A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

Separation and implantation of relativistic86Kr-fragments at the FrS; half-life measurement by ion-β time-correlations

Neutron-rich Co and Fe isotopes produced by⁸⁶Kr projectile fragmentation at 500 MeV/u were separated and identified using the fragment separator (FrS) in a bunched energy mode.⁶⁶Co and⁶⁵Fe ions were selectively implanted in a double PIN-diode array where the-decay signals were measured. The half-lives were deduced from time correlations between implantation and-decay signals. The remeasurement of the⁶⁶Co half-life confirms the isotope identification. The value of the⁶⁵Fe half-life was found to be 0.45±0.15 s.     

Photoconductivity of erbium-doped germanium

We have applied the technique of Photo Thermal Ionization Spectroscopy (PTIS) to the study of an erbium-doped p-Ge epitaxial layer, grown by MBE on an undoped n-type germanium substrate. The Er-doped Ge layer shows continuum photoconductivity response in the far-infrared region extending from 70 cm^–1 to 900 cm^–1. This type of epitaxial Er-doped Ge layers is a potentially attractive system for photoconductivity detectors of far-infrared radiation. Below 900 cm^–1 three acceptor-like charged states can be distinguished with ionization energies of 9, 26.6 and 50 meV. Additionally, a study of the photoconductive response of the same sample for radiation from 1000 cm^–1 to 10000 cm^–1, i.e., for radiation energies well inside the forbidden gap to energies above it, shows a wealth of levels, some of which have previously been associated with erbium.On leave from: Instituto de Física, Universidad Autónoma de Puebla, Puebla, México     

Bone-ablation mechanism using CO2 lasers of different pulse duration and wavelength

Bone ablation using different pulse parameters and four emission lines of 9.3, 9.6, 10.3, and 10.6 m of the CO₂ laser exhibits effects which are caused by the thermal properties and the absorption spectrum of bone material. The ablation mechanism was investigated with light- and electron-microscopy at short laser-pulse durations of 0.9 and 1.8 s and a long pulse of 250 s. It is shown that different processes are responsible for the ablation mechanism either using the short or the long pulse durations. In the case of short pulse durations it is shown that, although the mineral components are the main absorber for CO₂ radiation, water is the driving force for the ablation process. The destruction of material is based on explosive evaporation of water with an ablation energy of 1.3 kJ/cm³. Histological examination revealed a minimal zone of 10–15 m of thermally altered material at the bottom of the laser drilled hole. Within the investigated spectral range we found that the ablation threshold at 9.3 and 9.6 m is lower than at 10.3 and 10.6 m. In comparison the ablation with a long pulse duration is determined by two processes. On the one side, the heat lost by heat conduction leads to carbonization of a surface layer, and the absorption of the CO₂ radiation in this carbonized layer is the driving force of the ablation process. On the other side, it is shown that up to 60% of the pulse energy is absorbed in the ablation plume. Therefore, a long pulse duration results in an eight-times higher specific ablation energy of 10 kJ/cm³.     

Description of the turbidity measurements near the phase transition temperature of poly(N-isopropyl acrylamide) copolymers: the effect of pH, concentration, hydrophilic and hydrophobic content on the turbidity

Absorbance values between 300 and 800 nm of aqueous solutions of poly(N-isopropyl acrylamide-co-itaconic acid-9.80), poly(N-isopropyl acrylamide-co-itaconic acid-52.05) and poly(N-isopropyl acrylamide)s containing Tegomer H-Si 2111 end groups and/or blocks were measured using a Shimadzu 160-A UV-visible spectrometer. Turbidities obtained from these absorbance values were used to interpret the macromolecular phase transition from a hydrophilic to a hydrophobic structure of the polymers. The effects of comonomer type and content, concentration of the solutions, pH and temperature on the coil-globule transition were discussed in terms of turbidity form factor, β related to size and shapes of particles and calculated by using the simplified form of Debye equation.The results presented in this work show that the presence of Tegomer H-Si 2111 (Si containing end groups and/or blocks) or high amount of itaconic acid (IA) in the chains prevent a collapse transition from hydrated extended coils to hydrophobic globules, which aggregate and form a separate phase (β<2). Furthermore, it was observed that in the case of concentrated solutions intermolecular hydrophobic interactions between isopropyl groups overcame the repulsive forces resulting from the ionized carboxylic acid groups of IA or surface active nature of Si containing hydrophobic groups (β>2). This stage of the transition corresponds to macroscopic phase separation after an intramolecular process.     

Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.     

1－N－（苯并咪唑－1－乙酰基）－4－苯基－3－氨基硫脲金属配合物的合成及结构表征

合成了新配体１－Ｎ－（苯并咪唑－１－乙酰基）－４－苯基－３－氨基硫脲（ＢＰＭＳ），将其与Ｍｎ（Ⅱ）、Ｃｏ（Ⅱ）、Ｎｉ（Ⅱ）、Ｃｕ（Ⅱ）、Ｃｄ（Ⅱ）、Ｚｎ（Ⅱ）、ＵＯ２（Ⅱ）等金属的醋酸盐反应，合成了７个新配合物。所有化合物均经元素分析、ＩＲ、１ＨＮＭＲ和热重分析等表征。红外光谱表明，配体以四齿方式通过烯醇式羰基氧原子、烯醇式硫羰基硫原子以及Ｃ＝Ｎ１和Ｃ＝Ｎ２的氮原子与金属配位     

纳米级NiTiO3粉体的合成

以Ｈ２ＴｉＯ３，Ｈ２Ｏ２及ＮｉＣｌ２为主要原料，用化学共沉淀法制备了纳米级ＮｉＴｉＯ３。确定了反应物Ｈ２ＴｉＯ３，Ｈ２Ｏ２，ＮＨ３的最佳摩尔比为１：８：２，用不同的退火温度和退火时间对样品处理得到相应粒径的纳米级粉体。