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Inequality for Variance of Weighted Sum of Correlated Random Variables
Variance Covariance Random Variable Chebyshev!ˉs Inequality Correlated Random Variable Positive Semidefinite Matrix Law of Large Numbers
2012/11/23
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also gi...
On an inequality for the Riemann zeta-function in the critical strip
Riemann zeta-function size of the Riemann zeta-function new inequalities critical strip
2012/6/30
By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\zeta(1-s)| <= |\zeta(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. Moreover, we est...
Harnack inequality for fractional sub-Laplacians in Carnot groups
Carnot groups heat kernel fractional powers of sub-Laplacian Harnack inequality
2012/6/21
In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a techn...
Log-Harnack Inequality for Gruschin Type Semigroups
Gruschin semigroup log-Harnack inequality coupling regular conditional probability
2012/6/19
By constructing a coupling in two steps and using the Girsanov theorem under a regular conditional probability, the log-Harnack inequality is established for a large class of Gruschin type semigroups ...
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
Geometric PDEs Variational Methods Min-max Schemes
2012/6/14
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical sing...
An Optimal Inequality For The Tangent Function
inequality tangent function power series expansion
2012/5/24
In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents invol...
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfet...
Positive integer n is between two adjacent prime numbers square, the well-established number of product even distribution of the formula (S) andformula (L), According to the prime number theorem, Mert...
An operator inequality associated with Hilbert's type integral inequality
mathematical analysis integral operator Beta function Hilbert's type integral inequality
2011/9/29
In the paper, by using the way of weight functions and the theory of operators, we define a new Hilbert-type integral operator and obtain its norm. As applications, a Hilbert-type operator inequality ...
A New Extension of Hilbert-type Integral Inequality with Two Pairs of Conjugate Exponents
mathematical analysis Hilbert's type integral inequality conjugate exponent Holder inequality equivalent form
2011/9/29
In the paper, by introducing two pairs of conjugate exponents(p，q) and (r，s), we establish a new generalizations of the Hilbert-type ineqaulity with a best constant. As application, the reverse and it...
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
GNS inequality Log-HLS inequality critical mass Keller-Segel equation Analysis of PDEs
2011/9/23
Abstract: Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev inequality...
Abstract: In this note we give some results of the following type. Let z_j (j=1,...,n) be distinct complex numbers on the unit circle, but not equal to 1. Then the limes inferior of the real parts of ...
A generalized Young inequality and some new results on fractal space
Dfractal real line number system fractional set generalized Young inequality
2011/9/21
Abstract: Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequalit...
Estimates for the asymptotic behavior of the constants in the Bohnenblust--Hille inequality
Absolutely summing operators Bohnenblust–Hille Theorem Functional Analysis
2011/9/20
Abstract: A classical inequality due to H.F. Bohnenblust and E. Hille states that for every positive integer $n$ there is a constant $C_{n}>0$ so that $$(\sum\limits_{i_{1},...,i_{n}=1}^{N}|U(e_{i_{^{...
Chevet type inequality and norms of submatrices
Chevet type inequality norms of submatrices Probability
2011/9/15
Abstract: We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of "symmetric expone...