Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators.     

Periodic solutions for a Lotka–Volterra mutualism system with several delays

In the present paper, a Lotka–Volterra type mutualism system with several delays is studied. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions of the mutualism system. Our method is based on Mawhin’s coincidence degree and novel estimation techniques for the a priori bounds of unknown solutions. Our results are different from the existing ones such as those in of Yang et al. [F. Yang, D. Jiang, A. Ying, Existence of positive solution of multidelays facultative mutualism system, J. Eng. Math. 3 (2002) 64–68] and Chen et al. [F. Chen, J. Shi, X. Chen, Periodicity in a Lotka–Volterra facultative mutualism system with several delays, J. Eng. Math. 21 (3) (2004) 403–409].     

Effect of external Gaussian random field on phonon spectrum of linear atomic chains

We present the theoretical study of the effect of external random field characterized by a Gaussian probability distribution function on the continuous phonon spectrum of one-dimensional (1D) chain, based on the Jacobian matrix method. The cumulative effect of the random field and simple isotopic defect is studied analytically and numerically. The Gaussian random field removes a square-root divergence appearing in the phonon spectrum of ideal 1D chain. The impurity phonon DOS shows strong dependence on the variance and the mean of the random field and exhibits very different behavior from the non-random case: the continuous spectrum is expanded and the δ-peak, describing discrete impurity vibrations in the non-random chain with the impurity, falls into a continuous zone.     

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer n_M such that for all finitely generated Λ-modules N, if Ext_Λⁱ(M,N)=0 for all i?0, then Ext_Λⁱ(M,N)=0 for all i?n_M. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.     

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     

Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data

Lin and Zhang (J. Roy. Statist. Soc. Ser. B 61 (1999) 381) proposed the generalized additive mixed model (GAMM) as a framework for analysis of correlated data, where normally distributed random effects are used to account for correlation in the data, and proposed to use double penalized quasi-likelihood (DPQL) to estimate the nonparametric functions in the model and marginal likelihood to estimate the smoothing parameters and variance components simultaneously. However, the normal distributional assumption for the random effects may not be realistic in many applications, and it is unclear how violation of this assumption affects ensuing inferences for GAMMs. For a particular class of GAMMs, we propose a conditional estimation procedure built on a conditional likelihood for the response given a sufficient statistic for the random effect, treating the random effect as a nuisance parameter, which thus should be robust to its distribution. In extensive simulation studies, we assess performance of this estimator under a range of conditions and use it as a basis for comparison to DPQL to evaluate the impact of violation of the normality assumption. The procedure is illustrated with application to data from the Multicenter AIDS Cohort Study (MACS).     

The non-isotropic character of electric and dielectric properties of ammonium zinc chloride crystal

The dielectric constant, ε, and the d.c. conductivity, σ, were measured along the a-, b- and c-axes of (NH₄)₂ZnCl₄ (AZC) crystal in the 300-450 K temperature range. Crystals of AZC grown from aqueous solutions containing excess of ZnCl₂ were used. The value of the dielectric permittivity of AZC is extremely small compared to other ferroelectric crystals. Pronounced broad or step-like peaks at the phase transition temperatures were detected along the a- and b-axes, while ε along the c-axis is temperature independent up to the end of the measuring range. Reciprocal of the dielectric permittivity in the range of the commensurate to incommensurate phase transition obeys a relation similar to the Curie-Weiss law that is valid for second order ferroelectric/paraelectric phase transitions. The constants of the proposed relationship applied to the cooling run are given. The J-E characteristics along the three crystallographic axes were measured in the normal, incommensurate, commensurate and antiferroelectric phases. Hence, the type of conduction mechanism has been estimated. Parameters of Poole-Frenkel and Richardson-Schottky types of conduction mechanism have been determined. The effect of applied electric field on the conductivity measurement was also tested. Conductivity anomalies with different character were observed at the phase transition temperatures. The lnσ−1000/T dependence revealed thermal activation energy of conduction along the a-, b- and c-axes with different values in different phases of AZC.     

On the origin of irreproducible behaviour of Na1−xLixNbO3 solid solutions

The irreproducibility of electrical properties of Na_0.88Li_0.12NbO₃ solid solution on thermal cycling reported by M.A.L. Nobre and S. Lanfredi is explained by gradual decomposition of the supersaturated solid solution below ca. 800 °C.     

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.