A (2,1)-total labelling of a graph , is an assignment of integers to each vertex and edge such that: (i) any two adjacent vertices of G receive distinct integers, (ii) any two adjacent edges of G receive distinct integers, and (iii) a vertex and its incident edge receive integers that differ by at least 2. The span of a (2,1)-total labelling is the maximum difference between two labels. The minimum span of a (2,1)- total labelling of G is called the (2,1)-total number and denoted by A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label that, the vertices and edges of a cactus graph by 1   

As  is  known,  Meyer  introduced  the  concept  of  the  Perron  complements  of  nonnegative irreducible matrices. In addition, the Schur complements of generalized doubly diagonally dominant matrices were  introduced  by  Liu  etal.  [Linear  Algebra  Appl.,  378(2004):  231-244].  In  this  paper,  properties  of  the Perron complement of strictly generalized doubly diagonally dominate matrices are presented.

For underwater arc welding, it is much more complexity and difficulty to detect penetration depth than land arc welding. Based on least squares support vector machines (LSSVM), welding current, arc voltage, travel speed, contact-tube-to-work distance, and weld pool width are extracted as input units. Penetration depth is predicted in underwater flux-cored arc welding (FCAW). For improvement prediction performance, the LSSVM parameters are adaptively optimized. The experimental results show that this model can achieve higher identification precision and is more suitable to detect the depth of underwater FCAW penetration than back propagation neural networks (BPNN).

In this paper, we propose an algorithm for numerical solving an inverse nonlinear diffusion problem. The algorithm is based on the Laplace transform technique and the finite difference method in conjunction with the least-squares scheme. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. To show the efficiency and accuracy of the present method a test problem will be studied.

For dynamic optimization problems, the aim of an effective optimization algorithm is both to find the optimal solutions and to track the optima over time. In this paper, we advanced two kinds of cellular genetic algorithms inspired by the density dependence scheme in ecological system to solving dynamic optimization problems. Two kinds of improved evolution rules are proposed to replace the rule in regular cellular genetic algorithm, in which null cells are considered to the foods of individuals in population and the maximum of living individuals in cellular space is limited by their food. Moreover, in the second proposed rule, the competition scheme of the best individuals within the neighborhoods of one individual is also introduced. The performance of proposed cellular genetic algorithms is examined under three dynamic optimization problems with different change severities. The computation results indicate that new algorithms demonstrate their superiority respectively on both convergence and diversity.

S. S. Siddiqi and A. Nadeem [A proof of the smoothness of the 6-point interpolatory scheme, International Journal of Computer Mathematics, 83(5-6), 503-509, 2006] proved that Weissman's 6-point

  In  this  paper,  we  give  a  full-Newton  step  primal-dual  interior-point  algorithm  for  monotone horizontal linear complementarity problem. The searching direction is obtained by modification of the classic Newton direction, and which also enjoys the quadratically convergent property in the small neighborhood of $O(2\sqrt{n}{\rm log}\frac{n\mu^0}{\varepsilon})$.

In this paper, we introduce a piecewise modified matrix Padé-type approximation of hybrid order in the interval [0, 1]. It yields highly accurate results and exact values at some given points. The accuracy of this approximation increases as the order or the node increases. This method can be applied to approximate the exponential function. The explicit formula for computing the matrix exponential is presented. A numerical example is given to illustrate the effectiveness of this method.