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Full-Text Articles in Physical Sciences and Mathematics
Low-Dimensional Reality-Based Algebras, Rachel Victoria Barber
Low-Dimensional Reality-Based Algebras, Rachel Victoria Barber
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In this paper we introduce the definition of a reality-based algebra (RBA) as well as a subclass of reality-based algebras, table algebras. Using sesquilinear forms, we prove that a reality-based algebra is semisimple. We look at a specific reality-based algebra of dimension 5 and provide formulas for the structure constants of this algebra. We determine by looking at these structure constants and setting conditions on specific structural components when this particular reality-based algebra is a table algebra. In fact, this will be a noncommutative table algebra of dimension 5.
Smallest Eigenvalues For A Fractional Boundary Value Problem With A Fractional Boundary Condition, Angela Koester
Smallest Eigenvalues For A Fractional Boundary Value Problem With A Fractional Boundary Condition, Angela Koester
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We establish the existence of and then compare smallest eigenvalues for the fractional boundary value problems D_(0^+)^α u+λ_1 p(t)u=0 and $D_(0^+)^α u+λ_2 q(t)u=0,0< t< 1, satisfying the boundary conditions when n-1<α≤ n. First, we consider the case when 0<β
Self Dual Codes And The Indecomposable Building Blocks, Nathan John Russell
Self Dual Codes And The Indecomposable Building Blocks, Nathan John Russell
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Just like prime numbers are to integers, indecomposable codes are to self dual codes. This paper gives an explicit listing of the first few families of binary self dual codes, up to length 16. Binary self dual codes that are decomposable are given as a composition of indecomposable codes. The indecomposable codes are explicitly listed with generator matrices. The complete classifying process is outlined.
The Monochromatic Column Problem: The Prime Case, Loran Elizabeth Crowell
The Monochromatic Column Problem: The Prime Case, Loran Elizabeth Crowell
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Let p1, p2, . . . , pn be pairwise coprime positive integers and let P = p1p2 · · · pn. Let 0,1,...,m−1 be a sequence of m different colors. Let A be an n×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. A partial solution for the case when m is prime is given.