Boundary behavior of the Bergman kernel function on pseudoconvex domains with comparable Levi form

Let Ω be a smoothly bounded pseudoconvex domain in and let be a point of finite type. We also assume that the Levi form of bΩ is comparable in a neighborhood of z₀. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense.     

Fourier Transformation of the Renormalization-Invariant Coupling

We discuss integral transformations of the QCD renormalization-invariant coupling (running coupling constant). Special attention is paid to the Fourier transformation, i.e., to the transition from the space–time to the energy–momentum representation. Our first conclusion is that the condition for the possibility of such a transition provides one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to a way to translate some singular long-wave asymptotic behaviors to the infrared region of transferred momenta. Such a transition must be performed with the Tauberian theorem taken into account. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by numerical lattice simulation.     

Finite element approximation of spectral problems with Neumann boundary conditions on curved domains

This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain . Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain in the framework of the abstract spectral approximation theory.

     

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.     

Crystallization Behavior of Sol-Gel Derived Films by Self-Seeding Process

We propose the novel preparation method, Self-seeding Process, based on the following concept for low temperature crystallization of oxide films. Introduction of desirable inhomogeneity should give lowering of a crystallization temperature through heterogeneous nucleation accompanied with reduced activation energy. We carried out inspection of the above concept through use of PZT films. PZT gel films with the desirable inhomogeneity of microstructure were prepared, and their crystallization behaviors was examined. The PZT film was successfully crystallized at 500°C by the self-seeding process. The single phase (001) oriented PZT film with 0.55 m in thickness was obtained at 550°C for 5 min. The self-seeding process by microstructure control is efficient for the low temperature process of the oxide thin film.     

On Finite Groups and the Small Square Property

Let G be a finite group written multiplicatively and k a positive integer. If X is a non-empty subset of G, write X ² = |xy | x, y X . We say that G has the small square property on k-sets if |X ²| < k ² for any k-element subset X of G. For each group G, there is a unique m = m _G such that G has the small square property on (m + 1)-sets but not on m-sets. In this paper we show that given any positive integer d, there is a finite group G with m _G = d.     

Solving Nonconvex Planar Location Problems by Finite Dominating Sets

It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location.In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems.Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.     

Can a finite element method perform arbitrarily badly?

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the -norm and the nodal point errors converge arbitrarily slowly. With the -norm two cases need to be distinguished, and the usual duality principle does not characterize the error completely. The constructed elliptic problems are one dimensional.

     

Finite groups of matrices over group rings

We investigate certain finite subgroups of , where is a finite nilpotent group. Such a group gives rise to a -module; we study the characters of these modules to limit the structure of . We also exhibit some exotic subgroups .