Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

Structural aspects of antibody-antigen interaction revealed through small random peptide libraries

Summary Two small random peptide libraries, one composed of 4550 dodecapeptides and one of 8000 tripeptides, were synthesized in newly developed credit-card format miniPEPSCAN cards (miniPEPSCAN libraries). Each peptide was synthesized in a discrete well (455 peptides/card). The two miniPEPSCAN libraries were screened with three different monoclonal antibodies (Mabs). Two other random peptide libraries, expressed on the wall of bacteria (recombinant libraries) and composed of 10⁷ hexa- and octapeptides, were screened with the same three Mabs. The aim of this study was to compare the amino acid sequence of peptides selected from small and large pools of random peptides and, in this way, investigate the potential of small random peptide libraries. The screening of the two miniPEPSCAN libraries resulted in the identification of a surprisingly large number of antibody-binding peptides, while the screening of the large recombinant libraries, using the same Mabs, resulted in the identification of only a small number of peptides. The large number of peptides derived from the small random peptide libraries allowed the determination of consensus sequences. These consensus sequences could be related to small linear and nonlinear parts of the respective epitopes. The small number of peptides derived from the large random peptide libraries could only be related to linear epitopes that were previously mapped using small libraries of overlapping peptides covering the antigenic protein. Thus, with respect to the cost and speed of identifying peptides that resemble linear and nonlinear parts of epitopes, small diversity libraries based on synthetic peptides appear to be superior to large diversity libraries based on expression systems.Abbreviations ABTS 2,2-azino-di-3-ethylbenzthiazoline sulfonate - EGF epidermal growth factor - Mab monoclonal antibody - OD_ccd optical density obtained using CCD camera - RAMPO rabbit-antimouse peroxidase - SDS sodium dodecylsulfate - TGEV transmissible gastroenteritis virus     

Balancing domain decomposition for problems with large jumps in coefficients

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size . Computational experiments for two- and three-dimensional problems confirm the theory.

     

Influence of a background gas on expanding plasma clots

An expansion of finite plasma clots into the background neutral gas is studied numerically. The presented model includes the quasineutrality violation as well as the interpenetration of plasma and neutral gas at the boundary of the plasma. We estimate the region of plasma parameters where the model is correct. Space distributions of main plasma parameters, cooling of electrons and the process of inter-penetration of the plasma and the neutral gas are analysed as well as an empiric formula for electron temperature is found. Finally, it is shown that the most intensive plasma-gas inter-penetration occurs in the case where the initial plasma and gas densities are the same.     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Infinite products of finite simple groups

We classify the sequences of finite simple nonabelian groups such that has uncountable cofinality.

     

New hardware for radio frequency powered glow discharge spectroscopies and its capabilities for analytical applications

A new radio frequency (rf) hardware is developed for glow discharge spectroscopic methods. The resulting features and its capabilities for analytical applications are discussed. The electrical equipment developed allows to work as quickly, stably, reliably and easily as known from the direct current (dc) mode. Moreover, the rf power measurement has been improved. The hardware has been developed, optimised and tested for glow discharge optical emission spectroscopy (GDOES), but nevertheless it is possible to use it for all procedures applying glow discharge sources.     

Regioselective Synthesis of Mixed Indole 2,3-Bis(sulfides). A Study of the Mechanism of the Second Sulfenylation of Indole

Sulfenylation of indole using sulfenyl chlorides leads to the initial formation of a 3-indolyl sulfide, while excess reagent introduces a second sulfide at the 2-position of the ring. The mechanism of this second sulfenylation has not, to date, been rigorously elucidated. The development of the first, regioselective synthesis of mixed indole 2,3-bis(sulfides) has allowed the study of the sulfenylation of 3-indolyl sulfides using a different sulfenyl chloride. Our results afford evidence that the reaction proceeds via an intermediate 3,3-disulfenylated indolenine species, with subsequent migration of one of the sulfide groups to the 2-position.