Weierstrass逼近定理的应用

讨论 Weierstrass逼近定理的应用 .运用 Weierstrass逼近定理 ,我们对于连续偶函数和连续奇函数的性质进行了进一步的刻划 .     

On the Curve X(9)

Computations using theta functions with characteristic show that the modular curve X(9) is the complete intersection of two cubics. The holomorphic differentials and Weierstrass gap sequence are also computed.     

An action for a classical string,the equation of motion and group invariant classical solutions

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.      

Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations

This paper is based on the relations between projection Riccati equations and Weierstrass elliptic equation, combined with the Groebner bases in the symbolic computation. Then the novel method for constructing the Weierstrass elliptic solutions to the nonlinear evolution equations is given by using the above relations.     

Measures of Simultaneous Approximation for Quasi-Periods of Abelian Varieties

We examine various extensions of a series of theorems proved by Chudnovsky in the 1980s on the algebraic independence (transcendence degree 2) of certain quantities involving integrals of the first and second kind on elliptic curves; these extensions include generalizations to abelian varieties of arbitrary dimensions, quantitative refinements in terms of measures of simultaneous approximation, as well as some attempt at unifying the aforementioned theorems. In the process we develop tools that might prove useful in other contexts, revolving around explicit “algebraic” theta functions on the one hand, and Eisenstein's theorem and G-functions on the other hand.     

Time-optimal control problem for parabolic equations with control constraints and infinite number of variables

A time optimal control problem for parabolic equations withan infinite number of variables is considered. A time optimalcontrol problem is replaced by an equivalent one with a performanceindex in the form of integral form. Constraints on controlsare assumed. To obtain the optimality conditions for the Neumannproblem, the generalization of the Dubovitskii–Milyutintheorem given by Walczak (1984, Acta Universitatis LodziensisFolia Mathematica, 187–196; 1984, J. Optim. Theor. Appl.,42, 561–582) was applied.     

Weierstrass Multiplicative Points on a Compact Riemann Surface

We introduce Weierstrass multiplicative points and develop the theory of Weierstrass multiplicative points for multiplicative meromorphic functions and Prym differentials on a compact Riemann surface. We prove some analogs of the Weierstrass and Noether theorems on the gaps of multiplicative functions. We obtain two-sided estimates for the number of Weierstrass multiplicative points and q-points. We propose a method for studying the Weierstrass and Noether gaps and Weierstrass multiplicative points by means of filtrations in the Jacobi variety of a compact Riemann surface.     

Marginally Trapped Surfaces in L<Superscript>4</Superscript> and an Extended Weierstrass–Bryant Representation

Let E be the total space of a locally trivial torus bundle over a surface Σ_g of genus g > 1. Using Seiberg–Witten theory and spectral sequences, we prove that E carries a symplectic structure if and only if the homology class of the fiber [T²] is nonzero in H₂(E, R). Mathematics Subject Classifications (2000): 53C42, 53A10.