Sigma function solution of the initial value problem for Somos 5 sequences

The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.

     

Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

Isospectrality and galois projective geometries

We construct a series of pairs of domains in the plane and pairs of surfaces with boundary that are isospectral but not isometric. The construction is based on the existence of finite transformation groups that are spectrally equivalent but not isomorphic. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 660–664, May, 1998. This research was partially supported by the Russian Foundation for Basic Research and by INTAS under joint grant No. 96-01-00043.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

On Gouvêa's conjecture in the unobstructed case

In this article, for a residual modular representation defined over an arbitrary finite field, Gouvêa's conjecture which says that the universal deformation ring is isomorphic to a certain Hecke algebra is proven in the unobstructed case.     

过渡金属钼钒砷杂多化合物的合成与TPR,TPD研究

Seven transition metal molybdovanadoarsenic heteropoly compounds have been synthesized and characterized using IR, UV, TG-DTA, pH potential titration techniques. The molecular formulae of these compounds are pro-posed to be H_xM_yAsMO₁₀V₂O₄₀·zH₂O(x=1～3, y=1,2, M=Cr, Mn, Fe, Co, Ni, Cu, Zn).They are all keggin structure. Surface nature of these compounds have been investigated by temperature programmed desorption and temperature programmed reduction techniques. NH₃-TPD results show that in TPD profiles of the compounds there are two desorption peaks corresponding to weak acid sites of desorption, respectively. Desorbing activativon energy and preexponential factor of weak acid site of desorption for compounds have been calculated. H₂-TPR re-sults show that introducting transtion metal to molybdovanarsenic acid, the reduction peak temperatures of H₂-TPR shift regularly with increasing d electron numbers of transition metals. In addition, Zn and Cu heteropoly com-pounds have yet apparent effect of hydrogen spill over.     

Improved solid-phase peptide synthesis of ‘difficult peptides’ by altering the microenvironment of the developing sequence

Three types of resins, related to the spacer, environmental and microenvironmental models were prepared by grafting commercial AMP polymer with 2-[2-(2-aminoethylamino)-2-oxoethoxy]acetic acid. All resins were highly loaded and functionalized with Rink-amide linker. A comparative synthesis of the classic difficult sequence ACP (65-74) on the prepared resins by Fmoc/t-Bu chemistry is presented. The ‘microenviromental’ model resin afforded the crude peptide in the highest purity (98%).     

Multiple separatrix crossing in multi-degree-of-freedom Hamiltonian flows

Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem.