Related papers: Discrete Pauli pairs
For a family of second-order parabolic systems with bounded measurable, rapidly oscillating and time-dependent periodic coefficients, we investigate the sharp convergence rates of weak solutions in $L^2$. Both initial-Dirichlet and…
We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if $f$ is a probability density on $\R^n$ of the form $f(x)=\prod_{i=1}^n f_i(x_i)$, where each $f_i$ is a density on $\R$, say…
The stochastic time-fractional equation $\partial_t \psi -\Delta\partial_t^{1-\alpha} \psi = f + \dot W$ with space-time white noise $\dot W$ is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error…
Using a local analog of the Wiener-Levi theorem, we investigate the class of measures on Euclidean space with discrete support and spectrum. Also, we find a new sufficient conditions for a discrete set in Euclidean space to be a coherent…
We establish the rate of convergence in the strong law of large numbers of discrete Fourier Transform of the identically distributed random variables with finite moment of order p, where 1<p<2.
This study is motivated by a series of recent papers that show that, if a given deterministic sequence in the unit interval has a Poisson pair correlation function, then the sequence is uniformly distributed. Analogous results have been…
We compute the 't Hooft anomalies of discrete symmetries in the Pouliot type dual theories and check their anomaly matching conditions. The Pouliot type dual theories we will consider in this paper are two dual pairs; the dual pair of…
The main result of this paper is, that if we suppose that a function is absolutely continuous and uniformly H\"older continuous and that its finite difference function does not oscillate infinitely often on a bounded interval, then the…
The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the $q$-lattice setting is considered. We take up the task of initiating a systematic study of the corresponding moments of the density from two…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We extend Krylov and R\"{o}ckner's result \cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. To be more precise, let $b: [0,T]\times{\mathbb…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
In their work, Serre and Swinnerton-Dyer study the congruence properties of the Fourier coefficients of modular forms. We examine similar congruence properties, but for the coefficients of a modified Taylor expansion about a CM point…
We investigate the weak coupling limit of the Pauli- Fierz Hamiltonian within a mathematically rigorous framework. Furthermore, we establish the asymptotic behavior of the effective mass in this regime.
We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic…
Binary pulsars provide some of the tightest current constraints on modified theories of gravity and these constraints will only get tighter as radio astronomers continue timing these systems. These binary pulsars are particularly good at…
The influence of the low-frequency timing noise on the precision of measurements of the Keplerian and post-Keplerian orbital parameters in binary pulsars is studied. Fundamental limits on the accuracy of tests of alternative theories of…
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase transition in Bernoulli percolation. In addition to…
The behaviour of periodic points of discrete Euler top is studied. We derive invariant varieties of periodic points explicitly. When the top is axially symmetric they are specified by some particular values of the angular velocity along the…
The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a…