R-branch high-lying transition emission spectra of SbNa molecule

The calculation results of the R-branch transition emission spectra of(0–0) band of the A21 → X21 transition system of Sb Na molecule are presented in this paper. These R-branch high-lying transitional emission spectral lines are predicted by using the difference converging method(DCM). Our results show excellent agreement between DCM spectral lines and the experimental values, and the deviations are controlled within 0.0224 cm-1. What is more, based on the principle of over-determined linear equations, the prediction error is quantified in this work, which provides reliable theoretical support for our predicted DCM calculations. This work provides a lot of useful information for understanding the microstructure of Sb Na molecule.

DIFFERENCE SCHEME FOR AN INITIAL-BOUNDARY VALUE PROBLEM FOR LINEAR COEFFICIENT-VARIED PARABOLIC DIFFERENTIAL EQUATION WITH A NONSMOOTH BOUNDARY LAYER FUNCTION

In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter e is given, and error estimate and numerical result are also given.

A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED SELF-ADJOINT ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.

THE UNIFORMLY CONVERGENT DIFFERENCE SCHEMES FOR A SINGULAR PERTURBATION PROBLEM OF A SELFADJOINT ORDINARY DIFFERENTIAL EQUATION

In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of lite difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results.

Convergence of Y Chromosome STR Haplotypes from Different SNP Haplogroups Compromises Accuracy of Haplogroup Prediction

The paternally inherited Y chromosome has been widely used in forensics for personal identification, in anthropology and population genetics to understand origin and migration of human populations, and also in medical and clinical studies （Wang and Li, 2013; Wang et al., 2014）. There are two kinds of extremely useful markers in Y chromosome, single nucle- otide polymorphism （SNP） and short tandem repeats （STRs）. With a very low mutation rate on the order of 3.0 x 10-8 mutations/nucleotide/generation （Xue et al., 2009）, SNP markers have been used in constructing a robust phylogeny tree linking all the Y chromosome lineages from world pop- ulations （Karafet et al., 2008）. Those lineages determined by the pattern of SNPs are called haplogroups. That is to say, we have to genotype an appropriate number of SNPs in order to assign a given Y chromosome to a haplogroup. Compared with SNPs, the mutation rates of STR markers are about four to five orders of magnitude higher （Gusmgo et al., 2005; Ballantyne et al., 2010）. Typing STR has advantages of saving time and cost compared with typing SNPs in phylogenetic assignment of a Y chromosome （Wang et al., 2010）. A set of STR values for an individual is called a haplotype. Because of the disparity in mutation rates between SNP and STR, one SNP haplogroup could actually comprise many STR haplotypes （Wang et al., 2010）. It is most interesting that STR variability is clustered more by haplogroups than by populations （Bosch et al., 1999; Behar et al., 2004）, which indicates that STR haplotypes could be used to infer the haplogroup information of a given Y chromosome. There has been increasing interest in this cost- effective strategy for predicting the haplogroup from a given STR haplotype when SNP data are unavailable. For instance, Vadim Urasin＇s YPredictor （http：//predictor.ydna.ru/）, Whit Atheys＇ haplogroup predictor （http：//www.hprg.com/hapest5/） （Athey, 2005, 2006）, and haplogroup classifier of Arizona University （Schlecht et al., 2008） have been widely employed in previous studies for haplogroup prediction （Larmuseau et al., 2010; Bembea et al., 2011; Larmuseau et al., 2012; Tarlykov et al., 2013）.

CONVERGENCE OF A CONSERVATIVE DIFFERENCE SCHEME FOR THE ZAKHAROV EQUATIONS IN TWO DIMENSIONS

A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is proved in order O(h(2) + r(2)). In the proof, a new skill is used to deal with the term of difference quotient (e(j,k)(n))t. This is necessary, since there is no estimate of E(x, y, t) in L-infinity norm.