‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

Dynamic Analysis of an axially moving cable with time dependent tension and velocity isstudied in this paper. Tension force and the moving speed are assumed to be harmonic.It is found that there exists a specific value of speed in which natural frequency of the system approacheszero. This specific speed for such a critical condition is called critical speed and it will be proved thatincreasing ...

This article discusses a latent variable model for inference and prediction of symmetric relational data. The model, based on the idea of the eigenvalue decomposition, represents the relationship between two nodes as the weighted inner-product of node-specific vectors of latent characteristics. This “eigenmodel” generalizes other popular latent variable models, such as latent class and distance...

Variable elimination (VE), a central component of Bayesian network inference, starts and ends with clear structure and semantics, yet all intermediate distributions, whether normalized or unnormalized, are denoted as potentials. In this paper, a condition is given stating when intermediate distributions are defined with respect to the joint distribution. Theoretical and practical advantages of ...