CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

In this paper we prove the existence of conditional expectations in the noncom- mutative Lp（M, Ф）-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp（M, Ф）-spaces.

Noncommutative-Geometry Wormholes Based on the Casimir Effect

While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.

CONVERGENCE OF WEIGHTED AVERAGES OF MARTINGALES IN NONCOMMUTATIVE BANACH FUNCTION SPACES

Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.

SZEG TYPE FACTORIZATION THEOREM FOR NONCOMMUTATIVE HARDY-LORENTZ SPACES

We introduce noncommutative Hardy-Lorentz spaces and give the Szegō and inner-outer type factorizations of these spaces.

NONCOMMUTATIVE ORLICZ-HARDY SPACES

Let （Φ,Ψ） be a pair of complementary N-functions and HΦ（A） and HΨ（A） be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg＆#168;o and inner-outer type factorization theorems of Hp（A） to this case.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Accounting for Some Aspects of Dark Matter and Dark Energy via Noncommutative Geometry

The purpose of this paper is to seek a connection between noncommutative geometry, an offshoot of string theory, and certain aspects of dark matter and dark energy. The former case is based on a simple mathematical argument showing that the main manifestation of dark matter in connection with flat galactic rotation curves is also a consequence of noncommutative geometry. The latter case requires an examination of the local effect of noncommutative geometry and the subsequent extension to the global phenomenon of an accelerating Universe.

On Quantum Mechanics on Noncommutative Quantum Phase Space

In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.

Noncommutative Differential Calculus and Its Application on Discrete Spaces

我们在场军士在无限的集合和构造的函数空格的变化微分演算为差别建筑群证明 Poincar é词根的类似物的一个 homotopy 操作符。然后，水平、垂直的建筑群与全部的微分地图和垂直外面的衍生物被介绍。作为微分演算的申请，我们与 symplecticity 和精力的保存导出计划因为 Hamiltonian 系统和二维的积分与保存水流的无限的顺序当模特儿。然后有 symplectic 的 Euler Lagrange cohomology 保存结构在分离古典力学被给。

Parikh-Wilczek Tunneling as Massive Particles from Noncommutative Schwarzschild Black Hole

In this paper,we apply the tunneling of massive particle through the quantum horizon of a Schwarzschildblack hole in noncommutative spacetime.The tunneling effects lead to modified Hawking radiation due to inclusionof back-reaction effects.Our calculations show also that noncommutativity effects cause the further modifications tothe thermodynamical relations in black hole.We calculate the emission rate of the massive particles' tunneling from aSchwarzschild black hole which is modified on account of noncommutativity influences.The issues of information lossand possible correlations between emitted particles are discussed.Unfortunately even by considering noncommutativityview point,there is no correlation between different modes of evaporation at least at late-time.Nevertheless,as a resultof spacetime noncommutativity,information may be conserved by a stable black hole remnant.

One-loop renormalizability of noncommutative U(1) gauge theory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propa- gators in noncommutative U（1） gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to 02-order, but for a massive scalar field they are renormalizable only to O-order.

Quasideterminant Solutions of a Noncommutative Nonisospectral Kadomtsev-Petviashvili Equation

一个 noncommutative nonisospectral KadomtsevPetviashvili 方程的答案分别地以 quasiwronskian 和 quasigrammian 被给。这些答案被直接替换验证。一些获得的答案的动力学被说明。

Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.

Jacobson-Bourbaki Correspondence Theorem for Noncommutative Rings

In algebra, the Jacobson-Bourbaki theorem is especially useful for generalizations of the Galois theory of finite, normal and separable field extensions. It was obtained by Jacobson for fields and extended to division rings by Jacobson and Cartan who credited the result to unpublished work by Bourbaki. In 2005, the Jacobson-Bourbaki correspondence theorem for commutative rings was formulated by Winter. And this theorem for augmented rings was formulated by Kadison in 2012. In this paper, we prove the Jacobson-Bourbaki theorem for noncommutative rings which is finitely generated over their centers. We establish a bijective correspondence between the set of subdivisions which are right finite codimension in A and the set of Galois rings of the additive endomorphisms End A of A which is finitely generated over its center.

Noncommutative Multi-Solitons in a Modified Chiral Model in 2+1 Dimensions

Multi-soliton configurations of a Moyal-type noncommutative deformed modified 2＋1 chiral model have been constructed by dressing method several years ago. These configurations have no-scattering property. By making a second-order pole in the dressing ansatz, two-soliton configurations with genuine soliton-soliton interaction were constructed after that. We go on in this paper to construct a large family of multi-soliton configurations with scattering property by using the noncom- mutative extension of B/icklund transformations defined by Dai and Terng in a recent paper

On Symmetry Flows of Noncommutative Kadomtsev-Petviashvili Hierarchy

We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.

SZEG TYPE FACTORIZATION OF HAAGERUP NONCOMMUTATIVE HARDY SPACES

Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let A be a maximal subdiagonal algebra of M. We proved a Szeg type factorization theorem for the Haagerup noncommutative H;-spaces.

OUTER OPERATORS FOR THE NONCOMMUTATIVE SYMMETRIC HARDY SPACES ASSOCIATED WITH FINITE SUBDIAGONAL ALGEBRA

In this article, we extended main results on outer operators of [6] to the symmetric Hardy spaces, when associated subdiagonal algebra is finite.

A Relation of the Noncommutative Parameters in Generalized Noncommutative Phase Space

We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.