Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an in finite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.

Effect of Different Solvent Ratios (Water/Ethylene Glycol) on the Growth Process of CaMoO(4) Crystals and Their Optical Properties

In this paper, calcium molybdate (CaMoO(4)) crystals (meso- and nanoscale) were synthesized by the coprecipitation method using different solvent volume ratios (water/ethylene glycol). Subsequently, the obtained suspensions were processed in microwave-assisted hydrothermal/solvothermal systems at 140 degrees C for 1 h. These meso- and nanocrystals processed were characterized by X-ray diffraction (X R I)), Fourier transform Raman (FT-Raman), Fourier transform infrared (FT-IR). ultraviolet visible (UV-vis) absorption spectroscopies, held-emission gun scanning electron microscopy (FEG-SEM). transmission electron microscopy (TEM). and photoluminescence (PL) measurements. X RI) patterns and FT-Raman spectra showed that these meso- and nanocrystals have a scheelite-type tetragonal structure without the presence of deleterious phases. FT-IR spectra exhibited a large absorption band situated at around 827 cm(-1), which is associated with the Mo-O anti-symmetric stretching vibrations into the [MoO(4)] clusters. FEG-SEM micrographs indicated that the ethylene glycol concentration in the aqueous solution plays an important role in the morphological evolution of CaMoO(4) crystals. High-resolution TEM micrographs demonstrated that the mesocrystals consist of several aggregated nanoparticles with electron diffraction patterns of monocrystal. In addition, the differences observed in the selected area electron diffraction patterns of CaMoO(4) crystals proved the coexistence of both nano- and mesostructures, First-principles quantum mechanical calculations based on the density functional theory at the B3LYP level were employed in order to understand the band structure find density of states For the CaMoO(4). UV-vis absorption measurements evidenced a variation in optical band gap values (from 3.42 to 3.72 cV) for the distinct morphologies. The blue and green PI. emissions observed in these crystals were ascribed to the intermediary energy levels arising from the distortions on the [MoO(4)] clusters clue to intrinsic defects in the lattice of anisotropic/isotropic crystals.

Spontaneous recoherence of quantum states after decoherence

In this work, we identify the set of time-dependent pure states building the statistical mixture to which a system, initially in a pure state, is driven by the reservoir. This set of time-dependent pure states, composing what we term a pure basis, are those that diagonalize the reduced density operator of the system. Next, we show that the evolution of the pure-basis states reveals an interesting phenomenon as the system, after decoherence, evolves toward the equilibrium: the spontaneous recoherence of quantum states. Around our defined recoherence time, the statistical mixture associated with a special kind of initial states termed even-symmetric, spontaneously undergoes a recoherence process, by which the initial state of the system emerges from the mixture except for its reduced excitation drained into the reservoir. This phenomenon reveals that the reservoir only shuffle the original information carried out by the initial state of the system instead of erasing it. Moreover, as the spontaneously recohered state occurs only for asymptotic time, we also present a protocol to extract it from the mixture through specific projective measurements. The password to retrieve the original information stems is the knowledge of both the initial state itself and the associated pure basis. A definition of the decoherence time of an N-state superposition is also presented.

N-H...S=C hydrogen bond in O-alkyl N-methoxycarbonyl thiocarbamates, ROC(S)N(H)C(O)O)CH(3) (R = CH(3)(-), CH(3)CH(2)-)

Pure O-methyl N-methoxycarbonyl thiocarbamate CH(3)OC(S)N(H)C(O)OCH(3) (I) and O-ethyl N-methoxycarbonyl thiocarbamate, CH(3)CH(2)OC(S)N(H)C(O)OCH(3) (II), are quantitatively prepared by the addition reaction between the CH(3)OC(O)NCS and the corresponding alcohols. The compounds are characterized by multinuclear ((1)H and (13)C) and bi-dimensional ((13)C HSQC) NMR, GC-MS and FTIR spectroscopy techniques. Structural and conformational properties are analyzed using a combined approach involving crystallographic data, vibration spectra and theoretical calculations. The low-temperature (150 K) crystal structure of II was determined by X-ray diffraction methods. The substance crystallizes in the monoclinic space group P2(1)/n with a = 4.088(1)angstrom. b = 22.346(1)angstrom, c = 8.284(1)angstrom, beta = 100.687(3)degrees and Z = 4 molecules per unit cell. The conformation adopted by the thiocarbamate group -OC(S)N(H)- is syn (C=S double bond in synperiplanar orientation with respect to the N-H single bond), while the methoxycarbonyl C=O double bond is in antiperiplanar orientation with respect to the N-H bond. The non-H atoms in II are essentially coplanar and the molecules are arranged in the crystal lattice as centro-symmetric dimeric units held by N-H center dot center dot center dot S=C hydrogen bonds Id(N center dot center dot center dot S) = 3.387(1)angstrom, <(N-H center dot center dot center dot S) = 166.4(2)degrees]. Furthermore, the effect of the it electronic resonance in the structural and vibrational properties is also discussed. (C) 2009 Elsevier Ltd. All rights reserved.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Bimodal extension based on the skew-normal distribution with application to pollen data

This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic properties of this family of distributions and provides a stochastic representation which is useful for obtaining theoretical properties and to simulate from the distribution. Moreover, the singularity of the Fisher information matrix is investigated and maximum likelihood estimation for a random sample with no covariates is considered. The main motivation is thus to avoid using mixtures in fitting bimodal data as these are well known to be complicated to deal with, particularly because of identifiability problems. Data-based illustrations show that such model can be useful. Copyright (C) 2009 John Wiley & Sons, Ltd.

Epsilon Birnbaum-Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum-Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427-443, 2005). The extension allows generating Birnbaun-Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88-95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Bayesian density estimation using Skew Student-t-Normal mixtures

We present a Bayesian approach for modeling heterogeneous data and estimate multimodal densities using mixtures of Skew Student-t-Normal distributions [Gomez, H.W., Venegas, O., Bolfarine, H., 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18, 395-407]. A stochastic representation that is useful for implementing a MCMC-type algorithm and results about existence of posterior moments are obtained. Marginal likelihood approximations are obtained, in order to compare mixture models with different number of component densities. Data sets concerning the Gross Domestic Product per capita (Human Development Report) and body mass index (National Health and Nutrition Examination Survey), previously studied in the related literature, are analyzed. (c) 2008 Elsevier B.V. All rights reserved.

Involutions of RA Loops

Let L be an RA loop, that is, a loop whose loop ring over any coefficient ring R is an alternative, but not associative, ring. Let l bar right arrow l(theta) denote an involution on L and extend it linearly to the loop ring RL. An element alpha is an element of RL is symmetric if alpha(theta) = alpha and skew-symmetric if alpha(theta) = -alpha. In this paper, we show that there exists an involution making the symmetric elements of RL commute if and only if the characteristic of R is 2 or theta is the canonical involution on L, and an involution making the skew-symmetric elements of RL commute if and only if the characteristic of R is 2 or 4.

ANTISYMMETRIC ELEMENTS IN GROUP RINGS II

Let R be a commutative ring, G a group and RG its group ring. Let phi : RG -> RG denote the R-linear extension of an involution phi defined on G. An element x in RG is said to be phi-antisymmetric if phi(x) = -x. A characterization is given of when the phi-antisymmetric elements of RG commute. This is a completion of earlier work.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.