再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

Generalized matching theorems for closed coverings of convex sets

In this paper we use fixed point and coincidence theorems due to Park [8] to give matching theorems concerning closed coverings of nonempty convex sets in a real topological vector space. Our new results extend previously given ones due to Ky Fan [2], [3], Shih [10], Shih and Tan [11], and Park [7].     

Upper Critical Solution Temperature-Type Responsive Cyclodextrins with Characteristic Inclusion Abilities

Water-soluble and thermoresponsive macrocycles with stable inclusion toward guests are highly valuable to construct stimuli-responsive supramolecular materials for versatile applications. Here, we develop such macrocycles – ureido-substituted cyclodextrins (CDs) which exhibit unprecedented upper critical solution temperature (UCST) behavior in aqueous media. These novel CD derivatives showed good solubility in water at elevated temperature, but collapsed from water to form large coacervates upon cooling to low temperature. Their cloud points are greatly dependent on concentration and can be mediated through oxidation and chelation with silver ions. Significantly, the amphiphilicity of these CD derivatives is supportive to host-guest binding, which affords them inclusion abilities to guest dyes. The inclusion complexation remained nearly intact during thermally induced phase transitions, which is in contrast to the switchable inclusion behavior of lower critical solution temperature (LCST)-type CDs. Moreover, ureido-substituted CDs were exploited to co-encapsulate a pair of guest dyes whose fluorescence resonance energy transfer process can be switched by the UCST phase transition. We therefore believe these novel thermoresponsive CDs may form a new strategy for developing smart macrocycles and allow for exploring smart supramolecular materials.     

On solitary wave solutions to the nonlinear Schrödinger equations with two parameters

In this paper, we discuss the existence and multiplicity of positive solitary wave solutions for nonlinear Schrödinger equations with two parameters. The proof is based on the method of upper and lower solutions and the fixed point index.     

Boundary problems for fractional differential equations

In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.     

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.     

A Borinic Acid Polymer with Fluoride Ion‐ and Thermo‐responsive Properties that are Tunable over a Wide Temperature Range

A new type of smart borinic acid polymer with luminescence and multiple stimuli‐responsive properties is reported. In DMSO with small amounts of water, the homopolymer PBA shows a tunable upper critical solution temperature (UCST). As the amount of water increases from 0 to 2.5 % (v/v), the UCST rises linearly from 20 °C to 100 °C (boiling point of water). Thus, the thermal responsive behavior can be tuned over a wide temperature range. Furthermore, polymer solutions in DMSO show a reversible response to fluoride ions, which can be correlated to the presence of the Lewis acidic borinic acid groups. Upon addition of fluoride, the polymer becomes soluble because the functional R₂BOH groups are converted into ionic [R₂BF₂]^? groups, but turns insoluble again upon addition of H₂O, which reverses this process.     

多目标最优化恰当有效解的稳定性

主要研究当两种类型的参数扰动时,多目标最优化问题中恰当有效解的稳定性.在点集映射的连续性意义下,分析讨论这种稳定性问题并分别给出引起扰动的两参数u,v所对应的点集映射Q1(u)和Q2(v),同时严格证明了在两个闭凸锥U,V上Q1(u)和Q2(v)的连续性定理.最后,通过附注对其进行补充和改进.     

含参弱向量均衡问题的适定性

在实Hausdorff拓扑线性空间中研究了含参弱向量均衡问题的适定性.证明了在适当条件下由近似网定义的含参适定性等价于近似解映射的上半连续性,并给出了所研究问题各种适定的充分性条件.