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Articles 1 - 7 of 7
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Investigation Of The Effectiveness Of Interface Constraints In The Solution Of Hyperbolic Second-Order Differential Equations, Paul Jerome Silva
Investigation Of The Effectiveness Of Interface Constraints In The Solution Of Hyperbolic Second-Order Differential Equations, Paul Jerome Silva
Theses Digitization Project
Solutions to differential equations describing the behavior of physical quantities (e.g., displacement, temperature, electric field strength) often only have finite range of validity over a subdomain. Interest beyond the subdomain often arises. As a result, the problem of making the solution compatible across the connecting subdomain interfaces must be dealt with. Four different compatibility methods are examined here for hyperbolic (time varying) second-order differential equations. These methods are used to match two different solutions, one in each subdomain along the connecting interface. The entire domain that is examined here is a unit square in the Cartesian plane. The four compatibility …
The Proof Of Fermat's Last Theorem, Mohamad Trad
The Proof Of Fermat's Last Theorem, Mohamad Trad
Theses Digitization Project
Fermat, Pierre de, is perhaps the most famous number theorist who ever lived. Fermat's Last Theorem states that the equation xn + yn = zn has no non-zero integer solutions for x, y and z when n>2.
Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun
Affine Varieties, Groebner Basis, And Applications, Eui Won James Byun
Theses Digitization Project
No abstract provided.
The Edge-Isoperimetric Problem For The Square Tessellation Of Plane, Sunmi Lee
The Edge-Isoperimetric Problem For The Square Tessellation Of Plane, Sunmi Lee
Theses Digitization Project
The solution for the edge-isoperimetric problem (EIP) of the square tessellation of plane is investigated and solved. Summaries of the stabilization theory and previous research dealing with the EIP are stated. These techniques enable us to solve the EIP of the cubical tessellation.
Steiner Systems Of The Mathieu Group M₁₂, Kristin Marie Dillard
Steiner Systems Of The Mathieu Group M₁₂, Kristin Marie Dillard
Theses Digitization Project
A Steiner system T with parameters (5,6,12) is a collection of 6-element sets, called hexads, of a 12-element set [omega], such that any 5 of the 12 elements belong to exactly one hexad. In this project we construct a graph whose vertices are the orbits of S₁₂ on T x T, where T is the set of all Steiner systems S(5,6,12). Two vertices are joined if an orbit is taken into another under the action of a transposition. The number of hexads common to two Steiner systems are also given. We also prove that any two Steiner systems with parameters …
Constructible Circles On The Unit Sphere, Blaga Slavcheva Pauley
Constructible Circles On The Unit Sphere, Blaga Slavcheva Pauley
Theses Digitization Project
In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry.
Solutions To The Chinese Postman Problem, Kenneth Peter Cramm
Solutions To The Chinese Postman Problem, Kenneth Peter Cramm
Theses Digitization Project
Considering the Chinese Postman Problem, in which a mailman must deliver mail to houses in a neighborhood. The mailman must cover each side of the street that has houses, at least once. The focus of this paper is our attempt to discover the optimal path, or the least number of times each street is walked. The integration of algorithms from graph theory and operations research form the method used to explain solutions to the Chinese Postman Problem.