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Emergence of large densities and simultaneous blow-up in a two-species chemotaxis system with competitive kinetics
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
$ \begin{eqnarray*} \left\{\begin{array}{lll} u_t = \Delta u-\chi_1\nabla\cdot(u\nabla w)+\mu_1u(1-u-a_1v),\ \ \... |
Semidefinite programs (SDPs) -- some of the most useful and versatileoptimization problems of the last few decades -- are often pathological: theoptimal values of the primal and dual problems may differ and may not beattained. Such SDPs are both theoretically interesting and often impossible to solve;yet, the pathologi... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
April 2000 , Volume 6 , Issue 2
Select all articles
Export/Reference:
Abstract:
We improve Mather's proof on the existence of the connecting orbit around rotation number zero (Proposition 8.1 in [7]) in this paper. Our new proof not... |
Definition:Limit of Sequence/Real Numbers Definition
Let $\sequence {x_n}$ be a sequence in $\R$.
Let $\sequence {x_n}$ converge to a value $l \in \R$.
Then $l$ is a limit of $\sequence {x_n}$ as $n$ tends to infinity. This is usually written: $\displaystyle l = \lim_{n \mathop \to \infty} x_n$ Also see Also known as
A... |
Question:
Let {eq}f(x)= 0, if, x < 0, x, if, 0 \leq x \leq 10, 20-x ,if, 10 < x \leq 20, 0, if, x > 20; {/eq}
and {eq}g(x)=\int_0^xf(t)dt. {/eq}
Find an expression for {eq}g(x) when 10 < x < 20 . {/eq}
Answer Options:
1. {eq}g(x)=20x-\frac {1}{2}x^2-50 {/eq}
2. {eq}g(x)=20x-\frac {1}{2}x^2-100 {/eq}
3. {eq}g(x)=20x-\fr... |
Definition:Relative Complement Contents Definition
Then the set difference $S \setminus T$ can be written $\relcomp S T$, and is called the
relative complement of $T$ in $S$, or the complement of $T$ relative to $S$.
Thus:
$\relcomp S T = \set {x \in S : x \notin T}$ Also known as
Some authors call this
the complement ... |
ISSN:
1930-8337
eISSN:
1930-8345
All Issues
Inverse Problems & Imaging
February 2012 , Volume 6 , Issue 1
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Abstract:
We derive asymptotic expansions for the displacement at the boundary of a smooth, elastic body in the presence of small inhomogeneities. Both the body and the inclusi... |
If there is a discontinuity in the material such as a hole or a notch, the stress must flow around the discontinuity, and the flow lines will pack together in the vicinity of Strength of materials stress and strain discontinuity.
The concentration of stress will dissipate as we move away from the stress riser. The prop... |
Difference between revisions of "Lower attic"
From Cantor's Attic
Line 7: Line 7:
* [[Gamma | $\Gamma$]]
* [[Gamma | $\Gamma$]]
* [[Church-Kleene omega_1 | $\omega_1^{ck}$]]
* [[Church-Kleene omega_1 | $\omega_1^{ck}$]]
−
* [epsilon0#epsilon_alpha | the $\epsilon_\alpha$ hierarchy]]
+
* [epsilon0#epsilon_alpha | the $\... |
Determine the resultant couple moment of the two couples that act on the pipe assembly. The distance from A to B is d = 400 mm. Express the result as a Cartesian vector.
Solution:
Show me the final answer↓
To solve this problem, we will first express a position vector from A to B. Note that d = 400 mm as stated in the ... |
Is there a $n-th$an $n^{\text{th}}$ root function in Mathematica?
