一种求解半定规划的邻近外梯度算法

本文提出了一种求解半定规划的邻近外梯度算法.通过转化半定规划的最优性条件为变分不等式,在变分不等式满足单调性和Lipschitz连续的前提下,构造包含原投影区域的半空间,产生邻近点序列来逼近变分不等式的解,简化了投影的求解过程.将该算法应用到教育测评问题中,数值实验结果表明,该方法是解大规模半定规划问题的一种可行方法.     

含参集值向量拟均衡问题的适定性

首次对含参集值向量拟均衡问题的适定性进行了研究,并在适当的条件下建立了所研究问题适定性的充分条件.     

Heat‐Flow‐Driven Oligonucleotide Gelation Separates Single‐Base Differences

DNA phase transitions are often induced by the addition of condensation agents or by dry concentration. Herein, we show that the non‐equilibrium setting of a moderate heat flow across a water‐filled chamber separates and gelates DNA strands with single‐base resolution. A dilute mix of DNA with two slightly different gel‐forming sequences separates into sequence‐pure hydrogels under constant physiological solvent conditions. A single base change in a 36 mer DNA inhibits gelation. Only sequences with the ability to form longer strands are concentrated, further elongated, and finally gelated by length‐dependent thermal trapping. No condensation agents, such as multivalent ions, were added. Equilibrium aggregates from dry concentration did not show any sequence separation. RNA is expected to behave identically owing to its equal thermophoretic properties. The highly sequence‐specific phase transition points towards new possibilities for non‐equilibrium origins of life.     

Integrable couplings of fractional L‐hierarchy and its Hamiltonian structures

Based on a general isospectral problem of fractional order, a fractional bilinear form variational identity, the new integrable coupling of fractional L‐hierarchy and the Hamiltonian structures of the integrable coupling of fractional L‐hierarchy are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Some subgradient extragradient type algorithms for solving split feasibility and fixed point problems

In this paper, we consider the split feasibility problem (SFP) in infinite‐dimensional Hilbert spaces and propose some subgradient extragradient‐type algorithms for finding a common element of the fixed‐point set of a strict pseudocontraction mapping and the solution set of a split feasibility problem by adopting Armijo‐like stepsize rule. We derive convergence results under mild assumptions. Our results improve some known results from the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Macro‐hybrid mixed variational two‐phase flow through fractured porous media

Macro‐hybrid mixed variational models of two‐phase flow, through fractured porous media, are analyzed at the mesoscopic and macroscopic levels. The mesoscopic models are treated in terms of nonoverlapping domain decompositions, in such a manner that the porous rock matrix system and the fracture network interact across rock–rock, rock–fracture, and fracture–fracture interfaces, with flux transmission conditions dualized. Alternatively, the models are scaled to a macroscopic level via an asymptotic process, where the width of the fractures tends to zero, and the fracture network turns out to be an interface system of one less spatial dimension, with variable high permeability. The two‐phase flow is characterized by a fractional flow dual mixed variational model. Augmented two‐field and three‐field variational reformulations are presented for regularization, internal approximations, and macro‐hybrid mixed finite element implementation. Also abstract proximal‐point penalty‐duality algorithms are derived and analyzed for parallel computing. Copyright © 2016 John Wiley & Sons, Ltd.     

A Fibonacci quotient

In this article, we describe the outcome of a mathematical collaboration between a university lecturer and an undergraduate student. The resulting investigation concerned a particular divisibility property of the Fibonacci numbers, and indeed it seems that a new result was found in this regard. An interesting point to be made here is that, although the mathematical content was relatively straightforward, this joint exploration did, in a very modest sense, mirror certain key aspects of the research process.     

A pair of Fibonacci-like polynomials arising from a special mapping

We study here a pair of sequences of polynomials that arise from a particular iterated mapping on the plane. We show how these sequences come about, and give some of their interesting mathematical properties.     

An Optimal L∞–error Estimate for an Approximation of a Parabolic Variational Inequality

In this article, an optimal error estimate for parabolic variational inequalities is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimally L^∞-asymptotic behavior in uniform norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolutions.