Dynamical Behavior of a stochastic SIRS epidemic model

In this paper we study the Kernack - MacKendrick model under telegraph noise. The telegraph noise switches at random between two SIRS models. We give out conditions for the persistence of the disease and the stability of a disease free equilibrium. We show that the asymptotic behavior highly depends on the value of a threshold $\lambda$ which is calculated from the intensities of switching between environmental states, the total size of the population as well as the parameters of both SIRS systems. According to the value of $\lambda$, the system can globally tend towards an endemic case or a disease free case. The aim of this work is also to describe completely the omega-limit set of all positive solutions to the model. Moreover, the attraction of the omega-limit set and the stationary distribution of solutions will be pointed out.Comment: 16 page

Research on the Application of E-commerce to Small and Medium Enterprises (SMEs): the Case of India

SMEs account for a large proportion and play an important role in the development of each country in the world, including India. The globalization will bring many advantages for enterprises however SMEs will face fierce competition at the local, national and International level. In order to maintain and promote the important role of SMEs in the context of increased competition, SMEs have to change and adopt new technologies. E-commerce and digital technologies are bringing opportunities to help SMEs improve their competitiveness, narrow the gap with big enterprises thanks to their fairness and flexibility of the digital business environment.       According to UNIDO (2017), India is one of the countries successfully applying e-commerce to SMEs. Contributing to this success is the important role of the Indian government. Therefore, this paper focuses on researching the application of e-commerce to SMEs in terms of the role of government in promoting and creating an ecosystem for SMEs and e-commerce development

Luby Transform Coding Aided Iterative Detection for Downlink SDMA Systems

A Luby Transform (LT) coded downlink Spatial Division Multiple Access (SDMA) system using iterative detection is proposed, which invokes a low-complexity near-Maximum-Likelihood (ML) Sphere Decoder (SD). The Ethernet-based Internet section of the transmission chain inflicts random packet erasures, which is modelled by the Binary Erasure Channel (BEC), which the wireless downlink imposes both fading and noise. A novel log-Likelihood Ratio based packet reliability metric is used for identifying the channel-decoded packets, which are likely to be error-infested. Packets having residual errors must not be passed on to the KT decoder for the sake of avoiding LT-decoding –induced error propagation. The proposed scheme is capable of maintaining an infinitesimally low packet error ratio in the downlink of the wireless Internet for Eb/n0 values in excess of about 3dB

Local harmonic approaches with approximate cranking operators

Methods of large amplitude collective motion in the adiabatic limit are examined with a special emphasis on conservation laws. We show that the restriction to point transformations, which is a usual assumption of the adiabatic time-dependent mean-field theory, needs to be lifted. In order to facilitate the application of large amplitude collective motion techniques, we examine the possibility of representing the RPA normal-mode coordinates by linear combinations of a limited number of one-body operators. We study the pairing-plus-quadrupole model of Baranger and Kumar as an example, and find that such representations exist in terms of operators that are state-dependent in a characteristic manner

The software for oceanographic data management: VODC for PC 2.0

To manage and process a large amount of oceanographic data, users must have powerful tools that simplify these tasks. The VODC for PC is software designed to assist in managing oceanographic data. It based on 32 bits Windows operation system and used Microsoft Access database management system. With VODC for PC users can update data simply, convert to some international data formats, combine some VODC databases to one, calculate average, min, max fields for some types of data, check for valid data

Φ34\Phi^4_3 measures on compact Riemannian 33-manifolds

We construct the $\Phi^4_3$ measure on an arbitrary 3-dimensional compact Riemannian manifold without boundary as an invariant probability measure of a singular stochastic partial differential equation. Proving the nontriviality and the covariance under Riemannian isometries of that measure gives for the first time a non-perturbative, non-topological interacting Euclidean quantum field theory on curved spaces in dimension 3. This answers a longstanding open problem of constructive quantum field theory on curved 3 dimensional backgrounds. To control analytically several Feynman diagrams appearing in the construction of a number of random fields, we introduce a novel approach of renormalization using microlocal and harmonic analysis. This allows to obtain a renormalized equation which involves some universal constants independent of the manifold. We also define a new vectorial Cole-Hopf transform which allows to deal with the vectorial $\Phi^4_3$ model where $\Phi$ is now a bundle valued random field. In a companion paper, we develop in a self-contained way all the tools from paradifferential and microlocal analysis that we use to build in our manifold setting a number of analytic and probabilistic objects.Comment: references added, Section 6.2 adde