Based on lower record values, we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means, variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution (EMED), a new extension of moment exponential distribution, recently introduced by Hasnain (Exponentiated moment exponential distribution. Ph.D. Thesis, 2013). Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED. Finally, we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters. We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values. Monte Carlo simulations are performed to compare the performances of the proposed methods, and a data set has been analyzed for illustrative purposes.

In this paper, we propose a new biased estimator namely modified almost unbiased Liu estimator by combining almost unbiased Liu estimator (AULE) and ridge estimator (RE) in a linear regression model when multicollinearity presents among the independent variables. Necessary and sufficient conditions for the proposed estimator over the ordinary least square estimator, RE, AULE and Liu estimator (LE) in the mean squared error matrix sense are derived, and the optimal biasing parameters are obtained. To illustrate the theoretical findings, a Monte Carlo simulation study is carried out and a numerical example is used.

We consider the gauge transformations of a metric G-bundle over a compact Riemannian surface with boundary. By employing the heat flow method, the local existence and the long time existence of generalized solution are proved.

We present a smooth parametric surface construction method over polyhedral mesh with arbitrary topology based on manifold construction theory. The surface is automatically generated with any required smoothness, and it has an explicit form. As prior methods that build manifolds from meshes need some preprocess to get polyhedral meshes with special types of connectivity, such as quad mesh and triangle mesh, the preprocess will result in more charts. By a skillful use of a kind of bivariate spline function which defines on arbitrary shape of 2D polygon, we introduce an approach that directly works on the input mesh without such preprocess. For non-closed polyhedral mesh, we apply a global parameterization and directly divide it into several charts. As for closed polyhedral mesh, we propose to segment the mesh into a sequence of quadrilateral patches without any overlaps. As each patch is an non-closed polyhedral mesh, the non-closed surface construction method can be applied. And all the patches are smoothly stitched with a special process on the boundary charts which define on the boundary vertex of each patch. Thus, the final constructed surface can also achieve any required smoothness.

An (s, t)-partition of a graph $G=(V,E)$ is a partition of $V=V_1\cup V_2$ such that $\delta (G[V_1])\ge s$ and $\delta (G[V_2])\ge t$. It has been conjectured that, for sufficiently large n, every d-regular graph of order n has a $(\lceil \frac{d}{2}\rceil , \lceil \frac{d}{2}\rceil )$-partition (called an internal partition). In this paper, we prove that every d-regular graph of order n has a $(\lceil \frac{d}{2}\rceil , \lfloor \frac{d}{2}\rfloor )$ partition (called a weak internal partition) for $d\le 9$ and sufficiently large n.

A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with all Sylow q-subgroups of G for the primes q not dividing the order of H. Some criteria for p-supersolvability of a finite group are given, which are the generalizations of many recent results.