Is there a way to find $\sqrt[n]{x}$ with
Mathematica
Mathematica beside of
x^(1/n)as this is something different, because this is not always the same$$(-1)^{\frac{2}{4}}=i \neq 1= \sqrt[4]{(-1)^2}$$In the help I only found
Sqrt[x] which is the squareroo... |
Proof by Cases
Jump to navigation Jump to search
Proof by Cases is also known as the
Contents Sequent If we can conclude $\phi \lor \psi$, and: then we may infer $\chi$. $p \lor q, \left({p \vdash r}\right), \left({q \vdash r}\right) \vdash r$ Variants
The following forms can be used as variants of this theorem:
$\left... |
Tsukuba Journal of Mathematics Tsukuba J. Math. Volume 30, Number 1 (2006), 171-180. Remarks on the bordism intersection map Abstract
In this paper we give a characterization of the kernel of the bordism intersection map and we present some related results as the following. The set of bordism classes of $C^{\infty}$ ma... |
The Annals of Statistics Ann. Statist. Volume 4, Number 2 (1976), 384-395. Extension of the Gauss-Markov Theorem to Include the Estimation of Random Effects Abstract
The general mixed linear model can be written $y = X\alpha + Zb$, where $\alpha$ is a vector of fixed effects and $b$ is a vector of random variables. Ass... |
This vignette introduces
threshold graphs, a class of graphs with a unique centrality ranking and relevant functions from the
netrankr package to work with this class of graphs.
A threshold graph is a graph, where all nodes are pairwise comparable by neighborhood inclusion. Formally, \[ \forall u,v \in V: N(u) \subsete... |
We consider Real bundle gerbes on manifolds equipped with an involution andprove that they are classified by their Real Dixmier-Douady class inGrothendieck's equivariant sheaf cohomology. We show that the Grothendieckgroup of Real bundle gerbe modules is isomorphic to twisted KR-theory for atorsion Real Dixmier-Douady ... |
Pricing a call option with payoff function $C=\max\{S_T - S_{T/2}, 0\}$, where $S_T$ is geometric brownian motion. I appreciate any help! Please close this question if this is a duplicated question. Thanks all!
My approach is to take out $S_{T/2}$:
$$C = S_{T/2} \max\left\{\frac{S_T}{S_{T/2}} - 1, 0\right\}$$
Then we c... |
Contents MA 453 Fall 2008 Professor Walther News
Here are some basic pointers:
In order to do any editing, you must be logged in with your Purdue career account. If you look under MediaWiki FAQ, you get lots of instructions on how to work with Rhea. Some important things are under item 4 in that manual. If you want to ... |
Heat Transfer in Fully-Developed Internal Turbulent Flow From Thermal-FluidsPedia
Line 254: Line 254:
|{{EquationRef|(28)}}
|{{EquationRef|(28)}}
|}
|}
-
Since the buffer region is also very thin,
+
Since the buffer region is also very thin, <math>1-y/{{r}_{0}}</math> in eq. (5.321) is effectively equal to 1. Defining ... |
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... |
This is because cosmic strings are not gravitating matter in the usual sense but space-time defects. You will in fact obtain a flat space-time for every $\sigma = k/4, k \in \mathbb{Z}$ but in the coordinates you use this will be every time Minkowski but in a different set of coordinates.
You can see this by the canoni... |
Uplifting cardinals Uplifting cardinals were introduced by Hamkins and Johnstone in [1], from which some of this text is adapted.
An inaccessible cardinal $\kappa$ is
uplifting if and only if for every ordinal $\theta$ it is $\theta$-uplifting, meaning that there is an inaccessible $\gamma>\theta$ such that $V_\kappa\p... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Symbols:Greek/Rho Rho
The $17$th letter of the Greek alphabet.
Minuscules: $\rho$ and $\varrho$ Majuscule: $\Rho$
The $\LaTeX$ code for \(\rho\) is
\rho .
The $\LaTeX$ code for \(\varrho\) is
\varrho .
The $\LaTeX$ code for \(\Rho\) is
\Rho .
