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In this paper, we study the uniqueness of two difference polynomials of entire functions sharing one value, polynomial and small function. Our results of this paper are improvement of the previous theorems given by Chen and Chen [2], Liu, Liu and Cao [22] and Li et al. [19].

The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.

The properties of almost periodical functions and some new results have been published in [CA1], [CA2] and [CA3] In this paper we show some new definitions in order to analize some singularities. For this functions we find some uniqueness sets in $$\mathbb{R}$$ and $$\mathbb{R^{n}}$$. The paper finishes analizing the relation of this functions and the function sinc.

This is the first of two papers devoted to the proof of Zilber’s dichotomy for the case of difference-differential fields of characteristic zero. In this paper we use the techniques exposed in [9] to prove a weaker version of the dichotomy, more precisely, we prove the following: in DCFA the canonical base of a finite-dimensional type is internal to the fixed field of the field of constants. This will imply a weak version of Zilber’s dichotomy: a finite-dimensional type of SU-rank 1 is either 1-based or non-orthogonal to the fixed field of the field of constants.

Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labour scheduling. When modelling real problems, the problem of project scheduling with partially renewable resources, as many other combinatorial problems, gets such large dimensions that it is quite difficult to apply solution procedures. In this paper, we describe some powerful preprocessing techniques that reduce significantly the dimension of the problems and therefore improve the efficiency of any algorithm used for solving them. The paper shows the excellent results obtained by these techniques on a set of test instance taken from the literature. Keywords: Project Scheduling, Preprocessing, Partially Renewable Resources.

Many data analysis problems deal with non supervised partitioning of a data set, in non empty clusters well separated between them and homogeneous within the clusters. An ideal partitioning is obtained when any object can be assigned a class without ambiguity. The present paper has two main parts; first, we present different methods and heuristics that find the number of clusters for optimal partitioning of a set; afterwards, we propose a new heuristic and we perform different comparisons in order to evaluate the advantages on well known data sets; we end the paper with some concluding remarks. Keywords: Optimal partitioning, clustering, classification, heuristics.

Modeling wave reflection and transmission is important for a diversity of applications in physics and engineering. Examples can be found in acoustics and electromagnetism. Computational wave propagation requires high order accuracy both in space and time to get accurate phase and dissipation properties. In this paper we derive and evaluate a high order accurate method based on Discontinuous Galerkin Spectral Element Method (DGSEM) to compute reflection and transmission of electromagnetic waves traveling in two homogeneous and isotropic media, separated by a thin plane interfaz, with different physical properties of permittivity " and permeability . To discretize in Space we used DGSEM over a two dimensional Transverse Electric Maxwell Equations. We derived a Riemann solver to compute the numerical flux between the interfaces of two elements of the computational mesh and to add boundary conditions. To discretize in time we use a third order low storage Runge-Kutta of Williamson. Results when compared with the analytical solution, showed spectral convergence in space and third order convergence in time.

We study a three entries vector, called “stock market sentiment”, that summarizes bear, bull and neutral feeling about the future of the market. Following the paper about “mind or spirit” in Ulate (2006), we consider such sentiment a living being and we will study its change and dynamics using evolutionary game theory. We use a dynamical system of three differential equations to study the change in the vector, and later it will be compared with the Lotka Volterra system with two equations.

In this paper we prove a version of Fubini’s Theorem for null sets in the context of vector measures, in the spirit of the classical proof for sets in the Euclidean plane.

The HIV/AIDS has cost humanity countless material and human losses. Study its dynamics has become a priority for the global scientific community, with the idea of establishing an effective control policy and subsequently analyzing its eradication. This paper presents a model based on transition matrix of Markov chains with the objective to design a future strategy to reduce the appearance of new cases and decrease the lethality of this epidemic.

