Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g is a xed point free involution. If C is extremal of length a multiple of 24 all the involutions are xed point free, except the Golay Code and eventually putative codes of length 120. Connecting module theoretical properties of a self-dual code C with coding theoretical ones of the subcode C...

In the paper we examine data dependencies in the algorithm of back substitution in the problem of solving triangular systems of linear equations. The aim of the paper is to illustrate the structural blanks (SB) notation in consistency proof of data dependencies in loop programs. Data dependency semantics of programs is introduced and investigated. The introduced notation constitutes the theoret...

Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-modules an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann algebras on separable Hilbert spaces and the theory of von Neumann representations on self-dual Hilbert A-modules with countably generated Apre-dual Hilbert A-mod...

Let k be a fixed field of arbitrary characteristic and let ? basic connected Nakayama k-algebra without simple projective modules. In this article we prove that if V is an indecomposable finitely generated Gorenstein-projective left ?-module, then the versal deformation ring R(?,V) (in sense F. M. Bleher author) universal stable after taking syzygies. We also following result. ?=(?B0?) triangul...

The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism class of the syzygy module. Thus we can use this decomposition to compute the homological dimension...

The D-Egg, an acronym for ``Dual optical sensors in Ellipsoid Glass Gen2,'' is one of the modules designed future extensions IceCube experiment at South Pole. D-Egg has elongated-sphere shape to maximize photon-sensitive effective area while maintaining a narrow diameter reduce cost and time needed drilling deployment holes glacial ice depths up 2700 meters. design utilized Upgrade, next stage ...

Let k be a field, G an abelian group with a bicharacter, A a colour algebra; i.e., an associative graded k-algebra with identity, C a graded A-coring that is projective as a right A-module, C∗ the graded dual ring of C and Λ a left graded C-comodule that is finitely generated as a graded right C∗-module. We give necessary and sufficient conditions for projectivity and flatness of a graded modul...