Related papers: An intertwined Cauchy--Schwarz-type inequality bas…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
The notion of pairable functions is introduced and some of its properties are developed. In this connection the famous Euler identity is interpreted as a property of certain pairable functions and finite cyclic groups.
We give a short proof of Sjostrand's sign-imbalance identity for skew shapes using the domino Cauchy identity.
The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly…
This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under…
In the paper, the author establishes an integral representation for Cauchy numbers of the second kind, finds the complete monotonicity, minimality, and logarithmic convexity of Cauchy numbers of the second kind, and presents some…
Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well…
A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.
We obtain new inequalities with alternating signs of H\"{o}lder and Minkowski type.
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler-Lagrange equation…
We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
A new proof of the Wulff-Gage isoperimetric inequality for origin-symmetric convex bodies is provided. As its applications, we prove the uniqueness of log-Minkowski problem and a new proof of the log-Minkowski inequality of curvature…
Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper error bounds of such…
We present new generalizations of Cauchy-Schwarz (CS) inequalities to multiple vectors and use them to derive multi-operator quantum uncertainty relations and propose multi-operator squeezing.
Some identities that involve the elliptic version of the Cauchy matrices are presented and proved. They include the determinant formula, the formula for the inverse matrix, the matrix product identity and the factorization formula.
This article has two main objectives. The first one is to show Kuttler-Sigillito's type inequalities involving the mixed Neumann-Dirichlet, mixed Steklov-Dirichlet, and mixed Robin-Dirichlet eigenvalue problems. We will provide examples on…
For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.
In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, H\"{o}lder's inequality and Cauchy's…
In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.