A generalization of Tutte's 1-factor theorem to countable graphs

A criterion is proved for a countable graph to possess a perfect matching, in terms of “marriage” in bipartite graphs associated with the graph. In the finite case, this yields Tutte's 1-factor theorem. The criterion is conjectured to be valid for general graphs.     

On an obstruction for perfect matchings

Steffens [3] introduced a substructure (called below a “compressed set”) which prevents a graph from having a perfect matching, and proved that a countable graph possesses a perfect matching if and only if it does not contain such a substructure. In this paper we study some properties of compressed sets. Dedicated to Paul Erdős on his seventieth birthday     

On the equivalence of two conditions for the existence of transversals

There are two conditions which are known to be necessary for the existence of a transversal in any family of sets, but both are sufficient only if the family is countable. This paper proves that these conditions are always equivalent to each other. The families which are compatible with these conditions are characterised, in the sense that each of their subfamilies possesses a transversal if it satisfies the conditions. Using this, a conjecture of Podewski and Steffens is proved.     

Optimal design of a membrane separation process using signomial programming

A multistage membrane separation process for hydrogen recovery is described and formulated as a signomial programming problem. Two different configurations are examined. A 3-stage and a 5-stage process design problem are solved. The optimal solution to these programs is computed from an initial point that does not satisfy the mass balance or transport constraints of the process, using a primal-based geometric programming code. Also examined is the sensitivity of the optimal solution to changes in purity requirements. In all cases, computation times are very reasonable ranging from 2 to 4 seconds of IBM 370/165 CPU time.     

The relationship between naming reaction time and functional MRI parameters in Broca's area

We examined the correlation between behavioural reaction time and functional imaging parameters of the blood oxygenated level dependent (BOLD) response in Broca's Area during a word identification task, and whether the correlation [Magnetic Resonance Imaging 22 (2004) 451-455] varies as a function of four stimulus types: regular words (REGs) (e.g., hint), irregular words (IRRs) (e.g., pint), nonwords (NWs) (e.g., bint), and pseudohomophones (PHs) (e.g., pynt). Participants named letter strings aloud during a functional magnetic resonance imaging study. Naming reaction times were recorded during regular gaps in image acquisition, and BOLD parameters were extracted via a Tikhonov regularized BOLD analysis technique. The results revealed that only PH reaction times were correlated with BOLD width, providing evidence that Broca's area supports phonetic decoding accompanied with phonological lexical access. In addition, we advanced the development of equation-based models of cognitive behaviour and neurophysiology, whereby we showed that the relationship of mathematical independence that exists for predicting REG accuracy, given IRR and NW or PH naming accuracy, was present for naming reaction time, BOLD width, BOLD time to peak, and BOLD intensity. Therefore, we provide converging behavioural and neuroanatomical evidence for a mathematically independent relationship between sight vocabulary and phonetic decoding systems, consistent with a dual-route model of reading.     

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.     

On Atkin-Lehner Quotients of Curves

We study the erednik–Drinfeld p-adic uniformization ofcertain Atkin–Lehner quotients of Shimura curves overQ. We use it to determine over which local fields they haverational points and divisors of a given degree. Using a criterionof Poonen and Stoll, we show that the Shafarevich–Tategroup of their jacobians is not of square order for infinitelymany cases. 1991 Mathematics Subject Classification 11G18, 11G20,14G20, 14G35, 14H40.