In this paper we study the dynamics of HIV infection through the stochastic birth and death processes and ordinary differential equations representing a real system. For this specific case, a stochastic process is described to interpret the dynamics of HIV infection within a person’s organism in the initial stages of infection (post exposure or window period); that is to say, the initial time for the model corresponds with the very moment the virus enters the organism, and from then on the process of replication is taken into account and the incidences that the virus generates when it attacks the CD4+ T cells, which are integral parts of the patient’s immune system. The stochastic process allows one to deduce from first principles and create a basic model for HIV infection. The model is similar to those studied in the literature. It is a system based on ordinary differential equations with stochastic states. The state variables correspond to expected values (averages). We also find differential equations for the variance of the stochastic state of the variables, which provides additional information about the system. Finally, we present the local analytical study of the complete model and a numerical study of the system solutions using values of the parameters. The values of the parameters were obtained from secondary sources and were used to illustrate the analytical results.

In this paper an analysis of technical and scale efficiency of the academic units of the University of Costa Rica is presented. The methodology used is data envelopment analysis (DEA), since it allows to measure relative efficiency and provides information on how to improve each academic unit that is inefficient. The results are reported for three groupings: one based on the training process, another based on size (according to three inputs) and the third based on the knowledge area. Three inputs and three outputs are used. A sensitivity analysis through the development of four models is performed. The emphasis is on the mathematical model used, the output-oriented model, with variable returns of scale, solved each time with normalized data.

Fuzzy mathematics generalize concepts of traditional mathematics using fuzzy sets. This enables to study and model more properly phenomens characterized by imprecision. These generalizations includes concepts of algebra, analysis and topology. On the other side, cubical complexes have applications in digital image processing and in the study of dynamical systems, but in the actual literature there is not an extension of their properties using fuzzy sets. In this paper is proposed a generalization of the concept of cubical complex and of some of their properties, such as connectedness, polyhedral realization, connected component and holes, using fuzzy sets. The upper and lower trees of a fuzzy cubical complex are defined, which give information about the way in which its regional extrema are related. The homology groups of a fuzzy cubical complex are defined and it is shown that the rank of the 0-homology group of a given level is equal with the number of regional maxima of that level. Finally, it is shown how to associate a fuzzy cubical complex with a bidimensional digital grayscale image in order to study somo of its topological properties.

The main objective of this paper is to find the analytical solution of the autonomous equation y(k) = f (y) and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.

In this paper a novel fuzzy convergence system (SC) and its fundamentals are presented. The model was implemented on a monoobjetive PSO algorithm with three phases: 1) Stabilization, 2) generation and breadth-first search, and 3) generation and depth-first. The system SC-PSO-3P was tested with several benchmark engineering problems and with several CEC2006 problems. The computing experience and comparison with previously reported results is presented. In some cases the results reported in the literature are improved.

In this paper we give a complete description of the ordering relations in the set of catacondensed hexagonal systems, with respect to a vertex-degree-based topological index. As a consequence, extremal values of vertex-degree-based topological indices in special subsets of the set of catacondensed hexagonal systems are computed.

The recursion theory states that a decision problem is recursively solvable if there is a mechanical process to solve it. Within the context of formal logic, the decision problem consist to determine whether any wellformed formula of the system is a theorem or not. This paper first discusses, among other things, the famous problem of decision of the canonical first-order logic F0 (also called Entschei- dungsproblem) from a modern perspective. Then we study the decision problem of the partial propositional logics. It exploits the development achieved by recursion theory and semi-Thue production systems after the work of Post and Kleene in the 40’s and Davis in the early 70’s, among others, to explain a solution to these decision problems.

In this paper, we investigate the uniqueness problem on a conjecture of R. Brück concerning meromorphic function sharing the set of small functions with its derivative, and obtain some results which improve the theorems given by Zhang and Yang.

This paper introduces an adaptation of a multiobjective tabu/scatter search to deal with nonlinear discrete, mixed-integer constrained engineering optimization problems. The problem is reduced to a bi-objective problem (the objective function and the constraint violation function). This approach eliminates the use of penalties for constraint handling. Its performance was proved with different standard engineering optimization problems, including mathematical function minimization and structural engineering. The results show that the proposed method performs well in terms of efficiency and robustness.

In this paper we study the art of recent work Grosse-Erdmann & Kim [6], highlighting as a hypercyclic tuples of operators is a source to build bihypercyclic bilinear mappings.

In this paper the phenomenon of half-integer spin exemplification Paul AM Dirac made with a pair of scissors, an elastic cord and chair play. Four examples in which the same phenomenon appears and the algebraic structure of quaternions is related to one of the examples are described. Mathematical proof of the phenomenon using known topological and algebraic results are explained. The basic results of algebraic structures are described quaternions H , and an intrinsic relationship with the phenomenon half-integer spin and the Pauli matrices is established.

Unsupervised classifiers allow clustering methods with less or no human intervention. Therefore it is desirable to group the set of items with less data processing. This paper proposes an unsupervised classifier system using the model of soft graph coloring. This method was tested with some classic instances in the literature and the results obtained were compared with classifications made with human intervention, yielding as good or better results than supervised classifiers, sometimes providing alternative classifications that considers additional information that humans did not considered.

A hybridalgorithm which combines mathematical programming techniques (Kruskal’s algorithm and the strategy of maintaining arc consistency to solve constraint satisfaction problem “CSP”) and heuristic methods (musical composition method and DSATUR) to resolve the robust graph coloring problem (RGCP) is proposed in this paper. Experimental result shows that this algorithm is better than the other algorithms presented on the literature.

In the problem of scheduling of courses, it is generally assumed that the allocation of subjects to teaching periods is an input of the problem, which is defined by the academic authorities. This paper presents a methodology that makes use of linear programs with 0-1 integer variables, to establish the assignment of subjects to teaching periods, which takes into account the degree of difficulty of each subject and academic requirements of these, with the objective of minimizing the differences in degree of difficulty between the various academic periods.

In this paper a novel system of convergence (SC) is presented as well as its fundamentals and computing experience. An implementation using a novel mono-objetive particle swarm optimization (PSO) algorithm with three phases (PSO-3P): stabilization, generation with broad-ranging exploration and generation with in-depth exploration, is presented and tested in a diverse benchmark problems. Evidence shows that the three-phase PSO algoritm along with the SC criterion (SC-PSO-3P)can converge to the global optimum in several difficult test functions for multiobjective optimization problems, constrained optimization problems and unconstrained optimization problems with 2 until 120,000 variables.

The aspiration criterion is an imperative element in the Tabu Search, with aspiration-by-default and the aspiration-by-objective the mainly used criteria in the literature. In this paper a new aspiration criterion is proposed in order to implement a probabilistic function when evaluating an element classified as tabu which improves the current solution, the proposal is called Tabu Search with Probabilistic Aspiration Criterion (BT- CAP). The test case used to evaluate the performance of the Probabilistic Aspiration Criterion proposed consists on the 20 instances of the problem described in the First International Timetabling Competition. The results are compared with 2 additional variants of the Tabu Search Algorithm: Tabu Search with Default Aspiration Criterion (BT-CAD) and Tabu Search with Objective Aspiration Criterion (BT-CAO). Wilcoxon test was applied to the generated results, and it was proved with 99 % confidence that BT-CAP algorithm gets better solutions than the two other variants of the Tabu Search algorithm.

This paper deals with the study of an iterative method for solving a variational inclusion of the form 0 ∈ f (x)+F (x) where f is a locally Lipschitz subanalytic function and F is a set-valued map from Rn to the closed subsets of Rn. To this inclusion, we firstly associate a Newton then secondly an Inexact Newton type sequence and with some semistability and hemistability properties of the solution x∗ of the previous inclusion, we prove the existence of a sequence which is locally superlinearly convergent.

In this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.

This paper develops a methodology based on population genetics to improve the performance of two or more variables in job shop production systems. The methodology applies a genetic algorithm with special features in the individual selection when they pass from generation to generation. In comparison with the FIFO method, the proposed methodology showed better results in the variables makespan, idle time and energy cost. When compared with NSGA II, the methodology did not showed relevant differences in makespan and idle time; however better performance was obtained in energy cost and, especially, in the number of required iterations to get the optimal makespan.

