University. One of my reasons for choosing RAND rather than a more conventional academic appointment was my desire to be involved in applied rather than abstract mathematics. I could not have selected a better location to achieve this particular goal. George Dantzig had arrived recently and was in the process of applying linear programming techniques to a growing body of basic problems. Richard...

Modern Mixed-Integer Programming (MIP) solvers exploit a rich arsenal of tools to attack hard problems. It is widely accepted by the OR community that the solution of very hard MIPs can take advantage from the solution of a series of time-consuming auxiliary Linear Programs (LPs) intended to enhance the performance of the overall MIP solver. E.g., auxiliary LPs may be solved to generate powerfu...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

The first thing taught in Math 340 is Gaussian Elimination, i.e. the process of transforming a matrix to reduced row echelon form by elementary row operations. Because this process has the effect of multiplying the matrix by an invertible matrix it has produces a new matrix for which the solution space of the corresponding linear system is unchanged. This is made precise by Theorem 2.4 below. T...

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

We describe the clinical and pathologic observation of four patients with Porokeratosis of Mibelli. Allof them were women. They had four different forms of disease: Plaque type, functate form, Linear form and superficial disseminated form. In histologic features we observed a new change in basement membrane of epidermis in two patients. This change composed of Liquefaction degeneration of basal...