An extension of the dual complexity space and an application to Computer Science

In 1999, Romaguera and Schellekens introduced the theory of dual complexity spaces as a part of the development of a mathematical (topological) foundation for the complexity analysis of programs and algorithms [S. Romaguera, M.P. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311-322]. In this work we extend the theory of dual complexity spaces to the case that the complexity functions are valued on an ordered normed monoid. We show that the complexity space of an ordered normed monoid inherits the ordered normed structure. Moreover, the order structure allows us to prove some topological and quasi-metric properties of the new dual complexity spaces. In particular, we show that these complexity spaces are, under certain conditions, Hausdorff and satisfy a kind of completeness. Finally, we develop a connection of our new approach with Interval Analysis.     

Quasi-asymptotic contractions,set-valued dynamic systems,uniqueness of endpoints and generalized pseudodistances in uniform spaces

For set-valued dynamic systems in uniform spaces we introduce the concept of quasi-asymptotic contractions with respect to some generalized pseudodistances, describe a method which we use to establish general conditions guaranteeing the existence and uniqueness of endpoints (stationary points) of these contractions and exhibit conditions such that for each starting point each generalized sequence of iterations (in particular, each dynamic process) converges and the limit is an endpoint. The definition, result, ideas and techniques are new for set-valued dynamic systems in uniform, locally convex and metric spaces and even for single-valued maps.     

Numerical quenching for the semilinear heat equation with a singular absorption

In this paper we study the numerical approximation for the heat equation with a singular absorption. We prove that the numerical quenching rate coincides with the continuous one. We also see that the quenching time and the quenching set converge to the continuous one. In fact, under some restriction on the initial data, the numerical quenching coincides with the continuous one. Finally, we give some numerical results to illustrate our analysis.     

Quicksort algorithm: Application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words

In this paper, we apply an intuitionistic fuzzy quasi-metric version of a fixed point theorem, to obtain the existence of solution for a recurrence equation associated with the analysis of Quicksort algorithms.     

On the moments and distribution of discrete Choquet integrals from continuous distributions

We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means, ordered weighted averaging functions, and lattice polynomial functions as particular cases, our results encompass the corresponding results for these aggregation functions. After detailing the results obtained in [J.-L. Marichal, I. Kojadinovic, Distribution functions of linear combinations of lattice polynomials from the uniform distribution, Statistics & Probability Letters 78 (2008) 985–991] in the uniform case, we present results for the standard exponential case, show how approximations of the moments can be obtained for other continuous distributions such as the standard normal, and elaborate on the asymptotic distribution of the Choquet integral. The results presented in this work can be used to improve the interpretation of discrete Choquet integrals when employed as aggregation functions.     

A priori error estimation for the dual mixed finite element method of the elastodynamic problem in a polygonal domain, I

In this paper we analyze a new dual mixed formulation of the elastodynamic system in polygonal domains. In this formulation the symmetry of the strain tensor is relaxed by the rotation of the displacement. For the time discretization of this new dual mixed formulation, we use an explicit scheme. After the analysis of stability of the fully discrete scheme, L^∞ in time, L² in space a priori error estimates are derived for the approximation of the displacement, the strain, the pressure and the rotation. Numerical experiments confirm our theoretical predictions.     

Application of modified homotopy perturbation method for solving the augmented systems

In this paper, a new approach is proposed for solving the augmented systems. Based on the modified homotopy perturbation method, we construct the new iterative methods and derive the sufficient and necessary conditions for guaranteeing its convergence. Some numerical experiments show that this method is more simple and effective.     

Comparison of different spatial grids for numerical schemes of geophysical fluid dynamics

The generation of computational grids is an important component contributing to the efficiency of numerical schemes of atmosphere/ocean dynamics. In this study the problem of construction of the most uniform grids based on conformal mappings of spherical domains is considered. Stereographic, cylindrical and conic grids for computational rectangles are developed and their uniformity is compared. Numerical experiments with two schemes approximating shallow water equations are performed in order to assess the practical efficiency of the constructed grids and to compare the numerical results with analytical evaluations.     

Categories of models of R-mingle

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics.     

Mechanical properties and degradation studies of poly(D,L‐lactide‐co‐glycolide) 50:50/graphene oxide nanocomposite films

Poly(D,L‐lactide‐co‐glycolide) 50:50 (PLGA)/graphene oxide (GO) nanocomposite films were prepared with various GO weight fractions. A significant enhancement of mechanical properties of the PLGA/GO nanocomposite films was obtained with GO weight fractions. The incorporation of only 5 wt% of GO resulted in an ~2.5‐fold and ~4.7‐fold increase in the tensile strength and Young's modulus of PLGA, respectively. The thermomechanical behaviors of composite films were investigated by dynamic mechanical analysis. Results indicated that the values of T_g and storage moduli of the PLGA/GO composites were higher than those of the pristine PLGA. The improvement in oxygen barrier properties of composites was presumably attributed to the filler effect of the randomly dispersed GO throughout the PLGA matrix. In this work, we also studied in vitro biodegradation behavior. PLGA/GO composite films were hydrolyzed at 37°C for periods up to 49 days. Because of the presence of GO nanosheets, degradation of composite films took place more slowly with increasing GO amounts. Copyright © 2013 John Wiley & Sons, Ltd.