A note on the p-adic Kozyrev wavelets basis

We present a basis of p-adic wavelets for Sobolev-type spaces consisting of eigenvectors of certain pseudodifferential operators. Our result extends a well-known result due to S. Kozyrev.

Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces

In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.

A Spectral Gradient Projection Method for the Positive Semi-definite Procrustes Problem

This paper addresses the positive semi-deffnite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-deffnite positive matrices. These kinds of problems appear in many applications such as structure analysis, signal processing, among others. A non-monotone spectral projected gradient algorithm is proposed to obtain a numerical solution for the PSDP. The proposed algorithm employs the Zhang and Hager's non-monotone technique in combination with the Barzilai and Borwein's step size to accelerate convergence. Some theoretical results are presented. Finally, numerical experiments are performed to demonstrate the effectiveness and efficiency of the proposed method, and comparisons are made with other state-of-the-art algorithms.

Periodic solutions for a model of tumor volume with anti-angiogenic periodic treatment

In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give sufficient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.

Boundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences

The main result of this paper is the proof of the boundedness of the Maximal Function T* of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd, on Gaussian variable Lebesgue spaces Lp(.) (γd); under a condition of regularity on p(.) following [5] and [8]. As an immediate consequence of that result, the Lp(.) (γd)-boundedness of the Ornstein-Uhlenbeck semigroup {Tt}t≥ 0 in Rd is obtained. Another consequence of that result is the Lp(.) (γd)-boundedness of the Poisson-Hermite semigroup and the Lp(.) (γd)- boundedness of the Gaussian Bessel potentials of order β > 0.

Modeling the dengue fever transmission in a periodic environment

A mathematical model for dengue fever transmission is analyzed, which incorporates relevant biological and ecological factors: vertical transmission and seasonality in the interaction between the vector (Aedes aegypti females) and the host (human). The existence and uniqueness of a positive disease-free periodic solution is proved; the global stability of the disease-free solution and the effect of periodic migrations of mosquitoes carrying the virus on the transmission of dengue are analyzed utilizing the mathematical definition of the Basic Reproductive Number in periodic environments; finally, it is numerically corroborated with the help of the Basic Reproductive Number that dengue cannot invade the disease-free state if it is less than one and can invade if it is greater than one, however, in both threshold conditions when vertical transmission occurs, the number of infected people and carrier vectors rises, representing a mechanism for the persistence of dengue cases in a community throughout a natural year.

A Glivenko-Cantelli Bootstrap Theorem for the Foster-Greer-Thorbecke Poverty Index

We assume the Foster-Greer-Thorbecke (FGT) poverty index as an empirical process indexed by a particular Glivenko-Cantelli class or collection of functions and define this poverty index as a functional empirical process of the bootstrap type, to show that the outer almost sure convergence of the FGT empirical process is a necessary and sufficient condition for the outer almost sure convergence of the FGT bootstrap empirical process; that is: both processes are asymptotically equivalent respect to this type of convergence.

On L-O-supplemented modules

En esta nota nosotros introducimos los módulos L-⊕-suplementados, una generalizacion de los módulos ⊕-suplementados. Un módulo M se dice I-⊕-suplementado si para cada φ ∈ EndR (M), existe un sumando directo L de M tal que Imφ + L = M y Imφ ∩ L « L. Se demuestra que si M es un módulo I-⊕-suplementado con la condición D3 , entonces cada sumando directo de M es I-⊕-suplementado. Demostramos que si M = M1 ⊕ M2 es I-⊕-suplementado tal que M1 y M2 son proyectivos relativos, entonces M1 y M2 son I-⊕-suplementados. Estudiamos algunos anillos cuyos modulos son I-⊕-suplementados.

Coverings of Configurations, Prime Configurations, and Orbiconfigurations

This exploratory paper considers the notion of a covering of a configuration and G-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot G-cover other configurations, before considering orbiconfigurations. These are a generalized notion of a configuration in the spirit of an orbifold. We derive some specific results as to when configurations are prime as well as considering when an orbiconfiguration is bad - that is, when it cannot be G-covered by a configuration. A number of open questions are posited within.

Ineffable limits of weakly compact cardinals and similar results

It is proved that if an uncountable cardinal κ has an ineffable subset of weakly compact cardinals, then κ is a weakly compact cardinal, and if κ has an ineffable subset of Ramsey (Rowbottom, Jónsson, ineffable or subtle) cardinals, then κ is a Ramsey (Rowbottom, J\'onsson, ineffable or subtle) cardinal.