Minimal characters of the finite classical groups

Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical group we deter-mine the number of projective complex characters of G(q) of degree d(G(q)). In several cases we also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results we deduce the classification of quasi-simple irreducible complex linear groups of degree at most 2r r a prime divisor of the group order.     

Finite groups whose same degree characters are Galois conjugate

We classify the finite groups which satisfy the condition that any two nonprincipal complex irreducible characters of the same degree are Galois conjugate.     

Conditions for Permanence and Ergodicity of Certain SIR Epidemic Models

In this paper, we study sufficient conditions for the permanence and ergodicity of a stochastic susceptible-infected-recovered (SIR) epidemic model with Beddington-DeAngelis incidence rate in both of non-degenerate and degenerate cases. The conditions obtained in fact are close to the necessary one. We also characterize the support of the invariant probability measure and prove the convergence in total variation norm of the transition probability to the invariant measure. Some of numerical examples are given to illustrate our results.

     

On the stability of the solution mapping for parametric traffic network problems

In this paper, we introduce the parametric traffic network problems. Afterward, a key hypothesis is introduced by virtue of a parametric gap function to considered problems, and we prove that this hypothesis is not only sufficient but also necessary for the Hausdorff lower semicontinuity and Hausdorff continuity of the solution mapping for parametric traffic network problems.     

The superconducting fluctuation optical conductivity of iron-based superconductors

The European Physical Journal B - The physical properties of a quantum many-body system can, in principle, be determined by diagonalizing the respective Hamiltonian, but the dimensions of its...     

Efficiency in vector quasi-equilibrium problems and applications

In this paper, we give sufficient conditions for the existence of efficient solutions of a generalized vector quasi-equilibrium problem in topological vector spaces. The motivations for introducing this problem come from practical problems in traffic networks and the optimal control theory for discrete-time dynamical systems. The main results of the paper are proven with the help of a strongly monotonic function which can be constructed from the data of the problem under consideration. Some notions of cone-semicontinuity of set-valued maps, weaker than the usual concepts of semicontinuity, are also used in our study. As applications, we obtain existence results in vector quasi-optimization problems, Stampacchia set-valued vector quasi-variational inequality problems and Pareto vector quasi-saddle point problems. All these results are different from the corresponding ones in the literature.     

Determination of stresses and displacements in a thin annular disk subjected to diametral compression

Results of an analysis of the plane stress state of a thin annular disk subjected to uniform pressure on two diametrically opposite segments of the rim are presented. Some features of the stress distribution are investigated by means of both theoretical technique and experimental testing. Analytical expressions for the components of the displacement vector that correspond to the stress state of a ring under the action of diametral compression are established.     

Aggregate–disaggregate approach to an airfreight forwarder’s planning under uncertainty: a case study

Resource planning of airfreight forwarders is a complex endeavor, requiring decisions to be made in a dynamic and uncertain environment. Airfreight forwarders acquire airfreight spaces from three sources: allotment from carriers, retail from carriers and subcontracting to partners, all of which differ in terms of cost, flexibility and timing of booking. This real-life problem has many planning decisions (bookings in terms of carriers, route, time, ULDs, etc.). In this case study, we propose an aggregate–disaggregate approach and focus on the most critical decisions. A two-stage stochastic dynamic program first determines, in aggregates, the amount of allotment bookings, retail resources, and subcontracting or surplus co-loading. Then, a heuristic is used to disaggregate resource requirements into specific bookings. An analysis is provided to examine the relevant managerial issues. Based on real-life data, we show several patterns of aggregate resource bookings with respect to different levels of demand uncertainty and cost parameters. We show that resource disaggregation has to balance cost-effectiveness, capacity flexibility and routing flexibility of a resource plan.