Trigonometric Series with a Generalized Monotonicity Condition

In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.

Almost sure, L1-and L2-growth behavior of supercritical multi-type continuous state and continuous time branching processes with immigration

Under a first order moment condition on the immigration mechanism,we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration(CBI process)converges almost surely.If an x log(x)moment condition on the branching mechanism does not hold,then the limit is zero.If this x log(x)moment condition holds,then we prove L1 convergence as well.The projection of the limit on any left non-Perron eigenvector of the branching mean matrix is vanishing.If,in addition,a suitable extra power moment condition on the branching mechanism holds,then we provide the correct scaling for the projection of a CBI process on certain left non-Perron eigenvectors of the branching mean matrix in order to have almost sure and L1 limit.Moreover,under a second order moment condition on the branching and immigration mechanisms,we prove L2 convergence of an appropriately scaled process and the above-mentioned projections as well.A representation of the limits is also provided under the same moment conditions.

Modeling the impact of quarantine during an outbreak of Ebola virus disease

The quarantine of people suspected of being exposed to an infectious agent is one of the most basic public health measure that has historically been used to combat the spread of communicable diseases in human communities.This study presents a new deterministic model for assessing the population-level impact of the quarantine of individuals suspected of being exposed to disease on the spread of the 2014e2015 outbreaks of Ebola viral disease.It is assumed that quarantine is imperfect(i.e.,individuals can acquire infection during quarantine).In the absence of quarantine,the model is shown to exhibit global dynamics with respect to the disease-free and its unique endemic equilibrium when a certain epidemiological threshold(denoted byR 0)is either less than or greater than unity.Thus,unlike the full model with imperfect quarantine(which is known to exhibit the phenomenon of backward bifurcation),the version of the model with no quarantine does not undergo a backward bifurcation.Using data relevant to the 2014e2015 Ebola transmission dynamics in the three West African countries(Guinea,Liberia and Sierra Leone),uncertainty analysis of the model show that,although the current level and effectiveness of quarantine can lead to significant reduction in disease burden,they fail to bring the associated quarantine reproduction number(R Q0)to a value less than unity(which is needed to make effective disease control or elimination feasible).This reduction of R Q0 is,however,very possible with a modest increase in quarantine rate and effectiveness.It is further shown,via sensitivity analysis,that the parameters related to the effectiveness of quarantine(namely the parameter associated with the reduction in infectiousness of infected quarantined individuals and the contact rate during quarantine)are the main drivers of the disease transmission dynamics.Overall,this study shows that the singular implementation of a quarantine intervention strategy can lead to the effective control or elimination of Ebola viral disease in a community if its coverage and effectiveness levels are high enough.

Lower bounds on the minimum distance in Hermitian one-point differential codes

Korchmáros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2( H ) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ(D, mP ) where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2( H ) and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ(D, mP). Further improvements from G(P) were obtained by Korchmáros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.