A Class of Regular Simple ω2-semigroups-Ⅱ

In this paper, we study regular simple ω2-semigroups in which D｜Es = Wd by the generalized Bruck-Reilly extension and obtain its structure theorem.

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.

The Isomorphism Theorem of Regular Bisimple ω2-semigroups

In this paper we study the isomorphisms of two regular bisimple ω2- semigroups and obtain a criterion for two such semigroups to be isomorphic.

On Weakly P.P. Rings

We introduce, in this paper, the right weakly p.p. rings as the generaliza- tion of right p.p. rings. It is shown that many properties of the right p.p. rings can be extended onto the right weakly p.p. rings. Relative examples are constructed. As applications, we also characterize the regular rings and the semisimple rings in terms of the right weakly p.p. rings.

LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS

We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are HSlder continuous near boundary provided that the scaled mixed Lx,t^p,q-norm of the velocity vector field with 3/p ＋ 2/q 〈 2, 2 〈 q 〈 ∞ is sufficiently small near the boundary. Also, we will investigate that for this 3 2〈3 solution U ∈ Lx,t^p,q with 1 〈 3＋p ＋2/q＋≤3/2, 3 〈 p 〈 ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}（3/q＋2/q- 1）.

Regularity Criterion of Weak Solutions to the 3D Incompressible Hall-magnetohydrodynamic Equations

In this paper,we study the regularity criterion of weak solutions to the3 D incompressible Hall-magnetohydrodynamics,which is ifu and Bsatisfy the condition∫_0^T‖_（x3）u（t）‖^q_（LP）＋‖▽B‖^γ_（Lβ）dt〈∞ with 3/p＋2/q≤1,3/β＋2/γ≤1,p〉3,β〉3,then the weak solution（u,B） is a smooth one on（0,T].

WEAK REGULARIZATION FOR A CLASS OF ILL-POSED CAUCHY PROBLEMS

This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibilky method and regularized semigroups. Finally, an example is given.

REGULARITY OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR PROBLEM

We study the regularity of weak solutions to a class of second order parabolic system under only the assumption of continuous coefficients.We prove that the weak solution u to such system is locally Holder continuous with any exponent α∈(0,1)outside a singular set with zero parabolic measure.In particular,we prove that the regularity point in Q_(T) is an open set with full measure,and we obtain a general criterion for the weak solution to be regular in the neighborhood of a given point.Finally,we deduce the fractional time and fractional space differentiability of D_(u),and at this stage,we obtain the Hausdorff dimension of a singular set of u.

GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS

Global in time weak solutions to the α-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to α-model regularization for the three dimension compressible EulerPoisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies γ >4/3.

Determination of Time-Dependent Coefficients for a Weakly Degenerate Heat Equation

In this paper,we consider solving numerically for the first time inverse problems of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate heat equation,which vanishes at the initial moment of time,and/or the convection coefficient along with the temperature for a one-dimensional parabolic equation,from some additional information about the process(the so-called over-determination conditions).Although uniquely solvable these inverse problems are still ill-posed since small changes in the input data can result in enormous changes in the output solution.The finite difference method with the Crank-Nicolson scheme combined with the nonlinear Tikhonov regularization are employed.The resulting minimization problem is computationally solved using the MATLAB toolbox routine lsqnonlin.For both exact and noisy input data,accurate and stable numerical results are obtained.

REGULARITY OF H^1 ∩L^(n((γ-1)/(2-γ))) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R^N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R^N)∩L^(n(γ-1)/(2-γ))(Ω, R^N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n<γ<2, τ≤max((n+2)/(n-2), (γ-1)/(2-γ)-ε), (?)ε>0, b(x)∈L2n/(n+2), n^2/(n+2)+e(Ω), (?)ε>0.Remarks. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey Space.Let assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H^1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|^((n+2)/(n-2))+b, 0<γ≤1+2/n and the H^1∩L~∞ weak solutions of (1) under natural growth condition |B|≤α|p|~2+b with a smallness condition 2aM<λ(|u|≤M), which implys that the H^1∩L~∞ weak solutions have the same regularty in the case of 1+2/n<γ<2. In the case of γ=2, many counterexamples (see [2] showed that u must be in H^1L~∞, while in the case of 1+2/n<γ<2, we consider the H^1∩L^n(γ-1)/(2-γ) weak solutions of (1), weaken the instability conditions upon them (from L~∞ to L^n(γ-1)/(2-γ) and obtain the same regularity results. Finally we show that the exponent n(γ-1)/(2-γ) can not be docreased anymore for the sake of the regularity results.Delinition 1. We call u∈H^1∩L^n(γ-1)/(2-γ)(Q, R^N) be a weak solution of (1), providod that where We use the convention that repeated indices are summed. i, j go from 1 to N ann α, β from 1 to n.

