Etude des propriétés cristallographiques,diélectriques et d'optique non linéaire de quelques nouvelles phases de composition BaxLi5−2xNb5(1−y)Ta5yO15 et de structure bronzes oxygénés de tungstène quadratiques

Two series of phases with tetragonal bronze-like structure and composition Ba_xLi_5?2xT₅O₁₅ (T = Nb, Ta) have been isolated in the systems BaNb₂O₆LiNbO₃ and BaTa₂O₆LiTaO₃. All these phases show ferroelectric-paraelectric transitions. The Curie temperature increases with the lithium content. The value of T_C for Ba_2.03Li_0.94Nb₅O₁₅ is the highest ever observed for this type of structure: the obtained phases are potentially good materials for the harmonic generation of the 0.53-μm radiation. The optical yield of the niobate Ba_2.14Li_0.71Nb₅O₁₅ is about 2.5 times that of Ba₂NaNb₅O₁₅ and 250 times that of the K.D.P. The crystallographic and dielectric data of the system Ba_2.14Li_0.71Nb₅O₁₅Ba_2.14Li_0.71Ta₅O₁₅ characterize three domains, which are respectively antiferroelectric, ferroelectric, and paraelectric. The Curie temperature and the optical yield decrease with increasing tantalum content.     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.     

Silica-supported PtSn alloy doped with Ga, In or, Tl: Characterization and catalytic behaviour in n-hexane dehydrogenation

Silica-supported trimetallic catalysts containing Pt, Sn and a group 13 metal (PtSnM, M=Ga, In, Tl) were prepared by consecutive impregnation steps from cis-[PtCl₂(PPh₃)₂] and chloride precursors. X-ray diffraction (XRD), transmission electron microscopy (TEM), selected-area electron diffraction (ED) and energy dispersive X-ray analysis (EDX) showed large platelet-like particles of PtSn_1−xM_x phases. PtSnGa catalyst with a Pt/(Sn+Ga) molar ratio of 1.72 showed a bimodal particle distribution and a Pt phase was identified. Differences in surface structures were also revealed by the performance of catalysts in the dehydrogenation of n-hexane. For PtSnIn and PtSnTl (Pt/(Sn+M) molar ratio of about 1) the dehydrogenation was favoured. In contrast, PtSnGa catalyst yielded hydrogenolysis products. Photoelectron spectra showed the Pt 4f_7/2 level at a binding energy of 70.0–71.8 eV in all cases. Moreover, the FT-IR spectra of chemisorbed CO on the PtSnGa showed a slight shift in the ν(CO) toward higher values with respect to the monometallic catalyst, pointing to an electronic effect in accordance with photoelectron spectroscopy.     

Influence of the 4,6-O-benzylidene, 4,6-O-phenylboronate, and 4,6-O-polystyrylboronate protecting groups on the stereochemical outcome of thioglycoside-based glycosylations mediated by 1-benzenesulfinyl piperidine/triflic anhydride and N-iodosuccinimide/trimethylsilyl triflate

The effect of 4,6-O-benzylidene acetals, 4,6-O-phenylboronate esters, and 4,6-O-polystyrylboronate esters on the stereoselectivity of couplings to galacto-, gluco-, and mannopyranosyl thioglycosides, otherwise protected with benzyl ethers, has been investigated by the benzenesulfinyl piperidine/trifluoromethanesulfonic anhydride (BSP), diphenyl sulfoxide/trifluoromethanesulfonic anhydride (Ph(2)SO), and N-iodosuccinimide/trimethylsilyl trifluoromethanesulfonate (NIS/TMSOTf) methods. The BSP and Ph(2)SO methods give comparable results in all three systems whereas the NIS method affords significantly different stereoselectivities in both the gluco and manno, but not the galacto series. The benzylidene acetal and boronate esters influence the stereochemistry in a similar manner in the beta-selective manno series and the alpha-selective galacto series but show significant differences with the glucose donors. The differences between the glucose, galactose, and mannose series reflect the established differences in reactivity and, especially for mannose, those in the anomeric effect and are best interpreted in terms of changes in the relative energetics between the alpha- and beta-covalent triflate intermediates and the various contact ion pairs with which they are necessarily in equilibrium.     

Statistical Modeling of the Seismic Moments via Mathai Distribution

Mathai’s pathway model is playing an increasingly prominent role in statistical distributions. As a generalization of a great variety of distributions, the pathway model allows the studying of several non-linear dynamics of complex systems. Here, we construct a model, called the Pareto–Mathai distribution, using the fact that the earthquakes’ magnitudes of full catalogues are well-modeled by a Mathai distribution. The Pareto–Mathai distribution is used to study artificially induced microseisms in the mining industry. The fitting of a distribution for entire range of magnitudes allow us to calculate the completeness magnitude (Mc). Mathematical properties of the new distribution are studied. In addition, applying this model to data recorded at a Chilean mine, the magnitude Mc is estimated for several mine sectors and also the entire mine.     

The number of k‐SAT functions

We study the number SAT(k; n) of Boolean functions of n variables that can be expressed by a k‐SAT formula. Equivalently, we study the number of subsets of the n‐cube 2ⁿ that can be represented as the union of (n ? k)‐subcubes. In The number of 2‐SAT functions (Isr J Math, 133 (2003), 45–60) the authors and Imre Leader studied SAT(k; n) for k ≤ n/2, with emphasis on the case k = 2. Here, we prove bounds on SAT(k; n) for k ≥ n/2; we see a variety of different types of behavior. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 22: 227–247, 2003     

The Forwarding Indices of Random Graphs

A routing R of a graph G is a set of n(n ? 1) elementary paths R(u, v) specified for all ordered pairs (u, v) of vertices of G. The vertex-forwarding index ξ(G) of G, is defined by Where ξ(G, R) is the maximum number of paths of the routing R passing through any vertex of G and the minimum is taken over all the routings of G. Let G_p denote the random graph on n vertices with edge probability p and let m = np. It is proved among other things that, under natural growth conditions on the function p = p(n), the ratio Tends to 1 in probability as n tends to infinity.