19 citations · 35 across the 4 of their papers we have counts for
11 papers
Braid semistatistics and doubly regular R-matrix
S. Duplij, W. Marcinek
We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical…
Determinative degree and nucleotide sequence analysis by trianders
Diana Duplij, Steven Duplij
A new version of DNA walks, where nucleotides are regarded unequal in their contribution to a walk is introduced, which allows us to study thoroughly the "fine structure" of nucleo…
Bi-element representations of ternary groups
Andrzej Borowiec, Wieslaw A. Dudek, Steven Duplij
General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is b…
Basic concepts of ternary Hopf algebras
Andrzej Borowiec, Wieslaw A. Dudek, Steven Duplij
The theory of ternary semigroups, groups and algebras is reformulated in the abstract arrow language. Then using the reversing arrow ansatz we define ternary comultiplication, bial…
Regular graded algebras and obstructed categories with duality
Steven Duplij, Wladyslaw Marcinek
Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity instead of anticommutativity) are introduced and their proper…
Noninvertibility, semisupermanifolds and categories regularization
Steven Duplij, Wladyslaw Marcinek
The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction…