Oscillation of third-order nonlinear functional differential equations with mixed arguments

The objective of this paper is to offer sufficient conditions for the oscillation of all solutions and other asymptotic properties of the third-order nonlinear functional differential equation $$\left[a(t)\left[x''(t)\right]^{\gamma}\right]' =q(t)f \left(x\left[\tau(t)\right]\right)+p(t)h \left(x\left[\sigma(t)\right]\right)$$ with mixed arguments, where both cases ∫^∞ a ^?1/γ (s)?ds=∞ and ∫^∞ a ^?1/γ (s)?ds<∞ are dealt with. We deduce properties of the studied equations via new comparison theorems. Our results essentially improve and complement earlier ones. We also repair one interesting result of Grace et al.     

Self‐dual and self‐petrie‐dual regular maps

Regular maps are cellular decompositions of surfaces with the “highest level of symmetry”, not necessarily orientation‐preserving. Such maps can be identified with three‐generator presentations of groups G of the form G = 〈a, b, c|a² = b² = c² = (ab)^k = (bc)^m = (ca)² = … = 1〉; the positive integers k and m are the face length and the vertex degree of the map. A regular map (G;a, b, c) is self‐dual if the assignment b?b, c?a and a?c extends to an automorphism of G, and self‐Petrie‐dual if G admits an automorphism fixing b and c and interchanging a with ca. In this note we show that for infinitely many numbers k there exist finite, self‐dual and self‐Petrie‐dual regular maps of vertex degree and face length equal to k. We also prove that no such map with odd vertex degree is a normal Cayley map. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69:152‐159, 2012     

Binary and ternary recombination of para-H3(+) and ortho-H3(+) with electrons: state selective study at 77-200 K

Measurements in H(3)(+) afterglow plasmas with spectroscopically determined relative abundances of H(3)(+) ions in the para-nuclear and ortho-nuclear spin states provide clear evidence that at low temperatures (77-200 K) para-H(3)(+) ions recombine significantly faster with electrons than ions in the ortho state, in agreement with a recent theoretical prediction. The cavity ring-down absorption spectroscopy used here provides an in situ determination of the para/ortho abundance ratio and yields additional information on the translational and rotational temperatures of the recombining ions. The results show that H(3)(+) recombination with electrons occurs by both binary recombination and third-body (helium) assisted recombination, and that both the two-body and three-body rate coefficients depend on the nuclear spin states. Electron-stabilized (collisional-radiative) recombination appears to make only a small contribution.     

Trace elemental analysis by laser-induced breakdown spectroscopy—Biological applications

Laser-Induced Breakdown Spectroscopy (LIBS) is a sensitive optical technique capable of fast multi-elemental analysis of solid, gaseous and liquid samples. Since the late 1980s LIBS became visible in the analytical atomic spectroscopy scene; its applications having been developed continuously since then. In this paper, the use of LIBS for trace element determination in different matrices is reviewed. The main emphasis is on spatially resolved analysis of microbiological, plant and animal samples.     

Computational study of the mechanism of Bcl-2 apoptotic switch

In spite of attention devoted to molecular mechanisms of apoptosis, the details of functioning of one crucial component–the Bcl-2 apoptotic switch–are not completely understood. There are two competing mechanisms of its internal working—the indirect activation and the direct activation. In the absence of conclusive experimental data, we have used computational modeling to assess the properties of both mechanisms and their suitability to act as a biological switch. Since the two mechanisms form opposite poles of continuum of Bcl-2 molecular interaction models, we have constructed more general models including these two models as extreme cases. By studying the relationship between model parameters and the steady-state response we have found optimal interaction patterns which reproduce the behavior of the Bcl-2 apoptotic switch. Our results show, that stimulus–response ultrasensitivity is negatively affected by spontaneous activation of Bcl-2 effectors. We found that ultrasensitivity requires effectors activation, mediated by another subgroup of Bcl-2 proteins—activators. We have shown that the auto-activation of monomeric effector forms provides an ultrasensitivity enhancing feedback loop. Thorough robustness analysis revealed that the interaction pattern postulated in the direct activation hypothesis is able to conserve stimulus–response switching characteristics for wide range changes of its internal parameters. The robustness of the switch against the variation of the reaction parameter is strongly reduced for the intermediate hybrid model and even more for the indirect part of the models. Computer simulations of the more general model presented here suggest, that stimulus–response ultrasensitivity is an emergent property of the direct activation model that is unlikely to occur in the model of indirect activation. Introduction of indirect-model-specific interactions does not provide a better explanation of the Bcl-2 switch functionality compared to the direct model.     

Regularity inheritance in pseudorandom graphs

Advancing the sparse regularity method, we prove one‐sided and two‐sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox, and Zhao. These inheritance lemmas also imply improved H‐counting lemmas for subgraphs of bijumbled graphs, for some H.     

Large Cayley graphs and vertex‐transitive non‐Cayley graphs of given degree and diameter

For any d?5 and k?3 we construct a family of Cayley graphs of degree d, diameter k, and order at least k((d?3)/3)^k. By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide range of sufficiently large degrees and diameters. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 87–98, 2010     

Electrical and dielectric properties of glass system NaPO3–KHSO4

Glass samples have been prepared in the NaPO₃–KHSO₄ binary system with the classical melting, casting and annealing steps. Electrical and dielectrical properties of glass samples were studied. Measurements of DC and AC conductivity and complex electrical permittivity of xNaPO₃–(100 ? x)KHSO₄ glass system were carried out at temperatures ranging from room temperature to temperature located 15 °C below glass transition temperature T_g. Results showed that changes of NaPO₃ concentration considerably affect values of observed parameters. DC conductivity of glass increases as NaPO₃ concentration grows until concentration x = 60. However, beyond this value a sharp decrease of DC conductivity was observed. In addition relaxation times showed abrupt changes at concentration x = 60, corresponding to the lowest relaxation times at the temperature 90 °C.     

Roothaan INDO CI spin density calculation

Spin densities have been calculated by the Roothaan INDO CI method in the parametrization of Pople and Kaufman. The dependence of the spin densities on both the type and the number of configurations in CI has been followed. Results have been compared with the UHF and spin-projected UHF methods.