相关论文: A note on unique continuation for discrete harmoni…

An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra…

In this paper, we study the relationship between the dimension of linear space of harmonic function with growth bounded by a fixed-degree polynomial on a minimal submanifold in Euclidean space and that on its one cylindrical tangent cone at…

In this paper, we give a few results on the local behavior of harmonic functions on the Sierpinski triangle - more precisely, of their restriction to a side of the triangle. First we present a general formula that gives the H\"older…

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…

We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a Lipschitz bound. These unique-continuation-type results are…

Lattice gauge theories are considered with a partial axial gauge fixing along one direction only. This leaves a residual gauge symmetry that is still local in three directions but now global in one. It is found that this $N^{d-1}$ fold…

We examine supersymmetric theories with approximately conformal sectors. Without an IR cutoff the theory has a continuum of modes, which are often referred to as "unparticles." Making use of the AdS/CFT correspondence we find that in the…

The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…

In this paper we consider nonzero harmonic functions vanishing on some subsets of $\mathbb R^n$. We give a positive solution to Problem 151 from the Scottish Book posed by R. Wavre in 1936. In more detail, we construct a nonzero harmonic…

For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ f\left( x\right) $ is a sum of two functions $f\left( x\right) =f_{1}\left( x\right)…

We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on the square lattice. The fields are associated to the vertices and an equation Q(x_1,x_2,x_3,x_4)=0 relates four fields at one quad. Integrability of…

A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field…

Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $\sqrt{\log N}$. The level lines of such functions form a loop $O(2)$ model on the edges of the hexagonal…

A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under…

We construct numerical basis function sets on a lattice, whose spatial extension is scalable from single lattice sites to the continuum limit. They allow us to compute small and large bound states with comparable, moderate effort. Adopting…

A universal differential equation is a nontrivial differential equation the solutions of which approximate to arbitrary accuracy any continuous function on any interval of the real line. On the other hand, there has been much interest in…

We study the uniqueness of a vortex equation involving an entire function on the complex plane. As geometric applications, we show that there is a unique harmonic map $u:\mathbb{C}\rightarrow \mathbb{H}^2$ satisfying $\partial u\neq 0$ with…

Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…

Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann…