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.     

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.     

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.     

Hydrogen and deuterium diffusion in non-stoichiometric spinel

High pressure/temperature annealing experiments are used to determine diffusivities of H⁺ and D⁺ in non-stoichiometric spinel, a low-pressure analogue for nominally anhydrous minerals in Earth’s mantle. Data are fitted to the following Arrhenius law: Diffusivity (m²/s)?=?4?±?1?×?10^?12 exp(?54?±?2 kJ?mol^?1/RT). At low temperatures, H⁺ and D⁺ diffusion in non-stoichiometric spinel is charge balanced by flux of O vacancies, with infrared data consistent with protonation of both octahedral and tetrahedral O–O edges in non-stoichiometric spinel, and additional fine structure due to Mg–Al mixing and/or coupling of structurally incorporated H⁺ with cation vacancies. Absence of changes in the fine structure of O–H absorption bands indicates that H⁺ can become locally coupled and uncoupled to other defects during bulk diffusion. As such, proton conductivity in spinel group minerals, arising from faster flux of uncoupled H⁺, can only be calculated from H⁺ mobility data if the extent of defect coupling is constrained.     

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].     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

多集值信息表中的多粒度模糊决策论粗糙集

多粒度粗糙集和决策论粗糙集是Pawlak粗糙集的重要推广,目前已成为人工智能研究的热点.然而,它们大多处理的都是单值信息系统中的问题.而实际生活中绝大多数都是处理多值问题,为了解决这一问题,在多集值信息表中将多粒粗糙集与模糊决策论粗糙集相结合进行研究,提出了其在乐观,悲观情形下的上下近似,研究了一些相关性质并给出了多集值信息表中的多粒度模糊决策论粗糙集精度、粗度的概念,最后通过一个具体例子验证其有效性.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.