Identities for primal Menger algebras

This note gives a small set of identities for the primal unitary Menger algebra with n elements. It treats the constants uniformly.     

Descent generating polynomials and the Hermite–Biehler theorem

Journal of Algebraic Combinatorics - The subject of this paper are partial geometries $$pg(s,t,alpha )$$ with parameters $$s=d(d'-1), t=d'(d-1), alpha =(d-1)(d'-1)$$ , $$d, d'...     

Apollonian packings in seven and eight dimensions

Aequationes mathematicae - In an earlier work, we proposed a generalization for the Apollonian packing in arbitrary dimensions and showed that the resulting object in four, five, and six dimensions...     

最小化碳排放的共享单车迁移问题

本文考虑共享单车迁移问题, 它可看作是经典旅行售货商问题的一个新颖变形, 不同的是其目标函数为最小化碳排放。其中, 碳排放利用单车负载与其行驶路程的乘积进行刻画。我们提出了两个启发式算法：贪心和基于TSP的算法, 每个算法的核心思想均是优先减少单车负载。从理论上证明算法的可行性并给出数据实验以验证算法的实际性能。数据实验结果表明贪心算法优于基于TSP的算法, 这为共享单车企业进行日常单车分配提供了理论依据。     

Fluctuation Results for General Block Spin Ising Models

Journal of Statistical Physics - We study a block spin mean-field Ising model, i.e. a model of spins in which the vertices are divided into a finite number of blocks with each block having a fixed...     

Modelling Intra-City Time-Dependent Travel Speeds for Vehicle Scheduling Problems

Many research papers have presented mathematical models for vehicle scheduling. Several of these models have been embedded in commercial decision support systems for intra-city vehicle scheduling for launderies, grocery stores, banks, express mail customers, etc. Virtually all of these models ignore the important issue of time-dependent travel speeds for intra-city travel. Travel speeds (and times) in nearly all metropolitan areas change drastically during the day because of congestion in certain parts of the city road network. The assumption of constant (time-independent) travel speeds seriously affects the usefulness of these models. This is particularly true when time windows (earliest and latest stop time constraints) and other scheduling issues are important. This research proposes a parsimonious model for time-dependent travel speeds and several approaches for estimating the parameters for this model. An example is presented to illustrate the proposed modelling approach. The issue of developing algorithms to find near-optimal vehicle schedules with time-dependent travel speeds is also discussed. The modelling approach presented in this paper has been implemented in a commercial courier vehicle scheduling system and was judged to be ‘very useful’ by users in a number of different metropolitan areas in the United States.