Abstract We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet ...specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric colorable seeds. Consequently, we achieve a comprehensive characterization of ( n − 1 ) (n-1) -dimensional PL spheres with n + 4 n+4 vertices that possess a maximal Buchstaber number. A primary focus of this research is the fundamental categorization of non-singular complete toric varieties of Picard number 4. This classification serves as a valuable tool for addressing questions related to toric manifolds of Picard number 4. Notably, we have determined which of these manifolds satisfy equality within an inequality regarding the number of minimal components in their rational curve space. This addresses a question posed by Chen, Fu, and Hwang in 2014 for this specific case.
We prove that all homology 3-spheres are J 4 J_4 -equivalent, i.e. that any homology 3-sphere can be obtained from one another by twisting one of its Heegaard splittings by an element of the mapping ...class group acting trivially on the fourth nilpotent quotient of the fundamental group of the gluing surface. We do so by exhibiting an element of J 4 J_4 , the fourth term of the Johnson filtration of the mapping class group, on which (the core of) the Casson invariant takes the value 1 1 . In particular, this provides an explicit example of an element of J 4 J_4 that is not a commutator of length 2 2 in the Torelli group.
El manuscrito se centra en el desarrollo de un software para optimizar la producción de tilapias, abordando aspectos como el crecimiento, costo y rentabilidad. Utilizando herramientas tecnológicas ...avanzadas, se pretende facilitar la gestión de datos para los piscicultores, permitiendo procesos más eficientes, económicos y precisos. Los factores clave incluyen el peso, la temperatura, el crecimiento absoluto, el crecimiento térmico de los peces, y proyecciones mensuales de costos, producción y rentabilidad. El software, desarrollado en Java y utilizando la plataforma Eclipse, busca equilibrar agilidad y precisión en el tratamiento de datos. El trabajo se apoya en la revisión bibliográfica y entrevistas con piscicultores. Se emplea un enfoque de análisis de componentes principales y correlación de Pearson para asociar variables relevantes. Se evalúa la aplicación mediante datos históricos y pruebas piloto, ajustando funcionalidades para garantizar resultados fiables. Se destaca la importancia de interfaces amigables para usuarios no expertos en tecnología y se propone la expansión a aplicaciones móviles y la adaptación a otras especies de interés zootécnico.
Abstract Due to the fast growth of data that are measured on a continuous scale, functional data analysis has undergone many developments in recent years. Regression models with a functional response ...involving functional covariates, also called "function-on-function", are thus becoming very common. Studying this type of model in the presence of heterogeneous data can be particularly useful in various practical situations. We mainly develop in this work a Function-on-Function Mixture of Experts (FFMoE) regression model. Like most of the inference approach for models on functional data, we use basis expansion (B-splines) both for covariates and parameters. A regularized inference approach is also proposed, it accurately smoothes functional parameters in order to provide interpretable estimators. Numerical studies on simulated data illustrate the good performance of FFMoE as compared with competitors. Usefullness of the proposed model is illustrated on two data sets: the reference Canadian weather data set, in which the precipitations are modeled according to the temperature, and a Cycling data set, in which the developed power is explained by the speed, the cyclist heart rate and the slope of the road.
Further Study of 2-to-1 Mappings Over F 2 n Li, Kangquan; Mesnager, Sihem; Qu, Longjiang
IEEE transactions on information theory,
6/2021, Volume:
67, Issue:
6
Journal Article
The year's finest mathematical writing from around the world
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James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world-with glimpses at science, philosophy, music, art, and even crocheting. And there's much, much more.
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The aim of this paper is to prove new exact controllability properties of systems described by perturbations of the classical Kirchhoff plate equation. We first consider systems described by an ...abstract plate equation with a bounded control operator. The generator of these systems is perturbed by bounded operators which are not necessarily compact, thus not falling in the range of application of compactness-uniqueness arguments. Our first main result is abstract and can be informally stated as follows: if the system described by the corresponding unperturbed abstract wave equation, with the same control operator, is exactly controllable (in some time), then the considered perturbed plate system is exactly controllable in arbitrarily small time. The employed methodology is based, in particular, on frequency-dependent Hautus type tests for systems with skew-adjoint operators. When applied to systems described by the classical Kirchhoff equations, our abstract results, combined with some elliptic Carleman-type estimates, yield exact controllability in arbitrarily small time, provided that the system described by the wave equation in the same spatial domain and with the same control operator is exactly controllable. The same abstract results can be used to prove the exact controllability of the system obtained by linearizing the von Kármán plate equation around a real analytic stationary state. This leads, via a fixed-point method, to our second main result: the nonlinear system described by the von Kármán plate equations is locally exactly controllable around any stationary state defined by a real analytic function.
L'objectif de cet article est de prouver de nouvelles propriétés de contrôlabilité exacte de systèmes décrits par des perturbations de l'équation des plaques de Kirchhoff . Nous considérons d'abord les systèmes décrits par une équation de plaque abstraite avec un opérateur de contrôle borné. Le générateur de ces systèmes est perturbé par des opérateurs bornés qui ne sont pas nécessairement compacts, donc hors du domaine d'application des arguments compacité-unicité. Notre premier résultat principal est abstrait et peut être énoncé de manière informelle comme suit : si le système décrit par l'équation d'onde abstraite non perturbée correspondante, avec le même opérateur de contrôle, est exactement contrôlable (dans un certain temps), alors le système de plaques perturbées considéré est exactement contrôlable en un temps arbitrairement petit. La méthodologie employée est basée, en particulier, sur des tests de type Hautus dépendants de la fréquence pour des systèmes avec des opérateurs anti-adjoints. Lorsqu'ils sont appliqués à des systèmes décrits par les équations classiques de Kirchhoff, nos résultats abstraits, combinés à certaines estimations elliptiques de type Carleman, donnent une contrôlabilité exacte en un temps arbitrairement petit, à condition que le système décrit par l'équation d'onde dans le même domaine spatial et avec le même l'opérateur de contrôle soit exactement contrôlable. Les mêmes résultats abstraits peuvent être utilisés pour prouver la contrôlabilité exacte du système obtenu en linéarisant l'équation de la plaque de von Kármán autour d'un état stationnaire analytique réel. Ceci conduit, via une méthode de pont fixe, à notre second résultat principal : le système non linéaire décrit par les équations de von Kármán est localement exactement contrôlable autour de tout état stationnaire défini par une fonction analytique réelle.
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The ...proof uses results about normal forms of hyperbolic transseries in 19.
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