$\rho$ $\rho = \dfrac m V$
where:
$\rho_A$ $\rho_A = \dfrac m A$
where:
The $... |
Analysis of Rugates
\(n(x)=n_a+0.5 n_p A(x) \sin\left(\displaystyle\frac{4\pi x}{\lambda_0}\right)\)
\(A(x)=10 t^3-15 t^4+6 t^5 \)
\(t=\displaystyle\frac{2x}{TOT},\;\;\mbox{ if}\;\; x<\frac{TOT}{2} \)
\(t=\displaystyle\frac{2(TOT-x)}{TOT},\;\;\mbox{ if}\;\; x>\frac{TOT}{2}\)
Here
is total optical thickness. TOT
Design ... |
ISSN:
1930-5346
eISSN:
1930-5338
All Issues
Advances in Mathematics of Communications
May 2014 , Volume 8 , Issue 2
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Export/Reference:
Abstract:
A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and ... |
I was reading about energy usage in batteries and don't quite understand why it is measured in different units than home electrical usage. An ampere-hour does not include a measure of volts. But my understanding though is that a battery has a constant voltage (1.5V, 9V, ...) just as much as home electrical usage (120V,... |
I have real-valued functions $\{f_n\},f$ on a subset $X\subset \mathbb R^n$ that are equicontinuous and I have Borel measures $\{\mu_n\},\mu$. I have that
For each fixed $m$, $\int f_m d\mu_n\to\int f_md\mu$ and $\int f d\mu_n\to\int fd\mu$. $f_n\to f$ pointwise (so also uniformly since equicontinuous) $|f_n|\leq g\for... |
Complete Differentiable Semiclassical Spectral Asymptotics Chapter First Online: 14 September 2019 Abstract
For an operator
\(A:=A_h= A^0(hD) + V(x, hD)\) with a “potential” V decaying as \(|x|\rightarrow \infty \) we establish under certain assumptions the complete and differentiable with respect to \(\tau \) asymptot... |
I have a table called
AssignmentMarks that stores Student’s assignment marks for different subjects. This table has a column called
Marks varchar(10) which stores the marks. The marks can be like
1,
2, and also it can be
+,
- or
-+ which represents each sign a specific marks.
Note:
+ is
1 mark,
- is
-1 and
-+ is
0.5
Wh... |
The Friedmann equation expressed in natural units ($\hbar=c=1$) is given by $$\left(\frac{\dot a}{a}\right)^2 = \frac{l_P^2}{3}\rho(t) - \frac{k}{R^2}$$ where $t$ is the proper time measured by a comoving observer, $a(t)$ is the dimensionless scale factor, $l_P=\sqrt{8\pi G\hbar/c^3}$ is the reduced proper Planck lengt... |
According to Coulomb law, the electromagnetic force between point charges separated at zero distance is infinite. Does QED explains the same result, or there is any difference?
The use of 'point particles' to describe the results of classical electromagnetism is questionable if it is assumed the particles really are po... |
Learning Objectives
Describe the physics of rolling motion without slipping Explain how linear variables are related to angular variables for the case of rolling motion without slipping Find the linear and angular accelerations in rolling motion with and without slipping Calculate the static friction force associated w... |
Definition:Reflexive Closure Contents Definition The reflexive closure of $\mathcal R$ is denoted $\mathcal R^=$, and is defined as: $\mathcal R^= := \mathcal R \cup \set {\tuple {x, x}: x \in S}$
That is:
$\mathcal R^= := \mathcal R \cup \Delta_S$
where $\Delta_S$ is the diagonal relation on $S$.
The reflexive closure... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
Circle
The functions \(\sin (\theta)\) and \(\cos (\theta)\) are defined such that, if you drew a circle of radius \(r\) with a triangle inset like the one below, the lengths of the sides will have the listed values:
As the picture suggests, \(\sin \theta\) and \(\cos \theta\) have values that repeat when you increase ... |
I don’t think we’re clear on what simulation is NOT. RANDOMNESS IS NOT NECESSARY, for the simple reason randomness is merely a state of knowledge. Hence this classic post from 12 June 2017.
“Let me get this straight. You said
what makes your car go?”
“You heard me. Gremlins.”
“Grelims make your car go.”
“Look, it’s obv... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
@Rubio The options are available to me and I've known about them the whole time but I have to admit that it feels a bit rude if I act like an attribution vigilante that goes around flagging everything and leaving comments. I don't know how the process behind the scenes works but what I have done up to this point is lea... |
Consider the reaction scheme:
$$\ce{S + E ->[$k_1$] C1} \qquad \ce{C1 ->[$k_2$] E + P} \qquad \ce{S + C1 <=>[$k_3$][$k_4$]C2}$$
where $\ce{S}$ is the substrate, $\ce{E}$ is the enzyme, $\ce{P}$ is the product, $\ce{C1}$ and $\ce{C2}$ are enzyme substrate complexes. Let $[\ce{S}] = s$, $[\ce{E}] = e$, $[\ce{C1}] = c_1$,... |
Definition:Zero (Number) Contents Definition
Let $\left({S, \circ, \preceq}\right)$ be a naturally ordered semigroup.
