We introduced and studied GF-regular modules as a generalization of π-regular rings to modules as well as regular modules (in the sense of Fieldhouse). An R-moduleM is called GF-regular if for each x ∈ M and r ∈ R, there exist t ∈ R and a positive integer n such that rntrnx = rx. The notion of G-pure submodules was introduced to generalize pure submodules and proved that an RmoduleM isGF-regula...

The relationship between flow motion and tissue oxygenation was investigated during hemorrhage/retransfusion with and without dopamine in 14 pigs. During 45% bleed, jejunal microvascular hemoglobin O(2) saturation (HBjO(2)) and mucosal tissue Po(2) (Po(2)muc) were recorded in seven control and seven dopamine-treated animals. Mean arterial pressure and systemic O(2) delivery decreased during hem...

Let S be a d-dimensional separoid of (k− 1)(d+1)+1 convex sets in some ‘large-dimensional’ Euclidean space IE . We prove a theorem that can be interpreted as follows: if the separoid S can be mapped with a monomorphism to a d-dimensional separoid of points P in general position, then there exists a k-colouring ς:S → Kk such that, for each pair of colours i, j ∈ Kk, the convex hulls of their pre...

Suppose that M is a connected orientable n-dimensional manifold and m > 2n. If H(M, R) = 0 for i > 0, it is proved that for each m there is a monomorphism Hm(Wn, O(n)) → H m cont(Diff M, R). If M is closed and oriented, it is proved that for each m there is a monomorphism Hm(Wn, O(n)) → H m−n cont (Diff+ M, R), where Diff+ M is the group of orientation preserving diffeomorphisms of M . 2000 Mat...

A new eulytite-like orthophosphate Pb(3)Bi(PO(4))(3), was synthesized by the high temperature solution growth (HTSG) method and characterized by X-ray single crystal diffraction, powder diffraction and electron microscopy. It crystallizes in the acentric cubic space group (I4[combining macron]3d). The pure-phase powders of Pb(3)Bi(PO(4))(3), Ba(3)La(PO(4))(3) and Ba(3)Bi(PO(4))(3) were also pre...

Introduction One of the fundamental properties of typical AIS is its monomorphism. The C-shaped scoliosis is a “pure” 3D deformation, while S-shaped form consists of two 3D curves, etc. Mathematical modeling has shown a steady sequence of forming units of 3D deformation. Real clinical manifestations in the initial period of development of typical AIS are identical to changes, predicted by mathe...

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...