Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition

We study the initial-boundary value problem for a nonlinear wave equation given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u) , 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t), u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I under a certain local Lipschitzian condition on f, a global existence and uniqueness theorem is proved. The proof is based on the paper [10] associated to a contraction mapping theorem and standard arguments of density. In Part} 2, under more restrictive conditions it is proved that the solution u(t) and its derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page

The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.Comment: 18 page

Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type

This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy will blow up in finite time. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical resultsComment: 2

Characterization of O-glycan binding lectin from the red alga Hydropuntia eucheumatoides

The red alga, Hydropuntia eucheumatoides is one of the algal genera from which agar is commercially extracted, and is the main source of agar in the world. The lectin HEL from the red alga H. eucheumatoides was isolated by a combination of aqueous ethanol extraction, ethanol precipitation, ion exchange and filtration chromatography. Lectin gave a single band with molecular mass of 17,000 Da in both non-reducing and reducing SDS-PAGE conditions, therefore lectin exists in monomeric form. The hemagglutination activities of HEL were stable over a wide range of pH from 3 to 10, temperature up 60 oC and not affected by either the presence of EDTA or addition of divalent cations, indicating that lectin requires no metal for biological activity. The hemagglutination activities of HEL were not inhibited by monosaccharides and glycoproteins, D-glucose, D-mannose, D-galactose, D-xylose, N-acety-D-mannosamine, transferin, fetuin and yeast mannan, but strongly inhibited by monosaccharides containing  acetamido groups at equatorial C2 position, such as N-acetyl-galactosamine, N-acetyl-glucosamine, N-acetyl-neuraminic acid and glycoprotein porcine stomach mucin bearing O-glycans. Thus, lectin is specific for O-glycans and  may recognize the sequences GalNAcαSer/Thr, GalNAc(α1-3)[Fuc(α1-2)]Gal(β1-4)GlcNAc(β1-3)GalNAc- and GluNAc(α1-4)Gal- under interacting with the acetamido groups at equatorial C2 position of the terminal sugar residues in oligosaccharide structures of O-glycans. The red alga H. eucheumatoides could promise to be a source of valuable lectins for application in biochemistry and biomedicine

Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil

This paper is concerned with the linear ODE in the form $y'(t)=\lambda\rho(t)y(t)+b(t)$, $\lambda <0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $\rho(t)$, a linear drift in the coefficient $b(t)$ involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given.Comment: 18 page

FACTORS AFFECTING CAN THO RESIDENTS’ INTENTION TO VISIT DALAT IN THE COVID-19 ERA

The paper examines the factors affecting the intentions of Can Tho residents to travel to Dalat as the COVID-19 pandemic is gradually brought under control. The data were collected from a survey of 213 Can Tho residents and analyzed with Cronbach’s alpha, exploratory factor analysis, confirmatory factor analysis, and structural equation modeling. The results show that the intentions of Can Tho residents to travel to Dalat depend on four factors: (1) attitude toward Dalat tourism, (2) subjective norms, (3) perceived behavioral controls, and (4) perceived health risk. In particular, the attitudinal factor significantly influences Dalat travel intentions. Based on the research results, the article proposes four recommendations for managers, corresponding to the four influencing factors, to increase the intentions of Can Tho residents to travel to Dalat in the COVID-19 era

Exploiting No-Regret Algorithms in System Design

We investigate a repeated two-player zero-sum game setting where the column player is also a designer of the system, and has full control on the design of the payoff matrix. In addition, the row player uses a no-regret algorithm to efficiently learn how to adapt their strategy to the column player's behaviour over time in order to achieve good total payoff. The goal of the column player is to guide her opponent to pick a mixed strategy which is favourable for the system designer. Therefore, she needs to: (i) design an appropriate payoff matrix $A$ whose unique minimax solution contains the desired mixed strategy of the row player; and (ii) strategically interact with the row player during a sequence of plays in order to guide her opponent to converge to that desired behaviour. To design such a payoff matrix, we propose a novel solution that provably has a unique minimax solution with the desired behaviour. We also investigate a relaxation of this problem where uniqueness is not required, but all the minimax solutions have the same mixed strategy for the row player. Finally, we propose a new game playing algorithm for the system designer and prove that it can guide the row player, who may play a \emph{stable} no-regret algorithm, to converge to a minimax solution