Hypercontinuous Posets

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.     

Global dynamics for a model of a class of continuous‐time dynamical systems

In this paper, the global asympotic behavior of solutions of a class of continuous‐time dynamical system is studied. Not only do we obtain the ultimate boundedness of solutions of the system but we also obtain the rate of the trajectories of the system going from the exterior of the trapping set to the interior of the trapping set, which can be applied to study chaotic control and chaotic synchronization of the system. Copyright © 2015 John Wiley & Sons, Ltd.     

Approximating curves for non-expansive mappings and accretive operators

In this article, under the hypotheses that E is a reflexive Banach space which has a weakly continuous duality mapping J _? with gauge function ?, we investigate several alternative viscosity approximation methods for finding some common fixed points of infinite non-expansive mappings, and prove two strong convergence theorems.     

An extension of the well-posedness concept for fractional differential equations of Caputo’s type

It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution exists and that this solution continuously depends on the given function, the initial value, and the order of the derivative. Here, we extend this well-posedness concept to the extent that we also allow the location of the starting point of the differential operator to be changed, and we prove that the solution depends on this parameter in a continuous way too if the usual assumptions are satisfied. Similarly, the solution to the corresponding terminal value problems depends on the location of the starting point and of the terminal point in a continuous way too.     

在数学专业运筹学教学中引入计算机实践环节的探索

运筹学是应用数学的一个重要分支,在许多学科领域及工程问题中均有应用.自从运筹学在上世纪建立以来,其算法及理论的发展都受到了电子计算机的发展的极大影响.因此在本科运筹学教学中引入适当的计算机实践是非常必要的.这将有助于学生更加深入清晰地理解算法的工作步骤、算法建立的思想以及每个算法的优缺点.在本文中我们试着探讨了为何应在数学专业的运筹学教学中引入计算机实践环节,以及应当如何引入这些实践活动.     

Getting Ring‐Closing Metathesis off the Bench: Reaction‐Reactor Matching Transforms Metathesis Efficiency in the Assembly of Large Rings

Reported is the first study of the influence of reactor configuration on the efficiency of a challenging ring‐closing metathesis (RCM) reaction. With the intention of increasing the generality of RCM scaleup and reducing its dependence on substrate modification, macrocyclization of an unmodified, low effective‐molarity diene was explored using different reactor types, in conjunction with a commercial, homogeneous Grubbs catalyst. Optimized performance is compared for a conventional batch reactor (BR), a continuous plug‐flow reactor (PFR), and a continuous stirred‐tank reactor (CSTR). In the PFR, maximum conversion is achieved most rapidly, but product yields and selectivity are adversely affected by co‐entrapment of ethylene with the catalyst, substrate, and product in the traveling “plug”. Use of the CSTR, in which ethylene is efficiently swept out, affords an order‐of‐magnitude increase in total turnover numbers, and reduces the required catalyst loadings by 25× relative to the BR (to 0.2 mol %), while improving RCM yields and selectivity to quantitative levels. Continuous‐flow methodologies that support liberation of the ethylene co‐product thus show great promise for industrial uptake of RCM.