一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Study on properties of flame‐retardant cyanate esters modified with DOPO and triazine compounds

Ternary flame‐retardant modified cyanate ester blends (CEPG and CEPA) are formed by combining triazine compounds (TGIC or TAIC) and 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide with cyanate ester resin. The curing behaviors, thermal and mechanical properties, and the flame‐retardant properties are investigated. The results show that the CEPG and CEPA blends result in lower curing temperatures and glass transition temperatures than those of neat CE. Both of CEPG and CEPA blends significantly improve the flame‐retardant properties of CE resins, and UL‐94V‐0 rate is achieved for CEPG‐1.0 and CEPA‐0.5. The dielectric constant and loss of CEPA blends are lower than those of CEPG blend with the same phosphors content, and both of them are lower than those of neat CE. Therefore, the ternary flame‐retardant modified cyanate ester blends provide 2 ways for composites of producing printed circuit board with high flame‐retardant property and low dielectric constant and loss.     

The construction and approximation of feedforward neural network with hyp erb olic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tangent activation functionFirstly, an equation of partitions of unity for the hyperbolic tangent function is givenThen, two kinds of quasi-interpolation type neural network operators are constructed to approximate univariate and bivariate functions, respectivelyAlso, the errors of the approximation are estimated by means of the modulus of continuity of functionMoreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.     

Existence of positive solutions to a coupled system of fractional differential equations

We consider the following system of fractional differential equations where is the Riemann‐Liouville fractional derivative of order α,f,g : [0,1] × [0, ∞ ) × [0, ∞ ) → [0, ∞ ). Sufficient conditions are provided for the existence of positive solutions to the considered problem. Copyright © 2014 John Wiley & Sons, Ltd.     

An explicit counter-example for the shephard problem of convex bodies in ℝ n

Comparing the volume of the projection body of a double cone and that of the projection body of a ball, we give an explicit counter-example for the Shephard problem of convex bodies in Rⁿ (n ≥ 3) and an affirmative answer to the question of Zhang.     

Influences of Sr2+ Doping on Microstructure,Giant Dielectric Behavior,and Non-Ohmic Properties of CaCu3Ti4O12/CaTiO3 Ceramic Composites

The microstructure, dielectric response, and nonlinear current-voltage properties of Sr²⁺-doped CaCu₃Ti₄O₁₂/CaTiO₃ (CCTO/CTO) ceramic composites, which were prepared by a solid-state reaction method using a single step from the starting nominal composition of CCTO/CTO/xSrO, were investigated. The CCTO and CTO phases were detected in the X-ray diffraction patterns. The lattice parameter increased with increasing Sr²⁺ doping concentration. The phase compositions of CCTO and CTO were confirmed by energy-dispersive X-ray spectroscopy with elemental mapping in the sintered ceramics. It can be confirmed that most of the Sr²⁺ ions substituted into the CTO phase, while some minor portion substituted into the CCTO phase. Furthermore, small segregation of Cu-rich was observed along the grain boundaries. The dielectric permittivity of the CCTO/CTO composite slightly decreased by doping with Sr²⁺, while the loss tangent was greatly reduced. Furthermore, the dielectric properties in a high-temperature range of the Sr²⁺-doped CCTO/CTO ceramic composites can be improved. Interestingly, the nonlinear electrical properties of the Sr²⁺-doped CCTO/CTO ceramic composites were significantly enhanced. The improved dielectric and nonlinear electrical properties of the Sr²⁺-doped CCTO/CTO ceramic composites were explained by the enhancement of the electrical properties of the internal interfaces.     

Density functional study of α-graphyne derivatives: Energetic stability,atomic and electronic structure

The energetic stability, atomic and electronic structures of α-graphyne and its derivatives (α-GYs) with extended carbon chains were investigated by density functional (DF) calculations in this work. The studied α-GYs consist of hexagon carbon rings sharing their edges with carbon atoms N=1–10. The structure and energy analyses show that α-GYs with even-numbered carbon chains have alternating single and triple C–C bonds (polyyne), energetically more stable than those with odd-numbered carbon chains possessing continuous double C–C bonds (polycumulene). The calculated electronic structures indicate that α-GYs can be either metallic (odd N) or semiconductive (even N) depending on the parity of number of atoms on hexagon edges despite the edge length. The semiconducting α-graphyne derivatives are found to possess Dirac cones (DC) with small direct band gaps 2–40 meV and large electron velocities 0.554×10⁶–0.671×10⁶ m/s, 70–80% of that of graphene. Our DF studies suggest that introducing sp carbon atoms into the hexagon edges of graphene opens up an avenue to switch between metallic and DC electronic structures via tuning the parity of the number of hexagon edge atoms.     

Ethylene propylene diene monomer rubber‐based heat shielding materials for solid rocket motor: Impact of Kevlar fiber reinforcement on the thermal and mechanical properties

This work scrutinizes the utilization of ethylene propylene diene monomer rubber matrix (EPDM) with an embodiment of aramid fiber for the heat shielding applications in solid rocket motor (SRM). Aramid fibers are aromatic poly‐paraphenylene terephthalamide, here deployed are Kevlar fibers (KF). However, the literature that encompasses the thermal and mechanical behavior with the fiber loading is reported nowhere else. The effect of fiber addition on the surface morphology and density was thoroughly studied, and it revealed that the EHSMs were of lower density to act as an efficient payload for the SRM. In this regard, the thermal conductivity, heat capacity, thermal diffusivity, fire behavior, and mechanical properties of the EPDM/KF‐based EHSMs were explored. The results revealed that the EHSMs are thermally insulating and thermally stable material with balanced mechanical properties that can engender the thermal and mechanical strains of the rocket motor. Furthermore, other analytical techniques such as scanning electron microscopy and energy dispersive X‐ray spectroscopy have been exploited to monitor the performance of the char residues of the EHSM to delineate its performance in the fire atmosphere.