Generalized Projection Algorithms for Nonlinear Operators

In this paper, we prove three strong convergence theorems of modified Mann iteration for relatively asymptotically nonexpansive mappings, relatively nonexpansive mappings, and maximal monotone operators in a Banach space, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Matsushita, Kim, Martinez-Yanex, Xu, and some others.     

Relatively maximal monotone mappings and applications to general inclusions

Based on the relative maximal monotonicity frameworks, the approximation solvability of a general class of variational inclusion problems is explored, while generalizing most of the investigations on weak convergence using the proximal point algorithm in a real Hilbert space setting. Furthermore, the main result has been applied to the context of the relative maximal relaxed monotonicity frameworks for solving a general class of variational inclusion problems. It seems that the obtained results can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution inclusions, and the obtained results can further be applied to the Douglas–Rachford splitting method for finding the zero of the sum of two relatively monotone mappings as well.     

Strict stability in terms of two measures for impulsive differential equations with ‘supremum’

Strict stability for a nonlinear system of impulsive differential equations with ‘supremum’ is defined and studied. Razhumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations are the bases of the main proofs. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied. An example illustrating the usefulness of the obtained sufficient conditions is also included.     

Floquet theory for a Volterra integro-dynamic system

In this paper, we study periodic linear Volterra systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We discuss the relationship between the solution of the Volterra integro-dynamic system and the limiting equation of the corresponding system. We also develop integrability conditions of the resolvent of Volterra integro-dynamic systems.     

Opial's and wirtinger's type discrete inequalities in two independent variables

We develop discrete Taylor's formula in two independent variables and use it to establish Opial's type inequality involving higher order partial differences. This is followed by several variations of discrete Wirtinger's inequality in two independent variables     

Effect of Bi additive on structure and optical properties of amorphous BixIn25−xSe75 chalcogenide films

We report the structure and optical properties of thermally evaporated Bi_xIn_25?xSe₇₅ (0 ≤ x ≤ 7) films by using X-ray diffraction and optical spectroscopic techniques. The as-prepared samples were found to be amorphous by X-ray diffraction while the crystallization of Se, In₂Se₃ and Bi₂Se₃ phases has been observed upon annealing the films at 440 K. The enhancement in the main diffraction peak intensity was accepted as the increase in the crystalline character for the devitrified films with Bi content. The addition of 5 at.% of Bi results in the large change in the electrical parameters due to the carrier type reversal in the as-prepared samples. The red shift in the absorption edge along with a decrease in the transmittance has been observed for the as-prepared samples. The inverse relationship between optical gap and the tailing parameter (except x = 1) were observed with the increase in Bi content. The optical gap was found to increase up to x ≤ 1 and thereafter, resulted in the decrease in it for the thermally annealed samples. These results have been discussed in conjunction with the structural relaxation and impurity mediated heterogeneous crystallization of the film network.     

An analysis of 175 MeV Nickel ion irradiation and annealing effects on silicon NPN rf power transistors

In this study NPN rf power transistors were irradiated by 175 MeV Ni¹³⁺ ions in the dose range of 100 krad to 100 Mrad. Their characteristics such as excess base current (ΔI_B = I_Bpost ? I_Bpre), dc current gain (h_FE), transconductance (g_m) and collector-saturation current (I_CSat) were studied before and after irradiation. The damage factor (K) for h_FE was calculated using Messenger–Spratt relation. The base current (I_B) was found to increase significantly after irradiation and in turn decreases the h_FE. The g_m and collector current (I_C) in the saturation region (I_CSat) were found to decrease with increase in radiation dose. The results obtained here were also compared with that obtained by 140 MeV Si¹⁰⁺ ions, 100 MeV F⁸⁺ ions, 95 MeV O⁷⁺ ions and 50 MeV Li³⁺ ions irradiation studies in the same dose ranges to understand the LET effects. The recovery in the I–V characteristics of irradiated NPN transistors were studied by isothermal and isochronal annealing methods.     

The effects of a laser field on phase transitions in liquid crystals

We investigate theoretically some phase transitions in liquid crystals in the presence of a laser beam. We found, in non-absorbing nematics, a laser-induced one-way transition from a paranematic to a nematic phase. In absorbing nematics we found, in addition to this transition, a one-way transition from a nematic to a paranematic phase with increasing laser intensity. Further, we found a reentrant nematic or a reentrant paranematic via paranematic or nematic phase respectively. In the case of smectic A, laser absorption results in a coupling between the positional and orientational orders. As a result, the smectic A to nematic transition can change from second order to first order and the smectic C to smectic A transition can become first-order in the field of a laser.     

Estimating the entropy of liquids from atom–atom radial distribution functions: silica,beryllium fluoride and water

Molecular dynamics simulations of water, liquid beryllium fluoride and silica melt are used to study the accuracy with which the entropy of ionic and molecular liquids can be estimated from atom–atom radial distribution function data. The pair correlation entropy is demonstrated to be sufficiently accurate that the density–temperature regime of anomalous behaviour as well as the strength of the entropy anomaly can be predicted reliably for both ionic melts as well as different rigid-body pair potentials for water. Errors in the total thermodynamic entropy for ionic melts due to the pair correlation approximation are of the order of 10% or less for most state points, but can be significantly larger in the anomalous regime at very low temperatures. In the case of water, the rigid-body constraints result in larger errors in the pair correlation approximation, between 20 and 30%, for most state points. Comparison of the excess entropy, S _e, of ionic melts with the pair correlation entropy, S ₂, shows that the temperature dependence of S _e is well described by T ^?2/5 scaling across both the normal and anomalous regimes, unlike in the case of S ₂. The residual multiparticle entropy, ΔS = S _e ? S ₂, shows a strong negative correlation with tetrahedral order in the anomalous regime.     

Dielectric spectroscopy of a high-polarization ferroelectric liquid crystal

Dielectric spectroscopy investigations in the frequency range 50?Hz to 1?MHz have been carried out on a new ferroelectric liquid-crystalline material (S-(-)-4-(2-n-hexylpropionyloxy)biphenyl-4′-(3-methyl-4-decyloxy)benzoate) possessing a relatively large spontaneous polarization (P _s?～?240?nC?cm^?2) and containing a lateral methyl group on the aromatic ring of the alkoxybenzoate unit. The effect of temperature on the dielectric relaxation modes has been investigated in the SmC* and N* phases. From dielectric dispersion data, relaxation frequency and dielectric strength of all detected relaxation modes have been evaluated and discussed. A new surface-like mode of relaxation frequency ～11?kHz and dielectric strength 3.8, is seen to appear in the SmC* phase.