That is:
$\forall n \in S: 0 \preceq n$ Natural Numbers Integers Rational Numbers Real Numbers
Let $\C$ denote the set of complex numbers.
The
zero of $\C$ is the complex number: $0 + 0 i$ Also known as... |
During summer 2019, I was invited in the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge. I worked with Noemie Debroux and Angelica I. Aviles-Rivero on MRI reconstruction.
The Project
Due to technical difficulties, MRI data are incomplete, thus to recover a full image of the pat... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Hello guys! I was wondering if you knew some books/articles that have a good introduction to convexity in the context of variational calculus (functional analysis). I was reading Young's "calculus of variations and optimal control theory" but I'm not that far into the book and I don't know if skipping chapters is a goo... |
I'm studying the holographic entanglement entropy (HEE) in this paper (Ryu-Takayanagi, 2006). In section 6.3 they compute the HEE for a segment in a 2D CFT. To do so, they obtain the corresponding geodesic in the bulk (in the Poincaré patch) and compute its length.
I understand all that process, but I'm having some tro... |
Definition:Factorial Contents Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.
The
factorial of $n$ is defined inductively as: $n! = \begin{cases} 1 & : n = 0 \\ n \left({n - 1}\right)! & : n > 0 \end{cases}$
The
factorial of $n$ is defined as:
\(\displaystyle n!\) \(=\) \(\displaystyle \prod_{k \mathop = 1}^n ... |
Looking at the MO reputation league I found that it shows up 1767 screens, all screns but the last one show up 9x4=36 users and the last screen shows 27 users. So totally MO has 1766x36+27=63 603 users.
On the other hand, in the profile of the MO leader Hamkins we can find that he is 0,02% overall. But if MO indeed has... |
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... |
Communication, Networking, Signal and Image Processing (CS)
Question 5: Image Processing
August 2016 (Published in Jul 2019)
Problem 1 Calcualte an expression for $ \lambda_n^c $, the X-ray energy corrected for the dark current
$ \lambda_n^c=\lambda_n^b-\lambda_n^d $
Calculate an expression for $ G_n $, the X-ray atten... |
Given a modulus $n\in\mathbb{N}$ and another natural number $0<x<n$, what's an efficient algorithm to enumerate all pairs of natural numbers $(a,b)\in\mathbb{N}^2$ such that both $a$ and $b$ are less than $n$ and $$ab\equiv x \mod n\text?$$
Let's solve the problem for a specific $a$. Observe that $ab \equiv x \pmod{n}$... |
You have already got "practical" answers, so I intend to answer form another point of view.
There is a quite famous theorem due to Stone and von Neumann, later improved by Mackay, and finally by Dixmier and Nelson, roughly speaking establishing the following result within the most elementary version. (Another version o... |
I'm not quite sure that I understand how the generalized likelihood ratio test works for composite hypotheses; observe the example below:
Let $X_1,...,X_n$ be a random sample from an exponential distribution, $X_i\sim EXP(\theta) \implies E(X_i)=\theta$. Derive the generalized likelihood ratio test of $H_0:\theta=\thet... |
Another application of vol surfaces right here. A poor fit indicdates strongly the likelihood of bad data - particularly when the number of strikes is high as is the case for SPX.
Since you do not need a brilliant vol surface for pricing exotics, you needn't worry about smoothness at all points or arbitrage free consid... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
David E Speyer
Professor of Mathematics at the University of Michigan. My research interests are in combinatorial algebraic geometry, particularly Schubert calculus, matroids and cluster algebras. I also enjoy thinking about number theory and computational mathematics. Disclaimer: I will often ignore messages about old... |
Meaning of the Model Relationships It is often useful to divide all energy into mechanical and internal pieces. Change in total energy of a system is equal to the energy added to the system. Energy added can be separated into heat, Q, and work, W. When changes in energy are restricted to only the internalenergies, cons... |
1) Let us work in units where the speed-of-light $c=1$ is one.
