An efficient solution approach for real-world driver scheduling problems in urban bus transportation

The driver scheduling problem in public transportation is defined in the following way. There is a set of operational tasks, and the goal is to define the sequence of these tasks as shifts in such a way that every task must be assigned to a shift without overlapping. In real-world situations several additional constraints need to be considered, which makes large practical problems challenging to be solved efficiently. In practice it is also an important request with respect to a public transportation scheduling system to offer several versions of quasi-optimal solutions. In this paper we present an efficient driver scheduling solution methodology which is flexible in the above sense.     

Qualitative behaviour of a ratio-dependent predator–prey system

This paper deals with the qualitative properties of an autonomous system of differential equations, modeling ratio-dependent predator–prey interactions.This model differs from traditional ratio dependent models essentially in the predator mortality term, the death rate of the predator is not constant but instead increases when there is overcrowding.We incorporate delay(s) into the system. The most important observation is that as the delay(s) is (are) increased the originally asymptotic stable interior equilibrium loses its stability. Furthermore at a certain critical value a Hopf bifurcation takes place: small amplitude periodic solutions arise.     

On the multi‐colored Ramsey numbers of cycles

For a graph L and an integer k≥2, R_k(L) denotes the smallest integer N for which for any edge‐coloring of the complete graph K_N by k colors there exists a color i for which the corresponding color class contains L as a subgraph. Bondy and Erdos conjectured that, for an odd cycle C_n on n vertices, They proved the case when k = 2 and also provided an upper bound R_k(C_n)≤(k+ 2)!n. Recently, this conjecture has been verified for k = 3 if n is large. In this note, we prove that for every integer k≥4, When n is even, Sun Yongqi, Yang Yuansheng, Xu Feng, and Li Bingxi gave a construction, showing that R_k(C_n)≥(k?1)n?2k+ 4. Here we prove that if n is even, then © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 169‐175, 2012     

Numerical control of kohonen neural network for scattered data approximation

Surface reconstruction from scattered data using Kohonen neural network is presented in this paper. The network produces a topologically predefined grid from the unordered data which can be applied as a rough approximation of the input set or as a base surface for further process. The quality and computing time of the approximation can be controlled by numerical parameters. As a further application, ruled surface is produced from a set of unordered lines by the network. AMS subject classification 68U07, 65D17, 68T20     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

On the maximal number of certain subgraphs inK r -free graphs

Given two graphsH andG, letH(G) denote the number of subgraphs ofG isomorphic toH. We prove that ifH is a bipartite graph with a one-factor, then for every triangle-free graphG withn verticesH(G) H(T ₂(n)), whereT ₂(n) denotes the complete bipartite graph ofn vertices whose colour classes are as equal as possible. We also prove that ifK is a completet-partite graph ofm vertices,r > t, n max(m, r – 1), then there exists a complete (r – 1)-partite graphG* withn vertices such thatK(G) K(G*) holds for everyK _r -free graphG withn vertices. In particular, in the class of allK _r -free graphs withn vertices the complete balanced (r – 1)-partite graphT _r–1(n) has the largest number of subgraphs isomorphic toK _t (t < r),C ₄,K _2,3. These generalize some theorems of Turán, Erdös and Sauer.Dedicated to Paul Turán on his 80th Birthday     

Risk-Neutral Pricing for Arbitrage Pricing Theory

Journal of Optimization Theory and Applications - We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and...     

Strong approximations of the Hoeffding,Blum, Kiefer,Rosenblatt multivariate empirical process

Hoeffding (Ann. Math. Statist. 1948) and Blum, Kiefer and Rosenblatt (Ann. Math. Statist. 1961) constructed distribution free tests of independence based on a multivariate empirical process. We establish strong invariance principles for the latter and also for appropriate functionals of it.