An Extremal Characterization of the Incidence Graphs of Projective Planes

Let G be a 4-cycle free, bipartite graph on 2n vertices with partitions of equal cardinality n. Let c₆(G) denote the number of cycles of length 6 in G. We prove that for n 3, c₆(G) , where , with equality if and only if G is the incidence point-line graph of a projective plane.     

disjoint cycles containing specified independent vertices

Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ₂(G)n+k-1. Let v₁,…,v_k be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C₁,…,C_k with v_iV(C_i) for all 1ik.Then G has k vertex-disjoint cycles such that

(i) for all 1ik.

(ii) , and

(iii) At least k-1 of the k cycles are triangles.

The condition of degree sum σ₂(G)n+k-1 is sharp.

On the existence and uniqueness of limit cycles for generalized Liénard systems

In this paper, we consider a generalized Liénard system

     

Integrals of equivariant forms and a Gauss-Bonnet theorem for constructible sheaves

The Berline-Vergne integral localization formula for equivariantly closed forms ([N. Berline, M. Vergne, Classes caractéristiques équivariantes. Formules de localisation en cohomologie équivariante, C. R. Acad. Sci. Paris 295 (1982) 539-541], Theorem 7.11 in [N. Berline, E. Getzler, M. Vergne, Heat Kernels and Dirac Operators, Springer-Verlag, 1992]) is well-known and requires the acting Lie group to be compact. In this article, we extend this result to real reductive Lie groups G_R.As an application of this generalization, we prove an analogue of the Gauss-Bonnet theorem for constructible sheaves. If F is a G_R-equivariant sheaf on a complex projective manifold M, then the Euler characteristic of M with respect to F

     

Covering the alternating groups by products of cycle classes

Given integers k,l?2, where either l is odd or k is even, we denote by n=n(k,l) the largest integer such that each element of An is a product of k cycles of length l. For an odd l, k is the diameter of the undirected Cayley graph Cay(An,Cl), where Cl is the set of all l-cycles in An. We prove that if k?2 and l?9 is odd and divisible by 3, then . This extends earlier results by Bertram [E. Bertram, Even permutations as a product of two conjugate cycles, J. Combin. Theory 12 (1972) 368-380] and Bertram and Herzog [E. Bertram, M. Herzog, Powers of cycle-classes in symmetric groups, J. Combin. Theory Ser. A 94 (2001) 87-99].     

Limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method

By using the averaging method, we study the limit cycles for a class of quartic polynomial differential systems as well as their global shape in the plane. More specifically, we analyze the global shape of limit cycles bifurcating from a Hopf bifurcation and also from periodic orbits with linear center , . The perturbation of these systems is made inside the class of quartic polynomial differential systems without quadratic and cubic terms.     

Harnack-Thom theorem for higher cycle groups and Picard varieties

We generalize the Harnack-Thom theorem to relate the ranks of the Lawson homology groups with -coefficients of a real quasiprojective variety with the ranks of its reduced real Lawson homology groups. In the case of zero-cycle group, we recover the classical Harnack-Thom theorem and generalize the classical version to include real quasiprojective varieties. We use Weil's construction of Picard varieties to construct reduced real Picard groups, and Milnor's construction of universal bundles to construct some weak models of classifying spaces of some cycle groups. These weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors. We obtain some congruences involving the Picard number of a nonsingular real projective variety and the rank of its reduced real Lawson homology groups of divisors.

     

铈铁复合氧化物制备及其甲烷选择性氧化制合成气催化性能

用共沉淀法制备了CeO2-Fe2O3氧载体。在固定床反应器中研究了氧载体中晶格氧部分氧化甲烷的反应,并用空气为氧源进行了氧载体还原-氧化再生循环实验,通过XRD,O2-TPD,H2-TPR等手段对氧载体进行了表征。结果表明,CeO2-Fe2O3氧载体中的体相晶格氧适于部分氧化甲烷制合成气。新鲜的氧载体上存在二种氧：有强氧化性的吸附氧（包括弱吸附分子氧和表面晶格氧）和高选择性的体相晶格氧。在高温条件下（800℃）,CeO2-Fe2O3氧载体在消耗掉吸附氧后能均匀地释放出体相晶格氧将甲烷高选择性的氧化为CO和H2。循环实验表明,可以通过循环来提高合成气的选择性,经长时间的循环CeO2-Fe2O3氧载体上有CeFeO3出现,但其并未对选择性造成不利影响。     

Robust cycles in Kolmogorov–Lotka–Volterra class of models with intraspecific co-operation

Using the Andronov–Hopf bifurcation theorem and the Poincaré–Bendixson Theorem, we explore robust cyclical possibilities in Kolmogorov–Lotka–Volterra class of models with positive intraspecific cooperation (in the form of social networks) in the prey population. We find that this additional feedback effect of intraspecific cooperation introduces nonlinearities which modify the cyclical outcomes of the model. We show that the cyclical outcomes are more robust than in the existing literature in this area due to introduction of such non-linearities. We also demonstrate the possibilities of multiple limit cycles under certain situations.     

Closed form equilibrium evaluation of interest rate caps and related derivatives in a real business cycle setting

The objective of this study is to provide closed form solutions to financial derivatives on mean-reverting cash flows. The general equilibrium real business cycle specification implies that underlying prices follow geometric mean reversion processes. Option-pricing formulas are derived, in terms of macroeconomic parameters or observable market prices, both for consumption goods and interest rates. The framework offers a rich specification of the economy’s yield curve and caplet volatility surface, which seems to fit well with criteria suggested by the empirical literature. The methodology may be useful for studying the effects of real economy changes on financial markets.