Based on an accuracy analysis of two-stream approximations, an improved δ-Eddington ap-proximation is developed. The approximation has much better accuracy than all exiting two-stream ap-proximations as the optical d...
The orthogonality in Hilbert spaces is extended to the general Banach spaces and a concrete shift-invariant orthogonal family in L^1(R) is constructed. The corresponding projection approximation theorems and the algor...
The Lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.
LET D be the unit disk in the complex plane C and f be a sense preserving quasisymmetrichomeomorphism of D onto itself. Denote by Q a quadrilateral D (z1, z2, z3, z4 ) wit...
SUPPOSE θ∈[1,+ ∞) is any real number. The sequence B_θ={[nθ]|n∈N}is calledBeatty’s sequence determined by θ. Beatty sequences have been the subject of intensive inves-tigation in recent years on account of the...
This work was supported by the National Natural Science Foundation of China (Grant No. 19571028);the Guangdong Provincial Natural Science Foundation.
In this note, we consider (2) assuming that f satisfies the following conditions(f1) and(f2). We will develop a method entirely different from that in ref. [2] to prove that for anyweak sol...
The regular and smooth objects are always studied in conventional geometry. But very rough and irregular objects which have self-similarity, the fractal structure, are efficiently solved by fractal geometry. The self-...
Project supported in part by the Natural Science Foundation of Shanghai;the National Key Laboratory of Intelligent Technology and Systems of China.
Let the function n: R^R→R be defined by Recently, approximating continuous function of several variables by the composition and superposition 9oπ of the function π and a function of one variable g is arousing great...
Project supported in part by the National High-tech Project of China.
Suppose that ∏ is a maximization problem,and tha A is an approximation algorithmfor ∏.For every instance I of ∏,define R_A(I)=OPT(I)/A(I),where OPT(I)is the optimal value of I;A(I)is the value of approximate soluti...