On the geodesics in the Erez-Rosen spacetime

We discuss the problem of motion of test particles in a monopolequadrupole gravitational field and compare the results presented in different publications.     

A note on loop-soliton solutions of the short-pulse equation

It is shown that the N-loop soliton solution to the short-pulse equation may be decomposed exactly into N separate soliton elements by using a Moloney-Hodnett type decomposition. For the case N=2, the decomposition is used to calculate the phase shift of each soliton caused by its interaction with the other one. Corrections are made to some previous results in the literature.     

Explicit solutions of the Camassa–Holm equation

Explicit travelling-wave solutions of the Camassa–Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis–Procesi equation are given in an appendix.     

Development and applications of a preparative scale sample controlled thermogravimetric system

Journal of Thermal Analysis and Calorimetry -     

A computer study of the relationship between noise rating assessment and dB(A) levels

The paper discusses the merits of using a single dB(A) reading in preference to the more complicated and time-consuming process of deriving an NR number. It is shown that, for commonly-encountered spectra, there is a small numerical difference between the dB(A) and NR values. This difference depends upon spectral shape and the overall level of the noise. Octave bands above 1 kHz tend to make the dB(A) level less than the NR number, while the octave bands below 1 kHz generally have the opposite effect.     

The rapidly heated rigid-plastic cantilever

The concept of the expanding and contracting hinge produced by rapid thermal curvature is applied to the detailed analysis of a cantilever. In addition to a general study of the modes of deformation, the accelerations velocities and displacements are determined for a specific case. Although for the example chosen, less than 10% of the final plastic curvature occurs in the root hinge, a greatly simplified “strong beam” analysis which constrains all plastic deformation to the root hince gives a tip deflection only 6% less than the original value. The paper includes a discussion of the conditions which must be satisfied such that longitudinal inertia effects and elastic deflexions do not invalidate the analysis when it is applied to real materials.     

Preparation,Spectroscopic and Structural Investigations of Spiro Derivatives of Hexachlorocyclotriphosphazatriene

Abstract

Mono-(N₃P₃Cl₄Y₂), bis-(N₃P₃Cl₂Y₄) and tris-spiro derivatives (N₃P₃Y₆) have been prepared with ethylene, 1, 3-propylene and 1,4-butylene glycols (Y₂ = glycol residue). The ¹H NMR spectra of mono- and tris-derivatives are relatively simple; those of the bis- very complex due to the intrinsic asymmetry of the methylene protons. This effect is made use of in studying the replacement pattern of N₃P₃Cl₄ [O (CH₂)₃O] with primary and secondary amines. Homonuclear ¹H decoupling simplifies the spectra and allows an unambiguous distinction to be made between the different isomeric possibilities of the bis amino derivatives N₃P₃Cl₂R₂ [O(CH₂)₃O] where R = amino residue. Primary amines give geminal, secondary amines nongeminal trans-derivatives. The trans-structure of the bis-pyrrolidino derivative has been confirmed by X-ray crystallography.