WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES

In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.

POTENTIAL OPERATORS AND LAPLACE TYPE MULTIPLIERS ASSOCIATED WITH THE TWISTED LAPLACIAN

We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.

HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS

First of all, using the relations （2.3）, （2.4）, and （2.5）, we define a complex Clifford algebra Wn and the Witt basis. Secondly, we utilize the Witt basis to define the operators δ and δ on Kaehler manifolds which act on Wn-valued functions. In addition, the relation between above operators and Hodge-Laplace opeator is argued. Then, the Borel-Pompeiu formulas for W-valued functions are derived through designing a matrix Dirac operator D and a 2 × 2 matrix-valued invariant integral kernel with the Witt basis.

Multilinear Commutators of Sublinear Operators on Triebel-Lizorkin Spaces

In this sublinear operators paper, the boundedness of multilinear commutators related to with Lipschitz function on Triebel-Lizorkin spaces is given. As an application, we prove that the multilinear commutators of Littlewood-Paley operator and Bochner-Riesz operator are bounded on Triebel-Lizorkin spaces.

CERTAIN SUBCLASS OF p-VALENT MEROMORPHIC ANALYTIC FUNCTIONS INVOLVING CERTAIN INTEGRAL OPERATOR

The purpose of the present paper is to introduce a new subclass of p-valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.

Boundedness of Commutators Generated by Campanato-type Functions and Riesz Transforms Associated with Schrdinger Operators

Abstract： Let L=-△＋V be a SchrSdinger operator on Rn, n 〉 3, where △ is the Laplacian on Rn and V ≠ 0 is a nonnegative function satisfying the reverse HSlder＇s inequality. Let [b, T] be the commutator generated by the Campanatotype function b ∈∧Lβ and the Riesz transform associated with SchrSdinger operator T =△↓（-△ ＋ V）-1/2. In the paper, we establish the boundedness of [b, T] on Lebesgue spaces and Campanato-type spaces.

New 3-mode bosonic operator realization of SU(2) Lie algebra:From the point of view of squeezing

We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.

Integral Representations for the Solutions of the Generalized Schroedinger Equation in a Finite Interval

We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.

Vascular resection in pancreatic adenocarcinoma with portal or superior mesenteric vein invasion

AIM:To evaluate long-term survival after the Whipple operation with superior mesenteric vein/portal vein resection(SMV/PVR)in relation to resection length.METHODS:We evaluated 118 patients who underwent the Whipple operation for pancreatic adenocarcinoma at our Department of Hepatobiliary Pancreatic Surgery between 2005 and 2010.Fifty-eight of these patients were diagnosed with microscopic PV/SMV invasion by frozen-section examination and underwent SMV/PVR.In 28 patients,the length of SMV/PVR was≤3 cm.In the other 30 patients,the length of SMV/PVR was>3cm.Clinical and survival data were analyzed.RESULTS:SMV/PVR was performed successfully in 58patients.There was a significant difference between the two groups(SMV/PVR≤3 cm and SMV/PVR>3 cm)in terms of the mean survival time(18 mo vs 11 mo)and the overall 1-and 3-year survival rates(67.9%and14.3%vs 41.3%and 5.7%,P<0.02).However,there was no significant difference in age(64 years vs 58years,P=0.06),operative time(435 min vs 477 min,P=0.063),blood loss(300 mL vs 383 mL,P=0.071)and transfusion volume(85.7 mL vs 166.7 mL,P=0.084)between the two groups.CONCLUSION:Patients who underwent the Whipple operation with SMV/PVR≤3 cm had better long-term survival than those with>3 cm resection.

Bounded Plurisubharmonic Exhaustion Functions and Levi-flat Hypersurfaces

In this paper, we survey some recent results on the existence of bounded plurisubharmonic functions on pseudoconvex domains, the Diederich-Forn^ess exponent and its relations with existence of domains with Levi-flat boundary in complex manifolds.

A UTP semantic model for Orc language with execution status and fault handling

The Orc language is a concurrency calculus pro- posed to study the orchestration patterns in service oriented computing. Its special features, such as high concurrency and asynchronism make it a brilliant subject for studying web applications that rely on web services. The conventional se- mantics for Orc does not contain the execution status of ser- vices so that a program cannot determine whether a service has terminated normally or halted with a failure after it pub- lished some results. It means that this kind of failure cannot be captured by the fault handler. Furthermore, such a seman- tic model cannot establish an order saying that a program is better if it fails less often. This paper employs UTP methods to propose a denotational semantic model for Orc that con- rains execution status information. A failure handling seman- tics is defined to recover a failure execution back to normal. A refinement order is defined to compare two systems based on their execution failures. Based on this order, a system that introduces a failure recovery mechanism is considered bet- ter than one without. An extended operational semantics is also proposed and proven to be equivalent to the denotational semantics.