Sur une classe de structures kählériennes généralisées toriques

Cette thèse concerne le problème de trouver une notion naturelle de «courbure scalaire» en géométrie kählérienne généralisée. L'approche utilisée consiste à calculer l'application moment pour l'action du groupe des difféomorphismes hamiltoniens sur l'espace des structures kählériennes généralisées de type symplectique. En effet, il est bien connu que l'application moment pour la restriction de cette action aux structures kählériennes s'identifie à la courbure scalaire riemannienne. On se limite à une certaine classe de structure kählériennes généralisées sur les variétés toriques notée $DGK_{\omega}^{\mathbb{T}}(M)$ que l'on reconnaît comme étant classifiées par la donnée d'une matrice antisymétrique $C$ et d'une fonction réelle strictement convexe $\tau$ (ayant un comportement adéquat au voisinage de la frontière du polytope moment). Ce point de vue rend évident le fait que toute structure kählérienne torique peut être déformée en un élément non kählérien de $DGK_{\omega}^{\mathbb{T}}(M)$, et on note que cette déformation à lieu le long d'une des classes que R. Goto a démontré comme étant libre d'obstruction. On identifie des conditions suffisantes sur une paire $(\tau,C)$ pour qu'elle donne lieu à un élément de $DGK_{\omega}^{\mathbb{T}}(M)$ et on montre qu'en dimension 4, ces conditions sont également nécessaires. Suivant l'adage «l'application moment est la courbure» mentionné ci-haut, des formules pour des notions de «courbure scalaire hermitienne généralisée» et de «courbure scalaire riemannienne généralisée» (en dimension 4) sont obtenues en termes de la fonction $\tau$. Enfin, une expression de la courbure scalaire riemannienne généralisée en termes de la structure bihermitienne sous-jacente est dégagée en dimension 4. Lorsque comparée avec le résultat des physiciens Coimbra et al., notre formule suggère un choix canonique pour le dilaton de leur théorie.

A Numerically efficient power optimization scheme for coded OFDM systems in achieving minimum frame error rate

Coded OFDM is a transmission technique that is used in many practical communication systems. In a coded OFDM system, source data are coded, interleaved and multiplexed for transmission over many frequency sub-channels. In a conventional coded OFDM system, the transmission power of each subcarrier is the same regardless of the channel condition. However, some subcarrier can suffer deep fading with multi-paths and the power allocated to the faded subcarrier is likely to be wasted. In this paper, we compute the FER and BER bounds of a coded OFDM system given as convex functions for a given channel coder, inter-leaver and channel response. The power optimization is shown to be a convex optimization problem that can be solved numerically with great efficiency. With the proposed power optimization scheme, near-optimum power allocation for a given coded OFDM system and channel response to minimize FER or BER under a constant transmission power constraint is obtained

Hardware implementation of an analog neural nonderivative optimizer

Analog neural systems that can automatically find the minimum value of the outputs of unknown analog systems, described by convex functions, are studied. When information about derivative or gradient are not used, these systems are called analog nonderivative optimizers. An electronic circuit for the analog neural nonderivative optimizer proposed by Teixeira and Zak, and its simulation with software PSPICE, is presented. With the simulation results and hardware implementation of the system, the validity of the proposed optimizer can be verified. These results are original, from the best of the authors knowledge.

Funções convexas e desigualdades: uma abordagem no ensino médio

Pós-graduação em Matemática - IBILCE

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

About t-norms on type-2 fuzzy sets.

Walker et al. defined two families of binary operations on M (set of functions of [0,1] in [0,1]), and they determined that, under certain conditions, those operations are t-norms (triangular norm) or t-conorms on L (all the normal and convex functions of M). We define binary operations on M, more general than those given by Walker et al., and we study many properties of these general operations that allow us to deduce new t-norms and t-conorms on both L, and M.

Contribución al estudio de las negaciones, autocontradicción, t-normas y t-conormas en los conjuntos borrosos de tipo 2

