The system of partial differential equations which governs the
motion of a Newtonian fluid has been known for over a century. Yet,
due to the complexity of the equations, an analytical solution is known
only for a few simple geometries or a few special cases such as very
slow motion....
A technique of differentiation with respect to the distance to
the boundary of an outer parallel-body is applied to known measures of
sets of p-dimensional linear spaces which intersect a general convex
body in n-dimensional euclidean space in order to obtain an appropriate
definition of the measures of sets of...
A computationally efficient algorithm has been developed for
determining exact or approximate solutions for large scale generalized
fixed charge problems. This algorithm is based on a relaxation
of the Benders decomposition procedure, combined with a linear
mixed integer programming (MIP) algorithm specifically designed to
solve the problem associated with Benders...
The Cauchy problem for the evolution equation Mu’(t) + N(t,u(t)) = 0 is studied, where M and N(t,•) are, respectively, possibly degenerate and nonlinear monotone operators from a vector space to its dual. Sufficient conditions for existence and for uniqueness of solutions are obtained by reducing the problem to an...
We give a nonstandard method of integrating the equation Bu" + Cu’ + Au = f in Hilbert space by reducing it to a first order system in which the differentiated term corresponds to energy. Semigroup theory gives existence for hyperbolic and for parabolic cases. When C = εA, ε...
In this thesis the author extends the standard techniques of differential geometry to the case of distributional (in the sense of Schwartz) pseudoriemannian structures. A new definition of flows for distributional vector fields is developed using generalized paths which are essentially nonlinear-distributional measures, and an existence theorem is proved when...
Changes of density occur naturally in phase transition processes and introduce the bulk movement of material. It is customary in analyzing such problems to disregard this unpleasant complication and assume the densities to be equal. However, such changes are unavoidable and for one-dimensional problems the complexities introduced by this bulk...
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the one‐parameter family of hypersurfaces orthogonal to the curves, each of which inherits...