• Abstract

In order to relieve the deficiency of the usual cubic Hermite spline curves, the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed. The quartic Hermite spline curves not only have the same interpolation and continuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and $C^2$ continuity by the shape parameters when the interpolation conditions are fixed.

• Abstract

This paper presents several new Lyapunov-type inequalities for a system of first-order nonlinear differential equations. Our results generalize and improve some existing ones.

• Abstract

In the present paper, we consider a class of compact orientable 3-manifolds with one boundary component, and suppose that the manifolds are ∂-reducible and admit complete surface systems. One of our main results says that for a compact orientable, irreducible and ∂-reducible 3-manifold M with one boundary component F of genus n > 0 which admits a complete surface system S′ , if D is a collection of pairwise disjoint compression disks for ∂M, then there exists a complete surface system S for M, which is equivalent to S′ , such that D is disjoint from S. We also obtain some properties of such 3-manifolds which can be embedded in S³.

• Abstract

In this paper, the concept of C-left hyperideals is introduced in ordered semihypergroups, and several related properties are investigated. In particular, we discuss the relationships between the greatest left hyperideals and C-left hyperideals of ordered semihypergroups. Furthermore, we introduce the concept of left bases of an ordered semihypergroup, and give out the sufficient and necessary conditions of the existence of the greatest C-left hyperideal of an ordered semihypergroup by the properties of left bases. The result about C-left ideals in ordered semigroups is generalized to the ordered semihypergroups.

• Abstract

In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.

• Abstract

By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.

• Abstract

Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S, if and only if S is the strong semilattice of L-right cancellative planks; also if and only if S is a spined product of a right-e wlpp semigroup and a left normal band.

• Abstract

In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K^∞,bscp(SCP). We show that the existence of a right recollement of K^∞,bscp(SCP) with respect to K^−,bscp(SCP), K_scpac(SCP) and K^∞,bscp(SCP) has the homotopy category of strongly copure projective acyclic complexes as a triangulated subcategory in some case.