 1D Poisson solver which gives me the ground state energy $E_0$ and wave function.
If we now add a confinement dimension, can we estimate how $E_0$ is going ... |
Difference between revisions of "Talk:Gamma-function"
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$$
$$
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7) The function $ $ (Fig. c) is an entire function of order one and of maximal type; asymptotically, as $ $,
+
7) The function $$ (Fig. c) is an entire function of order one and of maximal type; asymptotically, as $$,
... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
In this question, all rings and algebras are commutative with identity.
Let $R$ be a ring, and let $A$ be an $R$-algebra with an $R$-subalgebra $B$. Suppose that we have an $R$-algebra homomorphism $\phi: B\to R$; then we can form the tensor product $A\otimes_B R$. My question is:
If the structure maps $R\to B$ and $R\... |
I tried:
$\lim_{x \rightarrow 0^+}(e^{\frac{1}{x}}x^2) = x^2 \cdot \frac{1}{e^{-\frac{1}{x}}} = \frac{x^2}{e^{-\frac{1}{x}}} = ???$
I thought maybe I could use $y = - \frac{1}{x}$, but I don't know what to do next.
I know the limit just by looking a the function: $\lim_{x \rightarrow 0^+} e^{\frac{1}{x}} = \infty $ and... |
STATEMENT OF THE PROBLEM
If $q^k n^2$ is an odd perfect number with Euler prime $q$, is $\sigma(q^k)/n + \sigma(n)/q^k$ bounded from above?
MOTIVATION
Let $\sigma=\sigma_{1}$ denote the classical sum-of-divisors function, and denote the abundancy index of $x \in \mathbb{N}$ by $I(x)=\sigma(x)/x$.
It is known that the i... |
The Black-Scholes option pricing model provides a closed-form pricing formula $BS(\sigma)$ for a European-exercise option with price $P$. There is no closed-form inverse for it, but because it has a closed-form vega (volatility derivative) $\nu(\sigma)$, and the derivative is nonnegative, we can use the Newton-Raphson ... |
Rotational Newton's Second Law
As we saw for linear motion, we can only go so far with energy conservation. If we want to analyze aspects of motion such as elapsed time and direction of motion, we need more than mechanical energy conservation to work with. In the linear case, we found that this meant that we had to use... |
1) Whenever one has a topological vector space (TVS) $V$ over some field $\mathbb{F}$, one can construct a dual vector space $V^*$ consisting of continuous linear functionals $f:V\to\mathbb{F}$.
2) Under relative mild conditions on the topology of $V$, it is possible to turn the dual vector space $V^*$ into a TVS. One ... |
Shouldn't the electric flux through a circular disc due to a point charge kept at some finite distance from it be zero as all field lines which enter it exit it also and hence the net would be zero?
Your disk isn't a closed surface, so Gauss's law doesn't apply here. The idea of field lines entering and exiting the sur... |
Difference between revisions of "Linear representation theory of symmetric group:S5"
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==Summary==
==Summary==
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{| class="sortable" border="1"
{| class="sortable" border="1"
! Item !! Value
! Item !! Value
|-
|-
−
| [[Degrees of ir... |
\frac {1 - \tau^{n}}{1 + \tau^{c}},\end{array}$ which, in turn, implies that, for example, 30% labor income tax rate is as distorting as 43% consumption tax rate and so forth.1 − 30 % 1 + 0 % ≈ 1 − 0 % 1 + 43 %$\begin{array}{}\displaystyle \frac {1 - 30\text\%}{1 + 0\text\%} \approx \frac {1 - 0\text\%}{1 + 43\text\%}\... |
This question make more sense when we don't limit outselves to real numbers.
For any $n = d + 1 > 1$ and $u = (u_0, u_1, \ldots, u_d) \in \mathbb{C}^n$, consider following product
$$\Lambda(u_0,\ldots,u_d) = \prod_{(\epsilon_1,\ldots,\epsilon_d) \in \{ \pm 1 \}^d}\left( \sqrt{u_0} + \sum_{k=1}^d \epsilon_k \sqrt{u_k} \... |
I want to do a cross product involving a vector of Pauli matrices $\vec \sigma = \left( {{\sigma _1},{\sigma _2},{\sigma _3}} \right)$; for example, $\vec \sigma \times \left( {1,2,3} \right)$.
s:= Table[PauliMatrix[i], {i, 1, 3}];Cross[s,{1,2,3}]
The code above will not work.
