Asymmetry and structural information in preferential attachment graphs

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd?s‐Rényi graphs are typically asymmetric, real networks are highly symmetric. So a natural question is whether preferential attachment graphs, where in each step a new node with m edges is added, exhibit any symmetry. In recent work it was proved that preferential attachment graphs are symmetric for m = 1, and there is some nonnegligible probability of symmetry for m = 2. It was conjectured that these graphs are asymmetric when m ≥ 3. We settle this conjecture in the affirmative, then use it to estimate the structural entropy of the model. To do this, we also give bounds on the number of ways that the given graph structure could have arisen by preferential attachment. These results have further implications for information theoretic problems of interest on preferential attachment graphs.     

Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information

Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type‐II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max‐probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an EM‐algorithm–type approach, respectively. In all cases, we illustrate the results by simulations of the five‐component bridge system and the 10‐component parallel system, respectively.     

Comparative study on two 2-pyrazoline derivatives with experimental and theoretical methods

Two 2-pyrazoline derivatives of 1-phenyl-3-(4-chlorophenyl)-5-(2-chlorophenyl)-2-pyrazoline (1) and 1-phenyl-3-(4-methylphenyl)-5-(2-chlorophenyl)-2-pyrazoline (2) have been synthesized and characterized by elemental analysis, IR, UV–Vis, and fluorescence spectra. The crystal structure of 2 has been determined by X-ray single crystal diffraction. For the two compounds, density functional theory (DFT) calculations of the structures and natural population atomic charge analysis have been performed at B3LYP/6-311G** level of theory. By using TD-DFT method, electron spectra of 1 and 2 have been predicted, which are in good agreement with the experimental ones. Comparative studies on 1 and 2 indicate that the change of substituted groups in 3-phenyl ring of pyrazoline ring will change the peak intensity and peak locations both in electron spectra and fluorescence spectra.     

The maximum surplus in a finite‐time interval for a discrete‐time risk model with exchangeable,dependent claim occurrences

This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed.     

Pseudo almost periodic in distribution solutions to impulsive partial stochastic functional differential equations

In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we obtain the existence and the exponential stability of piecewise pseudo almost periodic in distribution mild solutions for impulsive partial neutral stochastic functional differential equations under non-Lipschitz conditions. Moreover, an example is given to illustrate the general theorems.     

Experimental and theoretical comparative studies on two 2-pyrazoline derivatives

Two 2-pyrazoline derivatives of 1-phenyl-3-(4-methylphenyl)-5-phenyl-2-pyrazoline (1) and 1-phenyl-3-(4-methylphenyl)-5-(2,4-dichlorophenyl)-2-pyrazoline (2) have been synthesized and characterized by elemental analysis, IR, UV–vis and fluorescence spectroscopy. The crystal structure of 2 has been determined by X-ray single crystal diffraction. For the two compounds, density functional theory (DFT) calculations of the structures and natural population atomic charge analysis have been performed at B3LYP/6-311G** level of theory. By using TD-DFT method, electron spectra of 1 and 2 have been predicted, which suggests the B3LYP/6-311G** method can approximately simulate the electron spectra for the system presented here. Comparative studies on 1 and 2 indicate that the change of substituent in 5-phenyl ring of pyrazoline ring influences the peak location and intensity in electronic and fluorescence spectra.     

An exploration of conformational search of leucine molecule and their vibrational spectra in gas phase using ab initio methods

An extensive exploration of the conformational space has been carried out to characterize all possible gas phase structures of leucine. A total of 324 unique trial structures for canonical leucine were generated by considering all possible combinations of single bond rotamers. All trial structures were optimized at the B3LYP/6-311G* level of the DFT method. A total of 77 unique and stationary canonical conformers were found. Further, 15 most stable conformers were reoptimized at B3LYP/6-311++G** level and their respective relative energies, vertical ionization energies, hydrogen bonding patterns, rotational constants and dipole moments were calculated. A single point energy calculations for leucine conformers have also been done at both B3LYP/6-311++G(2df, p) and MP2/6-311++G(2df, p) levels. The good agreement between our estimates of rotational constants for two most stable conformers and available experimental measurements supports the reliability of the B3LYP/6-311++G** level of theory for describing the conformational behavior of leucine molecule. The proton affinity and gas phase basicity were also determined. Using the statistical approach, conformational distributions at various temperatures have also been performed and analyzed. Vibrational spectra were also calculated. It is also observed that zwitterions of leucine are not stable in gas phase.     

Stabilization of elasticity–viscoporosity system by linear boundary feedback

The initial boundary value problem for linear elastodynamic system for viscoporous materials is considered. Exponential decay of solutions via the linear boundary feedback is established. Existence of solutions is obtained through the method of c₀‐semigroups. Exponential stabilization is derived via a proper collection of ideas of observability inequality, energy identity and c₀‐semigroup of contractions. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear damped Timoshenko systems with second sound—Global existence and exponential stability

In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms being present in the equation for transverse displacement and rotation angle—a frictional damping and a dissipation through hyperbolic heat conduction modelled by Cattaneo's law, respectively. The global existence of small, smooth solutions and the exponential stability in linear and nonlinear cases are established. Copyright © 2008 John Wiley & Sons, Ltd.     

Global eigenvalue distribution regime of random matrices with an anharmonic potential and an external source

We consider ensembles of random Hermitian matrices with a distribution measure determined by a polynomial potential perturbed by an external source. We find the genus-zero algebraic function describing the limit mean density of eigenvalues in the case of an anharmonic potential and a diagonal external source with two symmetric eigenvalues. We discuss critical regimes where the density support changes the connectivity or increases the genus of the algebraic function and consequently obtain local universal asymptotic representations for the density at interior and boundary points of its support (in the generic cases). The investigation technique is based on an analysis of the asymptotic properties of multiple orthogonal polynomials, equilibrium problems for vector potentials with interaction matrices and external fields, and the matrix Riemann-Hilbert boundary value problem. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 34–57, April, 2009.