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By using the fixed-point index theory and Leggett-Williams fixed-point theorem, we study the existence of multiple solutions to the three-point boundary value problem , ; ; , where , are constants, is a parameter, and , are given functions. New existence theorems are obtained, which extend and complement some existing results. Examples are also given to illustrate our results.

We discuss the existence of minimal and maximal positive solutions for fractional differential equations with multipoint boundary value conditions, and new results are given. An example is also given to illustrate the abstract results.

A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.

This paper studies the spontaneous combustion process of two kinds of oil shale to grasp the characteristics and mechanism of spontaneous combustion, which provides a theoretical basis for preventing spontaneous combustion of oil shale. Based on thermal analysis and low-temperature adsorption, the risk of spontaneous combustion of Wangqing oil shale (WQOS) and Beipiao oil shale (BPOS) (China) are studied. Based on the thermal analysis data, advanced kinetics and technology solution (AKTS) software is used to predict and evaluate the risk of spontaneous combustion. The kinetic model, which is obtained by combining the Gaussian fitting method with the peak analysis method, can effectively describe the combustion of the volatilization. The results show that, the combustion process of the volatilization can be divided into three stages. The predicted results show that, for the same initial temperature, the tendency of spontaneous combustion of BPOS is greater than that of WQOS, which is consistent with the results of thermal analysis and static oxygen absorption. [ABSTRACT FROM AUTHOR]

In this work, we are pleased to investigate multiple positive solutions for a system of Caputo fractional p -Laplacian boundary value problems, and we also provide an example for illustrating our main results. [ABSTRACT FROM AUTHOR]

In this paper, the laboratory-scale permeable pavement layers, including a surface permeable brick layer, coarse sand bedding layers (thicknesses = 2, 3.5, and 5 cm), and single-graded gravel sub-base layers (thicknesses = 15, 20, 25, and 30 cm), were built to evaluate stormwater infiltration and surface runoff pollution reduction performance. And, the infiltration rate (I) and concentrations of suspended solids (SS), total phosphorus (TP), chemical oxygen demand (COD), ammonia nitrogen, and total nitrogen (TN) were measured under the simulated rainfall intensity of 72.4 mm/h over duration of 60 min. The results indicate that the thickness factor primarily influences the infiltration rate and pollutant removal rate. The highest steady infiltration rate was for surface brick layer 51.0 mm/h, for 5-cm sand bedding layer 32.3 mm/h, and for 30-cm gravel sub-base layer 42.3 mm/h, respectively. The SS average removal rate was relative higher (79.8∼98.6 %) for all layers due to the interception and filtration. The average removal rates of TP and COD were for surface layer 71.2 and 24.1 %, for 5-cm bedding layer 54.8 and 9.0 %, and for 20-cm sub-base layer 72.2 and 26.1 %. Ammonia nitrogen and TN cannot steadily be removed by layers according to the experiment results. The optimal thickness of bedding sands was 5 cm, and that of sub-base gravels was 20∼30 cm. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

Two new Ni(II) complexes of 2,6-bis[1-(2,6-diethylphenylimino)ethyl]pyridine (L1), 2,6-bis[1-(4-methylphenylimino)ethyl]pyridine (L2) have been synthesized and structurally characterized. Complex Ni(L1)Cl2 · CH3CN (1), exhibits a distorted trigonal bipyramidal geometry, whereas complex Ni(L1)(CH3CN)Cl2 (2), is six-coordinate with a geometry that can best be described as distorted octahedral. The catalytic activities of complexes 1, 2, Ni{2,6-bis[1-(2,6-diisopropyl-phenylimino)ethyl]pyridine} Cl2 · CH3CN (3), and Ni{2,6-bis[1-(2,6-dimethylphenylimino) ethyl]pyridine}Cl2 · CH3CN (4), for ethylene polymerization were studied under activation with MAO. [ABSTRACT FROM AUTHOR]