In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(t) = f(t, u(t));u(a) − u(b) = λi ∈ R; i = 0, ..., n− 1. Where f is a Carathéodory function. We obtain sufficient conditions in f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n ≥ 3 either α ≤ β or α ≥ β. For this, we study...

In this paper highly transitive subgroups of the symmetric group on the natural numbers are studied using combinatorics and the Baire category method. In particular, elementary combinatorial arguments are used to prove that given any nonidentity permutation α on N there is another permutation β on N such that the subgroup generated by α and β is highly transitive. The Baire category method is u...

a group is called morphic if for each normal endomorphism α in end(g),there exists β such that ker(α)= gβ and gα= ker(β). in this paper, we consider the case that there exist normal endomorphisms β and γ such that ker(α)= gβ and gα = ker(γ). we call g quasi-morphic, if this happens for any normal endomorphism α in end(g). we get the following results: g is quasi-morphic if and only if, for any ...

There are multiple polymorphic crystalline forms (such as α, β, γ, δ) of Poly(vinylidene fluoride) (PVDF). These crystal phases are different from each other due to two main factors: the relative orientations of the polymorphic molecules in crystal structures and the sequential orders of the torsion angles. Most of the previous research has been focused on the αand β-phases, since α-crystal is ...

– in this paper we consider some (α ,β ) -metrics such as generalized kropina, matsumoto and f (α β )2α = + metrics, and obtain necessary and sufficient conditions for them to be einstein metrics when βis a constant killing form. then we prove with this assumption that the mentioned einstein metrics must beriemannian or ricci flat.

In this paper, properties of ideal I semiprime ring R with multiplicative generalized (α,β)- reverse derivation determined not necessarily additive map d is studied. We previous studies for different derivations to F. show that [β(p),d(p)]I=0 all p∈I or [d(p)],α(p)]I=0 under the given conditions. Also, we give relationship between and anti-automorphism α automorphism β R. Under conditions, exam...

A novel Cu(II)-catalyzed cyclization of α-diazo-β-oxoamides with amines has been developed, constituting a straightforward method to construct pyrrol-3(2H)-one rings. The intramolecular hydrogen bonding effect in α-diazo-β-oxoamides plays an essential role in this reaction. A plausible reaction mechanism involving divergent generation and subsequent [2 + 3] cyclization of ketene and α-diazoimin...

Inspired by Fu et al. work [12] on modeling the exclusive-or differential property of the modulo addition as an mixed-integer programming problem, we propose a method with which any finite automaton can be formulated as an mixed-integer programming model. Using this method, we show how to construct a mixed integer programming model whose feasible region is the set of all differential patterns (...

Human telomerase reverse transcriptase (hTERT) is an essential component required for telomerase activity and telomere maintenance. Several alternatively spliced forms of hTERT mRNA have been reported in human primary and tumor cells. Currently, however, there is no sensitive and accurate method for the simultaneous quantification of multiple alternatively spliced RNA transcripts, such as in th...