Razumikhin Type Theorems on Boundedness

ＲａｚｕｍｉｋｈｉｎＴｙｐｅＴｈｅｏｒｅｍｓｏｎＢｏｕｎｄｅｄｎｅｓｓＺｈａｎｇＳｈｕｎｉａｎ（张书年）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｈａｉＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２００２４...     

Extensional Σ-Spaces in Type Theory

Synthetic Domain Theory provides a setting for denotational semantics following Dana Scott's slogan domains as sets in which all functions are continuous. Several approaches can be found in the literature, but they are either model-dependent or if they use an axiomatic setting then not uniformly and not explicitly. We present a completely logical approach to Synthetic Domain Theory (SDT), axiomatizing (complete) Extensional PERs. On these grounds some basic domain theory is developed. Special attention is devoted to admissibility. The axiomatic approach is advantageous since it allows for easy formalization and comparison to other axiomatic settings.The consistency of the theory is shown by providing an appropriate realizability model. It is discussed how to get from this special kind of SDT {à la Scott} to a more general form which unifies several approaches.     

On the Problem of Heilbron Type

ＯｎｔｈｅＰｒｏｂｌｅｍｏｆＨｅｉｌｂｒｏｎＴｙｐｅ￥ＴｉａｎＺｈｅｎｇｐｉｎｇ（田正平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＲｏｙａｌＨｏｌｌｏｗａｙａｎｄＢｅｄｆｏｒｄＮｅｗＣｏｌｅｇｅ，ＵｎｉｖｅｒｓｉｔｙｏｆＬｏｎｄｏｎ，Ｅｇｈ...     

On Grauert–Riemenschneider Type Criteria

Let(X, ω) be a compact Hermitian manifold of complex dimension n. In this article,we first survey recent progress towards Grauert–Riemenschneider type criteria. Secondly, we give a simplified proof of Boucksom's conjecture given by the author under the assumption that the Hermitian metric ω satisfies ?■ω~l= for all l, i.e., if T is a closed positive current on X such that ∫_XT_(ac)~n 0, then the class {T } is big and X is Kahler. Finally, as an easy observation, we point out that Nguyen's result can be generalized as follows: if ?■ω = 0, and T is a closed positive current with analytic singularities,such that ∫_XT_(ac)~n 0, then the class {T} is big and X is Kahler.     

Chaos for Subshifts of Finite Type

This paper deals with chaos for subshifts of finite type. We show that for any subshift of finite type determined by an irreducible and aperiodic matrix, there is a finitely chaotic set with full Hausdorff dimension. Moreover, for any subshift of finite type determined by a matrix, we point out that the cases including positive topological entropy, distributional chaos, chaos and Devaney chaos are mutually equivalent.     

Near Difference Sets of Type 2

Since cyclic difference sets have numerous important applications in thetheories as well as in the practice of experiment designs and communication, theyhave been studied in detail, and a certain number of generalizations andvariants have been investigated extensively. In 1973, H.J. Ryser proposed a     

On Gagliardo–Nirenberg Type Inequalities

We present a Gagliardo–Nirenberg inequality which bounds Lorentz norms of a function by Sobolev norms and homogeneous Besov quasinorms with negative smoothness. We prove also other versions involving Besov or Triebel–Lizorkin quasinorms. These inequalities can be considered as refinements of Sobolev type embeddings. They can also be applied to obtain Gagliardo–Nirenberg inequalities in some limiting cases. Our methods are based on estimates of rearrangements in terms of heat kernels. These methods enable us to cover also the case of Sobolev norms with \(p=1\) .     

On an Inequality of Jenkins Type

ＯｎａｎＩｎｅｑｕａｌｉｔｙｏｆＪｅｎｋｉｎｓＴｙｐｅ￥ＷｅｉＨａｎｂａｉ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２００４３３，Ｐ．Ｒ．Ｃ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐｅｐｅｒ，ｔｈｅａｕ...     

Some Hardy Type Inequalities in R~n

Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.     

On Projection Pursuit Type Density Estimation

ＯｎＰｒｏｊｅｃｔｉｏｎＰｕｒｓｕｉｔＴｙｐｅＤｅｎｓｉｔｙＥｓｔｉｍａｔｉｏｎ＊）ＳｏｎｇＬｉｘｉｎｇ（宋立新）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）ＬｕＳｕｊｕａｎ（吕...     

Lie Bialgebras of Generalized Virasoro-like Type

In this paper, Lie bialgebra structures on generalized Virasoro-like algebras are studied. It is proved that all such Lie bialgebras are triangular coboundary.     

Type Ⅱ codes over finite rings

In this paper,we generalize the concept of Type Ⅱ codes to arbitrary finite rings. We focus on Type Ⅱ codes over finite chain rings and use the Chinese Remainder Theorem on these codes to study Type Ⅱ codes over principal ideal rings.     

Finite Type Non—Minimal Submanifolds

The notion of finite type xubmanifolds was introduced by B.Y.Chen.In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds.The characteristic theorems of 2-type Chen submanifolds、mass-symmetric hypersurfaces and Dupin hypersurfaces in Es^m are obtained.The classification theorems of 3-type hypersurfaces and null 2-type curves in Es^m are also proved.     

Inequalities of Fejér-Jackson Type

 We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of the classical Fejér-Jackson inequality: For all integers n ⩾ 2 and real numbers x ∈ (0,π) we have

Jump Type Cahn-Hilliard Equations with Fractional Noises

The authors explore a class of jump type Cahn-Hilliard equations with fractional noises. The jump component is described by a （pure jump） Lévy space-time white noise. A fixed point scheme is used to investigate the existence of a unique local mild solution under some appropriate assumptions on coefficients.     

Hardy-Rellich Type Inequalities Associated with Dunkl Operators

In this paper, the authors obtain the Dunkl analogy of classical L~p Hardy inequality for p>N+2γ with sharp constant((p-N-2γ)/p)~p, where 2γ is the degree of weight function associated with Dunkl operators, and L pHardy inequalities with distant function in some G-invariant domains. Moreover they prove two Hardy-Rellich type inequalities for Dunkl operators.     

Approximation by Szasz-Mirakjan Type Operators in L''''

M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:     

Burr Type Ⅻ分布的统计推断

该文讨论了两参数Burr Type Ⅻ分布基于逐次定数截尾样本的参数估计,导出了有关参数的点估计和区间估计.我们利用模拟方法对所给点估计和参数的最大似然估计作了比较,模拟结果显示所给点估计优于常用的最大似然估计.最后,用一个实际例子说明本文所给方法.     

Integrals of Cauchy Type in C Space

The earliest paper to study boundary behavior of the integrals of the Cauchy-Martinelli type was[1]. But up to the present, not many boundary behaviors for the integrals of the Cauchy-Fantappi type are discussed. In this paper, we study the boundary behavior for the following form