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The goal of this article considers a class of semilinear fractional evolution hemivariational inequalities control systems described by the Riemann-Liouville fractional derivative in separable reflexive Banach spaces. At first, the existence of Riemann-Liouville fractional semilinear evolution hemivariational inequalities with nonconvex feedback control constraint is discussed by applying fractional operator theory and Schauder's fixed point theorem. Then, we show that the set of the original system's trajectories can be approximated by the set of the upper semicontinuous convex valued regularization of the original feedback system's trajectories under certain hypotheses. Also, an example is given to illustrate our main results at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a Riemann-Liouville fractional differential control system with mixed nonconvex feedback constraints on the control. At First, the existence results for Riemann-Liouville fractional semilinear differential control systems are discussed by using Schauder's fixed point theorem. Under some reasonable assumptions, we prove that the relaxation problem has an optimal solution, and that for each optimal solution there has a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously. Finally, we give an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

We are concerned with control systems described by a class of semilinear fractional evolution hemivariational inequalities in separable reflexive Banach spaces. The constraint on the control is a nonconvex valued multivalued function which is lower semicontinuous with respect to the variable states. Along with the original system we also consider the system in which the constraint on the control is the upper semicontinuous convex valued regularization of the original constraint. We obtain the existence results of the control systems and the relaxation property among the solution sets of these systems. In the end, an example is provided to illustrate the application of the obtained theory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a control system of nonlinear evolution hemivariational inequalities with mixed nonconvex constraints on the control. First, we investigate the relaxed problem for the hemivariational inequalities systems with feedback control and the integrand convexicated with respect to the control. Second, under some general conditions, the existence of optimal solution of the relaxed problem for hemivariational inequalities control systems is proved. Furthermore, we show that for every optimal solution there exists a minimizing sequence of the original problem converging to the optimal solution with respect to trajectories and the functional in appropriate topologies simultaneously. Finally, an example is provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

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A control system described by fractional evolution integro-differential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both two systems.

We consider a control system described by fractional semilinear evolution equations with a mixed multivalued control constraint whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraint on the control is the closed convex hull of the original constraint. We obtain existence results for the control systems and study relations between the solution sets of the two systems. An example is given to illustrate the abstract results.

A control system described by fractional evolution integro-differ-ential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both two systems. [ABSTRACT FROM AUTHOR]

Magnetite-silica core-shell nanoparticles (Fe3O4@SiO2 NPs) were prepared from silicon powder by direct oxidation without using any expensive precursors (such as TEOS) and organic solvents. The as-prepared Fe3O4@SiO2 NPs were characterized by TEM, DLS, XRD, FT-IR, zeta potential and NMR Analyzer. The results show that the Fe3O4@SiO2 NPs are monodispersed core-shell nanostructures with single cores that were uniformly coated by silica shells. The relaxation property indicates that Fe3O4@SiO2 NPs have desirable characteristics for T2 MRI contrast agents. This facile and green method is promising for large-scale production, which would open new opportunities for preparing core-shell nanostructures for biomedical applications. [ABSTRACT FROM AUTHOR]

Adaptive finite element method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property is the central part of this paper. In terms of coefficient inverse problems with single measurement data, the authors consider the adaptivity as the second stage of a two-stage numerical procedure. The first stage delivers a good approximation of the exact coefficient without an advanced knowledge of a small neighborhood of that coefficient. This is a necessary element for the adaptivity to start iterations from. Numerical results for the two-stage procedure are presented for both computationally simulated and experimental data. [ABSTRACT FROM AUTHOR]

Abstract: We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously. [Copyright &y& Elsevier]

Abstract: The electronic structure of the defect in quartz is investigated for the first time by the pulsed electron paramagnetic resonance spectroscopy. The temperature dependence of the longitudinal and transverse relaxations and the possible mechanisms lying behind are carefully characterized. With the pulsed electron–nuclear double resonance spectroscopy, a magnetically coupled proton is confirmed to exist in the center. The observed long over 260 μs at 60 K, as well as the well-separated energy levels arising from the proton-coupled electron–nuclear structure, makes center a good candidate for quantum memory in quantum computing. [Copyright &y& Elsevier]

Abstract: Nanostructured bismuth sulfide thin films were prepared onto glass substrates with particle size of 21nm by thermal evaporation using readily prepared bismuth sulfide nanocrystallite powder. The X-ray diffraction pattern revealed that bismuth sulfide thin films exhibit orthorhombic structure. The existence of quantum confinement effect was confirmed from the observed band gap energy of 1.86eV. AC and DC electrical conductivity of Al/BiSnc/Al structures was investigated in the frequency range 0.5–100kHz at different temperatures (303–463K) under vacuum. The AC conductivity (σ ac) is found to be proportional to angular frequency (ω s). The obtained experimental result of the AC conductivity showed that the correlated barrier hopping model is the appropriate mechanism for the electron transport in the nanostructured bismuth sulfide thin films. DC conduction mechanism in these films was studied and possible conduction mechanism in the bismuth sulfide thin films was discussed. [Copyright &y& Elsevier]

We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem. [ABSTRACT FROM AUTHOR]

Abstract: We establish the existence of infinitely many weak solutions for the general one-dimensional forward–backward diffusion equation under the homogeneous Neumann boundary condition by rephrasing it as a first-order differential inclusion problem. [Copyright &y& Elsevier]