一类具有偏差变元的Liénard型方程的周期解

利用重合度理论研究了一类具偏差变元的Liénard型方程x″+f1(x)|x′|2n+f2(t,x(t),x(t-0τ(t)))x′+g(t,x(t-1τ(t)))=p(t).获得了该方程存在ω-周期解的若干新结论,改进推广了有关文献中的已有结果.     

一类具分布式偏差变元的双曲型向量泛函微分方程解的H-振动性

研究了一类具有分布式偏差变元的中立型向量双曲泛函微分方程解的H-振动性.给出了判别解的H-振动性的一些充分条件.     

EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION

By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differential equation with deviating arguments are obtained.     

High dimensional limit theorems and matrix decompositions on the Stiefel manifold

The main purpose of this paper is to investigate high dimensional limiting behaviors, as m becomes infinite (m → ∞), of matrix statistics on the Stiefel manifold V_{k, m}, which consists of m × k (m ≥ k) matrices X such that X′X = I_k. The results extend those of Watson. Let X be a random matrix on V_{k, m}. We present a matrix decomposition of X as the sum of mutually orthogonal singular value decompositions of the projections P X and P X, where and are each a subspace of R^m of dimension p and their orthogonal compliment, respectively (p ≥ k and m ≥ k + p). Based on this decomposition of X, the invariant measure on V_{k, m} is expressed as the product of the measures on the component subspaces. Some distributions related to these decompositions are obtained for some population distributions on V_{k, m}. We show the limiting normalities, as m → ∞, of some matrix statistics derived from the uniform distribution and the distributions having densities of the general forms f(P X) and f(m^1/2P X) on V_{k, m}. Subsequently, applications of these high dimensional limit theorems are considered in some testing problems.     

A multiclass,multicriteria logit-based traffic equilibrium assignment model under ATIS

This paper presents a multiclass, multicriteria (cost versus time) logit-based traffic equilibrium assignment model in road networks served by advanced traveler information systems (ATIS). All users are differentiated by their own value of time (VOT) that follows some probability distribution. Users of each class, having their own VOT, are further divided into two groups, equipped and unequipped with ATIS respectively. The travel disutility received by each user is defined as a linear bi-criteria combination of travel time and monetary travel cost. It is assumed that all users make their route choices in a logit-based stochastic manner, but the equipped users have lower perception variation on the travel disutility than the unequipped due to the ATIS service. The model is formulated as a fixed-point problem and solved by the method of successive averages in conjunction with logit assignment. Numerical results show that the traditional single-class and/or single-criterion models may overestimate or underestimate the benefit from ATIS services.     

Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument

In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the notion of pseudo almost periodic vector sequences.     

A class of boundary value problems for first-order impulsive integro-differential equations with deviating arguments

This paper is concerned with a class of boundary value problems for nonlinear mixed impulsive integro-differential equations with deviating arguments. We establish a new comparison principle and use the method of upper and lower solutions together with the monotone iterative technique. Under suitable conditions, we obtain the existence results of extremal solutions for the problems. An example is also given to illustrate our results.     

A fuzzy clustering approach to real-time demand-responsive bus dispatching control

Quick response (QR) to passenger needs is a key objective for advanced public transportation systems (APTS), and it has become increasingly important for contemporary metropolitan bus operations to gain a competitive advantage over private transportation. This paper presents a real-time control methodology for demand-responsive bus operations that respond quickly to passenger needs. The proposed method primarily involves two levels of functionality: (1) short-term forecasting of passenger demands using time-series prediction models, and (2) identification of service strategies coupled with the associated bus service segments using fuzzy clustering technologies in response to variances in passenger demand attributes and traffic conditions. The proposed bus operations method identifies the demand-responsive vehicle service strategies primarily according to the predicted up-to-date attributes of passengers’ demands, rather than deterministic passenger arrival rates, which were generally used in previous literature. In addition, the variation of traffic conditions along bus lines is considered in the proposed method. Results from numerical studies using real data of passengers’ demands, including passenger volume at each bus stop and the passenger origin-destination (O-D) patterns, are presented to demonstrate the effectiveness of the proposed method for real-world applications.     

COMPARISON AND OSCILLATION THEOREMS FOR AN ADVANCED TYPE DIFFERENCE EQUATION

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