Let Δ be an abelian group. By considering the notion multiplication of Δ-graded modules (see [7]) over a commutative Δ-graded ring with unity, we introduce the notion of product of two Δ-graded submodules which we use to characterize the Δ-graded prime submodules of a multiplication Δ-graded module. Finally we proved a graded version of Nakayama lemma for multiplication Δ-graded modules.

A (δ, g)-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all (δ, g)-cages with odd girth g ≥ 9 are r-connected, where (r − 1) ≤ δ + √ δ − 2 < r and all (δ, g)-cages with even girth g ≥ 10 are r-connected, where r is the largest integer satisfying r(r−1) 2 4 + 1 + 2r(r − 1) ≤ δ. Those results support a conjecture of Fu, Huang and...

Internet Electron. J. Mol. Des. 2003, 1, 000–000 Abstract In order to separate the effect of substituents into two parts, referring to the interaction of the reacting molecules and the solvation, the δ∆G, δ∆H and δ∆S reaction constants were defined and determined from the dependence of ∆G, ∆H and ∆S activation parameters on the σ substituent constants, by analogy with the Hammett equation. The ...

Let G(V,X) be a finite and simple graph of order n size m. The complement G, denoted by G¯, is the obtained removing lines G adding that are not in G. A self-complementary if only it isomorphic to its complement. In this paper, we define δ-complement δ′-complement as follows. For any two points u v with degu=degv remove between add which thus called degu≠degv δ(δ′)-self-complementary G≅Gδ(G≅Gδ′...

Water availability is the most influential factor affecting plant carbon (δ(13)C) and nitrogen (δ(15)N) isotope composition in arid and semi-arid environments. However, there are potential differences among locations and/or species in the sensitivity of plant δ(13)C and δ(15)N to variation in precipitation, which are important for using stable isotope signatures to extract paleo-vegetation and ...

by John Alan Engbers For graphs G and H, an H-coloring of G, or homomorphism from G to H, is an edge-preserving map from the vertices of G to the vertices of H. H-colorings generalize such graph theory notions as proper colorings and independent sets. In this dissertation, we consider four questions involving H-colorings of graphs. Recently, Galvin [27] showed that the maximum number of indepen...

in order to reduce the operating temperature of solid oxide fuel cells (sofcs), novel electrolyte materials based on ceo2 and baceo3 are being developed in the scientific realm. in this context, we propose a new methodology for preparing the nano-ceramic composite materials such as bace0.9gd0.9o3-δ – ce0.9gd0.9o2-δ (bcgo–cgo) and bace0.8sm0.2o3-δ – ce0.8sm0.2o2-δ (bcso – cso) as possible elec...

We first measured the δ(13)C and δ(15)N values of root holoparasite Cynomorium songaricum and its hosts from 19 sites across four provinces in northwest China, in an attempt to investigate their nutritional relationship at the Tibetan plateau and the surrounding Gobi desert. Our study showed that the δ(13)C of C. songaricum closely mirrored the values of its hosts, Nitraria tangutorum and N. si...