Los conjuntos borrosos de tipo 2 (T2FSs) fueron introducidos por L.A. Zadeh en 1975 [65], como una extensión de los conjuntos borrosos de tipo 1 (FSs). Mientras que en estos últimos el grado de pertenencia de un elemento al conjunto viene determinado por un valor en el intervalo [0, 1], en el caso de los T2FSs el grado de pertenencia de un elemento es un conjunto borroso en [0,1], es decir, un T2FS queda determinado por una función de pertenencia μ : X → M, donde M = [0, 1][0,1] = Map([0, 1], [0, 1]), es el conjunto de las funciones de [0,1] en [0,1] (ver [39], [42], [43], [61]). Desde que los T2FSs fueron introducidos, se han generalizado a dicho conjunto (ver [39], [42], [43], [61], por ejemplo), a partir del “Principio de Extensión” de Zadeh [65] (ver Teorema 1.1), muchas de las definiciones, operaciones, propiedades y resultados obtenidos en los FSs. Sin embargo, como sucede en cualquier área de investigación, quedan muchas lagunas y problemas abiertos que suponen un reto para cualquiera que quiera hacer un estudio profundo en este campo. A este reto se ha dedicado el presente trabajo, logrando avances importantes en este sentido de “rellenar huecos” existentes en la teoría de los conjuntos borrosos de tipo 2, especialmente en las propiedades de autocontradicción y N-autocontradicción, y en las operaciones de negación, t-norma y t-conorma sobre los T2FSs. Cabe destacar que en [61] se justifica que las operaciones sobre los T2FSs (Map(X,M)) se pueden definir de forma natural a partir de las operaciones sobre M, verificando las mismas propiedades. Por tanto, por ser más fácil, en el presente trabajo se toma como objeto de estudio a M, y algunos de sus subconjuntos, en vez de Map(X,M). En cuanto a la operación de negación, en el marco de los conjuntos borrosos de tipo 2 (T2FSs), usualmente se emplea para representar la negación en M, una operación asociada a la negación estándar en [0,1]. Sin embargo, dicha operación no verifica los axiomas que, intuitivamente, debe verificar cualquier operación para ser considerada negación en el conjunto M. En este trabajo se presentan los axiomas de negación y negación fuerte en los T2FSs. También se define una operación asociada a cualquier negación suprayectiva en [0,1], incluyendo la negación estándar, y se estudia, junto con otras propiedades, si es negación y negación fuerte en L (conjunto de las funciones de M normales y convexas). Además, se comprueba en qué condiciones se cumplen las leyes de De Morgan para un extenso conjunto de pares de operaciones binarias en M. Por otra parte, las propiedades de N-autocontradicción y autocontradicción, han sido suficientemente estudiadas en los conjuntos borrosos de tipo 1 (FSs) y en los conjuntos borrosos intuicionistas de Atanassov (AIFSs). En el presente trabajo se inicia el estudio de las mencionadas propiedades, dentro del marco de los T2FSs cuyos grados de pertenencia están en L. En este sentido, aquí se extienden los conceptos de N-autocontradicción y autocontradicción al conjunto L, y se determinan algunos criterios para verificar tales propiedades. En cuanto a otras operaciones, Walker et al. ([61], [63]) definieron dos familias de operaciones binarias sobre M, y determinaron que, bajo ciertas condiciones, estas operaciones son t-normas (normas triangulares) o t-conormas sobre L. En este trabajo se introducen operaciones binarias sobre M, unas más generales y otras diferentes a las dadas por Walker et al., y se estudian varias propiedades de las mismas, con el objeto de deducir nuevas t-normas y t-conormas sobre L. ABSTRACT Type-2 fuzzy sets (T2FSs) were introduced by L.A. Zadeh in 1975 [65] as an extension of type-1 fuzzy sets (FSs). Whereas for FSs the degree of membership of an element of a set is determined by a value in the interval [0, 1] , the degree of membership of an element for T2FSs is a fuzzy set in [0,1], that is, a T2FS is determined by a membership function μ : X → M, where M = [0, 1][0,1] is the set of functions from [0,1] to [0,1] (see [39], [42], [43], [61]). Later, many definitions, operations, properties and results known on FSs, have been generalized to T2FSs (e.g. see [39], [42], [43], [61]) by employing Zadeh’s Extension Principle [65] (see Theorem 1.1). However, as in any area of research, there are still many open problems which represent a challenge for anyone who wants to make a deep study in this field. Then, we have been dedicated to such challenge, making significant progress in this direction to “fill gaps” (close open problems) in the theory of T2FSs, especially on the properties of self-contradiction and N-self-contradiction, and on the operations of negations, t-norms (triangular norms) and t-conorms on T2FSs. Walker and Walker justify in [61] that the operations on Map(X,M) can be defined naturally from the operations onMand have the same properties. Therefore, we will work onM(study subject), and some subsets of M, as all the results are easily and directly extensible to Map(X,M). About the operation of negation, usually has been employed in the framework of T2FSs, a operation associated to standard negation on [0,1], but such operation does not satisfy the negation axioms on M. In this work, we introduce the axioms that a function inMshould satisfy to qualify as a type-2 negation and strong type-2 negation. Also, we define a operation on M associated to any suprajective negation on [0,1], and analyse, among others properties, if such operation is negation or strong negation on L (all normal and convex functions of M). Besides, we study the De Morgan’s laws, with respect to some binary operations on M. On the other hand, The properties of self-contradiction and N-self-contradiction have been extensively studied on FSs and on the Atanassov’s intuitionistic fuzzy sets (AIFSs). Thereon, in this research we begin the study of the mentioned properties on the framework of T2FSs. In this sense, we give the definitions about self-contradiction and N-self-contradiction on L, and establish the criteria to verify these properties on L. Respect to the t-norms and t-conorms, Walker et al. ([61], [63]) defined two families of binary operations on M and found that, under some conditions, these operations are t-norms or t-conorms on L. In this work we introduce more general binary operations on M than those given by Walker et al. and study which are the minimum conditions necessary for these operations satisfy each of the axioms of the t-norm and t-conorm.

Epiconvergence D'une Suite De Sommes En Niveaux De Fonctions Convexes

We consider the problem of minimizing the max of two convex functions from both approximation and sensitivity point of view.This lead up to study the epiconvergence of a sequence of level sums of convex functions and the related dual problems.

Motzkin Decomposable Sets

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. We have provided several characterizations of the larger class of closed convex sets, Motzkin decomposable, in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed. Another result establishes that a closed convex set is Motzkin decomposable if and only if the set of extreme points of its intersection with the linear subspace orthogonal to its lineality is bounded. We characterize the class of the extended functions whose epigraphs are Motzkin decomposable sets showing, in particular, that these functions attain their global minima when they are bounded from below. Calculus of Motzkin decomposable sets and functions is provided.

Duality in Constrained DC-Optimization via Toland’s Duality Approach

2000 Mathematics Subject Classification: 90C48, 49N15, 90C25

Dense Subdifferentiability and Trustworthiness for Arbitrary Subdifferentials

2000 Mathematics Subject Classification: 49J52, 49J50, 58C20, 26B09.

A holistic attempt to predicating excess aftermarket returns of IPOs over a 90-day period post IPO

Double Degree

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

Sensing Cloud Optimization applied to a non-convex constrained economical dispatch

Conferência: 39th Annual Conference of the IEEE Industrial-Electronics-Society (IECON) - NOV 10-14, 2013

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.