In this paper we consider a monopoly producing a consumer good of high demand. Its market price depends on the volume of the produced goods described by the Cobb-Douglas production function. A production-sales activity of the firm is modeled by a nonlinear differential equation with two bounded controls: the share of the profit obtained from sales that the company reinvests into expanding own production, and the amount of short-term loans taken from a bank for the same purpose. The problem of maximizing discounted total profit on a given time interval is stated and solved. In order to find the optimal production and sales strategies for the company, the Pontryagin maximum principle is used. In order to investigate the arising two-point boundary value problem for the maximum principle, an analysis of the corresponding Hamiltonian system is applied. Based on a qualitative analysis of this system, we found that depending on the initial conditions and parameters of the model, both, singular and bang- bang controls can be optimal. Economic analysis of the optimal solutions is discussed.

In N-body simulations of cold dark matter, it has been found that three-parameter models, particularly the Einasto profile, yield better fits to a wide range of dark matter haloes than two parameter models like the Navarro-Frenk-White profile. Recently, the analytical properties of the Einasto profile has been studied, allowing closed expressions for its surface mass density and lensing properties in terms of the Fox H and Meijer G functions, using a Mellin transform formalism. These expressions are valid for all values of the Einasto index in terms of the Fox H function, and valid for integer and half-integer values of Einasto index in terms of the Meijer G function. In this paper, we derive expressions for lensing properties of the Einasto profile for all rational values of the Einasto index in terms of the Meijer G function. Equivalency between these expressions and other recent results is also discussed

This paper presents multiobjective tabu/scatter search architecture with preference information based on reference points for problems of contin- uous nature. Features of this new version are: its interactive behavior, its deterministic approximation to Pareto-optimality solutions near the refer- ence point, and the possibility to change progressively the reference point to explore different preference regions. The approach does not impose any restrictions with respect to the location of the reference points in the objective space. On 2-objective to 10-objective optimization test problems the modified approach shows its efficacy and efficiency to find an adequate non-dominated set of solutions in the preferred region.

This paper applies a geographically weighted statistical regression (GWR) model to young Nicaraguan immigrant homicides in Costa Rica during the period 1998-2008 and identifies possible covariates. The pa- rameters for the GWR model are: Yi(g)=β0(g)+β1(g)x1 +β2(g)x2 +...+βk(g)xk +ε, which may be obtained from the solution of β(g) = (XT W (g)X)−1 XT W (g)Y. The GWR model is a more adequate model than the classic models, such as the log-linear Poisson model. In the GWR model, poverty was the most significant variable. The map of the estimators associated with the percentage of poor households suggests that the relationship between poverty and mortality by homicide for young Nicaraguan immigrants is stronger in the Caribbean region and neighboring zones. When the GWR model was run for homicides among young Costa Ricans, this effect was not observed, as it was among Nicaraguan immigrants.

Kullback-Leibler information allow us to characterize a family of dis- tributions denominated Kullback-Leibler-Symmetric, which are distance functions and, under some restrictions, generate the Jensen’s equality shown by [1], in this paper denominated Jensen-Equal. On the other hand, [5] and [7] showed that graph theory gives conditions to define a new mea- surable space and, therefore, new distances, in particular, the distance characterized by [2], denominated Geodesic Distance. The interaction of these ideas allow us to define a new distribution, denominated Geodesic Distri- bution which, under graph theory as center and radius of a graph, we can to develop optimization methodologies based in probabilities of attendance. We obtain many applications and the proposal method is very adaptive. To illustrate, we apply this distribution in spatial statistics.

In this paper we show that the space of the so-called regularized functions defined on some rectangle in the plane is a Banach space. Moreover, under suitable hypotheses we give a necessary and sufficient condition for the Nemytskii operator to map the space of regularized functions into itself.

