In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theore...In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.展开更多
In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equa...In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.展开更多
Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding...Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.展开更多
In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u...In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.展开更多
In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic fi...In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.展开更多
文摘In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.
文摘In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.
基金Supported by the National 973 High Technology Projects (No. G1998030420)
文摘Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.
基金Project supported by the National Natural Science Foundation of China (No.10271095), the Gansu Provincial Natural Science Foundation of China (No.ZS031-A25-003-Z) and the NWNU-KJCXGC-212 Foundation
文摘In this paper the existence results of positive ω-periodic solutions are obtained forsecond order ordinary differential equation-u'(t)=f(t,u(t)) (t∈R), and also for firstorder ordinary differential equation u'(f)=f(t,u(t)) (t∈R), where f: R×R^+→Ris a continuous function which is ω-periodic in t. The discussion is based on the fixedpoint index theory in cones.
基金supported by National Science Foundation of USA(Grant No.DMS1115530)National Natural Science Foundation of China(Grant No.11171359)the Fundamental Research Funds for the Central Universities of China
文摘In this paper, we report our recent advances on vertex centered finite volume element methods （FVEMs） for second order partial differential equations （PDEs）. We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both HI and L2 norms along with study of superconvergence properties.
