On positive solutions for a class of quasilinear elliptic systems

We investigate the existence and properties of solutions for a class of systems of Dirichlet problems involving the perturbed phi-Laplace operators. We apply variational methods associated with the Fenchel conjugate. Our results cover both sublinear and superlinear cases of nonlinearities.     

Face numbers of generalized balanced Cohen-Macaulay complexes

A common generalization of two theorems on the face numbers of Cohen-Macaulay (CM, for short) simplicial complexes is established: the first is the theorem of Stanley (necessity) and Bj?rner-Frankl-Stanley (sufficiency) that characterizes all possible face numbers of a-balanced CM complexes, while the second is the theorem of Novik (necessity) and Browder (sufficiency) that characterizes the face numbers of CM subcomplexes of the join of the boundaries of simplices.     

Parallel mean curvature surfaces in symmetric spaces

We present a reduction-of-codimension theorem for surfaces with parallel mean curvature in symmetric spaces.     

Concordant and Monotone Morphisms

Concordant-dissonant and monotone-light factorisation systems on categories, ways to construct them, and conditions for them to coincide, as well as their examples are studied in this article. These factorisation systems are constructed from a reflection induced from a ground adjunction and a specified prefactorisation system. Furthermore, we give additional conditions, under which the monotone-light and the concordant-dissonant factorisations coincide for sub-reflections of the induced reflection. The adjunctions given by right Kan extensions, from the category of presheaves on sets, turn out to be very well-behaved examples, provided they satisfy the cogenerating set condition, which allows to describe the four classes of morphisms in the reflective and concordant-dissonant (= monotone-light) factorisations. It is also noticed that the faithfulness of the composite of the left-adjoint with the Yoneda embedding can be seen as a generalisation of the cogenerating set condition. Using this generalisation it is possible to present a convenient simplified version of the sufficient conditions above for the case of an adjunction from the category of presheaves on sets into a cocomplete category, satisfying the faithfulness of the abovementioned composite. Then, the same is done for induced sub-reflections from categories of models of (limit) sketches; in particular this explains why the monotone-light factorisation for categories via preordered sets is just the restriction of the same factorisation for simplicial sets via ordered simplicial complexes.     

An Interactive Method for 0-1 Multiobjective Problems Using Simulated Annealing and Tabu Search

This paper presents an interactive method for solving general 0-1 multiobjective linear programs using Simulated Annealing and Tabu Search. The interactive protocol with the decision maker is based on the specification of reservation levels for the objective function values. These reservation levels narrow the scope of the search in each interaction in order to identify regions of major interest to the decision maker. Metaheuristic approaches are used to generate potentially nondominated solutions in the computational phases. Generic versions of Simulated Annealing and Tabu Search for 0-1 single objective linear problems were developed which include a general routine for repairing unfeasible solutions. This routine improves significantly the results of single objective problems and, consequently, the quality of the potentially nondominated solutions generated for the multiobjective problems. Computational results and examples are presented.     

The analyticity of a generalized Ruelle’s operator

In this work we propose a generalization of the concept of Ruelle’s operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle’s operator. Our operator generalizes both the Ruelle operator proposed in [2] and the Perron Frobenius operator defined in [7]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle’s operator and present some examples.     

Virtual element methods for parabolic problems on polygonal meshes

The virtual element method (VEM) is a recent technology that can make use of very general polygonal/polyhedral meshes without the need to integrate complex nonpolynomial functions on the elements and preserving an optimal order of convergence. In this article, we develop for the first time, the VEM for parabolic problems on polygonal meshes, considering time‐dependent diffusion as our model problem. After presenting the scheme, we develop a theoretical analysis and show the practical behavior of the proposed method through a large array of numerical tests. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 2110–2134, 2015