Sea levels are rising around the world, and this is a particular concern along most of the coasts of the United States. A 1989 EPA report shows that sea levels rose 5-6 inches more than the global average along the Mid-Atlantic and Gulf Coasts in the last century. The main reason for this is coastal land subsidence. This sea level rise is considered more as relative sea level rise than global sea level rise. Thus, instead of studying sea level rise globally, this paper describes a statistical approach by using factor analysis of regional sea level rates of change. Unlike physical models and semi-empirical models that attempt to approach how much and how fast sea levels are changing, this methodology allows for a discussion of the factor(s) that statistically affects sea level rates of change, and seeks patterns to explain spatial correlations.

Many real-world problems can be expressed as an instance of the constrained nonlinear optimization problem (CNOP). This problem has a set of constraints specifies the feasible solution space. In the last years several algorithms have been proposed and developed for tackling CNOP. In this paper, we present a cultural algorithm for constrained optimization, which is an adaptation of “Musical Composition Method” or MCM, which was proposed in [33] by Mora et al. We evaluated and analyzed the performance of MCM on five test cases benchmark of the CNOP. Numerical results were compared to evolutionary algorithm based on homomorphous mapping [23], Artificial Immune System [9] and anti-culture population algorithm [39]. The experimental results demonstrate that MCM significantly improves the global performances of the other tested metaheuristics on same of benchmark functions.

Suppose that a vector is produced jointly. We will consider the problem of dividing the cost of production among a group of components. In this paper we characterized a solution through two axioms, s-sensibility and separability. The sensibility is a concept related to the variations of a solution due to slight changes of the cost function and the separability is standard. We study the discrete cost sharing problem. We provide a axiomatic solution.

This paper presents didactic strategies in a ludic tone to explore the methodology of Monte Carlo and analizes the implementations that have been performed in several educational scenarios. These proposals allow us to put into action concepts of probability and statistics in an amusing and attractive way by conducting cooperative “experiments-games” that are based on the use of real and virtual objects. Each strategy is aimed to teachers of high school and teacher training institutes, and also for early stages at University level, in order to be modified, recreated, and enhanced according to the specific areas of application.

In this paper, we consider the problem of one-sided conditional and unconditional interval estimation for the scale and shape parameters in a two-parameter Weibull model. The statistical inference is based upon the pivots advocated in Bain and Engelhardt, the likelihood ratio method and Birnbaum statistic. Simulation results illustrating the performance of these interval estimating methods are discussed and displayed. Empirical point estimate results obtained with the maximum likelihood, generalized moment and generalized probability weighted moment methods are also presented.

There is evidence that signals from financial markets, such as stock indices, interest rates or commodities, have a multifractal nature. In recent years, many efforts have been made to relate the inefficiency of markets with the multifractal characteristics of this corresponding signals. These characteristics are summarized in the knowledge of the spectrum of singularities or multifractal spectrum that relates to the set of singular points of the signal with its corresponding Hausdorff dimension. The novel approach proposed in this paper, to study the dynamics of financial markets, is to analyze the evolution of the set of singular points or Hölder exponents of the series of exchanges, measured daily. We examined the “logarithmic returns” of stock indices from 9 countries in developed markets and 12 belonging to emerging markets from February 2006 to March 2009.The analysis reveals that the temporal variation of the local Hölder exponent point reflects the evolution of the crisis and identifies the historical events which have occurred during this phenomenon, from the minimum values of the Hölder exponent.

This paper describes a general procedure to do Bayesian inference based on the likelihood evaluation of the stochastic general equilibrium models (MEGE) through Markov Chain Monte Carlo methods (MCMC). The proposed methodology involves log linearizing the model, transformed into state space form, then use the Kalman filter to evaluate the likelihood function and finally apply the Metropolis Hastings algorithm to estimate the posterior distribution parameters. Technique is illustrated using the stochastic growth of basic model, considering quarterly data on the Venezuelan economy between the first quarter of (1984) through the third quarter of (2004). The empirical analysis made allows us to conclude that the algorithms used to estimate the model parameters work efficiently and low computational cost, the estimates obtained are consistent, that is, estimates of the predictions adequately reflect the behavior of the product, employment, consumption and investment per capita in the country. The graphs of the estimated histograms show bimodal and skewed distributions.

