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The Solutions to Elmsley’s Problem
Order formula the highest position p primary group theory card tricks edge
2015/7/8
We give a formula for the optimal sequence of perfect shuffles to bring a card at position p to the top (or indeed, to any position). This solves a fifty-year-old problem of Elmsley. The ar...
A remark on the definitions of viscosity solutions for the integro-differential equations with L{é}vy operators
remark definitions of viscosity solutions integro-differential equations
2011/1/21
In this note, we shall consider the following problem F(x, u,∇u,∇2u)−ZRN [u(x+z)−u(x)−1|z|<1h∇u(x).
Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems
Closed-Form Solutions Nuclear Norm Minimization Problems
2010/11/24
It is an efficient and effective strategy to utilize the nuclear norm approximation to learn low-rank matrices, which arise frequently in machine learning and computer vision. So the exploration of n...
Multiplicity of solutions for homogeneous elliptic systems with critical growth
homogeneous elliptic systems critical growth
2010/11/24
In this paper we are concerned with the number of nonnegative solutions of the elliptic system $$ {array}{ll} -\Delta u = Q_u(u,v) + 1/2{2^*} H_u(u,v),& {in} \Omega,\vdois\ -\Delta v = Q_v(u,v) + 1/{2...
Null Asymptotics of Solutions of the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation
the Einstein-Maxwell Equations General Relativity
2010/11/15
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christ...
Response solutions for arbitrary quasi-periodic perturbations with Bryuno frequency vector
quasi-periodic perturbations Bryuno frequency vector
2010/11/9
We study the problem of existence of response solutions for a real-analytic one-dimensional system, consisting of a rotator subjected to a small quasi-periodic forcing. We prove that at least one res...
Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions
Positive solutions parabolic system cross-diffusion nonlocal initial conditions
2010/11/19
The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equation...
Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems
stationary solutions multivariate stochastic recursions related limit theorems
2010/11/12
Let $\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\R^d$. We study the Markov chain $\{X_n^x\}_{n=0}^\8$ on $\R^d$ defined by the recursion $X_n^x = \Phi_n(X^x_{n-1})$, $n\ge 0$, $X_0=x\in\...
Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
Schrö dinger equations 4d applications
2010/11/9
We consider the energy critical nonlinear Schr\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to t...
alphaCertified: certifying solutions to polynomial systems
alphaCertified certifying polynomial systems
2010/11/11
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial syste...
$L^\infty$ solutions for a model of polytropic gas flow with diffusive entropy
Polytropic gas di usive entropy
2010/12/1
We establish the global existence of L1 solutions for a model of polytropic gas ow with di usive entropy. The result is obtained by showing the convergence of a class of nite di erence schemes, whic...
Elliptic N-soliton-type solutions, i.e. solutions emerging from the application of N consecutive B\"acklund transformations to an elliptic seed solution, are constructed for all equations in the ABS l...
Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings
Generalized vector quasi-equilibrium problem Upper semi-continuity Lower semi-contin-uity Fixed point Existence
2007/12/12
Let $X,Y$ be two finite-dimensional topological vector spaces, $Z$ a Hausdorff topological vector space, $K\subset X$ and $D\subset Z$ be two nonempty sets, $C$ be a pointed, closed, and convex cone i...
New Solutions of the Einstein-Dirac Equation in Dimension n=3
Solutions the Einstein-Dirac Equation Dimension n=3
2010/11/1
The aim of this short note is to announce the existence of a one-parameter family of left-invariant metrics on $S^3$ admitting WK-spinors. This family contains the two non-Einstein Sasakian metrics w...
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
Similarity Solutions and Collapse Attractive Gross-Pitaevskii Equation
2010/11/2
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling con...