On the efficacy of pseudo-coordinates—Part 2: moving boundary constraints

In this paper an argument is presented in favor of utilizing felicitous or natural coordinates in the model formulation of complex hybrid parameter multiple body mechanical systems (HPMBS). Specifically for this paper, HPMBS that consist of continuua that are subjected to spatially and temporally varying non-holonomic boundary conditions. This is the second paper of a two part series of papers that is presented to clarify the novelty and usefulness of a recently developed Gibbs-Appell type projection based HPMBS modeling tool. The purpose of the paper is to show that with the novel use of pseudo-coordinates and speeds (as defined by the author) it is completely natural to provide minimal configuration space dimensionality yet still retain rigorous analytical formulation tractability.Presented in this work, as a demonstrative arguing point, is the development of the hybrid parameter motion equations for a rolling flexible-disk material cutting device. This device consists of a circular flexible continuum (the cutter) along with the requisite mounting rigid hub and handle. This non-holonomically constrained device is modeled executing spatial motion constrained to the plane via moving constraints applied to the boundary of the planar continuum. Also included in this work are numerical results bolstering the claims made herein. These numerical results demonstrate that the methodology elucidated provides low-order models suitable for modeling complicated devices. These low-order models are in contrast to the current modeling trend of ever-increasing degrees of freedom.     

Field desorption mass spectra of involatile sulphonic acids,sulphonates and dyestuff materials

Abstract-Useful field desorption mass spectra can be obtained from involatile sulphonic acids and sulphonates, even when large dyestuff molecules are involved. Unusual cluster ions are commonly found, which can be singly or doubly charged. Most ions can be assigned, however, and the great potential of field desorption mass spectrometry in the identification of these involatile species is clearly established.     

207Pb(p,p') measurements at 135 and 61 MeV,the effective interaction and core polarization

Data at Einp = 61 and 135 MeV for neutron-hole transitions are used to study the proton-neutron part of the assumed NN force. Collective core-polarization strengths (A_L) from the present fits at 135 MeV are consistent with those extracted from the (e, e') reaction for two L = 2 transitions and one L = 4 transition. This is not the case at 61 MeV where the A_L values needed to fit the (p, p') data are much smaller for transitions to the $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole states. A fully microscopic DWBA fit is successful for the L = 3 transition to the doublet at 2.64 MeV of excitation at E_p = 61 MeV, but fails at 135 MeV; a fully microscopic DWIA calculation provides a reasonable fit to the data at 135 MeV.     

An entropy-theoretic proof of the Sucheston zero-one law

The purpose of this note is to provide a new proof to the following reformulation of the Sucheston zero-one law: An automorphism T of a Lebesgue space X is mixing if and only if, for every subsequence A of the sequence of natural numbers and every partition α of X having finite entropy, there exists a subsequence B = {b(j)} of A such that Λ_{r = 1}^∞ V_{j = r}^∞T^b(j)(α) is the trivial partition.     

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.