New convolutions weighted by Hermite functions and their applications

We introduce eight new convolutions weighted by multi-dimensional Hermite functions, prove two Young-type inequalities, and exhibit their applications in different subjects. One application consists in the study of the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are here obtained.publishe

On integral operators and equations generated by cosine and sine Fourier transforms

In this paper, we study some properties of a class of integral operators that depends on the cosine and sine Fourier transforms. In particular, we will exhibit properties related with their invertibility, the spectrum, Parseval type identities and involutions. Moreover, a new convolution will be proposed and consequent integral equations will be also studied in detail. Namely, we will characterize the solvability of two integral equations which are associated with the integral operator under study. Moreover, under appropriate conditions, the unique solutions of those two equations are also obtained in a constructive way.publishe

Doubly Stochastic Yule Cascades (Part I): The explosion problem in the time-reversible case

Motivated by the probabilistic methods for nonlinear differential equations introduced by McKean (1975) for the Kolmogorov-Petrovski-Piskunov (KPP) equation, and by Le Jan and Sznitman (1997) for the incompressible Navier-Stokes equations, we identify a new class of stochastic cascade models, referred to as {\it doubly stochastic Yule cascades}. We establish non-explosion criteria under the assumption that the randomization of Yule intensities from generation to generation is by an ergodic time-reversible Markov chain. In addition to the cascade models that arise in the analysis of certain deterministic nonlinear differential equations, this model includes the multiplicative branching random walks, the branching Markov processes, and the stochastic generalizations of the percolation and/or cell aging models introduced by Aldous and Shields (1988) and independently by Athreya (1985)

Prevalence and risks of fascioliasis among adult cohorts in Binh Dinh and Quang Ngai provinces-central Viet Nam

Fascioliasis (liver fluke disease) has raised significant public health concerns in the 15 regional provinces of Central Vietnam, accounting for 93% of the national incidence of the disease. No control measures to date have proven effective. Annual reports show increasing incidence of fascioliasis but they are incomplete. This cross-sectional study was conducted to identify the prevalence of fascioliasis and to describe its associated risks in three communes in Central Vietnam. 500 human blood samples were examined (ELISA); and a survey of knowledge, attitude and practice (KAP) was conducted for 600 randomly selected adults per commune. The findings suggest that overall seroprevalence was 7.75% (95% CI 6.54-9.16%). Among the infected cases, people aged from 18-59 years (85.6%) and farmers (68.0%) accounted for majority of infection. Less than half of participants in all three communes (24.6% - 46.0%) knew the causes of fascioliasis; and considerable proportions ate improperly boiled vegetables (28.2-33.8%), drank unboiled water (23.5-42.5%), and did not own a household toilet (14.2-20.5%). Relatively high prevalence and risks of fascioliasis were found in Central Vietnam, supporting the need for comprehensive intervention measures including selective treatment, health education, and multisectoral approaches to reduce the morbidity associated with fascioliasis and thus improve the health status of the people

The Higgs Sector of the Minimal 3 3 1 Model Revisited

The mass spectrum and the eigenstates of the Higgs sector of the minimal 3 3 1 model are revisited in detail. There are discrepancies between our results and previous results by another author.Comment: 20 pages, latex, two figures. One note and one reference are adde

Heisenberg uncertainty principles for an oscillatory integral operator

The main aim of this work is to obtain Heisenberg uncertainty principles for a specific oscillatory integral operator which representatively exhibits different parameters on their sine and cosine phase components. Additionally, invertibility theorems, Parseval type identities and Plancherel type theorems are also obtained

On a Class of Integral Equations Involving Kernels of Cosine and Sine Type

We consider a class of integral equations characterized by kernels of cosine and sine type and study their solvability. Moreover, we analyse the integral operator T, which is generating those equations, by identifying its characteristic polynomial, characterizing its invertibility, spectrum, Parseval type identity and involution properties. Additionally, a new convolution is here introduced, associated with T, for which we deduce a corresponding factorization property