In Ref. 1 is derived the radial geodesic equation for a particle in the equatorial plane
$$\tag{7.47} (\frac{dr}{d\lambda})^2+2V(r)~=~E^2, $$
with potential
$$ \tag{7.48} 2V(r)~:=~(1-\frac{r_s}{r})((\frac{L}{r})^2+\epsilon). $$
Here $\epsilon=0$ for a massl... |
Difference between revisions of "Inaccessible"
m (Linked to Indescribables)
m (→Hyper-inaccessible and more: by)
(7 intermediate revisions by 2 users not shown) Line 3: Line 3:
Inaccessible cardinals are the traditional entry-point to the large cardinal hierarchy, although weaker notions such as the [[worldly]] cardina... |
Mathematica makes it very easy to to plot the contour lines for a function of two real variables using
ContourPlot. It also makes it very easy to plot the streamlines of vector fields using
Stream Plot. However, I need to plot "contour lines" which can not come from either method.
Simply put, a "ridge system" is like a... |
Authors
Mats Granath
Johan Schött
Published in Physical Review B. Condensed Matter and Materials Physics Volume 90 Pages 235129 ISSN 1098-0121 Publication year 2014 Published at
Department of Physics (GU)
Pages 235129 Language en Links
dx.doi.org/10.1103/PhysRevB.90.2351...
Subject categories Condensed Matter Physics
W... |
The process of solving rational inequalities is close to the method of solving polynomial inequality.
In solving the rational inequality ,special attention needs to be given to the denominator.
Points to Remember:
Never multiply both sides by denominator
Always bring all the terms to one side and make another side zero... |
Let $\sum a_n x^n$ be a power series whose radius of convergence is $0<R<\infty$.
What is the radius of convergence, $R'$ of $\sum \frac {n^n}{n!} a_n x^n$?
If I know $\lim_{n\rightarrow\infty} \frac {a_{n+1}}{a_n}$ exists. this would be an easy problem, since (after simplification):
$\frac1{R'}=\lim_{n\rightarrow\inft... |
We considered the pentagonal numbers which begin :
\(1, 5, 12, 22, 35, 51, 70, 92, 117, 145, …\)
That is :
\(\displaystyle P_n = \frac {n(3n-1)}{2}\) for \(n = 1, 2, 3, … \)
Now consider the following sequence :
\(2, 5, 8, 11, 14, 17, 20, 23, 26, 29, …\)
which begins at \(2\) and has a common difference of \(3\) betwee... |
I have to show that:
\begin{equation} P_{t,T}(K)=e^{-r(T-t)} \int_0^{\infty}\left(K-S\right)^+ q_T^S(S)dS \end{equation}
is equivalent to: \begin{equation} P_{t,T}(K)=e^{-r(T-t)}\int_{-\infty}^{K}\left(\int_{-\infty}^y q_T^S(z)dz\right)dy \end{equation}
Breeden and Litzenberger have shown that using Leibniz integration... |
Question:
Pat made the substitution {eq}x - 4 = 6 \sin(t){/eq} in an integral and integrated to obtain {eq}\int f(x) dx = 12 t - 2 \sin(t) \cos(t) + C{/eq}.
Complete Pat's integration by doing the back substitution to find the integral as a function of {eq}x{/eq}
Integration by substitution
When we make an integration ... |
I'm not sure about your calculation but Matlab yields the correct result. In this problem, the common approach is to use
Routh-Hurwitz criterion and search for a row of zeros that yields the possibility for imaginary axis roots. For convert the system to the closed-loop transfer function, hence $$\frac{K}{s^4 + 10s^3 +... |
Spring 2018, Math 171 Week 10 Poisson Process Conditioning
Let \(N(t)\) be a Poisson process with rate \(\lambda\). Fix \(0 \le n\), \(s \le t\).
Compute \(\mathbb{P}(N(s)=m \mid N(t) = n)\) for \(m \le n\). Give the name and parameters of the distribution.
(Answer) Binomial(\(n,\frac{s}{t}\))
Compute \(\mathbb{E}[N(s)... |
I am trying to uderstand the behavior of Dirac spinors in terms of the scalar perturbations of the FRW metric and I was wondering:
Can the perturbation of the spin connection $\delta \omega^{a}_{b \mu}$ be determined by perturbing the first structure equation $de^{a} = -\omega^{a}_{b}\wedge e^{b}$ ? More explicitly, ca... |
Difference between revisions of "User:Nikita2"
m
m
(15 intermediate revisions by the same user not shown) Line 3: Line 3: −
I am Nikita Evseev
+
I am Nikita Evseev Novosibirsk, Russia.
My research interests are in [[Mathematical_analysis | Analysis]] and [[Sobolev space|Sobolev spaces]].
