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- Function spaces<br />Banach spaces<br />Isometrics (Mathematics)<br />Cayley algebras (1)
- Industrial location -- Mathematical models<br />Heuristic algorithms<br />Heuristic programming (1)
- Industrial location -- Mathematical models<br />Industrial sites -- Location -- Mathematical models (1)
- Quasi-uniform spaces<br />Completeness theorem (1)
- Transportation, Automotive -- Dispatching -- Mathematical models<br />Traffic engineering -- Mathematical models<br />Heuristic algorithms (1)
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Completeness And Related Topics In A Quasi-Uniform Space, John Warnock Carlson
Completeness And Related Topics In A Quasi-Uniform Space, John Warnock Carlson
Doctoral Dissertations
"Completions and a strong completion of a quasi-uniform space are constructed and examined. It is shown that the trivial completion of a T₀ space is T₀ . Examples are given to show that a T₁ space need not have a T₁ strong completion and a T₂ space need not have a T₂ completion. The nontrivial completion constructed is shown to be T₁ if the space is T₁ and the quasi-uniform structure is the Pervin structure. It is shown that a space can be uniformizable and admit a strongly complete quasi-uniform structure and not admit a complete uniform structure. Several counter-examples …
Heuristic Algorithms For The Generalized Vehicle Dispatch Problem, Leland Ray Miller
Heuristic Algorithms For The Generalized Vehicle Dispatch Problem, Leland Ray Miller
Doctoral Dissertations
"A heuristic algorithm, called the sweep algorithm, is developed for the vehicle dispatch problem with distance and load constraints for each vehicle. A mathematical development and a step procedure for the sweep algorithm is given. Also given are eight problems and their solutions derived by the sweep algorithm. The solutions for this algorithm are compared with solutions from other vehicle dispatch algorithms, and the sweep algorithm is found to give better results for almost every problem. Various modifications are also presented for the sweep algorithm. A mathematical formulation is given for the vehicle dispatch problem with arbitrary cost functions at …
Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers, James E. Jamison
Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers, James E. Jamison
Doctoral Dissertations
"In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert …
A Coordinate Oriented Algorithm For The Traveling Salesman Problem, Joseph Sidney Greene
A Coordinate Oriented Algorithm For The Traveling Salesman Problem, Joseph Sidney Greene
Doctoral Dissertations
"The traveling salesman problem may be stated as follows: "A salesman is required to visit each of n given cities once and only once, starting from any city and returning to the original place of departure. What route should be chosen in order to minimize the total distance traveled?" A new algorithm is developed which gives a good approximation to the solution for a large number of cities using reasonable computer time and which will converge to the exact solution if allowed to continue. This algorithm is a branch and bound technique which utilizes the distance between cities in its …
A Heuristic Algorithm For Determining A Constructive Suboptimal Solution To The Combinatorial Problem Of Facility Allocation, Harry Kerry Edwards
A Heuristic Algorithm For Determining A Constructive Suboptimal Solution To The Combinatorial Problem Of Facility Allocation, Harry Kerry Edwards
Doctoral Dissertations
"The major problem in plant layout is to determine the most economical relative location of facilities. There are two distinct types of suboptimal solutions to this combinatorial problem: construction and improvement. The writer has developed Modular Allocation Technique (MAT) which is the first useful construction suboptimal technique. The MAT general algorithm, a theorem relating the MAT solution to the optimal solution and an example problem are given. A computer program has been written that will apply MAT to the allocation problem for a maximum of 40 facilities. Results are given to demonstrate how MAT solutions may be used as initial …
Search Algorithms For The Simple Plant Location Problem, John Bruce Prater
Search Algorithms For The Simple Plant Location Problem, John Bruce Prater
Doctoral Dissertations
"Two algorithms are developed, one exact, one approximate, for finding solutions to the simple plant location problem. Theorems are proved which give sufficient conditions for the inclusion of a plant in the optimal solution. The exact algorithm which is developed is similar to the Branch and Bound method. The approximate technique consists of a directed search through the solution tree for the problem, followed by terminal iterations. The terminal iterations are justified by empirical results obtained from a preliminary version of the technique and a theorem which is proved. Statistics from the results of applying the algorithm to a large …