The solvable radical of Sylow factorizable groups

Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of |G|. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of |G|. Received: 26 January 2005     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.     

Combinatorial Lie bialgebras of curves on surfaces

Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6) (1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of curves on a surface. When the surface has non-empty boundary, this vector space has a basis of cyclic reduced words in the generators of the fundamental group and their inverses. We give a combinatorial algorithm to compute this Lie bialgebra on this vector space of cyclic words. Using this presentation, we prove a variant of Goldman's result relating the bracket to disjointness of curve representatives when one of the classes is simple. We exhibit some examples we found by programming the algorithm which answer negatively Turaev's question about the characterization of simple curves in terms of the cobracket. Further computations suggest an alternative characterization of simple curves in terms of the bracket of a curve and its inverse. Turaev's question is still open in genus zero.     

Effects of vitrification suppression on structure morphology, conductivity and dielectric properties of vanadium phosphate glasses

Vitrification suppression in the (V₂O₅)_1−x (P₂O₅)_x glasses where x=0.10, 0.15, 0.20, and 0.25 was controlled by changing the rate of quenching glasses. The structure variations occurring in the glasses were detected by differential thermal analysis and optical microscope. The results implied the separation and growth of V₂O₅ orthorhombic microcrystal in the samples with x=0.10 and 0.15 whereas other samples did not illustrate remarkable changes in their microstructure. However, in temperature range between 300 and 473 K a semiconducting behavior for all samples appears during the study of electrical conductivity-temperature dependence. A decrease in conductivity values accompanied with some variations in activation energies by reducing quenching rate was observed. The conductivity results suggested that the conduction occurs by the phonon assisted hopping of a small polaron between V⁴⁺ and V⁵⁺ states at relatively higher temperature range above θ_D/2. Whereas at relatively low temperatures the conduction may occur by electron jumping between filled and empty states at Fermi level in the disordered matrix besides polaronic conduction. Reasonable values for the density of localized states, carrier concentration and carrier mobility were estimated and discussed. Also, dielectric constant and dielectric loss were studied as a function of frequency at different temperatures confirming the structure variations in the glass system.     

Optical and electric properties of Nb-doped anatase TiO2 single crystal

Nb-doped anatase TiO₂ single crystal has been grown by chemical vapour transport method. Raman spectra shows that the obtained crystal with Nb of 0.08 wt% has typical anatase structure. An absorption band was observed at around 2.2 eV, which seems to be due to the d-d transition in the conduction band. The electron paramagnetic resonance and electric resistivity measurements show that the doped niobium makes quite shallow donor level whose orbital is d_xy-like centered at the titanium position of anatase.     

Photoluminescence characteristics of ZnTiO3: Bi nanocrystals

The photoluminescence properties of the Bi³⁺ in sol-gel derived ZnTiO₃ nanocrystals have been investigated. An ultra-violet emission at 360 nm and a visible emission band at 506 nm have been observed, originating from two kinds of emission centers. The former is ascribed to the ³P₁-¹S₀ transition of Bi³⁺ and the latter to the recombination of the electrons with the photo-generated holes trapped in the zinc vacancies. In all cases the latter contribution is predominant.     

EPR investigations of oxidation effects in (V1−xMox)2−δO3

Electron paramagnetic resonance (EPR) investigations has been carried out on the new family of molybdenum doped vanadium sesquioxides (V_1−xMo_x)_2−δO₃. The oxidation effects were monitored from the rate of paramagnetic V⁴⁺ created when the sample is exposed to the air. The effects of the oxidation time, sample temperature, and annealing at 1000 °C under a diluted hydrogen atmosphere on the EPR signal features are analyzed. The V⁴⁺ concentration in the oxidized samples is determined and the relaxation effects driven by the conduction electrons are pointed out from the thermal behaviour of the EPR line features. EPR spectra of all the oxidized samples also reveal a small ferromagnetic contribution strongly correlated with the V⁴⁺ content.     

Charmless Hadronic Decays B→VV in the Topcolor-Assisted Technicolor Model

Based. On the effective Hamiltonian with the generalized factorization approach, we calculate the branchingratios and CP asymmetries of B → VV decays in the Topcolor-assisted Technicolor (TC2) model. Within the consideredparameter space we find that: (a) for the penguin-dominated B → K* φ and K*0 φ decays, the new physics enhancementsto the branching ratios are around 40%; (b) the measured branching ratios of B →K* φ and K*0φ decays prefer therange of 3 Neffc 5; (c) the SM and TC2 model predictions for the branching ratio B(B →ρ ρ0) are only about halfof the Belle‘s measurement; and (d) for most B → VV decays, the new physics corrections on their CP asymmetries are generally small or moderate in magnitude and insensitive to the variation of mπ and Neffc.     

催化荧光法测定痕量草酸

在硫酸介质中 ,草酸能催化重铬酸钾氧化罗丹明B褪色 ,使体系荧光猝灭 ,建立了催化荧光法测定草酸的新方法。催化反应在 50℃水浴中进行 1 0min ,为假零级反应。测定草酸的线性范围为 0 4～ 1 2 0mg·L- 1 ,其回归方程为ΔF =8 42c(mg·L- 1 ) 3 81 ,r=0 9983 ,检出限为 0 1 6mg·L- 1 。试验了 30种共存物质的干扰情况。此法用于生物样品中草酸含量的测定 ,结果满意。     

Study of relaxor-like behaviour of laser ablated (Pb, La)Tio3 thin films

Lanthanum modified lead titanate (PLT) thin films are one of the potential candidates for the pyroelectric and memory applications due to their excellent dielectric, pyroelectric and ferroelectric properties. PLT thin films with 25 at.% of La were deposited on platinum coated Si substrates by the laser ablation technique. The phase transition studies were done in the temperature range of −40 to 150 °C as a function of frequency and ac field. A diffused phase transition with the shifting of the maximum dielectric permittivity (?_max) to higher temperatures with the increase of frequency and dielectric dispersion with frequency at the lower temperatures were observed. The variation of the temperature corresponding to maximum dielectric constant T_m, with frequency follows the Vogel-Fulcher relation, which is the characteristic of the relaxor-like behavior of the material. With the increase of ac drive, the T_max was shifted to lower value.