My research interests are in [[... |
Definition:Prime Decomposition Contents Definition
Let $n > 1 \in \Z$.
\(\displaystyle n\) \(=\) \(\displaystyle \prod_{p_i \mathop \divides n} {p_i}^{k_i}\) \(\displaystyle \) \(=\) \(\displaystyle {p_1}^{k_1} {p_2}^{k_2} \cdots {p_r}^{k_r}\)
where:
$p_1 < p_2 < \cdots < p_r$ are distinct primes $k_1, k_2, \ldots, k_r... |
Rule of Simplification/Proof Rule Contents Proof Rule
As a proof rule it is expressed in either of the two forms:
$(1): \quad$ If we can conclude $\phi \land \psi$, then we may infer $\phi$. $(2): \quad$ If we can conclude $\phi \land \psi$, then we may infer $\psi$. It can be written: $\displaystyle {\phi \land \psi \... |
Time scales of epidemic spread and risk perception on adaptive networks
Li-Xin Zhong, Tian Qiu, Fei Ren, Ping-Ping Li, Bi-Hui Chen
arXiv:1011.1621
Incorporating dynamic contact networks and delayed awareness into a contagion model with memory, we study the spreading patterns of infectious diseases in connected populati... |
Symmetry and asymptotic behavior of ground state solutions for schrödinger systems with linear interaction
HLM, CEMS, Academy of Mathematics and Systems Science, the Chinese, Academy of Sciences, Beijing 100190, School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
$\left\{ {... |
I am working with the following TransformedDistribution:
Dist = TransformedDistribution[2 v S1 + 2 v S2 - v c, {S1 \[Distributed] BinomialDistribution[1/2 (c + t), p], S2 \[Distributed] BinomialDistribution[1/2 (c - t), 1 - p]}]
This random variable has neat expressions for mean, variance, skewness, and kurtosis:
(-1 +... |
$$\mathrm{molarity} = \frac{\text{amount of solute}}{\text{volume of solution}} $$ and amount of substance is based on quantity (larger mass means larger amount), so how come it is an intensive property. Shouldn't it be an extensive property?
Concentration is an intensive property. The value of the property does not ch... |
I wouldn't have asked this question if I hadn't seen this image:
From this image it seems like there are reals that are neither rational nor irrational (dark blue), but is it so or is that illustration incorrect?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professi... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
Questions on more advanced topics of number theory, such as quadratic residues, primitive roots, prime numbers, non-linear Diophantine equations, etc. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.
Number theory is concerned with the study of natural numbers. One of... |
I used
Plot[NIntegrate[...]...] to plot a function of 5 different variables. It took really long. Right now I need to integrate this function one more time over the 5th variable and plot the result. Can someone tell me if there is an option to
Nintegrate the plot to speed things up? Maybe there's a way to convert the p... |
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why?
@amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a... |
Chaudhuri, Nirmalendu and Ramaswamy, Mythily (2001)
Existence of positive solutions of some semilinear elliptic equations with singular coefficients. In: Proceedings of the Royal Society of Edinburgh: Mathematics, 131 (6). pp. 1275-1295.
PDF
full.pdf
Restricted to Registered users only
Download (266kB) | Request a copy... |
Automata Theory- Brzozowski Algebraic Method
A LaTeX typeset copy of this tutorial is below for download:
Brzozowski_Algebraic_Method.pdf
(126.4K)
Number of downloads: 1369
I. Introduction
Recall that a language is regular if and only if it is accepted by some finite state automaton. In other words, each regular expres... |
Difference between revisions of "Filter"
(→The club filter, the non-stationary ideal and saturation)
(→The club filter, the non-stationary ideal and saturation)
Line 54: Line 54:
* $2^{\aleph_0}=\aleph_{\omega_1}$ implies $2^{\aleph_1}\leq\aleph_{\omega_2}$.
* $2^{\aleph_0}=\aleph_{\omega_1}$ implies $2^{\aleph_1}\leq\... |
I have come up with the following understanding about Expectation of RV.
Please, correct me if I am wrong.
