Combinatorics of Nilpotents in Symmetric Inverse Semigroups

We show how several famous combinatorial sequences appear in the context of nilpotent elements of the full symmetric inverse semigroup . These sequences appear either as cardinalities of certain nilpotent subsemigroups or as the numbers of special nilpotent elements and include the Lah numbers, the Bell numbers, the Stirling numbers of the second kind, the binomial coefficients and the Catalan numbers.AMS Subject Classification: 05A15, 20M18, 20M20, 05A19.     

Modelling of the frictional heating generated in rolling contact

The transformation of the frictional energy into the heating is a problem of continued technical interest. This problem in the case of the pure sliding contact is widely discussed in many papers. In the case of rolling contact, the frictional heating is due to the slip between the rollers. Since the value of slip is unknown, the problem is more complicated, it becomes non-linear. The paper presents a new mathematical model of the generation of the heat during the rolling problem. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of pore distribution on the statistics of peak stress and overall properties of porous material

This paper addresses the effect of pore distribution on the overall properties and local stress fields in a porous material. Thermal and elastic fields in materials with uniform microstructure are compared with those of materials containing distinguishable clusters of circular or elliptic shape. The numerical simulation combines multipole expansion of local fields with the multi-particle unit cell method. Our work demonstrates that statistics of the peak stresses follow Gumbel’s rule derived for statistics of extreme values and are directly related to statistics of nearest neighbors. Based on this correspondence, an analytical expression for statistics of maximal stresses in a porous material with arbitrary microstructure is constructed in terms of porosity and statistics of minimal distances between the nearest neighbors. At the same time, the numerical analysis indicates that overall elastic constants and thermal (or electrical) conductivity are almost insensitive to the actual distribution of pores – uniform or with distinguishable pore clusters – at least in the examined interval of porosity (up to 50%).     

Effective dimension of finite semigroups

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to numerous examples.     

Diagonals of separately pointwise Lipschitz mappings

It is proved that, for a metric space X and a normed space Z, the diagonals of pointwise Lipschitz mappings f : X ²? →?Z are exactly stable pointwise limits of pointwise Lipschitz mappings. The joint Lipschitz property of separately pointwise Lipschitz mappings f : X?×?Y?→?Z, where X, Y, and Z are metric spaces, is investigated.     

On the sum of a narrow and a compact operators

Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm. It is proved that for every Köthe F-space X and for every locally convex F-space Y   the sum _T1+_T2$T_1+T_2$ of a narrow operator _T1:X→Y$T_1:X\to Y$ and a compact narrow operator _T2:X→Y$T_2:X\to Y$ is a narrow operator. This gives a positive answers to questions asked by M. Popov and B. Randrianantoanina [6, Problems 5.6 and 11.63].     

Simultaneous identification of historical pigments Prussian blue and indigo in paintings by electrospray mass spectrometry

A new analytical protocol for identification of Prussian blue (PB) and indigo was proposed. Pigments useful for dating of artworks were detected by flow injection analysis/electrospray ionization mass spectrometry after alkalization of their suspensions in water, decomposition of PB to iron (III) hydroxide and hexacyanoferrate (II) and reduction of indigo to soluble leucoindigo using sodium dithionite. Limits of detection (PB 47 pg, indigo 59 pg) complied with requirements for analysis of microsamples of historical paintings. Potential of the developed method was proven in analysis of blue samples of two oil paintings from the 20^th century. Further, PB was confirmed in a microsample from a painting of ‘Crucifixion’, St. Sebestian church on St. Hill in Mikulov, Czech Republic. Copyright © 2013 John Wiley & Sons, Ltd.