An efficient algorithm to solve connectivity problem on trapezoid graphs

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs withn vertices andm edges takesO(K(G)mn ^1.5) time, whereK(G) is the vertex connectivity ofG. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takesO(n ²) time andO(n) space for a trapezoid graph.     

Vibrational and electronic spectra of 9,10-dihydrobenzo(a)pyren-7(8H)-one and 7,8,9,10-tetrahydrobenzo(a)pyrene: an experimental and computational study

The molecular geometries, vibrational and UV-vis spectra of 9,10-dihydrobenzo(a)pyrene-7(8H)-one (9,10-H(2)BaP) and 7,8,9,10-tetrahydrobenzo(a)pyrene (7,8,9,10-H(4)BaP) were investigated using density functional theory (DFT-B3LYP), with the triple-ζ 6-311+G(d,p) and Dunning's cc-pVTZ basis sets. From the comparison of infrared experimental and calculated infrared, and Raman data comprehensive assignments are made. The calculated infrared frequencies below 1800 cm(-1) are in good agreement with experimental data, with an average deviation of <4 cm(-1). Using the B3LYP/6-311+G(d,p)//TD-B3LYP/6-311G(d,p) level of theory, transition energies, and oscillator strengths of the 30 lowest electronic absorption bands are assigned to π-π* transitions, with good qualitative agreement between experimental and simulated absorption data. In addition, the HOMO-LUMO gaps and their chemical hardness were analyzed.     

Central limit theorem for quadratic forms for sparse tables

Sufficient conditions for asymptotic normality for quadratic forms in {n_t − np_t} are given, where {n_t} are the observed counts with expected cell means {np_t}. The main result is used to derive asymptotic distributions of many statistics including the Pearson's chi-square.     

A Domain Embedding Method Using the Optimal Distributed Control and a Fast Algorithm

We propose a domain embedding method to solve second order elliptic problems in arbitrary two-dimensional domains. The method is based on formulating the problem as an optimal distributed control problem inside a disc in which the arbitrary domain is embedded. The optimal distributed control problem inside the disc is solved rapidly using a fast algorithm developed by Daripa et al. [3,7,10–12]. The arbitrary domains can be simply or multiply connected and the proposed method can be applied, in principle, to a large number of elliptic problems. Numerical results obtained for Dirichlet problems associated with the Poisson equation in simply and multiply connected domains are presented. The computed solutions are found to be in good agreement with the exact solutions with moderate number of grid points in the domain.     

Evidence of Dynamical Fluctuation of Target Residues in Relativistic Nuclear Interaction at 14.5 AGeV

An analysis of data of target fragments of ²⁸Si-AgBr (at 14.5 AGeV) reveals the existence of emission asymmetry in the azimuthal plane, which is found to depend on the number of target fragments. The comparison with the data of ³²S-AgBr (at 200 AGeV) and ¹⁶O-AgBr (at 60 AGeV) interactions indicates that emission asymmetry depends on the projectile mass and energy.     

A data dependent approach to density estimation

Summary A data dependent approach to density estimation is proposed here. The proposed method requires boundedness and some weak integrability condition on the unknown density, but not any assumption of smoothness. Applications to histogram, kernel, spline and orthogonal series methods are discussed.     

A family of maximal subgroups containing the Sylow subgroups and some solvability conditions

Archiv der Mathematik -     

Pressure dependence of elastic properties of wurtzite ZnO crystal

We present the pressure dependence of elastic properties of the wurtzite phase of ZnO undergoing wurtzite to the rocksalt phase transition. A simple Landau theory is developed to describe the structural phase transition between wurtzite to rocksalt phases observed in ZnO. We have defined the necessary order parameter of the wurtzite to the rocksalt phase transition. We present a detailed analysis of the pressure dependence of the elastic and shear constants of the wurtzite phase of ZnO. The theoretical predictions are in the line with experimental results.     

Evidence of pressure dependence tricritical point at the nematic–smectic-A transition

We examine the effect of pressure on the nematic to smectic-A N–SmA) transition within the Landau phenomenological theory. The influence of pressure on the N–SmA transition is discussed by varying the coupling between the orientational and translational order parameters. The possibility of the tricritical point at the N–SmA transition is discussed in a phenomenological way. The theoretical predictions are found to be in good qualitative agreement with experimental results.