On permutations of order dividing a given integer

We give a detailed analysis of the proportion of elements in the symmetric group on n points whose order divides m, for n sufficiently large and m≥n with m=O(n).      

Acoustic analysis of voice in multiple sclerosis patients

The objective is to investigate the presence of dysphonic symptoms in multiple sclerosis (MS) patients and to compare quantitative acoustic parameters in multiple sclerosis patients and normal individuals. The method of study was an 8-month controlled cross-sectional that was carried out with 106 individuals (30 MS, 76 controls). Both groups included males and females from 20 to 55 years. Exclusion criteria were prior vocal disorder, laryngeal microsurgery, recent endotracheal intubation, tumors, laryngeal, lung or mediastinal metastases, respiratory disease, and other associated neurological diagnoses. For dysphonic symptoms (qualitative variables), associations were assessed using Mantel-Haenszel's chi2 test, with Yates correction or the Fisher exact test when necessary. Statistical significance was set at p< or =0.05. Dysphonia was observed in 70% of MS individuals versus 33% of controls (p=0.01). Association was found between MS and dysphonia (OR: 2.2, CI 95%: 1.13-4.25). Fundamental frequency was higher among MS patients (p=0.01). Fundamental frequency deviation was significantly higher in MS women (but not men) than controls (p=0.00). Jitter was higher in MS men than in all other groups (p=0.00). Results suggest that evaluation and treatment of MS patients should be revised, evaluating voice alterations in relation to other signs. MS seems to intensify gender effect on fundamental frequency deviation, noise, and jitter, with MS women presenting fewer voice variations than men.     

Hereditarily Optimal Realizations of Consistent Metrics

One of the main problems in phylogenetics is to find good approximations of metrics by weighted trees. As an aid to solving this problem, it could be tempting to consider optimal realizations of metrics—the guiding principle being that, the (necessarily unique) optimal realization of a tree metric is the weighted tree that realizes this metric. And, although optimal realizations of arbitrary metrics are, in general, not trees, but rather weighted networks, one could still hope to obtain a phylogenetically informative representation of a given metric, maybe even more informative than the best approximating tree. However, optimal realizations are not only difficult to compute, they may also be non-unique. Here we focus on one possible way out of this dilemma: hereditarily optimal realizations. These are essentially unique, and can be described in a rather explicit way. In this paper, we recall what a hereditarily optimal realization of a metric is and how it is related to the 1-skeleton of the tight span of that metric, and we investigate under what conditions it coincides with this 1-skeleton. As a consequence, we will show that hereditarily optimal realizations for consistent metrics, a large class of phylogentically relevant metrics, can be computed in a straight-forward fashion. Received August 26, 2004     

Isoconversional kinetic analysis of stoichiometric and off-stoichiometric epoxy-amine cures

The curing reaction of stoichiometric and off-stoichiometric diglycidyl ether of bisphenol A (DGEBA) and 1,3-phenylene diamine (m-PDA) mixtures was studied by differential scanning calorimetry, thermogravimetric analysis and rheological measurements. In order to highlight the side reactions such as etherification and homopolymerization, the neat DGEBA and DGEBA/DMBA (N,N-dimethylbenzylamine) mixture were examined. The classical model-fitting and the advanced isoconversional methods were used to determine the activation energy of the different reactions. The advanced isoconversional method leads to a good agreement between isothermal, nonisothermal and rheological results. The effective activation energies of primary amine epoxy reaction, etherification and homopolymerization were estimated to about 55-60, 104 and 170 kJ mol⁻¹, respectively.     

Nanostructured silicon as a photonic material

Photonics applications of silicon are presented. In particular it is demonstrated that silicon when rendered low dimensional, e.g. in form of nanocrystals or quantum wires, can be turned into an active photonic materials which shows light amplification characteristics, non-linear optical effects, photon confinement in both one and two dimensions, photon trapping with evidences of light localization, and gas sensing properties.     

Deformations in Mathematics and Physics

This text is my introductory talk given at the Workshop “Deformations and Contractions in Mathematics and Physics” in Oberwolfach in January 2006. The author is grateful for the Mathematisches Forschungsinsitut Oberwolfach for being able to organize this Meeting. The work was partially supported bt grants OTKA T043641 and T043034.