Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

Measurement of the K α to L α and K β to L β intensity ratios of seven elements in the atomic number range 52≤ Z ≤62 using photoionization at 59.5 keV1

The Kα to Lα and Kβ to Lβ intensity ratios of seven elements have been measured following photoionization at 59.5 keV by using a Si (Li) detector (FWHM=155 eV at 5.96 keV). The intensity ratios were determined by measuring K and L x-rays emitted from a standard target of a given element. The theoretical values of the Kα to Lα and Kβ to Lβ intensity ratios were calculated using theoretically tabulated values of shell/subshell photoionization cross sections, fluorescence yields, Coster-Kronig transition probabilities, and radiative decay rates for ηKLi≠ and ηKLi=0. The measured values are in good agreement with theoretical results. From Optika i Spektroskopiya, Vol. 97, No. 2, 2004, pp. 186–189. Original English Text Copyright ? 2004 by A. Kü?ük?nder, S?ğüt, E. Kü?ük?nder, Büyükkasap. This article was submitted by the authors in English.     

The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

A nodal coupling of finite and boundary elements

This article presents and analyzes a simple method for the exterior Laplace equation through the coupling of finite and boundary element methods. The main novelty is the use of a smooth parametric artificial boundary where boundary elements fit without effort together with a straight approximate triangulation in the bounded area, with the coupling done only in nodes. A numerically integrated version of the algorithm is also analyzed. Finally, an isoparametric variant with higher order is proposed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 555–570, 2003     

Microperforated insertion units: An alternative strategy to design microperforated panels

Microperforated panels (MPPs) coupled to a rigid wall have been proposed recently as an alternative to porous absorbers in situations having concerns with bacterial contamination and small particles discharge, like food, pharmaceutical and microelectronic industries. There exists also an increasing interest for MPP absorbers in the transportation industry and civil engineering. In general, an optimally designed MPP with good broadband absorption requires many submillimetric holes distributed over a panel of also submillimetric thickness. Such thin plates or foils become so fragile that they need to be protected from mechanical damage. In this paper, an alternative strategy is investigated which allows the design of MPPs with panels of millimetric thickness while maintaining their acoustic performance. These absorbers, named microperforated insertion units (MIUs), avoid the structural problems of the classical MPPs. An assessment of the sound absorption properties of these structures is presented. Comparisons between calculations and measurements are also made under two experimental conditions: plane waves at normal incidence (impedance tube) and free field (anechoic room).