On Closed Ideals of βG

For every discrete group G, the Stone-Cech compactification βG has a natural structure of a right topological semigroup. Using the concept of Boolean group ideal on G, we propose a way of constructing closed ideals of the semigroup βG. In particular, we show that, for every infinite Abelian group G of cardinality κ, there are distinct closed ideals in βG.     

On t-Dimension over Strong Mori Domains

In this note we prove that if R is a strong Mori domain with t-dim R = n and with countably many prime v-ideals, then there is a chain of rings between R and R^w R1=R belong to R2……belong to Rn lohtuin in R^w such that each R, is also a strong Mori domain and t-dim Rk=n - k ＋ 1 for k = 1,2,..., n.     

On Right Hereditary Rings and Dedekind Domains

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On Extensions of Semilocal Prüfer Domains

One of the most important results of Chevalley's extension theorem states that every valuation domain has at least one extension to every extension field of its quotient field. We state a generalization of this result for Prüfer domains with any finite number of maximal ideals. Then we investigate extensions of semilocal Prüfer domains in algebraic field extensions. In particular, we find an upper bound for the cardinality of extensions of a semilocal Prüfer domain. Moreover, we show that any two extensions of a semilocal Prüfer domain are incomparable (by inclusion) in an algebraic extension of fields.     

On the Bergman Kernels of Some Special Reinhardt Domains

We consider the Reinhardt domains of the following types:E_1 = {z = (z_1,z_2)∈C~2: |z_1}~(2K)+ |z_2|<1,K>0},E_2 = {z = (z_1,z_2)∈C~2: |z_1| + |z_2|<1},E_3 = {z = (z_1,z_2,z_3)∈ C~3: |z_1| + |z_2|~2 + |z_3|~2<1},E_4 = {z = (z_1,z_2,z_3)∈ C~3: |z_1| + |z_2| + |z_3|~2<1},E_5 = {z = (z_1,z_2,z_3)∈ C~3: |z_1| + |z_2| + |z_3|<1}.     

On Iterates of Holomorphic Self-Maps in Weakly Pseudoconvex Domains

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On ∈-Derivations and Local ∈-Derivations

In this paper, we describe ∈-derivations in certain graded algebras by their actions on elements satisfying some special conditions. One of the main results is applied to local ∈-derivations on some certain graded algebras.     

On the Simultaneous Basis Property in Prüfer Domains

In this paper we prove that if D is a Prüfer domain such that given a proper invertible integral ideal A of D there exists a nonempty finite set of finitely generated maximal ideals that contain A, then D has the simultaneous basis property. This result is used to study two old open problems: "Does every Prüfer domain have the PA-property?", and "Is every Bézout domain an elementary divisor domain?". We include also a new different proof of the simultaneous basis property for valuations domains.     

On the p—Local Rank of Finite Groups

In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1.     

On the Collision Local Time of Fractional Brownian Motions

In this paper, the existence and smoothness of the collision local time are proved for two independent fractional Brownian motions, through L2 convergence and Chaos expansion. Furthermore, the regularity of the collision local time process is studied.     

On Singular Sets of Local Solutions to p-Laplace Equations

The author proves that the right-hand term of a p-Laplace equation is zero on the singular set of a local solution to the equation. Such a result is used to study the existence of an optimal control problem.     

On Homogenization of Problems in Domains of the “Infusorium” Type

In the paper, we consider problems in perforated domains with rapidly oscillating boundary. We assume that the oscillating boundary has a special structure. The width of the hills has the same size as the cell of periodicity inside the domain and the order of the height of the hills is bigger. Under these assumptions we construct the homogenized problem, prove the homogenization theorem, construct the correctors, and obtain estimates of the deviation of the solution to the initial problem from the leading terms of the asymptotic series.     

On Indirect Proof of Local Index Theorem for Signature Operator

In proving the local index theorem of the signature operator, people used aGilkey theorem, which was described on page 284 in [1], and thought it as the keypoint for the proof. Now we point out that things could be otherwise. Let us begin with some notions. Let R be a set of letters R_(i_1, ...i_3, ), where s= 4,5,6,..., and 1≤i_1,…,i≤2n, and let g be a set of letters g_(ij) with 1≤i,j≤2n,and let 1/(detg) be a letter. A polynomial in R,g, 1/(detg) means a polynomial in finite     

On the Weak＊ Drop Property for Polar of Closed Bounded Convex Sets

We define and study the weak* drop property for the polar of a closed bounded convex set in a Banach space which is both a generalization of the weak* drop property for dual norm in a Banach space and a characterization of the sub-differentialmapping x→эp(x) from S(X) into 2^S(X*) that is norm upper semi-continuous and norm compact-valued.     

On the Non-Existence of the Closed Orbit for a Liénard System

A sufficient condition for a Liénard system to have no non-trivial closed orbits is given by transforming the system into another system called the Bogdanov—Takens system. The result here (Theorem 2) is a partial improvement of that of Wang and Yu [2].AMS Subject Classification (2000), 34C07, 34C25, 34C26, 34D20     

A Local Tb Theorem for Square Functions in Domains with Ahlfors–David Regular Boundaries

We prove a local Tb theorem for square functions, in which we assume L ^p control of the pseudo-accretive system, with p>1 extending the work of S. Hofmann to domains with Ahlfors–David regular boundaries.     

On Hawking’s Local Rigidity Theorem for Charged Black Holes

We show the existence of the Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein–Maxwell space–time without assuming the underlying space–time is analytic. This extends a result of Friedrich et al. (Commun Math Phys 204:691–707, 1971), which holds in the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field T which is tangent to the horizon and not vanishing on the bifurcate sphere, then space–time must be locally axially symmetric without the analyticity assumption. This axial symmetry plays a fundamental role in the classification theory of stationary black holes.     

On Calabi’s Strong Maximum Principle via Local Semi-Dirichlet Forms

We give a stochastic proof of an extension of E. Calabi??s strong maximum principle under some geometric conditions in the framework of strong Feller diffusion processes associated to local regular semi-Dirichlet forms with lower bounds. As a corollary, our notion of subharmonicity implies a notion of viscosity subsolution in a stochastic sense. We can apply our result to singular geometric object like Alexandrov space, limit space under spectral distance of Riemannian manifolds with uniform lower Ricci curvature bound and so on.     

On the Asymptotic Behavior of Faber Polynomials for Domains With Piecewise Analytic Boundary

Let φ(z) be an analytic function on a punctured neighborhood of ∞, where it has a simple pole. The nth Faber polynomial F _n (z) (n=0,1,2,…) associated with φ is the polynomial part of the Laurent expansion at ∞ of [φ(z)] ⁿ . Assuming that ψ (the inverse of φ) conformally maps |w|>1 onto a domain Ω bounded by a piecewise analytic curve without cusps pointing out of Ω, and under an additional assumption concerning the “Lehman expansion” of ψ about those points of |w|=1 mapped onto corners of ∂ Ω, we obtain asymptotic formulas for F _n that yield fine results on the limiting distribution of the zeros of Faber polynomials.