The convergence theorem for the Henstock integral of fuzzy number valued functions is given. Especially,a convergence theorem of the Kaleva′s integral is given,which is a extension of a lot of convergence theorems for Kaleva′s integral.
The Advances of the Calculus of Fuzzy Number Valued Functions
Let g and f be two integer valued functions defined on V(G) such that 4≤g(x)≤f(x) for every x∈V(G). In this paper, it is proved that for any path P with length 2m of an (mg+m-1,mf-m+1) graph G, there exists a (g,f) factorization of G 2 orthogonal to P.
On an arbitrary subset of K-quasi-additive fuzzy measures space, aim at an given -integrable fuzzy number valued function, we establish the K-quasi-additive fuzzy number valued integrals, and regard all of this kind of integrals as set functions being taken valued fuzzy number valued on the measurable spaces, applying the integrals transformation theormem, we discuss their null-additivity and absolute continuity etc.
ECJ which we use to implement GA and do numerical experiment is introduced in this thesis(2)A clonal selection algorithm based on clone selection principle to solve numerical function optimization is proposed.
In this paper the existence and uniqueness of the solution of the boundary value problem for the ordinary differential equation (u—scalar function) and the asymptotic expansion of the solution with respect to the small parameter were discussed, taking the smoothing of discontinuous solutions of Riemann problem for quasilinear hyperbolic differential equations as a background. The asymptotic expansion of the solution of the equation for the given initial values was also given in passing.
本文以准线性双曲型方程Riemann问题间断解展平为背景,讨论了常微分方程边值问题 e d~2u/dξ~2=F(ξ,u)du/dξ (u——数值函数)u(-∞,∈)=u~-(∈),u(∞,∈)=u~+(∈)解的存在性、唯一性和解对小参数∈的渐近展开,顺便,也给出了方程满足初值条件 l(ξ_0,∈)=a(∈),u＇(ξ_0,∈)=b(∈)/∈的解之渐近展开式。
An elementary proof of an operational property of pure function in a matrix is dealt with by means of the polynomial expression in tnis article, i. e. Let A be an nxn-matrix in complex field. (λ), ψ(a)==f[(a)] be complex functions, pure functions of matrix A-(A), ψ(A) are defined, B = (A), then f[B] is also defined and ψ(A)=f[B]=f[(A)].
A post-processing code INETPL, using M150 computer in Tsinghua University, was presented. The basic rules and methods to develop the three-dimensional depictions, two-dimentional isograms and one-dimensional graphs of two- dimensional arrays were described.