Definition:Expected value of a RV says that, if a random experiment is repeated n number of times, what would be the value that you expect to see most of the times.Expected value of a Random Variable is a value. I... |
IMO transaction data is a better approach, because you have both sides of the trade agreeing that the price is "right." The literature tends to decompose the transaction price $P$ into a true/efficient price $P^e$ plus micro-structure noise, which I think originates from Hasbrouck '93 in the Review of Financial Studies... |
Electronic Journal of Probability Electron. J. Probab. Volume 17 (2012), paper no. 8, 35 pp. Distributional properties of exponential functionals of Lévy processes Abstract
We study the distribution of the exponential functional $I(\xi,\eta)=\int_0^{\infty} \exp(\xi_{t-}) d \eta_t$, where $\xi$ and $\eta$ are independe... |
One of the forms of algebraic expressions is power expression. It is in the form of a
n, where a is called as the base, and n is called as the exponent. The word exponent is so common that the power expressions are described as exponential expressions.
The value of the expression is the product of the base when multipl... |
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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... |
ISSN:
1930-5346
eISSN:
1930-5338
All Issues
Advances in Mathematics of Communications
May 2016 , Volume 10 , Issue 2
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Abstract:
For projective varieties defined over a finite field ${\mathbb F}_q$ we show that they contain a unique subvariety that satisfies the Finite Field Nullstel... |
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... |
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... |
Let \( A_{a, b} = \{ (x, y) \in \mathbb{Z}^2 : 1 \leq x \leq a, 1 \leq y \leq b \} \). Consider the following property, which we call Property R:
“If each of the points in \(A\) is colored red, blue, or yellow, then there is a rectangle whose sides are parallel to the axes and vertices have the same color.”
Find the ma... |
ISSN:
1930-8337
eISSN:
1930-8345
All Issues
Inverse Problems & Imaging
February 2011 , Volume 5 , Issue 1
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Export/Reference:
Abstract:
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show... |
Definition:Norm/Vector Space Definition $\norm{\,\cdot\,}: V \to \R_{\ge 0}$
satisfying the (vector space) norm axioms:
\((N1)\) $:$ Positive definiteness: \(\displaystyle \forall x \in V:\) \(\displaystyle \norm x = 0 \) \(\displaystyle \iff \) \(\displaystyle x = \mathbf 0_V \) \((N2)\) $:$ Positive homogeneity: \(\d... |
OpenCV 4.0.1
Open Source Computer Vision
GMat cv::gapi::concatHor (const GMat &src1, const GMat &src2) Applies horizontal concatenation to given matrices. More... GMat cv::gapi::concatHor (const std::vector< GMat > &v) GMat cv::gapi::concatVert (const GMat &src1, const GMat &src2) Applies vertical concatenation to give... |
Difference between revisions of "Vopenka"
(Added not necessarily weakly compact and external links section.)
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==External links==
==External links==
− + +
* [http://mathoverflow.net/questions/45602/can-vopenkas-principle-be-violated-definably Math Overflow question and answer about formalisations]
{{Ref... |
Global asymptotic stability in a chemotaxis-growth model for tumor invasion
Department of Mathematics, Tokyo University of Science, Tokyo 162-8601, Japan
$ \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v) + ru -\mu u^\alpha, \qquad x\in \Omega, \ t>0, \\ \ v_t = \Delta v + wz, \qquad x\in \Omega, \ t>... |
Difference between revisions of "Weakly compact"
(Many Minor Fixes)
Line 61: Line 61:
A transitive set $M$ is a $\kappa$-model of set theory if
A transitive set $M$ is a $\kappa$-model of set theory if
−
$|M|=\kappa$, $M^{\lt\kappa}\subset M$ and $M$ satisfies
+
$|M|=\kappa$, $M^{\lt\kappa}\subset M$ and $M$ satisfies ... |
1Department of Computer and Inst. Tech. Edu., Faculty of Education, Agri Ibrahim Cecen University, Agri, Turkey
2Department of Mathematics, Faculty of Science, Ege University, 35100 Bornova-Izmir, Turkey
Abstract
An exponential dominating set of graph $G = (V,E )$ is a subset $S\subseteq V(G)$ such that $\sum_{u\in S}(... |
Boundedness in a quasilinear fully parabolic Keller-Segel system via maximal Sobolev regularity
1.
Department of Mathematics and Informatics, Graduate School of Science, Chiba University, 1-33, Yayoi-cho, Inage, Chiba 263-8522, Japan
2.
Department of Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-k... |
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