Left and right centers in quasi-Poisson geometry of moduli spaces

We introduce left central and right central functions and left and right leaves in quasi-Poisson geometry, generalizing central (or Casimir) functions and symplectic leaves from Poisson geometry. They lead to a new type of (quasi-)Poisson reduction, which is both simpler and more general than known quasi-Hamiltonian reductions. We study these notions in detail for moduli spaces of flat connections on surfaces, where the quasi-Poisson structure is given by an intersection pairing on homology.     

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non‐uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.     

Development of a general approach to the synthesis of a library of isoflavonoid derivatives

Isoflavonoids are a class of organic compounds that act primarily as antioxidants. They are produced almost exclusively by various members of the bean family including soybeans, tofu, peanuts, chick peas, and alfalfa. The antioxidant characteristics that isoflavonoids exhibit help hinder the progression of certain cancers, primarily breast, prostate, and colon cancer. We have developed a three-five step synthesis for obtaining a suite of isoflavonoid derivatives. The synthesis involves an enamine formation, a ring closure and halogenation, a Suzuki coupling, and finally a global deprotection to obtain the respective isoflavonoid derivatives.     

Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency.     

On the Propagation of Regularity and Decay of Solutions to the k-Generalized Korteweg-de Vries Equation

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u ₀ ∈ H ^3/4+ (?) whose restriction belongs to H ^l ((b, ∞)) for some l ∈ ?⁺ and b ∈ ? we prove that the restriction of the corresponding solution u(·, t) belongs to H ^l ((β, ∞)) for any β ∈ ? and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves.     

广义次指数密度的两个新的等价条件

得到了广义次指数密度的两个新的等价条件,刻划了它们的卷积封闭性和卷积根封闭性.     

Euler方程的解在Besov空间上的存在性和惟一性

利用交换子及不可压缩流的性质,得到了Eu ler方程在Besov空间的端点情形时存在性和惟一性.     

Recombination induced hypergraphs: A new approach to mutation-recombination isomorphism

Natural selection acts on genetic variation that comes from two principal sources: mutation and recombination. Because of the inherent differences between mutation and recombination, it is often assumed that they are qualitatively different ways to explore the genotype space. In this paper a new way of constructing recombination spaces is introduced and the topological features of the resulting hypergraphs are analyzed. It is shown that types which are neighbors in the point mutation space are also neighbors in the recombination space, i.e., mutation and recombination spaces are homomorphic. This implies that the shapes of the fitness functions explored by mutation and recombination are similar. However, the potential of one- and two-point recombination operators to explore the fitness landscape may differ dramatically from uniform recombination operators or mutation operators because of the limited number of recombinant types they can produce. © 1996 John Wiley & Sons, Inc.