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Estimates In The Generalized Morrey Space For Linear Parabolic Systems, Matthew Scott Mcbride
Estimates In The Generalized Morrey Space For Linear Parabolic Systems, Matthew Scott Mcbride
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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.
Mutually Orthogonal Latin Squares Based On Z3X Z9, James Michael Carter
Mutually Orthogonal Latin Squares Based On Z3X Z9, James Michael Carter
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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 = Z3x 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 Z3x Z3, so that the action of f is to create the quotient group K = G/<(0, 3)>. …