Let B be a commutative algebra and A B-algebra (determined by an homomorphism ?:B?A). M. D. Staic introduced Hochschild like cohomology H•((A,B,?);A) called secondary cohomology, to describe the non-trivial deformations of A. J. Laubacher et al later obtained natural construction new chain complex C¯•(A,B,?) in process introducing cyclic (co)homology. In this paper, we establish connection betw...

We prove that every [Formula: see text]H-thin link has no text]-torsion for text] in its Khovanov homology. Together with previous results by Lee [The support of the Khovanov’s invariants alternating knots, preprint (2002), arXiv:math.GT/0201105; An endomorphism invariant, Adv. Math. 197(2) (2005) 554–586, arXiv:math.GT/0210213] and author [Torsion homology, Fund. 225 (2014) 343–364, arXiv:math...

Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose ...

We consider the q-hypergeometric equation with q = 1 and α, β, γ ∈ Z. We solve this equation on the space of functions given by a power series multiplied by a power of the logarithmic function. We prove that the subspace of solutions is twodimensional over the field of quasi-constants. We get a basis for this space explicitly. In terms of this basis, we represent the q-hypergeometric function o...

Following Jiang Guanghao and Xu Luoshan’s concept of conjugative, dually conjugative, normal and dually normal relations on sets, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasiregular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually ...

There exist different schemes of model reduction for parametric ordinary differential systems arising from chemical reaction systems. In this paper, we focus on some schemes which rely on quasi-steady states approximations. We show that these schemes can be formulated by means of differential and algebraic elimination. Our formulation is simpler than the classical ones. It permitted us to obtai...

It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises of whether the same statement is true for non-oscillating trajectories of real analytic vector fields. We show, under certain assumptions, that such a trajectory generates an o-minimal and model-complete structure together with th...

Let X be a minuscule Schubert variety. In this article, we use the combinatorics of quivers to define new quasi-resolutions of X . We describe in particular all relative minimal models π̂ : X̂ → X of X and prove that all the morphisms π̂ are small (in the sense of intersection cohomology). In particular, all small resolutions of X are given by the smooth relative minimal models X̂ and we describe a...

We prove that every polarity of PG(2k − 1, q), where k ≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to PGk(2k, q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. P...