Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 135-139).

No description available.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [104]-115).

No description available.

In this thesis some problems in mathematical programming have been studied. Chapter 1 contains a brief review of the problems studied and the motivation for choosing these problems for further investigation. The development of two algorithms for finding all the vertices of a convex polyhedron and their applications are reported in Chapter 2. The linear complementary problem is studied in Chapter 3 and an algorithm to solve this problem is outlined. Chapter 4 contains a description of the plant location problem (uncapacited). This problem has been studied in some depth and an algorithm to solve this problem is presented. By using the Chinese representation of integers a new algorithm has been developed for transforming a nonsingular integer matrix into its Smith Normal Form; this work is discussed in Chapter 5. A hybrid algorithm involving the gradient method and the simplex method has also been developed to solve the linear programming problem. Chapter 6 contains a description of this method. The computer programs written in FORTRAN IV for these algorithms are set out in Appendices Rl to R5. A report on study of the group theory and its application in mathematical programming is presented as supplementary material. The algorithms in Chapter 2 are new. Part one of Chapter 3 is a collection of published material on the solution of the linear complementary problem; however the algorithm in Part two of this Chapter is original. The formulation of the plant location problem (uncapacited) together with some simplifications are claimed to be original. The use of Chinese representation of integers to transform an integer matrix into its Smith Normal Form is a new technique. The algorithm in Chapter 6 illustrates a new approach to solve the linear programming problem by a mixture of gradient and simplex method.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 117-121).

No description available.

Thesis: M.S., Massachusetts Institute of Technology, Department of Mathematics, 1979 / Bibliography: leaf 61. / by Paulo Arruda Villela. / M.S. / M.S. Massachusetts Institute of Technology, Department of Mathematics

In financial markets, spread option is a derivative security with two underlying assets and the payoff of the spread option depends on the difference of these assets. We consider American style spread option which allows the owners to exercise it at any time before the maturity. The complexity of pricing American spread option is that the boundary of the corresponding partial differential equation which determines the option price is unknown and the model for the underlying assets is two-dimensional.In this dissertation, we incorporate the stochasticity to the interest rate and assume that it satisfies the Vasicek model or the CIR model. We derive the partial differential equations with terminal and boundary conditions which determine the American spread option with stochastic interest rate and formulate the associated free boundary problem. We convert the free boundary problem to the linear complimentarity conditions for the American spread option, so that we can go around the free boundary and compute the option price numerically. Alternatively, we approximate the option price using methods based on the Monte Carlo simulation, including the regression-based method, the Lonstaff and Schwartz method and the dual method. We make the comparisons among the option prices derived by the partial differential equation method and Monte Carlo methods to show the accuracy of the result.

The aims of this thesis are to study the fracture behaviour in unreinforced masonry, to carry out a limited experimental program on three-point bending (TPB) masonry panels and to develop a time-dependent fracture formulation for the study of mode I fracture in quasi-brittle materials. A micro-model for fracture in unreinforced masonry is developed using the concept of the discrete crack approach. All basic masonry failure modes are taken into account. To capture brick diagonal tensile cracking and masonry crushing, a linear compression cap is proposed with a criterion for defining the compression cap. The failure surface for brick and brick-mortar interfaces are modelled using a Mohr-Coulomb failure surface with a tension cut-off and a linear compression cap. The fracture formulation, in nonholonomic rate form within a quasi-prescribed displacement approach, is based on a piecewise-linear constitutive law and is in the form of a so-called ?linear complementarity problem? (LCP). The proposed model has been applied to simulating fracture in masonry shear walls and masonry TPB panels. An experimental program was undertaken to investigate the failure behaviour of masonry panels under TPB with relatively low strength mortar. The basic material parameters were obtained from compression, TPB and shear tests on bricks, mortar and brick-mortar interfaces. The experimental results showed that the failure of masonry TPB panels is governed by both tensile and shear failure rather than just tensile failure. The simulation of the masonry TPB tests compared well with the experimental results. In addition, the LCP fracture formulation is enhanced to study the time-dependent mode I fracture in quasi-brittle materials. Two main time-dependent sources, the viscoelasticity of the bulk material and the crack rate dependent opening, are taken into account. A simplified crack rate model is proposed to include the rate-dependent crack opening. The model is applied to predicting time-dependent crack growth in plain concrete beams under sustained loading. The model captures the essential features including the observed strength increase with loading rate, the load-deflection and load-CMOD responses, the deflection-time and CMOD-time curves, the predicted time to failure and the stress distributions in the fracture zone.