Consider the singular perturbation problem for εu(t; ε) + u(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε) ds+ f(t; ε) , where t ≥ 0, u(0; ε) = u0(ε), u (0; ε) = u1(ε), and w(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t) , t ≥ 0 , w(0) = w0 , in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear opera...

In this paper, we study ε-generalized weak s...

AIMS The aim of this study was to establish the degree of structural and functional adaptations in the left (LA) and right atria (RA) in elite male athletes engaged in 'high dynamic : high static' (HDHS) and 'low dynamic : high static' (LDHS) sporting disciplines compared with sedentary controls. METHODS AND RESULTS Eighteen male, elite HDHS athletes (13 boxers and 7 triathletes), 18 male, el...

We consider the problem of maximizing the secure connectivity in wireless ad hoc networks, and analyze complexity of the postdeployment key establishment process constrained by physical layer properties such as connectivity, energy consumption and interference. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing ...

Maximum-a-Posteriori (MAP) inference lies at the heart of Graphical Models and Structured Prediction. Despite the intractability of exact MAP inference, approximate methods based on LP relaxations have exhibited superior performance across a wide range of applications. Yet for problems involving large output domains (i.e., the state space for each variable is large), standard LP relaxations can...

We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in [0, 1]. Similar notions have been considered for kernels; we extend them to more general types of ranges. We then consider approximations of these range spaces through ε-nets and εsamples (aka ε-approximations). We characterize when size ...

There are many chemical molecules whose names are Cannabigerol (CBG), cannabidol (CBD), cannabichromene (CBC), tetrahydrocannabivarin (THCV), cannabigerovarinic acid (CBGV) and cannabidiolic acid (CBDA) derived from Marijuana. Theoretical methods were used to compare the chemical and biological activities of the six major molecules. Molecules were compared with their chemical activities using m...