Fast broadcasting and gossiping in radio networks

We establish an O(nlog²n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of Ω(nlogn). The fastest previously known algorithm for this problem works in time O(n^3/2). Using our broadcasting algorithm, we develop an O(n^3/2log²n) algorithm for gossiping in the same network model.     

The existence of global in space variables solution for non-linear subelliptic equation of floating water

The existence of global in space variables solutions for a class of non-linear subelliptic evolution operators is proved. A Cauchy problem and an initial-boundary value problem are considered using the contraction theorem and Galerkin methods.     

Additive Schwarz Method for Mortar Discretization of Elliptic Problems with <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript> Nonconforming Finite Elements

An additive Schwarz preconditioner for nonconforming mortar finite element discretization of a second order elliptic problem in two dimensions with arbitrary large jumps of the discontinuous coefficients in subdomains is described. An almost optimal estimate of the condition number of the preconditioned problem is proved. The number of preconditioned conjugate gradient iterations is independent of jumps of the coefficients and is proportional to (1+log(H/h)), where H,h are mesh sizes. AMS subject classification (2000) 65N55, 65N30, 65N22     

Weakened constraints from b-->sgamma on supersymmetry flavor mixing due to next-to-leading-order corrections

We examine the process B-->X(s)gamma in minimal supersymmetry (SUSY) with general squark flavor mix-ings. We include all relevant next-to-leading order (NLO) QCD corrections and dominant NLO SUSY effects from the gluino. We find that gluino-squark corrections to down-type quark masses induce large NLO corrections to the dominant Wilson coefficients whose size is often similar to those at LO, es-pecially at large tan(beta. For micro>0, destructive interference and suppression by the renormalization group running lead to a "focusing effect" of reducing the size of gluino corrections to the branching ratio, and also of reducing the LO sensitivity to flavor mixings among squarks. Constraints from B(B-->X(s)gamma) on the SUSY-breaking scale can become significantly weakened relative to the minimal flavor violation case, even, at large tan(beta, for small flavor mixings. The case of micro<0 also becomes allowed.     

The study of atropoisomers of meso-tetrakis[2.2]paracyclophanylporphyrin

Theoretical considerations of atropoisomers of the title compound have revealed the existence of a large number of stable isomeric species. Syntheses, carried out according to two procedures at widely separated temperatures, resulted in the formation of mixtures of atropoisomers in good yield. Two isomeric fractions have been separated and characterized. Some analytical methods have been worked out and have proved useful in separational techniques.     

5,7,12,14-Tetramethyldimethoxybenzo[b,i][1,4,8,11]tetraazacyclodecine,a new tumoricidal pseudo-porphyrin

The title compound, a mixture of two isomers differing in the position of a methoxy substituent in one benzene ring, was obtained in a Ni-templated synthesis directly as a water soluble dihydrochloride of the free base. The cyclic voltametry study indicated that in a neutral solution the reduction and oxidation are irreversible one electron processes, the latter leading to cation radical undergoing polymerization, a process followed by deposition of a film on the electrode. In 1,2-dichloroethane the cation radical is oxidized to a dication, both species being much less stable than those originating from meso-tetraphenylporphyrin. The title compoud at 2.5 × 10^?5 M in Tris buffer showed a 50% inhibition of the growth of malignant melanoma cells as compared to a 44% inhibition shown by a water soluble meso-monomethoxy-tris(N-methylpyridinium)porphyrin. The exposure to light for 30 minutes at 2.5 times smaller concentration increased the inhibition caused by the pseudo-porphyrin from 9% to 49%.     

