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We obtain simple proofs of certain inequalites for bivariate means.

The Calder\'on-Zygmund inequality is a cornerstone of harmonic analysis and partial differential equations. In this article, we establish various Calder\'on-Zygmund inequalities on evolving Riemannian manifolds with bounded curvature. We…

We estimate the concentration functions of $n$-fold convolutions of one-dimensional probability measures. The main result is a supplement to the results of G\"otze and Zaitsev (1998). We show that the estimation of concentration functions…

Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…

We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…

In this paper we obtain some existence result of solution for general variational inequalities. As applications several coincidence and fixed point results are provided.

The Gaussian product inequality is a long-standing conjecture. In this paper, we investigate the three-dimensional inequality $E[X_1^{2}X_2^{2m_2}X_3^{2m_3}]\ge E[X_1^{2}]E[X_2^{2m_2}]E[X_3^{2m_3}]$ for any centered Gaussian random vector…

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.

We present a gauge invariant way to compute one loop corrections to processes involving the production and decay of unstable particles.

We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…

We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.

We study some new invariant measures arising from local inverse iterates. Examples are also given.

We examine versions of the classical inequalities of Paley and Zygmund for functions of several variables. A sharp multiplier inclusion theorem and variants on the real line are obtained.

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions.

We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.

We establish an inequality of different metrics for algebraic polynomials.

Some new Gruss type inequalities in inner product spaces and applications for integrals are given.

Identities and inequalities for the cosine and sine functions are obtained.

In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction. We study properties of the uncertainty product and give an…