Multiplication for solutions of the equation

Linear first-order systems of partial differential equations (PDEs) of the form f=Mg, where M is a constant matrix, are studied on vector spaces over the fields of real and complex numbers. The Cauchy–Riemann equations belong to this class. We introduce on the solution space a bilinear *-multiplication, playing the role of a nonlinear superposition principle, that allows for algebraic construction of new solutions from known solutions. The gradient equation f=Mg is a simple special case of a large class of systems of PDEs, admitting a *-multiplication of solutions. We prove that any gradient equation has the exceptional property that the general analytic solution can be expressed as *-power series of certain simple solutions.     

(2+1)维Boussinesq方程的新的周期解

利用Hirota方法及Riemann theta函数得到了(2+1)维Boussinesq方程的新的周期解.在极限情况下,该周期解退化为孤子解. 关键词： Hirota方法 Riemann theta 函数 (2+1)维Boussinesq方程 周期解     

Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary： Shocks and Contact Discontinuities

In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.     

Conservation Laws Possessing Contact Characteristic Fields with Singularities

In many applications, there arise systems of two nonlinear conservation laws with a single linearly degenerate characteristic field, or contact field, the speed of which may coincide with that of the genuinely nonlinear characteristic field along a curve. Along this coincidence curve, the contact field may have isolated singular points. We prove that under generic assumptions the singular points can be centers or saddles for the contact field. We construct the local Riemann solution for each of the two generic cases. This work sheds light on the classification of local Riemann solutions of systems of two conservation laws with a linearly degenerate characteristic field.     

Quasi-range-preserving Operator

Ｑｕａｓｉ－ｒａｎｇｅ－ｐｒｅｓｅｒｖｉｎｇＯｐｅｒａｔｏｒＬａｉＣｈｕｎｈｕｉ（赖春晖）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇｚｈｏｕＴｅａｃｈｅｒｓ，Ｃｏｌｌｅｇｅ，ＺｈａｎｇｚｈｏｕＦｕｊｉａｎ，３６３０００）Ａｂｓｔｒａ...     

On Vortex Methods for Initial Boundary Value Problems

ＯｎＶｏｒｔｅｘＭｅｔｈｏｄｓｆｏｒＩｎｉｔｉａｌＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓ￥ＺｈａｎｇＰｉｎｇｗｅｎ（张平文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｉｎｇ，１００８７１）Ａｂｓｔｒ...     

The Held—Karp algorithm and degree-constrained minimum 1-trees

In this note we propose to find a degree-constrained minimum 1-tree in the Held—Karp algorithm [5, 6] for the symmetric traveling-salesman problem, and show that it is reduced to finding a minimum common basis of two matroids.     

Some experiments with the pathological linear programs of N. Zadeh

Computational results are presented which show that N. Zadeh's pathological examples for the simplex algorithm apparently take a number of pivots approximately proportional to the number of columns in the tableau when its column order is randomized.     

OnQ-matrices

In a recent paper [1], Aganagic and Cottle have established a constructive characterization for aP ₀-matrix to be aQ-matrix. Among the principal results in this paper, we show that the same characterization holds for anL-matrix as well, and that the symmetric copositive-plusQ-matrices are precisely those which are strictly copositive.     

Periods of Harmonic Prym Differentials on a Compact Riemann Surface

We study the period classes of closed, harmonic, and holomorphic Prym differentials on a compact Riemann surface of any genus g2 for arbitrary characters of its fundamental group. We prove that the harmonic Prym vector bundle of harmonic Prym differentials and the Gunning cohomology bundle are real-analytically isomorphic over the base of nontrivial normalized characters for every compact Riemann surface of genus g2.