In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.

in this paper we use a class of stochastic functional kolmogorov-type model with jumps to describe the evolutions of population dynamics. by constructing a special lyapunov function, we show that the stochastic functional differential equation associated with our model admits a unique global solution in the positive orthant, and, by the exponential martingale inequality with jumps, we dis...

In this paper we consider Jessen’s functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as ...

BACKGROUND Leg-length inequality is most often divided into two groups: anatomic and functional. Part I of this review analyses data collected on anatomic leg-length inequality relative to prevalence, magnitude, effects and clinical significance. Part II examines the functional "short leg" including anatomic-functional relationships, and provides an outline for clinical decision-making. METHO...

BACKGROUND Part II of this review examines the functional "short leg" or unloaded leg length alignment asymmetry, including the relationship between an anatomic and functional leg-length inequality. Based on the reviewed evidence, an outline for clinical decision making regarding functional and anatomic leg-length inequality will be provided. METHODS Online databases: Medline, CINAHL and Mant...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

For the functional A[ f ] = ∑k=1 ak f (zk) , we give necessary and sufficient conditions over the real numbers zk , such that, the inequality A[ f ] 0 , holds for some classes of convex functions. Then, we deduce an inequality related to Alzer’s inequality and a weighted majorization inequality.