Reduced products which are not saturated

Summary IfT is a complete theory of Boolean algebra, then we writeA ⊲_T B to denote that for every cardinal κ and every κ-regular filter over a setI such that the Boolean algebra 2 _F ^I of all subsets ofI reduced byF is a model ofT, the reduced powerA _F ^I isK ⁺-saturated wheneverB _F ^I isK ⁺-saturated. The relation ⊲_T generalizes the relation ◃ introduced by Keisler. As in the case of Keisler's ◃ it happens that ⊲_T’s are relations between complete theories, i.e. ifA≡B thenA ⊲_T B andB ⊲_T A. In this paper some examples of theories which are maximal (minimal) with respect to ⊲_T’s are provided and the relations ⊲_T are compared with each other. Presented by J. Mycielski     

X-ray structure of isomeric 3-chloro-4-(methylthio)- and 4-chloro-3-(methylthio)quinolines

The crystal and molecular structures of two isomeric 3,4- and 4,3-chloro-(methylthio)quinolines have been determined. For 3-chloro-4-(methylthio)-quinoline (3-Cl–4-MeS–Q); triclinic, space group ,a=7.199(3),b=7.919(3),c=8.921(3) Å, =89.74(3), =74.29(3), =78.55(3)°. For 4-chloro-3-(methylthio)quinoline (4-Cl–3-MeS–Q): monoclinic, space group P2₁/n,a=12.860(4),b=5.424(2),c=13.434(4) Å, =90.84(3)°. The values of the Cl...S distance as well as those for the Cl–C–C(S) and (Cl)C–C–S angles indicate the attractive interaction between ortho-situated heteroatoms in isomer 4-Cl–3-MeS–Q contrary to the effects observed in the case of 3-Cl–4-MeS–Q. The conclusions were confirmed by calculations of atomic charges withab initio method 4-31G basis set, which show positively charged sulfur atom in 4-Cl–3-MeS–Q and negatively charged sulfur in 3-Cl–4-MeS–Q.Part XXX in the series of Azinyl Sulfides.     

Optimisation of sample pre-treatment method for the determination of triclosan in marine sediments by high-performance liquid chromatography and marine benthic quality assessment in the southern Baltic Sea

This study comprises optimisation of sample preparation and HPLC analytical procedure for the determination of a personal care product ingredient, triclosan (TCS), in marine sediments. The testing of several varying pre-treatment parameters confirmed that ultrasonic extraction is an effective method for the isolation of TCS from marine sediments, and that the choice of extraction solvent appeared to be of major importance. The selection of the mobile-phase composition and the absorption wavelength was made for the high-performance liquid chromatography analysis step. Based on the validated method, a preliminary assessment of the benthic ecosystem quality with regards to TCS contamination has been demonstrated in the southern Baltic Sea – a semi-enclosed sea, characterised by poor water exchange, thus particularly susceptible to anthropopression. TCS has been identified and quantified in situ in marine bottom sediments, sediment dwelling isopod – Saduria entomon L. and estimated in silico in pore waters based on the equilibrium partition theory in order to assess the potential exposure and uptake from the aqueous phase. TCS concentrations identified in the bottom sediments of the Gdansk Basin, as the natural habitat for studied S.entomon L., appear to be threatening to the benthic environment. Particularly when considering S. entomon L. as a major nutrition source for cod (Gadus morhua) undergoing the feminisation process, since the recent studies prove TCS to have a potential to induce critical alterations in the endocrine system of marine ichthyofauna.     

Phase diagram of the TbBr(3)-RbBr binary system: thermodynamic and transport properties of the Rb(3)TbBr(6) compound

Phase equilibria in the TbBr3-RbBr binary system were established from differential scanning calorimetry (DSC) measurements. This binary system is characterized by two compounds, namely Rb3TbBr6 and RbTb2Br7, and two eutectics located at the TbBr3 mole fractions, x = 0.117 (728 K) and x = 0.449 (718 K), respectively. Rb3TbBr6 undergoes a solid-solid phase transition at 728 K and melts congruently at 1047 K with the related enthalpies 7.8 and 58.7 kJ mol(-1), respectively. RbTb2Br7 melts incongruently at 803 K. It undergoes also a solid-solid phase transition at 712 K, a temperature very close to that (718 K) of the second eutectic, and much attention was paid in evidencing and separating these transition and eutectic effects. Separate investigations of the thermodynamic and transport properties were performed on the Rb3TbBr6 compound. These heat capacity and electrical conductivity experimental results suggest an order-disorder mechanism in the alkali-metal cation sublattice whereas the TbBr6 octahedra, forming the anionic sublattice, retain their normal lattice positions.