The dipole field model

We provide a rigorous discussion of the dipole field model which significantly improves previous treatments and clarifies the general mathematical properties of the model as a prototype of four-dimensional QFT with confining infrared singularity. By exploiting the Krein-Hilbert structure associated with the local and covariant quantization of the model, we can characterize, in a simple way, the possible physical interpretation, prove that the breaking of spacetime translation is inevitable in the physical space (mechanisms of confinement), identify a nontrivial physical vacuum sector, and discuss the breaking of symmetries and the existence and role of translationally invariant field operators, etc.     

Error for the modified secant method

New error bounds for the modified secant method are provided. We show that our error estimates are better than the ones already existing in the literature, under similar assumptions.     

On the regularization of projection methods for solving III-posed problems

Summary In this paper we consider a class of regularization methods for a discretized version of an operator equation (which includes the case that the problem is ill-posed) with approximately given right-hand side. We propose an a priori- as well as an a posteriori parameter choice method which is similar to the discrepancy principle of Ivanov-Morozov. From results on fractional powers of selfadjoint operators we obtain convergence rates, which are (in many cases) the same for both parameter choices.     

A conjecture of Gy. Petruska

Summary We give a negative answer to a conjecture of Gy. Petruska.     

Impression creep characterization of 90Pb-10Sn microelectronic solder balls at subsolvus and supersolvus temperatures

The creep behavior of Pb-10wt.%Sn, a common high-lead solder used in microelectronic packaging, was studied by impression creep testing of ball-gridarray (BGA) solder balls attached to an organic substrate, both above and below the solvus temperature (408 K). Below the solvus temperature, the solder microstructure consists of roughly equiaxed grains of the Pb-rich solid solution α, which contains <5wt.%Sn in solution, with a coarse dispersion of Sn-rich β precipitates. Here, the creep behavior of the solder is controlled by dislocation climb via dislocation core diffusion, yielding n≈4 and Q≈60 kJ/mole. Above the solvus temperature, where the entire 10wt.%Sn is in solution, the creep mechanism becomes controlled by viscous glide of dislocations, limited by solute drag, with n≈3 and Q≈92 kJ/mole. Based on experimental data, creep equations for the as-reflowed solder in the two temperature regimes are given. Comparison of the present data with those available in the literature showed good agreement with the proposed laws.     

An iterative substructuring algorithm for equilibrium equations

Summary The topic of iterative substructuring methods, and more generally domain decomposition methods, has been extensively studied over the past few years, and the topic is well advanced with respect to first and second order elliptic problems. However, relatively little work has been done on more general constrained least squares problems (or equivalent formulations) involving equilibrium equations such as those arising, for example, in realistic structural analysis applications. The potential is good for effective use of iterative algorithms on these problems, but such methods are still far from being competitive with direct methods in industrial codes. The purpose of this paper is to investigate an order reducing, preconditioned conjugate gradient method proposed by Barlow, Nichols and Plemmons for solving problems of this type. The relationships between this method and nullspace methods, such as the force method for structures and the dual variable method for fluids, are examined. Convergence properties are discussed in relation to recent optimality results for Varga's theory ofp-cyclic SOR. We suggest a mixed approach for solving equilibrium equations, consisting of both direct reduction in the substructures and the conjugate gradient iterative algorithm to complete the computations.Dedicated to R. S. Varga on the occasion of his 60th birthdayResearch completed while pursuing graduate studies sponsored by the Department of Mathematical Sciences, US Air Force Academy, CO, and funded by the Air Force Institute of Technology, WPAFB, OHResearch supported by the Air Force under grant no. AFOSR-88-0285 and by the National Science Foundation under grant no. DMS-89-02121     

Groups with a positive law on commutators

Let p be a prime number and let G be a finitely generated group that is residually a finite p-group. We prove that if G satisfies a positive law on all elements of the form [a,b][c,d]ⁱ, a,b,c,d∈G and i?0, then the entire derived subgroup G^′ satisfies a positive law. In fact, G^′ is an extension of a nilpotent group by a locally finite group of finite exponent.     

Subsystem entropy for ? sofic shifts

We prove that any ?^d shift of finite type with positive topological entropy has a family of subsystems of finite type whose entropies are dense in the interval from zero to the entropy of the original shift. We show a similar result for ?^d sofic shifts, and also show every ?^d sofic shift can be covered by a ?^d shift of finite type arbitrarily close in entropy.     

Quantified functional analysis and seminormed spaces: A dual adjunction

In this work we investigate the natural algebraic structure that arises on dual spaces in the context of quantified functional analysis. We show that the category of absolutely convex modules is obtained as the category of Eilenberg-Moore algebras induced by the dualization functor [−,R] on locally convex approach spaces. We also establish a dual adjunction between the latter category and the category of seminormed spaces.     

Boussinesq–Cerruti problems for the hexagonally symmetric system of elasticity in n–dimensional half-space

The Poisson matrices of the analoga to the Boussinesq–Cerruti boundary value problems for the operator of transversely isotropic elastostatics in n–dimensional half-space are computed by Fourier transformation and given in explicit form. (Received: May 4, 2004; revised: January 30, 2006)