Under the analysis of signals disturbed by noise, in this paper we propose a working methodology aimed to seize the best estimate of combining Kalman filtering with the characterization that is achieved by applying a multiresolution analysis (MRA) using wavelets. From the standpoint of Kalman filtering this combined procedure is quasi-optimal, but the change to be made allows the simultaneous implementation of a scheme of wavelet denoising; with this decreases the computational cost of applying both procedures separately. Our proposal is to process the signal by successive non-overlapping intervals, combining the process for calculating the optimal filter with a MRA using the Haar wavelet. The method takes advantage of the combined use of both tools (Kalman-Haar) and is free from edge problems related to the signal segmentation.

Tide charts, based upon harmonic analysis, is the general method of choice for predicting water levels. In the shallow waters of the Gulf of Mexico, however, tide charts are woefully inadequate for the prediction of water levels. We have developed a number of models for the prediction of water levels. In this paper we summarize these methods and discuss the development of an axiomatic tool that we use to measure the quality of predictions of water levels in the estuaries and shallow waters of the Gulf of Mexico. This quality measure is based upon the preference rankings of National Ocean Service criteria by experts in the field.

The risk free rate on bonds is a very important quantity that allows calculation of premium values on bonds. This quantity of stochastic nature has been modeled with different degrees of sophistication. This paper reviews the major models utilized in the estimation of the risk free rate and gives an example of the behavior generated by one of these models.

Tide tables are the method of choice for water level predictions in most coastal regions. However, for many locations along the coast of the Gulf of Mexico, tide tables do not meet United States National Ocean Service (NOS) standards. Wind forcing has been recognized as the main variable not included. The performance of the tide tables is particularly poor in shallow embayments. Recent research has shown that Artificial Neural Network (ANN) models including input variables such as previous water levels, tidal forecasts, wind speed, wind direction, wind forecasts and barometric pressure can greatly improve over the tide charts for locations including open coast and deep embayments. In this paper, the ANN modeling technique is applied to a shallow embayment, the station of Rockport, located near Corpus Christi, Texas. The ANN model performance is compared against the NOS tide charts and the persistence model for the years 1997 to 2001. The performance is assessed using NOS criteria including Central Frequency (CF of 15 cm), Maximum Duration of Positive Outliers (MDPO), and Maximum Duration of Negative Outliers (MDNO). Over the study period, the performances of the three models (tide table, persistence, ANN) are respectively CF’s of 85%, 95.8% and 96.9%, MDPOs of 16, 14 and 5.9 hours, and MDNOs of 72.8 hours, 0.6 and 9.5 hours.

One of the most important tasks in image processing problem and machine vision is object recognition, and the success of many proposed methods relies on a suitable choice of algorithm for the segmentation of an image. This paper focuses on how to apply texture operators based on the concept of fractal dimension and cooccurence matrix, to the problem of object recognition and a new method based on fractal dimension is introduced. Several images, in which the result of the segmentation can be shown, are used to illustrate the use of each method and a comparative study of each operator is made.

Ramírez (2001) introduced the generalized robust coloring problem (GRCP), this problem lets solve timetabling problems which considers constraints such as: two events can not be assigned at the same time and there must be at least d days between two events.The GRCP deals with a robust coloring for a given graph with a fixed number of colors, not necessarily the chromatic number and considers the distance between colors as the penalization of complementary edges. It was shown that the problem is NP-complete, so it is necessary to use approximate methods to find good solutions in a reasonable time. This paper presents a hybrid of a genetic algorithm with a local search for cases of 30-120 hours per week; it is shown that for some cases the found solution is optimal and in other cases the solutions are very promising.