A COMPLETE SOLUTION OF HOSOYA'S MYSTERY

ＺＨＡＮＧＦＵＪＩ（张福基）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉａｍｅｎ３６１００５，Ｃｈｉｎａ）ＣＨＥＮＲＯＮＧＳＩ（陈荣斯）（ＣｏｌｌｅｇｅｏｆＦｉｎａｎｃｅａｎｄＥｃｏｎｏｍｉｃｓ，Ｆｕｚｈｏ...     

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

ＳＯＭＥＫＩＮＤＳＯＦＬＩＡＰＵＮＯＶＦＵＮＣＴＩＯＮＡＬＩＮＳＴＡＢＩＬＩＴＹＴＨＥＯＲＹＯＦＲＦＤＥＤＵＸＵＥＴＡＮＧ（杜雪堂）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ４１００...     

HORMANDER MULTIPLIER THEOREM ON SU(2)

ＨＲＡＮＤＥＲＭＵＬＴＩＰＬＩＥＲＴＨＥＯＲＥＭＯＮＳＵ（２）￥ＦＡＮＤＡＳＨＡＮ；ＸＵＺＥＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｕｈｕｉＵｎｉｖｅｒｓｉｔｙｔＨｅｆｅｉ２３００３９，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ａｂｏｕｎｄ...     

ASYMPTOTIC BEHAVIOR OF OPERATORS OF PROBABILISTIC TYPE IN L_p SPACES

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＯＰＥＲＡＴＯＲＳＯＦＰＲＯＢＡＢＩＬＩＳＴＩＣＴＹＰＥＩＮＬ_ｐＳＰＡＣＥＳ￥ＣＨＥＮＷＥＮＺＨＯＮＧ；ＣＵＩＺＨＥＮＬＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉ?..     

A SUFFICIENT CONDITION FOR NON－COEXISTENCE OF ONE DIMENSIONAL MULTICOLOR CONTACT PROCESSES

ＡＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＮＯＮ－ＣＯＥＸＩＳＴＥＮＣＥＯＦＯＮＥＤＩＭＥＮＳＩＯＮＡＬＭＵＬＴＩＣＯＬＯＲＣＯＮＴＡＣＴＰＲＯＣＥＳＳＥＳＬＩＵＸＩＵＦＡＮＧ（刘秀芳）ＷＡＮＧＪＵＮ（王军）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

A strong limit theorem for generalized Cantor-like random sequences

ＡＳＴＲＯＮＧＬＩＭＩＴＴＨＥＯＲＥＭＦＯＲＧＥＮＥＲＡＬＩＺＥＤＣＡＮＴＯＲ－ＬＩＫＥ　ＲＡＮＤＯＭ　ＳＥＱＵＥＮＣＥＳＬＩＵＷＥＮ（刘文）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｙｓｉｃｓ,ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅ...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

TURNING POINT PROBLEMS FOR THE THIRD ORDER DIFFERENTIAL EQUATIONS EXHIBITING RESONANCE

ＴＵＲＮＩＮＧＰＯＩＮＴＰＲＯＢＬＥＭＳＦＯＲＴＨＥＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＥＸＨＩＢＩＴＩＮＧＲＥＳＯＮＡＮＣＥＸＩＡＯＣＨＥＮＧＹＯＵ（肖成猷）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉ...     

BLOW-UP AT THE BOUNDARY FOR DEGENERATE DIFFUSION EQUATION

ＢＬＯＷ－ＵＰＡＴＴＨＥＢＯＵＮＤＡＲＹＦＯＲＤＥＧＥＮＥＲＡＴＥＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮ￥ＣａｏＺｈｅｎｃｈａｏ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＸｉａｍｅｎＵｎｉｖ．Ｘｉａｍｅｎ３６１００５）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｃｏｎｓｉ...     

A COMPLETE METRIC OF POSITIVE CURVATURE ON R~n AND EXISTENCE OF CLOSED GEODESICS

ＡＣＯＭＰＬＥＴＥＭＥＴＲＩＣＯＦＰＯＳＩＴＩＶＥＣＵＲＶＡＴＵＲＥＯＮＲ~ｎＡＮＤＥＸＩＳＴＥＮＣＥＯＦＣＬＯＳＥＤＧＥＯＤＥＳＩＣＳ￥ＺＨＵＤＡＸＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｌＴｉａｎｊ?..     

RECOGNIZING ESSENTIALLY DISCONNECTED BENZENOIDS WITH FIXED DOUBLE BONDS

ＲＥＣＯＧＮＩＺＩＮＧＥＳＳＥＮＴＩＡＬＬＹＤＩＳＣＯＮＮＥＣＴＥＤＢＥＮＺＥＮＯＩＤＳＷＩＴＨＦＩＸＥＤＤＯＵＢＬＥＢＯＮＤＳ￥ＬＩＮＫＥＲＯＮＧ；Ｓ．Ｊ．ＣＹＶＩＮ；Ｂ．Ｎ．ＣＹＶＩＮ；ＣＨＥＮＲＯＮＧＳＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａ...     