The only way I can think of is to use the ... |
> I'm really just getting ready to explain how they show up in logic: first in good old classical "subset logic", and then in the weird new "partition logic".
I am pretty excited to read what's next!
I wanted to a few puzzles I ran into a while ago related to these topics.
First, a some definitions...
**Definition.** A... |
name: Leon Derczynski
status: Assistant Professor of Computer Science
ErhvervsForsker: 2019-2022, InnovationsFonden PhD 1,07M DKK. Deep Learning Generative Models for Content Structuring.
Role: PI for ITU.
NLPL: 2017-2020, NordForsk. www.nlpl.eu. Nordic Language Processing Laboratory. A cross-Nordic collaboration of hi... |
Quasilinear nonhomogeneous Schrödinger equation with critical exponential growth in R^n
DOI: http://dx.doi.org/10.12775/TMNA.2015.029
Abstract
In this paper, using variational methods, we establish the existence and multiplicity of weak solutions for nonhomogeneous quasilinear elliptic equations of the form -\Delta_n u... |
Getting Started¶
MathJax allows you to include mathematics in your web pages, either using LaTeX, MathML, or AsciiMath notation, and the mathematics will be processed using javascript to produce HTML, SVG or MathML equations for viewing in any modern browser.
There are two ways to access MathJax: the easiest way is to ... |
I've been trying to wrap my head around the current I measured through the collector branch vs. the expected calculation for collector current and believe I have a knowledge gap in what to do.
The setup of the circuit is shown above with the LED being a blue LED with a forward voltage given as 0.3 V which seems implaus... |
Let $C([0,\infty), R)$ be the canonical space of continuous functions. Assume $(\Omega, \mathcal{F}, \{\mathcal{F}_{t}\}_{t\geq 0})$ is a measurable space with a filtration. Let $P, Q$ be two probability measures on $(\Omega, \mathcal{F})$. Assume $X_{t}$ and $Y_{t}$ are two stochastic processes adapted to $\{\mathcal{... |
What is a Prime Number?
An integer, say $ p $ , [ $ \ne {0} $ & $ \ne { \pm{1}} $ ] is said to be a prime integer iff its only factors (or divisors) are $ \pm{1} $ & $ \pm{p} $ .
As?
Few easy examples are:
$ \pm{2}, \pm{3}, \pm{5}, \pm{7}, \pm{11}, \pm{13} $ …….etc. This list goes up to infinity & mathematicians are tr... |
There are proofs that treat the cases of real and non-real $\chi$ on an equal footing. One proof is in Serre's Course in Arithmetic, which the answers by Pete and David are basically about. That method is using the (hidden) fact that the zeta-function of the $m$-th cyclotomic field has a simple pole at $s = 1$, just li... |
Current browse context:
astro-ph.CO
Change to browse by: Bookmark(what is this?) Astrophysics > Cosmology and Nongalactic Astrophysics Title: Distinguishing between $Λ$CDM and modified gravity with future observations of cosmic growth rate
(Submitted on 30 Dec 2015)
Abstract: A probability of distinguishing between $\L... |
Mathematics CUI: LaTeX Resources
This page contains LaTeX template of CIIT Mathematics, MSc Project and MS Thesis templates.
Templates
Download a zip file given below and extract it by right clicking on the file.
MSc Project Template: cui-math-project.zip MS Thesis Template: cui-ms-thesis.zip Installing latex
Three sep... |
As @DeanB said, the assignment shows exactly how to do what you are asking. It seems you are just stuck on some sort of mental block, it happens to everyone!
For the low-pass circuit:
You are given the following schematic:
And an equation that describes its transfer function, then they even solved for the cutoff freque... |
The key for producing a nice tone, is a mix of two facts: first, offering the air stream a somehow geometrical regular hole, where a stationary wave can be born with a certain frequency and other possible frequencies are filtered out, and second, a low enough stream velocity, so that no turbulences can happen and the f... |
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We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from... |
Let $(T_t)$ be a strongly continuous semigroup of positive operators on $C(K)$, where $K$ is a compact space. Assume also that $T_t1 =1 $ for every $t\geq 0$. (This is also called a Feller Semigroup.)
Since $K$ is compact we know that there exists a probability measure $\mu$ on $K$ satisfying $\mu T^*_t = \mu $ for eve... |
The explicit formula for cup product on group cohomology is as simple as can be. For simplicity let's consider integer coefficients $H^*(G;\mathbb{Z})$, although this works for any coefficients as long as they're untwisted.
