Discrete distributions of orderk on a binary sequence

Summary This paper considers discrete distributions of orderk based on a binary sequence which is defined as an extension of independent trials with a constant success probability and is more practical than the independent trials. Some results on calculation of probabilities and characteristics of the distributions are obtained as well as their formal expressions. Examples and an application are also given. The Institute of Statistical Mathematics     

具非线性控制变量的非自治松驰系统时间最优追踪控制问题中的若干结果

本文讨论了一类广义非自治离散松驰系统的时间最优控制问题，将R^n中点曲线的目标约束推广为凸集值函数的超曲线约束．在证明了松驰系统与原系统可达集相等的基础上，得到了最优控制的存在性．由凸集分离定理及终端时间闺值函数方程，我们获得了最大值原理及最优控制时间的确定方法．较之Hamilton方法，本文的条件更一般．离散松驰系统的相关结论可以用于分散控制．     

时滞Duffing型方程周期解的存在唯一性

该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t)$ 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t)$ 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t) g(x(t-τ(t,x(t))))=f(t)周期解的存在性,得到了方程周期解存在的充分条件和必要条件．研究了当滞量为常值时,方程周期解的存在唯一性．并且给出了所研究问题的一个应用实例．     

Fourier and barycentric formulae for equidistant Hermite trigonometric interpolation

We consider the Hermite trigonometric interpolation problem of order 1 for equidistant nodes, i.e., the problem of finding a trigonometric polynomial t that interpolates the values of a function and of its derivative at equidistant points. We give a formula for the Fourier coefficients of t in terms of those of the two classical trigonometric polynomials interpolating the values and those of the derivative separately. This formula yields the coefficients with a single FFT. It also gives an aliasing formula for the error in the coefficients which, on its turn, yields error bounds and convergence results for differentiable as well as analytic functions. We then consider the Lagrangian formula and eliminate the unstable factor by switching to the barycentric formula. We also give simplified formulae for even and odd functions, as well as consequent formulae for Hermite interpolation between Chebyshev points.     

Periodic solutions of second order nonlinear difference equations with discrete -Laplacian

We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second order difference equations involving discrete -Laplacian. We obtain in particular upper and lower solutions theorems, Ambrosetti–Prodi type multiplicity results, sharp existence conditions for nonlinearities which are bounded from below or from above and necessary and sufficient conditions for the existence of positive periodic solutions when the nonlinearity is singular at 0.     

Strong and uniform mean stability of cosine and sine operator functions

It is first observed that a uniformly bounded cosine operator function C() and the associated sine function S() are totally non-stable. Then, using a zero-one law for the Abel limit of a closed linear operator, we prove some results concerning strong mean stability and uniform mean stability of C(). Among them are: (1) C() is strongly (C,1)-mean stable (or (C,2)-mean stable, or Abel-mean stable) if and only if 0ρ(A)σ_c(A); (2) C() is uniformly (C,2)-mean stable if and only if S() is uniformly (C,1)-mean stable, if and only if , if and only if , if and only if C() is uniformly Abel-mean stable, if and only if S() is uniformly Abel-mean stable, if and only if 0ρ(A).     

The estimation of moments of an unknown error distribution in the discrete pulse transform

Intuition suggests that the variance of additive noise contaminating a signal can be estimated by investigation of the highest resolution level in a local Nonlinear Multiresolution Analysis. In the case of the Discrete Pulse Transforms with LULU-operators well known elegant identities between B-splines lead to some surprisingly simple and useful results.     

Coherent multiperiod risk adjusted values and Bellman’s principle

Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as in decision-making. We finally deduce risk measurements for the final value of locked-in positions and repeat a warning concerning Tail-Value-at-Risk.     

On solving the discrete location problems when the facilities are prone to failure

The classical discrete location problem is extended here, where the candidate facilities are subject to failure. The unreliable location problem is defined by introducing the probability that a facility may become inactive. The formulation and the solution procedure have been motivated by an application to model and solve a large size problem for locating base stations in a cellular communication network. We formulate the unreliable discrete location problems as 0–1 integer programming models, and implement an enhanced dual-based solution method to determine locations of these facilities to minimize the sum of fixed cost and expected operating (transportation) cost. Computational tests of some well-known problems have shown that the heuristic is efficient and effective for solving these unreliable location problems.     

A goal programming approach to vehicle routing problems with soft time windows

The classical vehicle routing problem involves designing a set of routes for a fleet of vehicles based at one central depot that is required to serve a number of geographically dispersed customers, while minimizing the total travel distance or the total distribution cost. Each route originates and terminates at the central depot and customers demands are known. In many practical distribution problems, besides a hard time window associated with each customer, defining a time interval in which the customer should be served, managers establish multiple objectives to be considered, like avoiding underutilization of labor and vehicle capacity, while meeting the preferences of customers regarding the time of the day in which they would like to be served (soft time windows). This work investigates the use of goal programming to model these problems. To solve the model, an enumeration-followed-by-optimization approach is proposed which first computes feasible routes and then selects the set of best ones. Computational results show that this approach is adequate for medium-sized delivery problems.