PARTIAL REGULARITY FOR THE NAVIER-STOKES-FOURIER SYSTEM

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary conditions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.

On GP-V-rings and Characterizations of Strongly Regular Rings

The purpose of this paper is to characterize strongly regular rings via MERT rings and weakly one-sided ideals. Many important equivalent conditions on strongly regular rings are shown.

On Weak Regular-semigroups

In this paper, a special kind of partial algebras called projective partial groupoids is defined. It is proved that the inverse image of all projections of a fundamental weak regular *-semigroup under the homomorphism induced by the maximum idempotent-separating congruence of a weak regular *-semigroup has a projective partial groupoid structure. Moreover, a weak regular *-product which connects a fundamental weak regular *-semigroup with corresponding projective partial groupoid is defined and characterized. It is finally proved that every weak regular *-product is in fact a weak regular *-semigroup and any weak regular *-semigroup is constructed in this way.

The Smoothness of Weak Solutions to the System of Second Order Differential Equations with Non-negative Characteristics

In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.

Regularity for weakly(K_(1),K_(2))-quasiregular mappings

In this paper, we first give the definition of weakly (K1,K2-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse H?lder inequality, we obtain their regularity property: For anyq 1 that satisfies $0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1$ , there existsp 1=p 1(n,q 1,K 1,K 2)>n, such that any (K1, K2)-quasiregular mapping $f \in W_{loc}^{1,q_1 } (\Omega ,R^n )$ is in fact in $W_{loc}^{1,p_1 } (\Omega , R^n )$ . That is, f is (K1,K2)-quasiregular in the usual sense.

不可压MHD方程组的一个条件正则性准则

研究了三维不可压MHD方程组弱解的条件正则性问题.主要考虑速度场水平方向的分量uh和磁场水平方向的分量bh,当uh和bh满足一定的条件时,弱解是光滑的.

一类非齐次椭圆方程组非常弱解的正则性

研究一类非齐次项是p-Laplace算子的椭圆方程组非常弱解的正则性。结合Hodge分解以及偏微分方程正则性理论的证明技巧,建立了具有p-Laplace型椭圆方程组的非常弱解与经典意义下的弱解之间的关系。

基于目标最优双向建模的柯西约束反演方法研究及应用

初始模型构建和反演算法是影响反演可靠性与精度的两个关键因素。针对勘探程度低、钻井少且井距大带来的低频模型构建不合理、储层与围岩反射系数差异小所造成的反演预测精度低的问题,建立了基于目标最优双向建模的柯西约束反演方法。该方法基于地震反演预测目标,在利用岩相统计分析敏感地震属性的基础上将岩石物理垂向低频趋势与敏感地震属性的横向变化相结合,提高低频模型指示砂体横向边界的能力,实现了更加符合区域地质认识的目标最优双向初始模型构建;结合目标最优双向初始模型,采用三参数柯西先验分布对反演参数进行正则化约束,利用柯西分布长尾巴特征保护弱反射信息,提高薄层反演的垂向预测精度。XH凹陷A区块中深层勘探的实际资料应用结果表明,基于目标最优双向建模的柯西约束反演结果与研究区潮坪、三角洲的沉积环境特征吻合,并通过提高储层预测的纵、横向分辨能力有效指导了A区块的勘探实践。

GV-Noether环及其弱GV-内射模

给出了GV-Noether环的Cartan-Eilenberg-Bass定理.引进了弱GV-内射模并刻画了DW-环和VN正则环.特别地,证明了环R是VN正则环当且仅当任意弱GV-内射R-模是绝对纯R-模,当且仅当任意弱GV-内射R-模是余平坦R-模.给出了GV-Noether环的Megibben定理.通过提供一些例子区别Noether环,GV-Noether环和w-Noether环.