An integral transformation for integer programming problems

It is shown that every integer programming problem can be transformed into an equivalent integer program with free variables in polynomial time. The transformation is advantageous because the equivalent problem it generates can be solved very easily in some restricted cases.     

Numerical Modeling of Functional Fatigue in NiTi Wires

Motivated by the high potential of shape memory alloys (SMA) in several industrial applications, we investigate the material response under cyclic loading. In particular, the focus is set on the modelling of functional fatigue, which results in the deterioration of the specific features of SMA. In fact, functional fatigue restricts SMA in terms of its applicability for real structures and workpieces. This necessitates the development of material models which take this phenomenon into account. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximation by Gamma type operators

In this study, we introduce newly defined Gamma operators which preserve constants and e^2μ·, μ>0 functions. In accordance with this purpose, we focus on their approximation properties such as uniform convergence, rate of convergence, asymptotic formula, and saturation results. Superior properties of introduced operators have been tested both theoretically and numerically in certain senses to highlight the performance of the new constructions of Gamma operators.     

Optimal production in a competitive market under yield uncertainty

Motivated by the U.S. influenza vaccine market, we study the impact of random yield and production capacity on the number of firms, total supply, consumer surplus and social welfare in a market with identical suppliers. We formulate a two-stage game with endogenous entry, where each entering firm aims to maximize its profit under yield uncertainty subject to a production capacity constraint. We show that if firms produce full capacity in the equilibrium, then there are fewer firms in the equilibrium compared to the social optimum even for small levels of yield uncertainty. Furthermore, we prove that if firms do not produce full capacity in the equilibrium, they will not produce full capacity in the social optimum.     

NEW DYNAMIC INEQUALITIES FOR DECREASING FUNCTIONS AND THEOREMS OF HIGHER INTEGRABILITY

In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, P′olya, D'Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.     

Convergence behavior of interior-point algorithms

We show that most interior-point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition. These algorithms include all path-following algorithms and some potential reduction algorithms. The result also holds for the monotone complementarity problem if a strict complementarity solution exists. In general, the limit point is a solution that maximizes the number of its nonzero components among all solutions.Research supported in part by NSF Grant DDM-8922636, the Iowa Business School Summer Grant, and the Interdisciplinary Research Grant of the University of Iowa Center for Advanced Studies.     

Coverings and Ring-Groupoids

We prove that the set of homotopy classes of the paths in a topological ring is a ring object (called ring groupoid). Using this concept we show that the ring structure of a topological ring lifts to a simply connected covering space.     

A rational approximation based on Bernstein polynomials for high order initial and boundary values problems

We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann [1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ C^d+2[a, b].