Nonautonomous saddle-node bifurcations: Random and deterministic forcing

We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing by measure-preserving dynamical systems and for deterministic forcing by homeomorphisms of compact metric spaces. Additional assumptions like ergodicity or minimality of the forcing process then yield further information about the dynamics.The main difference to the unforced situation is that at the critical bifurcation parameter, two alternatives exist. In addition to the possibility of a unique neutral invariant graph, corresponding to a neutral fixed point, a pair of so-called pinched invariant graphs may occur. In quasiperiodically forced systems, these are often referred to as ‘strange non-chaotic attractors’. The results on deterministic forcing can be considered as an extension of the work of Novo, Núñez, Obaya and Sanz on nonautonomous convex scalar differential equations. As a by-product, we also give a generalisation of a result by Sturman and Stark on the structure of minimal sets in forced systems.     

A forcing relation of braids from Nielsen fixed point theory

In this paper, we focus our attention on the connections between the braid group and Nielsen fixed point theory. A new forcing relation between braids is introduced, and we show that it can be fulfilled by using Nielsen fixed point theory.     

Non-convex sweeping processes involving maximal monotone operators

By using a regularization method, we study in this paper the global existence and uniqueness property of a new variant of non-convex sweeping processes involving maximal monotone operators. The system can be considered as a maximal monotone differential inclusion under a control term of normal cone type forcing the trajectory to be always contained in the desired moving set. When the set is fixed, one can show that the unique solution is right-differentiable everywhere and its right-derivative is right-continuous. Non-smooth Lyapunov pairs for this system are also analysed.     

On fixed points of stratified maps

Nielsen fixed point theory deals with the fixed point sets of self maps on compact polyhedra. In this note, we shall extend it to stratified maps, to consider fixed points on (noncompact) strata. The extension was motivated by our recent work on the braid forcing problem in which the deleted symmetric products are indispensable. The stratified viewpoint is theoretically as natural as the equivariant Nielsen fixed point theory, while it can be more tractable computationally and more flexible in applications. This work was partially supported by an NSFC grant and a BMEC grant.     

A trace formula for the forcing relation of braids

The forcing relation of braids has been introduced for a 2-dimensional analogue of the Sharkovskii order on periods for maps of the interval. In this paper, by making use of the Nielsen fixed point theory and a representation of braid groups, we deduce a trace formula for the computation of the forcing order.     

A note on “Monte Carlo analysis of convertible bonds with reset clause”

Kimura and Shinohara [T. Kimura, T. Shinohara, Monte Carlo analysis of convertible bonds with reset clauses, European Journal of Operational Research 168 (2006) 301–310] analyze the value of a non-callable convertible bond with a reset clause. For a reset convertible bond, the conversion ratio is not fixed but depends on the underlying stock price. However, their model does not consider a dilution effect which can result due to changes in the number of shares into which the bond is converted. In this paper, we have developed a new pricing formula for reset convertible bonds that adjusts for dilution.     

Characterization of reducible hexagons and fast decomposition of elementary benzenoid graphs

A benzenoid graph is a finite connected plane graph with no cut vertices in which every interior region is bounded by a regular hexagon of a side length one. A benzenoid graph G is elementary if every edge belongs to a 1-factor of G. A hexagon h of an elementary benzenoid graph is reducible, if the removal of boundary edges and vertices of h results in an elementary benzenoid graph. We characterize the reducible hexagons of an elementary benzenoid graph. The characterization is the basis for an algorithm which finds the sequence of reducible hexagons that decompose a graph of this class in O(n²) time. Moreover, we present an algorithm which decomposes an elementary benzenoid graph with at most one pericondensed component in linear time.     

None of the coronoid systems can be isometrically embedded into a hypercube

A graph that can be isometrically embedded into a hypercube is called a partial cube (or binary Hamming graph). Klavžar, Gutman and Mohar [S. Klavžar, I. Gutman, B. Mohar, Labeling of benzenoid systems which reflects the vertex-distance relations, J. Chem. Inf. Comput. Sci. 35 (1995) 590–593] showed that all benzenoid systems are partial cubes. In this article we show that none of the coronoid systems (benzenoid systems with “holes”) is a partial cube.     

Chaos in periodically forced discrete-time ecosystem models

Natural populations whose generations are non-overlapping can be modelled by difference equations that describe how the populations evolve in discrete time-steps. These ecosystem models are, in general, nonlinear and contain system parameters that relate to such properties as the intrinsic growth-rate of a species. Typically, the parameters are kept constant. In this study, in order to simulate cyclic effects due to changes in environmental conditions, periodic forcing is applied to system parameters in four specific models, comprising three well-known, single-species models due to May, Moran–Ricker, and Hassell, and also a Maynard Smith predator–prey model. It is found that, in each case, a system that has simple (e.g., periodic) behavior in its unforced state can take on extremely complicated behavior, including chaos, when periodic forcing is applied, dependent on the values of the forcing amplitudes and frequencies. For each model, the application of forcing is found to produce an effective increase in the parameter space over which the system can behave chaotically. Bifurcation diagrams are constructed with the forcing amplitude as the bifurcation parameter, and these are observed to display rich structure, including chaotic bands with periodic windows, pitch-fork and tangent bifurcations, and attractor crises.