Van der Waerden spaces and Hindman spaces are not the same

A Hausdorff topological space is van der Waerden if for every sequence in there is a converging subsequence where contains arithmetic progressions of all finite lengths. A Hausdorff topological space is Hindman if for every sequence in there is an IP-converging subsequence for some infinite .

We show that the continuum hypothesis implies the existence of a van der Waerden space which is not Hindman.

     

A marginal cost analysis for prevetive replacement policies

Some well known preventive replacement policies are each characterized by a single parameter which governs the sequence of planned replacements. In this paper we define and compute for any one of these policies the marginal cost of a planned replacement in terms of the policy parameter. This function is used to obtain the equation of optimality, with respect to two common objective functions: the expected cost per unit time and the expected total discounted costs, and to investigate the existence of a unique finite solution. Moreover, the marginal cost notion provides reasoning to the mathematical results of the models and thereby clarifies the effect of the various components of the model on these results. This better insight into models is perhaps the most important benefit of a marginal cost analysis.     

Raman spectroscopic study of the effect of take-up speed on conformation,orientation, and crystallinity in PET fibers

The dependence of the Raman spectrum of PET fibers on take-up speed (TUS) during high-speed spinning is examined. It is found that conformational change, orientation, and crystallinity, all different functions of TUS as a processing variable, are reflected in the spectra. The data, as well as those from thermal annealing of PET fibers, are shown to be consistent with those from other techniques, leading to a set of equations from which a number of properties of the PET fibers can be determined from the Raman spectrum alone.     

Surface defect centres in irradiated AgCl studied by X-ray photoelectron spectroscopy

Irradiation of silver chloride with both UV and soft X-rays during X-ray photoelectron spectroscopic measurements at ca. 300K produces a new thermally-stable chlorine centre; however, at temperatures below ca. 180K the rate of production of this species is immeasurably slow. Cadmium doping experiments indicate that the centre is closely associated with cation vacancies.     

Structural requirements in chiral diphosphine-rhodium complexes. II. N.M.R. determination of E,Z-geometry in prochiral substrates used in asymmetric hydrogenation reactions: α-acetamidocinnamic acids,esters, and parent azlactones.

Using n.m.r. the configuration of the stable 4-benzylidene-2-methyl-2-oxazolin-5-one, substituted derivatives, and the corresponding acids and esters derived from the parent stable azlactones were all found to be of Z-stereochemistry.     

Application of a singular perturbation expansion to the solution of certain Fokker-Planck equations

We show that a singular perturbation expansion for the solution of a parabolic equation can be applied to some Fokker-Planck equations arising in the analysis of the effects of noise on laser operations. A generalization to the approximate solution of the Smoluchowski equation, when diffusion is a small effect, is given.     

Laryngeal Granular Cell Tumor

Granular cell tumor (GCT) of the larynx is an uncommon, benign laryngeal neoplasm. Abrikossoff first described the tumor in 1926 as myoblastoma. The origin of this tumor has been debated in the literature. Most of the authors believe that the tumor is of neural origin due to the characteristic immunohistochemical-staining pattern. The authors describe two cases of laryngeal GCTs located in different sites with a review of the histological and clinical features, the differential diagnosis, and the treatment and the prognosis of the tumor.