A unified three point approximating subdivision scheme

In this paper,we propose a three point approximating subdivision scheme,with three shape parameters,that unifies three different existing three point approximating schemes.Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed.The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.     

On constructing total orders and solving vector optimization problems with total orders

In this paper, we introduce a construction method of total ordering cone on \mathbbRⁿ{\mathbb{R}^n} . It is shown that any total ordering cone on \mathbbRⁿ{\mathbb{R}^n} is isomorphic to the cone \mathbbRⁿ_lex{\mathbb{R}^n_{lex}} . Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented.     

How much do we “pay” for using default parameters?

This paper explores the potential benefit of using tuned parameter settings for integer programming instances. Three metrics are considered for selecting parameters: Time-to-Optimality, Proven-Gap and Best-Integer-Solution. Good parameter settings for each metric are found using the open-source software tool Selection Tool for Optimization Parameters. Computational tests are presented using CPLEX solver (version 9.0) on MIPLIB test instances, showing substantial improvements over the default parameter setting. Although the benefit of a tuned parameter setting on an individual instance is outweighed by the cost of identifying the tuned setting, these results indicate that substantial benefit may be achieved in cases where the cost of tuning parameter settings is justified.     

A penalty continuation method for the ∓∞ solution of overdetermined linear systems

A new algorithm for the ∓_∞ solution of overdetermined linear systems is given. The algorithm is based on the application of quadratic penalty functions to a primal linear programming formulation of the ∓_∞ problem. The minimizers of the quadratic penalty function generate piecewise-linear non-interior paths to the set of ∓_∞ solutions. It is shown that the entire set of ∓_∞ solutions is obtained from the paths for sufficiently small values of a scalar parameter. This leads to a finite penalty/continuation algorithm for ∓_∞ problems. The algorithm is implemented and extensively tested using random and function approximation problems. Comparisons with the Barrodale-Phillips simplex based algorithm and the more recent predictor-corrector primal-dual interior point algorithm are given. The results indicate that the new algorithm shows a promising performance on random (non-function approximation) problems.     

On some classes of p-valent functions involving Carlson-Shaffer operator

Let , be a class of functions analytic in the open unit disc E. We use Carlson-Shaffer operator for p-valent functions to define and study certain classes of analytic functions. Inclusion results, a radius problem and some other interesting properties are discussed.     

Irregular Boundary Value Problems with Discontinuous Coefficients and the Eigenvalue Parameter

In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation contains an abstract linear operator which is (usually) unbounded in the space Lq(−1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation is also studied.     

Semiperfect Modules with Respect to a Preradical

In an earlier paper [8] the authors introduced strongly and properly semiprime modules. Here properly semiprime modules M are investigated under the condition that every cyclic submodule is M-projective (self-pp-modules). We study the idempotent closure of M using the techniques of Pierce stalks related to the central idempotents of the self-injective hull of M. As an application of our theory we obtain several results on (not necessarily associative) biregular, properly semiprime, reduced and Firings. An example is given of an associative semiprime PSP ring with polynomial identity which coincides with its central closure and is not biregular (see 3.6). Another example shows that a semiprime left and right FP-injective Pl-ring need not be regular (see 4.8). Some of the results were already announced in [7].     

On Complex Split Quaternion Matrices

In this paper, we present some important properties of complex split quaternions and their matrices. We also prove that any complex split quaternion has a 4 × 4 complex matrix representation. On the other hand, we give answers to the following two basic questions “If AB =  I, is it true that BA =  I for complex split quaternion matrices?” and “How can the inverse of a complex split quaternion matrix be found?”. Finally, we give an explicit formula for the inverse of a complex split quaternion matrix by using complex matrices.     

Solutions of the SIR models of epidemics using HAM

In this paper, we investigate the accuracy of the Homotopy Analysis Method (HAM) for solving the problem of the spread of a non-fatal disease in a population. The advantage of this method is that it provides a direct scheme for solving the problem, i.e., without the need for linearization, perturbation, massive computation and any transformation. Mathematical modeling of the problem leads to a system of nonlinear ODEs. MATLAB 7 is used to carry out the computations. Graphical results are presented and discussed quantitatively to illustrate the solution.     

Generating the surface mapping class group by two elements

Wajnryb proved in 1996 that the mapping class group of an orientable surface is generated by two elements. We prove that one of these generators can be taken as a Dehn twist. We also prove that the extended mapping class group is generated by two elements, again one of which is a Dehn twist. Another result we prove is that the mapping class groups are also generated by two elements of finite order.