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Semi-Symmetric Algebras: General Constructions. Part II

Iliev, Valentin Vankov (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 15A69, 15A78.In [3] we present the construction of the semi-symmetric algebra [χ](E) of a module E over a commutative ring K with unit, which generalizes the tensor algebra T(E), the symmetric algebra S(E), and the exterior algebra ∧(E), deduce some of its functorial properties, and prove a classification theorem. In the present paper we continue the study of the semi-symmetric algebra and discuss its graded dual, the corresponding canonical bilinear form,...

Sensor Location Problem for a Multigraph

Pilipchuk, L. A., Vishnevetskaya, T. S., Pesheva, Y. H. (2013)

Mathematica Balkanica New Series

MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow...

Several results on chordal bipartite graphs

Mihály Bakonyi, Aaron Bono (1997)

Czechoslovak Mathematical Journal

The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that,...

Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs

Weige Xi, Ligong Wang (2016)

Discussiones Mathematicae Graph Theory

Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained...

Sign patterns that allow eventual positivity.

Berman, Abraham, Catral, Minerva, Dealba, Luz Maria, Elhashash, Abed, Hall, Frank J., Hogben, Leslie, Kim, In-Jae, Olesky, Dale D., Tarazaga, Pablo, Tsatsomeros, Michael J., van den Driessche, Pauline (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Signatura of magic and Latin integer squares: isentropic clans and indexing

Ian Cameron, Adam Rogers, Peter D. Loly (2013)

Discussiones Mathematicae Probability and Statistics

The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin squares are included, including the order eight Franklin subset which is of direct relevance...

Simple multilinear algebras and hermitian operators

T. S. R. Fuad, Jon D. Phillips, Xiaorong Shen, Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

The paper studies multilinear algebras, known as comtrans algebras, that are determined by so-called T -Hermitian matrices over an arbitrary field. The main result of this paper shows that the comtrans algebra of n -dimensional T -Hermitian matrices furnishes a simple comtrans algebra.

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