The blow-up of critical anisotropic equations with critical directions

We investigate blow-up theory for doubly critical anisotropic problems in bounded domains of the Euclidean space.     

Spectral Models for Orthonormal Wavelets and?Multiresolution Analysis of L 2(?)

Spectral representations of the dilation and translation operators on L ²(?) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.     

Extending and relating different approaches for solving fuzzy quadratic problems

Quadratic programming problems are applied in an increasing variety of practical fields. As ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy quadratic programming problems. This work presents two methods used to solve linear problems with uncertainties in the set of constraints, which are extended in order to solve fuzzy quadratic programming problems. Also, a new quadratic parametric method is proposed and it is shown that this proposal contains all optimal solutions obtained by the extended approaches with their satisfaction levels. A few numerical examples are presented to illustrate the proposed method.     

Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis

Angiogenesis is a key process in the tumoral growth which allows the cancerous tissue to impact on its vasculature in order to improve the nutrient’s supply and the metastatic process. In this paper, we introduce a model for the density of metastasis which takes into account for this feature. It is a two-dimensional structured population equation with a vanishing velocity field and a source term on the boundary. We present here the mathematical analysis of the model, namely the well-posedness of the equation and the asymptotic behavior of the solutions, whose natural regularity led us to investigate some basic properties of the space W_div(W)={V ? L¹;  div(GV) ? L¹}{W_{rm div}(Omega)=left{Vin L^1;;{rm div}(GV)in L^1right}}, where G is the velocity field of the equation.     

Mixed integer nonlinear programming tools: a practical overview

We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties.     

Generalized GIPSCAL re-revisited: a fast convergent algorithm with acceleration by the minimal polynomial extrapolation

Generalized GIPSCAL, like DEDICOM, is a model for the analysis of square asymmetric tables. It is a special case of DEDICOM, but unlike DEDICOM, it ensures the nonnegative definiteness (nnd) of the model matrix, thereby allowing a spatial representation of the asymmetric relationships among ??objects??. A fast convergent algorithm was developed for GIPSCAL with acceleration by the minimal polynomial extrapolation. The proposed algorithm was compared with Trendafilov??s algorithm in computational speed. The basic algorithm has been adapted to various extensions of GIPSCAL, including off-diagonal DEDICOM/GIPSCAL, and three-way GIPSCAL.     

Axiomatizability of positive algebras of binary relations

We consider all positive fragments of Tarski??s representable relation algebras and determine whether the equational and quasiequational theories of these fragments are finitely axiomatizable in first-order logic. We also look at extending the signature with reflexive, transitive closure and the residuals of composition.     

The constructive characterization of (��,?)-edge-connected digraphs

We give a constructive characterization for (??, ?)-edge-connected digraphs, proving a conjecture of Frank.