Gluings of modular lattices

The notions of gluing, tolerance relations, and Mal'cev products of varieties have been used by various authors to investigate varieties of lattices. In this paper the authors introduce a general framework for all these concepts and apply it to varieties of modular and Arguesian lattices.     

Frequency–energy plots of steady-state solutions for forced and damped systems,and vibration isolation by nonlinear mode localization

We study the structure of the periodic steady-state solutions of forced and damped strongly nonlinear coupled oscillators in the frequency–energy domain by constructing forced and damped frequency – energy plots (FEPs). Specifically, we analyze the steady periodic responses of a two degree-of-freedom system consisting of a grounded forced linear damped oscillator weakly coupled to a strongly nonlinear attachment under condition of 1:1 resonance. By performing complexification/averaging analysis we develop analytical approximations for strongly nonlinear steady-state responses. As an application, we examine vibration isolation of a harmonically forced linear oscillator by transferring and confining the steady-state vibration energy to the weakly coupled strongly nonlinear attachment, thereby drastically reducing its steady-state response. By comparing the nonlinear steady-state response of the linear oscillator to its corresponding frequency response function in the absence of a nonlinear attachment we demonstrate the efficacy of drastic vibration reduction through steady-state nonlinear targeted energy transfer. Hence, our study has practical implications for the effective passive vibration isolation of forced oscillators.     

Multi-mode resource availability cost problem with recruitment and release dates for resources

This paper investigates the multi-mode resource availability cost problem with recruitment and release dates for resources. This problem is a more realistic model and extended case of the resource availability cost problem. The project contains activities interrelated by finish–start precedence relations with zero time lags, which require a set of renewable resources. First, a mixed integer programming formulation is proposed for the problem. Then, simulated annealing (SA) algorithm is proposed to obtain a satisfying solution for this NP-hard problem. The effectiveness of the proposed algorithm is demonstrated through comprehensive experimentation based on 300 test problems. The results are analyzed and discussed.     

A distance on curves modulo rigid transformations

We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy functional which, roughly speaking, measures the extent to which the jet field of the first curve needs to be rotated to match up with the jet field of the second curve. We show that this energy functional attains a global minimum on the appropriate function space, and we derive a set of first-order ODEs for the minimizer.     

Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV–KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar–Nepomnyashchy and Johnson–Noble–Rodrigues–Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.     

q-ENGEL SERIES EXPANSIONS AND SLATER'S IDENTITIES

Abstract

Dedicated to the memory of John Knopfmacher (1937–1999)

We describe the q-Engel series expansion for Laurent series discovered by John Knopfmacher and use this algorithm to shed new light on partition identities related to two entries from Slater's list. In our study Al-Salam/Ismail and Santos polynomials play a crucial r?ole.     

Lagrangian distributions and connections in multisymplectic and polysymplectic geometry

We discuss the interplay between lagrangian distributions and connections in (generalized) symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic structures on fiber bundles, which is relevant for the covariant hamiltonian formulation of classical field theory. In particular, we generalize Weinstein?s tubular neighborhood theorem for symplectic manifolds carrying a (simple) lagrangian foliation to this situation. In all cases, the Bott connection, or an appropriately extended version thereof, plays a central role.     

Prospective elementary teachers’ claiming in responses to false generalizations

When faced with a false generalization and a counterexample, what types of claims do prospective K-8 teachers make, and what factors influence the type and prudence of their claims relative to the data, observations, and arguments reported? This article addresses that question. Responses to refutation tasks and cognitive interviews were used to explore claiming. It was found that prospective K-8 teachers’ claiming can be influenced by knowledge of argumentation; knowledge and use of the mathematical practice of exception barring; perceptions of the task; use of natural language; knowledge of, use of, and skill with the mathematics register; and abilities to technically handle data or conceptual insights. A distinction between technical handlings for developing claims and technical handlings for supporting claims was made. It was found that prudent claims can arise from arguer-developed representations that afford conceptual insights, even when searching for support for a different claim.     

Integral geometry of translation invariant functionals,II: The case of general convex bodies

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures.     

Der fàltungsalgorithmus für dreidimensionale radon–probleme †

Filtered backprojection is an efficient numerical method for inversion of the Radon and x-ray transform. It can be adapted to the three dimensional case ([10], [11]). In this paper we present a method to calculate convolution kernels for filtered backprojection in three dimensions.     

Extrapolation applied to certain discretization methods solving the initial value problem for hyperbolic differential equations

Summary The procedurediwiex presented in this paper provides an approximate solution to Cauchy's initial value problem for general hyperbolic systems of first order. The procedurecharex can be applied to the initial value problem for a hyperbolic system of quasi-linear differential equations. This second method is a kind of method of characteristics. It produces a solution for the whole domain of determinancy. Both procedures use extrapolation to the limit. Editor's Note. In this fascile, prepublication of algorithms from the Approximations series of the Handbook for Automatic Computation is continued. Algorithms are published in ALGOL 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones     

A partition relation for partially ordered sets

We introduce a partition relation which is an alternate for measuring how badly the ordinary partition relation fails, we develop its corresponding partition calculus and we determine its status for various typical partially ordered sets.     

On convolution equations with semi-almost periodic symbols on a finite interval

This note concerns a class of Wiener-Hopf operators on a finite interval, acting between Sobolev multi-index spaces. Necessary and sufficient conditions for such an operator to be Fredholm are given, as well as a formula for the index. The argument is based on a reduction procedure of convolution operators on a finite interval to operators of the same type on the half-line.supported by the Netherlands organization for scientific research (NWO)supported in part by NSF Grant 9101143     

Boundedness and Regularity Properties of Semismooth Reformulations of Variational Inequalities

The Karush-Kuhn-Tucker (KKT) system of the variational inequality problem over a set defined by inequality and equality constraints can be reformulated as a system of semismooth equations via an nonlinear complementarity problem (NCP) function. We give a sufficient condition for boundedness of the level sets of the norm function of this system of semismooth equations when the NCP function is metrically equivalent to the minimum function; and a sufficient and necessary condition when the NCP function is the minimum function. Nonsingularity properties identified by Facchinei, Fischer and Kanzow, 1998, SIAM J. Optim. 8, 850–869, for the semismooth reformulation of the variational inequality problem via the Fischer-Burmeister function, which is an irrational regular pseudo-smooth NCP function, hold for the reformulation based on other regular pseudo-smooth NCP functions. We propose a new regular pseudo-smooth NCP function, which is piecewise linear-rational and metrically equivalent to the minimum NCP function. When it is used to the generalized Newton method for solving the variational inequality problem, an auxiliary step can be added to each iteration to reduce the value of the merit function by adjusting the Lagrangian multipliers only. This work is supported by the Research Grant Council of Hong Kong This paper is dedicated to Alex Rubinov on the occasion of his 65th Birthday     

Prescribed Q-curvature problem on closed 4-Riemannian manifolds in the null case

The main objective of this short note is to give a sufficient condition for a non constant function k to be Q curvature candidate for a conformal metric on a closed Riemannian manifold with the null Q-curvature. In contrast to the prescribed scalar curvature on the two-dimensional flat tori, the condition we provided is not necessary as some examples show. The second author would like to thank Department of Mathematics, University of Paris XII for their invitation, hospitality and financial support during his visit. His research is partially supported by NUS research grant: R-146-000-077-112.     

Commutant lifting and interpolation: The time-varying case

We show how the commutant lifting theorem for nest algebras due to Paulsen and Power can be used to give a unified framework for the treatment of a variety of interpolation problems for nest algebras which have been considered recently in the literature. Applications include the treatment of robust control for time-varying systems.Partially supported by NSF grant DMS-9500912     

Relations between stochastic and parametric programming for decision problems with a random objective function

In this paper we study the relation between the general concept for an optimal solution for stochastic programming problems with a random objective function-the concept of an £-efficient solution-and the associated parametric problem, We show that it is possible under certain assumptions to obtain some or even all £-efficient solutions of the stochastic problem by solving the parametric problem with respect to a certain parameter set.     

Double coset decompositions and computational harmonic analysis on groups

In this paper we introduce new techniques for the efficient computation of a Fourier transform on a finite group. We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary finite group. We apply our general results to special linear groups and low rank symmetric groups, and obtain new efficient algorithms for harmonic analysis on these classes of groups, as well as the two-sphere.     

On nilpotent ideals in the cohomology ring of a finite group

In this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some generalizations and further applications.We then consider the essential cohomology conjecture, and show that it is related to group actions on connected graphs. We discuss an obstruction for constructing a fixed point free action of a group on a connected graph with zero “k-invariant” and study the class related to this obstruction. It turns out that this class is a “universal essential class” for the group and controls many questions about the groups essential cohomology and transfers from proper subgroups.