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...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Let X be a smooth projective minimal 3-fold of general type. We prove the sharp inequality K X ≥ 2 3 (2pg(X)− 5), an analogue of the classical Noether inequality for algebraic surfaces of general type.

1 We study relationships between Logarithmic Sobolev inequalities with one parameter of Davies-Simon type, energy-entropy inequality, Nash-type inequality and Sobolev-type inequalities. The inequalities of Sobolev-type apply in the general setting of symmetric sub-Markovian semigroups (and some generalizations). We provide several examples of application of theses results for ultracontractive s...

In this paper, the concept of the classical f -divergence (for a pair of measures) is extended to the mixed f divergence (for multiple pairs of measures). The mixed f -divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed f -divergence are established, such as permutation invariance and symmetry in distributions. An Alexan...

In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev sp...

We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the Brunn-Minkowski inequality (for Minkowski sums between generic sets and convex sets) and of the Gaussian concentration inequality. The former inequality is th...