This paper defined a new class of transformation graphs by introducing symbol“0”, and for a simple nonempty undirected graph $G$, investigated the connectedness and regularity of ten new transformation graphs of $G$. When $G$ is a regular graph, the spectra of transformation graphs of $G$ were determined in terms of the spectrum of $G$.
The existence of positive solution was studied for thenonlinear Sturm-Liouville boundary value problem, where thenonlinear term $f(t,u)$ may be singular at $t = 0,\,t = 1$. Byintroducing the integrations of height functions of nonlinear termon bounded set the growths of nonlinear term were described. Byapplying the Krasnoselskii fixed point theorem in degree theory andthe dominated convergence theorems in real variable, an existencetheorem of positive solution was proved when there are limitfunctions $\mathop {\lim }\limits_{u \to + 0} f(t,u) / u$ and$\mathop {\lim }\limits_{u \to + \infty } f(t,u) / u$.
Four kinds of Hagen-Rothe type convolutions were defined by introducing denominator factors. They have no closed expressions themselves. Two identities due to Andrews and Burge produced other four convolution formulas by means of reversals and linear combinations. Starting from these four formulae and using Gould-Hsu inversions, four pairs of reciprocal formulas with respect to Hagen-Rothe type convolutions were established.
A weak maximum principle for the variable exponent Laplace on a complete noncompact Riemannian manifold under suitable conditions about the growth of the volume was established, by which a Liouville type theorem for the variable exponent Laplace was proved.
This paper defined the $(r,s)$-differential operator of the algebra of Laurent polynomials over the complex numbers field. Let $\mathcal{D}_{r,s}$ be the associative algebra generated by $\{ t^{\pm 1} \}$ and the $(r,s)$-differential operator, which is called ($r,s$)-differential operators algebra. In this paper, the derivation algebra of $\mathcal{D}_{r,s}$ and its Lie algebra $\mathcal{D}_{r,s}^-$ were described and all the non-trivial 2-cocycles were determined.
The main successional stages including grassland, Pinus massoniana dominated forests, Schima superba dominated forests and Castanopsis fargesii dominated forests in the Tiantong region, were selected to examine temporal trends of soil profile and carbon density. The results showed: (1) soil physical and chemical properties exhibited contrasting temporal patterns, with proportion of soil particulates, soil organic matter and soil moisture (10~20 cm) displaying a gradual increasing trends through succession, and with soil pH and soil bulk density generally decreasing with time; (2) soil carbon density was the lowest in the intermediate layer (10~20 cm) along soil profile, and was “Ushaped” through succession; and (3) among soil properties, proportion of soil particulates was positively correlated with soil moisture and negatively correlated with soil bulk density; soil organic carbon positively correlated with soil carbon density. It is concluded that soil physical and chemical properties substantially improve during secondary succession of evergreen broadleaved forests.
Tributyltin (TBT) used to be widely used as biocides in antifouling paints, but now has been banned in different degrees due to its harmful effects on marine ecosystems. Based on rich references, this paper analyzed relationship between legislations against TBT and concentrations of TBT in marine sediment. At least 22 countries or areas have legislations against TBT and 59.1% of them are in Europe. Most of the legislations were published before 1991. IMO legislation to ban TBT totally will come into force on September 17, 2008. In the world scale, TBT in sediment did not show significant decrease during 1986 to 2006. In contrast, TBT in sediment was a little higher after 1990s’ than before. It was mainly due to the great development of marine transportations, the limited countries with legislation and the global pollution of TBT. As for the areas with registrations against TBT, TBT in sediment usually did not decrease significantly until 4～5 years later. Partial legislation of TBT had positive effect on controlling TBT pollution in small harbors. However, TBT pollution in sediment got worse in those countries without legislation of TBT in recent years. Due to the lag effect of TBT legislation and the slow degradation of TBT in sediment, it will take more decades for TBT concentrations to decrease in sediment and water, and for a ecosystem to recover effectively.
Poly(otoluidine) was synthesized by interfacial polymerization using iron chloride, ammonium persulfate, and a complex (composed by K2S2O8, CuSO4 and NaHSO3) as oxidant, respectively. The molecular structures,morphologies and electrochemical behaviors were detected by FTIR, UVVIS, SEM and Cyclic voltammetry. The results showed that poly(otoluidine) particles appeared as micro powder and their diameters were within several hundred nanometers. All the three polymers showed good electrochemical activity. When using FeCl3 as oxidant, the molecular weight and conjugated degree, as well as the electrochemical activity of the poly(otoluidine), were the best.
This paper gave a review of recent developments in the study of nullities of undirected simple graphs. The problem on nullity is very interesting in characterizing all kinds of properties of graphs as well as in determination of the stability of a molecule in chemistry. The results on bipartite graphs, trees, unicyclic graphs, bicyclic graphs, line graphs of trees were introduced. And thegraphs with large nullities were discussed.
This paper was concerned with a one-dimensional linear wave equation associated with nonlinear boundary conditions. The unique local solution to the wave equation was proved to exist. The result is that the nonlinearity at the boundary causes a finite time blow up of the solution, even for small initial data. And the upper bound to the blow up time is given in the paper
This research guaranteed orthogonal symmetry demonstration to any system function,ensured the formula of demonstration to system function variance.They are the kernel and foundation stone of statistical analysis of global symmetry.By studying how these symmetry functions work in the whole system function,the symmetry of system function can be understood better.As illustrated by the examples,it showed the symmetry of system function clearly by using the Monte-Carlo calculated value of contribution rate as the global sensitivity index of symmetry function.
中国综合性科技类核心期刊(北大核心)
