一类(QL)型随机微分方程解的轨道唯一性判别及其应用

考虑了一类拟左连续(QL)型随机微分方程(S.D.E.)解的轨道唯一性,应用随机分析方法获得了唯一性成立的一般判别定理,并在方程系数满足局部(或非)Lipschitz条件下给出了一些应用实例.     

Revising uniqueness for a nonlinear diffusion-convection equation

This paper provides a generalized and simplified proof of the uniqueness of a weak solution for nonlinear diffusion-convection problems of Stefan type with homogeneous boundary conditions and continuous convection.     

Regularity and uniqueness of a class of biharmonic map heat flows

We consider a class of weak solutions of the heat flow of biharmonic maps from \(\Omega \subset \mathbb{R }^n\) to the unit sphere \(\mathbb{S }^L\subset \mathbb{R }^{L+1}\) , that have small renormalized total energies locally at each interior point. For any such a weak solution, we prove the interior smoothness, and the properties of uniqueness, convexity of hessian energy, and unique limit at \(t=\infty \) . We verify that any weak solution \(u\) to the heat flow of biharmonic maps from \(\Omega \) to a compact Riemannian manifold \(N\) without boundary, with \(\nabla ^2 u\in L^q_tL^p_x\) for some \(p>\frac{n}{2}\) and \(q>2\) satisfying (1.12), has small renormalized total energy locally and hence enjoys both the interior smoothness and uniqueness property. Finally, if an initial data \(u_0\in W^{2,r}(\mathbb{R }^n, N)\) for some \(r>\frac{n}{2}\) , then we establish the local existence of heat flow of biharmonic maps \(u\) , with \(\nabla ^2 u\in L^q_tL^p_x\) for some \(p>\frac{n}{2}\) and \(q>2\) satisfying (1.12).     

On boundary uniqueness theorems for a linear elliptic equation with constant coefficients

For the solutions of an elliptic equation with constant coefficients, we prove uniqueness theorems that generalize the classical boundary uniqueness theorems for analytic functions.     

On the join of graphs and chromatic uniqueness

A graph is chromatically unique if it is uniquely determined by its chromatic polynomial. Let G be a chromatically unique graph and let K_m denote the complete graph on m vertices. This paper is mainly concerned with the chromaticity of K_m + G where + denotes the join of graphs. Also, it is shown that a large family of connected vertextransitive graphs that are not chromatically unique can be obtained by taking the join of some vertex-transitive graphs. © 1995 John Wiley & Sons, Inc.     

On a class of sets of uniqueness for double trigonometric series

We obtain a new class of sets of uniqueness for double trigonometric series in the case of rectangular convergence as well as prove the two-dimensional analog of Privalov’s theorem.     

On chromatic uniqueness of certain 5-partite graphs

Let P(G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G～H, if P(G,λ)=P(H,λ). We write [G]={H∣H～G}. If [G]={G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 5-partite graphs with 5n+3 vertices according to the number of 6-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, many new families of chromatically unique complete 5-partite graphs with certain star or matching deleted are obtained.     

On uniqueness theorem for a class of functions analytic in a halfplane

We obtain a uniqueness theorem for a class of analytic functions of exponential type in a halfplane.     

A uniqueness theorem for Delaunay graphs

We establish a necessary and sufficient condition for the congruence of two isomorphic Delaunay graphs.     

A uniqueness result for a nonlinear hyperbolic equation

Summary We prove the uniqueness of the solution of a Cauchy problem for a nonlinear and non-local hyperbolic equation, which arises in a model of the dynamic of cardiac muscle.The authors were supported by G.N.A.F.A., G.N.I.M. and I.A.N. of C.N.R. and by M.P.I.     

On the uniqueness criterion for solutions of the Sturm-Liouville equation

We consider the Sturm-Liouville equation $ - y'' + qy = \lambda ^2 y $ in an annular domain K from ? and obtain necessary and sufficient conditions on the potential q under which all solutions of the equation ?y″(z) + q(z)y(z) = λ ² y(z), z ∈ γ, where γ is a certain curve, are unique in the domain K for all values of the parameter λ ∈ ?.     

On uniqueness sets for an elliptic equation with constant coefficients

For the solutions of the elliptic equation

On the existence and uniqueness of smooth solution for a generalized Zakharov equation

The paper deals with the existence and uniqueness of smooth solution for a generalized Zakharov equation. We establish local in time existence and uniqueness in the case of dimension d=2,3. Moreover, by using the conservation laws and Brezis-Gallouet inequality, the solution can be extended globally in time in two dimensional case for small initial data. Besides, we also prove global existence of smooth solution in one spatial dimension without any small assumption for initial data.     

On chromatic uniqueness of two infinite families of graphs

In this paper, it is proven that for each k ≥ 2, m ≥ 2, the graph Θ_k(m,…,m), which consists of k disjoint paths of length m with same ends is chromatically unique, and that for each m, n, 2 ≤ m ≤ n, the complete bipartite graph K_m,n is chromatically unique. © 1993 John Wiley & Sons, Inc.     

On a class of graphs without 3-stars

M. Numata described edge regular graphs without 3-stars. Allμ-subgraphs of these graphs are regular of the same valency. We prove that a connected graph without 3-stars all of whoseμ- subgraphs are regular of valencyα > 0 is either a triangular graph, or the Shläfli graph, or the icosahedron graph.