Let's define group cohomology using inhomogeneous cochains; thus we take the abelian groups $C^n... |
Difference between revisions of "User:Nikita2"
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I am Nikita Evseev
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I am Nikita Evseev Novosibirsk, Russia.
My research interests are in [[Mathematical_analysis | Analysis]] and [[Sobolev space|Sobolev spaces]].
My research interests a... |
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Change to browse by: References & Citations Bookmark(what is this?) Condensed Matter > Mesoscale and Nanoscale Physics Title: The interplay of electron-photon and cavity-environment coupling on the electron transport through a quantum dot system
(Submitted on 15 Aug 2019)
Abstr... |
I'd like to use as definition of "exact (forward) linear prediction" that given a finite number of the first consecutive samples of a signal, all of the following samples can be predicted with zero residual error by a linear predictor with the same finite number of coefficients.
Your thinking is correct. Consider the
l... |
Liouville equation
The Liouville equation
$\def\phi{\varphi}\partial_t\partial_\tau\phi(t,\tau) = e^{\phi(t,\tau)}$ or$$\phi_{t\tau} = e^\phi\tag{a1}$$is a non-linear partial differentialequation (cf.Differential equation, partial)that can be linearized and subsequently solved. Namely, it can betransformed into the lin... |
The $GF$ in $GF(p^n)$ is
not a function — it just stands for "Galois field (of $p^n$ elements)".
As for what a Galois field
is, it's a finite set of things (which we might represent e.g. with the numbers from $0$ to $p^n-1$), with some mathematical operations (specifically, addition and multiplication, and their invers... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
Since the set over which you are minimizing is compact, there exists a minimizer. Since the set is convex and the objective function is convex, the set of minimizers is convex.
The KKT conditions now tell you what the form of any minimizer must be: Either $x_i = 0$ or the numbers $a_i/b_i \exp(-x_i/b_i)$ must all equal... |
Support
This page provides an explanation of the main topics related to wave forecast that at a first sight may appear tough to the majority of users.
What does UTC mean?
UTC stands for Coordinated Universal Time. For weather and ocean forecast purposes, we can say that it is equivalent to the Greenwich Mean Time (GMT)... |
Product . category theory Collection
context $F:\mathrm{Ob}_{{\bf C}^{\bf 2}}$ range $a,b:\mathrm{Ob}_{\bf 2},\ a\neq b$ definition $\langle Fa\times Fb, \pi\rangle := \mathrm{lim}\,F$ Discussion Elaboration
${\bf C}^{\bf 2}$ is the functor category with objects being functors in ${\bf 2}\longrightarrow{\bf C}$ and the... |
(50g) Simpson's rule for f(x,y)
11-17-2018, 09:27 PM (This post was last modified: 11-18-2018 11:14 PM by peacecalc.)
Post: #1
(50g) Simpson's rule for f(x,y)
Hello friends,
like Eddie Shore showed us HERE an algorithm for integration a function with two variables with the simpson rule and a matrix. He implemented this... |
Let us now take a closer look at the
hex-fractal we sliced last week. Chopping a level 0, 1, 2, and 3 Menger sponge through our slanted plane gives the following:
This suggests an iterative recipe to generate the hex-fractal. Any time we see a hexagon, chop it into six smaller hexagons and six triangles as illustrated ... |
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Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Just to expand on the comment of @Myself above...
Adjoining algebraics as matrix maths
Sometimes in mathematics or computation you can get away with adjoining an algebraic number $\alpha$ to some simpler ring $R$ of numbers like the integers or rationals $\mathbb Q$, and these characterize all of your solutions. If thi... |
In last week’s discussion of proofs by contradiction and nonconstructive proofs, we showed:
Theorem: There exist irrational numbers \(x\) and \(y\) with the property that \(x^y\) is rational.
However, our proof was
nonconstructive: it did not pinpoint explicit values for \(x\) and \(y\) that satisfy the condition, inst... |
The nearshore is defined as that part of the ocean where the depth is so small that wind-generated waves are influenced by the bottom. It is usual to identify the depth where the waves start to “feel” the presence of the bottom as the depth of approximately half the wave length. In deep waters the profile of swell wave... |
I've got the follow question which drives me almost crazy as the answer seems to be simple. Given a morphism $p:V\to S$ of schemes of finite type over some base field. Assume that $p$ has all the properties of a vector space over $S$ that is, there should be morphisms $+:V\times_S V \to V, \cdot: A^1_S \times_S V \to V... |
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