A Categorical Approach to Groupoid Frobenius Algebras

In this paper, we show that $\mathcal{G}$ -Frobenius algebras (for $\mathcal{G}$ a finite groupoid) correspond to a particular class of Frobenius objects in the representation category of $D(k[\mathcal{G}])$ , where $D(k[\mathcal{G}])$ is the Drinfeld double of the quantum groupoid $k[\mathcal{G}]$ (Nikshych et al. 2000).     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators

Numerical Algorithms - In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert...     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.     

An Initial-Boundary Value Problem for the Korteweg–de Vries Equation with Dominant Surface Tension

We consider the initial-boundary value problem (IBVP) for the Korteweg–de Vries equation with zero boundary conditions at x=0 and arbitrary smooth decreasing initial data. We prove that the solution of this IBVP can be found by solving two linear inverse scattering problems (SPs) on two different spectral planes. The first SP is associated with the KdV equation. The second SP is self-conjugate and its scattering function is found in terms of entries of the scattering matrix s(k) for the first SP. Knowing the scattering function, we solve the second inverse SP for finding the potential self-conjugate matrix. Consequently, the unknown object entering coefficients in the system of evolution equations for s(k,t) is found. Then, the time-dependent scattering matrix s(k,t) is expressed in terms of s(k)=s(k,0) and of solutions of the self-conjugate SP. Knowing s(k,t), we find the solution of the IBVP in terms of the solution of the Gelfand–Levitan–Marchenko equation in the first inverse SP.     

On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.