bbˉb\bar b Description with a Screened Potential

Recent lattice QCD calculations suggest a rather abrupt transition in the confinig potential from a linear to a constant behavior. We analyze the effects of such a fast deconfinement in the simplest non-relativistic system, bottomonium.Comment: 4 pages. Presented at MENU04, Beijing 2004. To be published by IJMP

Monoids Mon⟨a,b:aαbβaγbδaεbφ=b⟩\mathrm{Mon}\langle a,b:a^{\alpha}b^{\beta}a^{\gamma}b^{\delta}a^{\varepsilon}b^{\varphi}=b\rangle admit finite complete rewriting systems

The aim of this note is to prove that monoids $\mathrm{Mon}\langle a,b:aUb=b\rangle$, with $aUb$ of relative length 6, admit finite complete rewriting systems. This is some advance in the understanding the long-standing open problem whether the word problem for one-relator monoids is soluble

The Search for Maximal Values of min(A,B,C) / gcd(A,B,C) for A^x + B^y = C^z

This paper answers a question asked by Ed Pegg Jr. in 2001: "What is the maximal value of min(A,B,C)/ gcd(A,B,C) for A^x + B^y = C^z with A,B,C >= 1; x,y,z >= 3?" Equations of this form are analyzed, showing how they map to exponential Diophantine equations with coprime bases. A search algorithm is provided to find the largest min/gcd value within a given equation range. The algorithm precalculates a multi-gigabyte lookup table of power residue information that is used to eliminate over 99% of inputs with a single array lookup and without any further calculations. On inputs that pass this test, the algorithm then performs further power residue tests, avoiding modular powering by using lookups into precalculated tables, and avoiding division by using multiplicative inverses. This algorithm is used to show the largest min/gcd value for all equations with C^z <= 2^100.Comment: Body: 16 pages, Appendices: 11 pages, 5 tables, 1 figur

Towards a lattice determination of the B∗BπB^\ast B \pi coupling

The coupling $g_{B^\ast B \pi}$ is related to the form factor at zero momentum of the axial current between $B^\ast$- and $B$-states. This form factor is evaluated on the lattice using static heavy quarks and light quark propagators determined by a stochastic inversion of the fermionic bilinear. The \gBBP coupling is related to the coupling $g$ between heavy mesons and low-momentum pions in the effective heavy meson chiral lagrangian. The coupling of the effective theory can therefore be computed by numerical simulations. We find the value $g = 0.42(4)(8)$. Besides its theoretical interest, the phenomenological implications of such a determination are discussed.Comment: 20 pages, 6 figure

Термодинамический анализ процессов самораспространяющегося высокотемпературного синтеза керамических материалов

В статье приведены результаты термодинамического анализа применительно к процессам самораспространяющегося высокотемпературного синтеза керамических огнеупорных материалов в системе Al – SiO2 – C. Показана возможность определения максимальной температуры процесса и расчета состава продуктов синтеза. Установлено оптимальное соотношение компонентов в системе для получения материала, содержащего максимальное количество фаз корунда и карбида кремния, которое составляет, %: SiO2 – 40 – 60, Al – 30 – 40, С – 10 – 20