We generalize the notions of badly approximable (resp. singular) systems of m linear forms in n variables, and relate these generalizations to certain bounded (resp. divergent) trajectories in the space of lattices in Rm+n.

LetM be a connectedmatroid having a ground set E. Lemos andOxley proved that |E(M)| ≤ 2 c(M)c (M)where c(M) (resp. c(M)) is the circumference (resp. cocircumference) of M. In addition, they conjectured that one can find a collection of at most c(M) circuits which cover the elements ofM at least twice. In this paper, we verify this conjecture for regular matroids. Moreover, we show that a versio...

In this paper, we prove that f is an 1-sequence-covering (resp., 2sequence-covering) mapping from a locally separable metric space M onto a space X if and only if {(Xλ, {Pλ,n}) : λ ∈ Λ} is a double point-star wsn-cover (resp., double point-star so-cover) for X, where (f,M,X, {Pλ,n}) is an ls-Ponomarevsystem, and investigate further properties of mappings in the ls-Ponomarevsystem (f,M,X, {Pλ,n}).

In this Note, we prove three theorems. Throughout, F will denote a number field with absolute Galois group GF = Gal(F̄ /F ), and the adele ring AF = F∞ × AF,f . When ρ is an irreducible continuous 2– dimensional C representation of GF , one says that it is icosahedral, resp. octahedral, resp. tetrahedral, resp. dihedral when the projective image of ρ(GF ) is A5, resp. S4, resp. A4, resp. D2m for...

Let M be a graded leftA-module and M∗ the associate complex of M. Then : If is noetherian (resp. artinian) then strongly hopfian cohopfian); cohopfian), leftA-module, M, N submodule N∗ fully invariant subcomplex M∗. M∗/N∗ hopfian, hopfian. if all cohopfian, cohopfian.

We propose to replace Zadeh's DeMorgan-type negation in fuzzy logic by a Heyting-type negation which, unlike the former, preserves the law of the excluded contradiction and is more in line with negation in databases and logic programs. We show that the resulting system can be used for obtaining conservative extensions of relational and deductive databases (resp. normal logic programs).

In this paper, we give an algebra-combinatorics formula of the Möbius transform for an abstract simplicial complex K on [m] = {1, ...,m} in terms of the Betti numbers of the Stanley-Reisner face ring of K. Furthermore, we employ a way of compressing K to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex...

We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del to formalize paraconsistent fuzzy reasoning. The are interpreted matrices, where the common underlying structure is bi-lattice (twisted) product of $[0,1]$ interval. first (resp.\ second) coordinate encodes positive negative) information one has about a statement. propose constraint tableaux that provide modular framework...

In this paper, we concentrate on studying the generalization of almost interior Γ-hyperideals in ordered Γ-semihypergroups. The notion weakly Γ-semihypergroups is introduced. This concept generalizes Then, characterization having no proper provided. Next, introduce fuzzy Also, some properties are considered. Moreover, concepts and characterized. connections between strongly prime (resp., prime,...

In this paper, we give an algebra–combinatorics formula of the Möbius transform for an abstract simplicial complex K on [m] = {1, ...,m} in terms of the Betti numbers of the Stanley–Reisner face ring of K. Furthermore, we employ a way of compressing K to estimate the lower bound of the sum of those Betti numbers by using this formula. As an application, associating with the moment-angle complex...