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.     

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.     

Forecasting the partisan composition of the house as a function of seniority

This note examines the influence of seniority of the partisan composition of the House of Representatives. A model is developed to compute the re-election probabilities as a function of the levels of seniority. These estimates, together with the composition of the immediately preceding congress, are then used to estimate the composition of any congress and the results compared to the actual electoral outcomes. The end result is a partisan composition or the House independent of the short-term fluctuations created by issues relevant to the individual elections. In addition, measures of accuracy of the estimates are computed in order to assertain how much of the variation in the data is left to be explained by issue-oriented factors.     

On range and response: Dimensions of process flexibility

There are two dimensions to process flexibility: range versus response. Range is the extent to which a system can adapt, while response is the rate at which the system can adapt. Although both dimensions are important, the existing literature does not analytically examine the response dimension vis-a-vis the range dimension.     

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.     

*-Orderings on a ring with involution

The object of the paper is to extend part of the theory of *-orderings on a skewfield with involution to a general ring with involution. The valuation associated to a *-ordering is examined. Every *-ordering is shown to extend. *-orderings are shown to form a space of signs as defined by Brocker and Marshall. In case the involution is the identity, the ring under consideration is commutative and the *-orderings are just the usual orderings making up the usual real spectrum of a commutative ring as defined by Coste and Roy.     

Weighted estimates for parametrized Littlewood-Paley operators

In this paper, we obtain some boundedness on the weighted Lebesgue spaces and the weighted Hardy spaces for the parametrized Littlewood-Paley operators with the kernel Ω satisfying the logarithmic type Lipschitz conditions.     

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.     

Gauss-Tchebycheff quadrature formulas

Summary It is well known that the Tchebycheff weight function (1-x ²)^–1/2 is the only weight function (up to a linear transformation) for which then point Gauss quadrature formula has equal weights for alln. In this paper we describe explicitly all weight functions which have the property that then _k-point Gauss quadrature formula has equal weights for allk, where (n _k),n ₁<n ₂<..., is an arbitrary subsequence of . Furthermore results on the possibility of Tchebycheff quadrature on several intervals are given.     

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.     

贯穿剖分上样条空间维数的注记

本文利用ｂｌｏｓｓｏｍ形式的光滑拼接条件，得到了贯穿剖分上样条空间维数定理的一个新的证明方法．     

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.     

Self-intersections of curves on surfaces

Let M be a compact orientable surface with nonempty boundary (x(M)<0) and fundamental group . Let be a geodesic on M (with a fixed hyperbolic structure), and let W be a (cyclically reduced) word in a fixed set of generators of which represents . In this paper, we give an algorithm to count the number of self-intersections of in terms of W, generalizing a result of Birman and Series, where an algorithm was given to decide if was simple. Some applications of the algorithm to surfaces with one boundary and the Markoff spectrum are also given.