Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients.     

Complex impure systems: Sheaves,freeways, and chains

Fundamental to the approach of Complex Impure Systems is the definition of the concept of an s‐impure set as a set of perceptual beliefs or denotative significances (relative beings) of material and/or energetic real objects (absolute beings). But any Subject not only the subject S perceives objects O as significances, and he perceives the existing relations between these significances or, alternatively, he infers them. The study of these relations, conceived not as a singular relation between singular objects, but as sheaves of relations in both directions and forming relational freeways, will be studied here. In this work, we approach the structure of the system, from a synchronous point of view, as a first approach to this class of systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 387–400, 2016     

A New Method for Enumerating Independent Sets of a Fixed Size in General Graphs

We develop a new method for enumerating independent sets of a fixed size in general graphs, and we use this method to show that a conjecture of Engbers and Galvin [7] holds for all but finitely many graphs. We also use our method to prove special cases of a conjecture of Kahn [13]. In addition, we show that our method is particularly useful for computing the number of independent sets of small sizes in general regular graphs and Moore graphs, and we argue that it can be used in many other cases when dealing with graphs that have numerous structural restrictions.     

Forecasting portfolio returns using weighted fuzzy time series methods

We propose using weighted fuzzy time series (FTS) methods to forecast the future performance of returns on portfolios. We model the uncertain parameters of the fuzzy portfolio selection models using a possibilistic interval-valued mean approach, and approximate the uncertain future return on a given portfolio by means of a trapezoidal fuzzy number. Introducing some modifications into the classical models of fuzzy time series, based on weighted operators, enables us to generate trapezoidal numbers as forecasts of the future performance of the portfolio returns. This fuzzy forecast makes it possible to approximate both the expected return and the risk of the investment through the value and ambiguity of a fuzzy number.We incorporate our proposals into classical fuzzy time series methods and analyze their effectiveness compared with classical weighted fuzzy time series models, using historical returns on assets from the Spanish stock market. When our weighted FTS proposals are used to point-wise forecast portfolio returns the one-step ahead accuracy is improved, also with respect to non-fuzzy forecasting methods.     

Score sets in oriented 3-partite graphs

Let D(U, V, W) be an oriented 3-partite graph with |U|=p, |V|=q and |W|= r. For any vertex x in D(U, V, W), let d x and d-x be the outdegree and indegree of x respectively. Define aui (or simply ai) = q r d ui - d-ui, bvj(or simply bj) = p r d vj - d-vj and Cwk (or simply ck) = p q d wk - d-wk as the scores of ui in U, vj in V and wk in Wrespectively. The set A of distinct scores of the vertices of D(U, V, W) is called its score set. In this paper, we prove that if a1 is a non-negative integer, ai(2≤i≤n - 1) are even positive integers and an is any positive integer, then for n≥3, there exists an oriented 3-partite graph with the score set A = {a1,2∑i=1 ai,…,n∑i=1 ai}, except when A = {0,2,3}. Some more results for score sets in oriented 3-partite graphs are obtained.     

QSAR Modeling of Large Heterogeneous Sets of Molecules

Abstract

In aquatic toxicology, QSAR models are generally designed for chemicals presenting the same mode of toxic action. Their proper use provides good simulation results. Problems arise when the mechanism of toxicity of a chemical is not clearly identified. Indeed, in that case, the inappropriate application of a specific QSAR model can lead to a dramatic error in the toxicity estimation. With the advent of powerful computers and easy access to them, and the introduction of soft modeling and artificial intelligence in SAR and QSAR, radically different models, designed from large non-congeneric sets of chemicals have been proposed. Some of these new QSAR models are reviewed and their originality, advantages, and limitations are stressed.     

Gaussian basis sets for molecular applications

The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom‐centered, energy‐optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design. © 2012 Wiley Periodicals, Inc.     

Characterization and computation of control invariant sets for linear impulsive control systems

Impulsive control systems are suitable to describe and control a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they evolve freely in-between impulsive actions, which makes it difficult to guarantee its permanence in a given state-space region. In this work, we develop a method for characterizing and computing approximations to the maximal control invariant sets for linear impulsive control systems, which can be explicitly used to formulate a set-based model predictive controller. We approach this task using a tractable and non-conservative characterization of the admissible state sets, namely the states whose free response remains within given constraints, emerging from a spectrahedron representation of such sets for systems with rational eigenvalues. The so-obtained impulsive control invariant set is then explicitly used as a terminal set of a predictive controller, which guarantees the feasibly asymptotic convergence to a target set containing the invariant set. Necessary conditions under which an arbitrary target set contains an impulsive control invariant set (and moreover, an impulsive control equilibrium set) are also provided, while the controller performance are tested by means of two simulation examples.     

Continuous functions with impermeable graphs

We construct a Hölder continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We conclude that this function has impermeable graph—one of the key concepts introduced in this paper—and we present further examples of functions both with permeable and impermeable graphs. Moreover, we show that typical (in the sense of Baire category) continuous functions have permeable graphs. The first example function is subsequently used to construct an example of a continuous function on the plane which is intrinsically Lipschitz continuous on the complement of the graph of a Hölder continuous function with impermeable graph, but which is not Lipschitz continuous on the plane. As another main result, we construct a continuous function on the unit interval which coincides in a set of Hausdorff dimension 1 with every function of total variation smaller than 1 which passes through the origin.     

分担集合的亚纯函数的正规性*

本文研究了亚纯函数及其 k 阶导数分担两个不同集合的亚纯函数族的正规性问题.证明了如下结论: 设 F 是平面区域 D上的亚纯函数族, 其中函数的零点重数至少为 k+1. 设S₁, S₂是两个集合,且|S₁|=m, |S₂|=n, S₂ ≠ 0, 这里m, n是正整数. 如果任意f(z) ∈ F,满足f(z) ∈ S₁?f^(k)(z) ∈ S₂, z ∈ D, 则 F 在区域 D 上正规.本文的研究结果是对刘晓俊和庞学诚[刘晓俊, 庞学诚. 分担值与正规族 [J].数学学报(中文版),2007, 50(2):409--412] 2007年研究结果的改进.