Department: Mathematics ![[clear]](close-x.png "Remove this limiter")
6 matches in the database.
These are records: 1 - 6.
1.
Carter, James Michael.
Mutually orthogonal latin squares based on ℤ3× ℤ9.
Degree: MS, Mathematics, 2007, Wright State University
► This paper will investigate the number of mutually orthogonal latin squares, MOLS,…
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▼ This paper will investigate the number of mutually orthogonal latin squares, MOLS, that can be constructed using elements from the group G = ℤ3× ℤ9. In calculating this number, it is necessary to consider the group under the action of the homomorphism f : G → K defined by f ((g1, g2))=(g1mod 3, g2mod 3) so that K ≅ Im(G) is isomorphic to ℤ3× ℤ3, so that the action of f is to create the quotient group K = G/〈(0, 3)〉. Based on data from the group ℤ2× ℤ4, the elements of the image should be permuted and constants added before considering G′=f-1(K). The use of orthomorphisms will allow for the construction of orthogonal latin squares.
Advisors/Committee Members: Evans, Anthony.
Subjects: Mathematics
Keywords: orthomorphisms, latin squares
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2.
Gutman, Alex James.
Circulant Weighing Matrices.
Degree: MS, Mathematics, 2009, Wright State University
► The existence status of previously open cases of circulant weighing matrices will…
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▼ The existence status of previously open cases of circulant weighing matrices will be established using various techniques. The results fill in 52 missing entries in Strassler's Table of Circulant Weighing Matrices, which considers matrices of order 1 - 200 with weight k less than or equal to 100.
Advisors/Committee Members: Arasu, K.T.
Subjects: Mathematics
Keywords: matrices, circulant weighing matrices, weighing matrices, Strassler, multiplier, integer circulant weighing matrices
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3.
Hollon, Jeff R.
An Investigation of Group Developed Weighing Matrices.
Degree: MS, Mathematics, 2010, Wright State University
► A weighing matrix is a square matrix whose entries are 1, 0…
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▼ A weighing matrix is a square matrix whose entries are 1, 0 or -1 and has the property that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be developed by an abelian group. Through a combination of extending previous results and by giving explicit constructions we will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022. Further, some of the new results provide insight into the existence of matrices with larger weights and orders.
Advisors/Committee Members: Arasu, K. T.
Subjects: Mathematics
Keywords: group developed; group invariant; weighing matrix; abelian groups; circulant; hadamard; matrices
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4.
McBride, Matthew Scott.
Estimates in the Generalized Morrey Space for Linear Parabolic Systems.
Degree: MS, Mathematics, 2007, Wright State University
► The purpose of the this paper is to study the parabolic system…
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▼ The purpose of the this paper is to study the parabolic system u_t^{i} - D_α(a_ij^{αβ}D_βu^j) = -div f^i in the generalized Morrey Space L_φ^{2,λ} . We would like to understand the regularity of the solutions of this system. It will be shown that 1: if a_ij^{αβ} in C(Q_T) then Du in L_φ^{2,λ}, and 2: if a_ij^{αβ} in VMO(Q_T) then Du in L_φ^{2,λ}. Moreover we will be able to obtain estimates on the gradient of the solutions to the system, which will tell us about the regularity of the solutions.
Advisors/Committee Members: Huang, Qingbo.
Subjects: Mathematics
Keywords: z0; aαβ; ϕ
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5.
Parker, Keli Siqueiros.
Multilevel Hadamard Matrices.
Degree: MS, Mathematics, 2011, Wright State University
► Multilevel Hadamard Matrices (MHMs) have been examined by Trihn, Fan, and Gabidulin…
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▼ Multilevel Hadamard Matrices (MHMs) have been examined by Trihn, Fan, and Gabidulin for constructions of multilevel zero-correlation zone sequences, which in turn have useful application in quasi-synchronous code division multiple access (CDMA) systems. Subsequently, Adams, Crawford, Greeley, Lee and Murugan introduced a construction of full-rate circulant MHMs and proved the existence of an order n MHM with n elements of distinct absolute value for all n, thus determining the maximum number of distinct elements permissible in an order n MHM to be the greatest possible. We give a survey of MHMs, in particular examining the circulant case and the methods for studying such objects. We provide several observations regarding Adams' construction, discuss the characterization of circulant matrices H satisfying HHT = wI for orders 3 and 4, and give new constructions for other orders of MHMs.
Advisors/Committee Members: Arasu, K. T.
Subjects: Mathematics
Keywords: Hadamard Matrix; multilevel Hadamard matrix; weighing matrix; circulant matrices; zero correlation zone sequence
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6.
Phillips, Jason D.
Intersections of Deleted Digits Cantor Sets With Their Translates.
Degree: MS, Mathematics, 2011, Wright State University
► We define a family of deleted digits Cantor sets which satisfy specific…
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▼ We define a family of deleted digits Cantor sets which satisfy specific constraints on the generating set of digits. We explore the structure and dimension of the intersection of a deleted digits Cantor set with its translate by a real value t. These results apply directly to the traditional Middle Thirds Cantor set as well as regular and uniform Cantor sets. We show that this family includes certain irregular sets which have not been previously analyzed. Our methods not only reveal the upper and lower bounds for the Minkowski dimension, but also uncover a formula for calculating the dimension of these intersections when specific conditions are met.
Advisors/Committee Members: Pedersen, Steen.
Subjects: Mathematics
Keywords: deleted digits; Cantor sets; fractals; fractal dimension; fractional dimension
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