A Generalization of the Logarithmic Gross–Sobolev Inequality

Doklady Mathematics - A sharp integral inequality is proved that is used to derive a Sobolev interpolation inequality. A generalization of the logarithmic Sobolev inequality is proposed based on...     

The Improvement of Fischer's Inequality and Hadamard's Inequality

ＴｈｅＩｍｐｒｏｖｅｍｅｎｔｏｆＦｉｓｃｈｅｒ＇ｓＩｎｅｑｕａｌｉｔｙａｎｄＨａｄａｍａｒｄ＇ｓＩｎｅｑｕａｌｉｔｙＨｕａｎｇＬｉｐｉｎｇ（黄礼平）（ＤｅｐａｒｔｍｅｎｔｏｆＢａｓｉｃＳｃｉｅｎｃｅｓ，ＸｉａｎｇｔａｎＭｉｎｉｎｇＩｎｓｔｉｔｕｔｅ，...     

Models for CR-manifolds of type (1,K) for 3≤K≤7 and their automorphisms

Models similar to the tangent quadric are constructed for surfaces with one-dimensional complex tangent space. It is shown that these models possess the main properties of the tangent quadric. Their groups and algebras of automorphisms are found. Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 452–459, March, 2000.     

The Equivalence of the DFA and OFA Automate

ＴｈｅＥｑｕｉｖａｌｅｎｃｅ　ｏｆｔｈｅＰＦＡａｎｄＯＦＡＡｕｔｏｍａｔａＴｈｅＥｑｕｉｖａｌｅｎｃｅｏｆｔｈｅＰＦＡａｎｄＯＦＡＡｕｔｏｍａｔａ￥／／ＬｉＧｕｏｃａｉａｎｄＷａｎｇＣｈｕａｎｈｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

Weak-Type (1-1) Inequality for the Monge-Ampère SIO's

The purpose of this article is to prove a weak-type (1-1) estimate for a class of singular integral operators related to the real analysis of the Monge-Ampère equation. The method uses the theory of homogeneous spaces. It should be noted that the class of operators has been widened since [3] by replacing the Lipschitz type condition with a weaker Hölder-aalpha type condition ($0 < alpha leq 1$0 < alpha leq 1).     

The Equivalence between Property (ω) and Weyl’s Theorem

We call T ∈ B(H) consistent in Fredholm and index (briefly a CFI operator) if for each B ∈ B(H),T B and BT are Fredholm together and the same index of B,or not Fredholm together.Using a new spectrum defined in view of the CFI operator,we give the equivalence of Weyl’s theorem and property (ω) for T and its conjugate operator T* .In addition,the property (ω) for operator matrices is considered.     

The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space

Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.     

An Estimate of Inequality of Signature and Nullity for Links

ＡｎＥｓｔｉｍａｔｅｏｆＩｎｅｑｕａｌｉｔｙｏｆＳｉｇｎａｔｕｒｅａｎｄＮｕｌｌｉｔｙｆｏｒＬｉｎｋｓ￥ＬｉＱｉｓｈｅｎｇ（李起升）（Ｄｅｐｔ．ＯｆＭａｔｈ．ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｋａｉｆｅｎｇ４７５００１）Ａｂｓｔｒａｃｔ：Ａｎｉｎｅｑｕ...     

Hadamard Inequality and a Refinement of Jensen Inequality for Set—Valued Functions

We present the following set-valued analogue of the Hadamard inequality: Let Y be a Banach space, I be an open interval and let F: I ? cl(Y) be a continuous and convex set-valued function. Then $${F(a)+F(b)\over 2}\subset{1\over b-a}\int_a^b\ F(x)dx\subset F \bigg({a+b\over 2}\bigg)$$ , for every a, b ∈ I, a < b. Some refinement of Jensen inequality for set-valued functions is also given.     

The Discrete Subgroups and Jфrgensen’s Inequality for SL(m,Cp)

In this paper, we give discreteness criteria of subgroups of the special linear group on Qp or Cp in two and higher dimensions. J rgensen's inequality gives a necessary condition for a nonelementary group of Mbius transformations to be discrete. We give a version of Jфrgensen's inequality for SL(m, Cp).     

Annihilators and Associated Varieties of Aq(λ) Modules for U(p, q)

Vogan has conjectured that the cohomologically induced modules A _q() in the weakly fair range exhaust all unitary representations of U(p, q) with certain kinds of real integral infinitesimal character. To prove a statement like this, it is essential to identify these modules among the set of all irreducible Harish-Chandra modules. Barbasch and Vogan have parametrized this latter set in terms of their annihilators and asymptotic supports (or, equivalently, associated varieties). In this paper, we identify the weakly fair A _q() in this parametrization by combining known results about their asymptotic supports together with an explicit computation of their annihilators. In particular, this determines all vanishing and coincidences among the A _q() in the weakly fair range, and gives the Langlands parameters of these modules.     

Hypercontractivity, Nash inequalities and subordination for classes of nonlinear semigroups

A suitable notion of hypercontractivity for a nonlinear semigroup {T _t } is shown to imply Nash-type inequalities for its generator H, provided a subhomogeneity property holds for the energy functional (u,Hu). We use this fact to prove that, for semigroups generated by operators of p-Laplacian-type, hypercontractivity implies ultracontractivity. Then we introduce the notion of subordinated nonlinear semigroups when the corresponding Bernstein function is f(x)=x ^α , and write an explicit formula for the associated generator. It is shown that hypercontractivity still holds for the subordinated semigroup and, hence, that Nash-type inequalities hold as well for the subordinated generator.     

Combinatorial proofs for identities related to generalizations of the mock theta functions $$\omega (q)$$ω(q) and $$\nu (q)$$ν(q)

The Ramanujan Journal - The two partition functions $$p_\omega (n)$$ and $$p_\nu (n)$$ were introduced by Andrews, Dixit and Yee, which are related to the third-order mock theta functions $$\omega...     

Pitt’s Inequality and Logarithmic Uncertainty Principle for the Dunkl Transform on {\mathbb{R}}

We establish Pitt’s inequality and deduce Beckner’s logarithmic uncertainty principle for the Dunkl transform on \({\mathbb{R}}\) . Also, we prove Stein–Weiss inequality for the Dunkl–Bessel potentials.     

The Existence of Complete Mappings of SL(2, q), q≡1 Modulo 4

In 1955, Hall and Paige conjectured that any finite group with a noncyclic Sylow 2-subgroup admits complete mappings. For the groups GL(2, q), SL(2, q), PSL(2, q), and PGL(2, q) this conjecture has been proved except for SL(2, q), q odd. We prove that SL(2, q), q≡1 modulo 4 admits complete mappings.     

The Halász Inequality for Additive Function of Rational Argument

We obtain an upper bound for the quantity . Here I is an interval, is the set of rational numbers q=m/n I such that nx, and f(q) is an arbitrary real-valued additive function of rational argument. The interval I and function f may depend on x3.     

Congruences for the coefficients of the Gordon and McIntosh mock theta function $$\xi (q)$$ ξ ( q )

The Ramanujan Journal - Recently Gordon and McIntosh introduced the third order mock theta function $$\xi (q)$$ defined by $$\begin{aligned} \xi (q)=1+2\sum _{n=1}^{\infty...