On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number

Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc（G） = min{∑e∈E f（e）｜ f is an SCDF of G}. This paper will characterize all maxima] planar graphs G with order n ≥ 6 and γ′sc（G） =n.

On the Number of Limit Cycles in Small Perturbations of a Piecewise Linear Hamiltonian System with a Heteroclinic Loop

In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.

Thermodynamic performance of Dual-Miller cycle(DMC) with polytropic processes based on power output, thermal efficiency and ecological function

This study reports a new model of an air standard Dual-Miller cycle(DMC) with two polytropic processes and heat transfer loss.The two reversible adiabatic processes which could not be realized in practice are replaced with two polytropic processes in order to more accurately reflect the practical working performance. The heat transfer loss is taken into account. The expressions of power output, thermal efficiency, entropy generation rate(EGR) and ecological function are addressed using finite-time thermodynamic theory. Through numerical calculations, the influences of compression ratio, cut-off ratio and polytropic exponent on the performance are thermodynamically analyzed. The model can be simplified to other cycle models under specific conditions, which means the results have an certain universality and may be helpful in the design of practical heat engines. It is shown that the entropy generation minimization does not always lead to the best system performance.

CYCLE CONTR0L FUNCTIONS AND THE NUMBER 0F LIMIT CYCLES

The cycle coatrol function is defined and used to estimate tbe number of limit cycles for someplanar autonomous systems. Some sufficient conditions for the existence of no or at most one limitcycles are given.

Assessment of the Endothelial Function with Changed Volume of Brachial Artery by Menstrual Cycle

The endothelial function has been proven to be an important factor in the pathogenesis of atheroscle-rosis, hypertension and heart failure. The flow-mediated vasodilation (FMD) of the peripheral artery is an endothelium-dependent function. Brachial-artery ultrasound scanning is the popular method for evaluat-ing FMD.

Characterization of the genes involved in nitrogen cycling in wastewater treatment plants using DNA microarray and most probable number-PCR

To improve nitrogen removal performance of wastewater treatment plants （WWTPs）, it is essential to understand the behavior of nitrogen cycling communities, which comprise various microorganisms. This study characterized the quantity and diversity of nitrogen cycling genes in various processes of municipal WWTPs by employing two molecular-based methods：most probable number-polymerase chain reaction （MPN-PCR） and DNA microarray. MPN-PCR analysis revealed that gene quantities were not statistically different among processes, suggesting that conventional actwated sludge processes （CAS） are similar to nitrogen removal processes in their ability to retain an adequate population of nitrogen cycling microorganisms. Furthermore, most processes in the WWTPs that were researched shared a pattern：the nitS and the bacterial amoA genes were more abundant than the nirK and archaeal amoA genes, respectivelv. DNA microarray analysis revealed that several kinds of nitrification and denitrification genes were detected in both CAS and anaerobic-oxic processes （AO）, whereas limited genes were detected in nitrogen removal processes. Results of this study suggest that CAS maintains a diverse community of nitrogen cycling microorganisms; moreover, the microbial communities in nitrogen removal processes may be specific.