Analysis of the nonlinear vibration of a two-mass–spring system with linear and nonlinear stiffness

An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. The main contribution of this research is twofold. First, it introduces the transformation of two nonlinear differential equations for a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment of a nonlinear differential system by linearization coupled with Newton’s method. Secondly, the major section is the solving of the governing nonlinear differential equation where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using a first-order variational approach. The aforementioned approach proposed by J.H. He, who actually developed the method, is exactly He’s variational method. This approach is an explicit method with high validity for resolving strong nonlinear oscillation system problems. Two examples of nonlinear two-degree-of-freedom mass–spring systems are analyzed, and verified with published results and exact solutions. The method can be easily extended to other nonlinear oscillations and so could be widely applicable in engineering and science.     

Structural studies and T c dependence in La2−x Dy x Ca y Ba2Cu4+y O z type mixed oxide superconductors

A new series of mixed oxide superconductors with the stoichiometric composition La_2−x Dy _x Ca _y Ba₂Cu_4+y O _z (x=0.0 − 0.5, y=2x) has been studied for structural and superconductiong properties. Our earlier studies on La_2−x (Y/Er) _x Ca _y Ba₂Cu_4+y O _z series, show a strong dependence of T _c on hole concentration (p _sh). In the present work, the results of the analysis of the neutron diffraction measurements at room temprerature on x=0.3 and 0.5 samples are reported. It is interesting to know that Ca substitutes for both La and Ba site with concomitant displacement of La onto Ba site. Superconductivity studies show that maximum T _c is obtained for x=0.5, y=1.0 sample (T _c ∼ 75 K), for La_1.5Dy_0.5Ca₁Ba₂Cu₅O _z (La-2125).     

A market-based martingale valuation approach to optimum inventory control in a doubly stochastic jump-diffusion economy

We propose a novel market-based approach to optimum inventory control in a doubly stochastic jump-diffusion economy by modelling a commodity distributor’s inventory investment as a portfolio of forward commitments with explicit accounting of the jump-diffusion dynamics of demands, costs, and prices in open markets. We apply the robust real-asset martingale valuation methodology to derive a closed-form solution for the inventory value and a simple and intuitive optimality condition. Numerical analysis verifies this condition and demonstrates that the resulting optimum policy has robust properties in relation to the stylized effects.     

The analysis of alkyl-capped alcohol ethoxylates and alcohol ethoxycarboxylates from alcohol ethoxylates by atmospheric pressure chemical ionization mass spectrometry

Alcohol ethoxylates (AEs) are nonionic surfactants. They are industrially important compounds that have historically been difficult to analyze, with the best results to date achieved through derivatization (e.g., silylation) followed by analysis by gas chromatography/mass spectrometry (GC/MS). Recently, mass spectrometric techniques such as field desorption (FD), time-of-flight secondary ion mass spectrometry (TOF-SIMS), fast atom bombardment (FAB), electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI) have been employed to analyze surfynol(R) 4xx. In an effort to produce low-cost alkyl-capped AEs and anionic detergents from AEs, a fast and reliable measure of the product yields and conversions from AEs is required in research. We found that the product yields and conversions from reactions of AEs, obtained by the employment of atmospheric pressure chemical ionization (APCI), were in good agreement with those obtained from proton nuclear magnetic resonance spectroscopy ((1)H-NMR). Therefore, APCI can be used as a validated tool for studying AE reactions. Mixtures that contain either silylated or unsilylated ethoxylates and/or carboxylates yield the same APCI mass spectra. Copyright -Copyright 1999 John Wiley & Sons, Ltd.     

A new salicin derivative from the stem bark of Populus davidiana

Phytochemical study on the BuOH-soluble fraction of the stem bark of Populus davidiana resulted in the isolation of a new salicin derivative(1),named davidianoside.The structure was elucidated on the basis of extensive physicochemical and spectroscopic analyses.     

Thiol‐Directed Synthesis of Highly Fluorescent Gold Clusters and Their Conversion into Stable Imaging Nanoprobes

Fluorescent gold clusters (FGCs) with tunable emission from blue to red and quantum yields in the range of 6–17 % have been synthesized by simple modification of the conditions used for the synthesis of gold nanoparticles, namely by replacing the stronger reducing agent with a controlled amount of thiol. Various functional FGCs with hydrodynamic diameters of 5–12 nm have been successfully synthesized and used as cell labels. The results of our investigations strongly indicate that FGCs composed of Au⁰ are more stable imaging probes than commonly reported red/NIR‐emitting FGCs with a composition of Au⁰/Au^I, as this combination rapidly transforms into nonfluorescent large clusters on exposure to light. The FGC‐based nanoprobes reported herein exhibit stable fluorescence upon continuous light exposure and can be used as imaging probes with low cytotoxicity.     

Aspherical‐Atom Modeling of Coordination Compounds by Single‐Crystal X‐ray Diffraction Allows the Correct Metal Atom To Be Identified

Single‐crystal X‐ray diffraction (XRD) is often considered the gold standard in analytical chemistry, as it allows element identification as well as determination of atom connectivity and the solid‐state structure of completely unknown samples. Element assignment is based on the number of electrons of an atom, so that a distinction of neighboring heavier elements in the periodic table by XRD is often difficult. A computationally efficient procedure for aspherical‐atom least‐squares refinement of conventional diffraction data of organometallic compounds is proposed. The iterative procedure is conceptually similar to Hirshfeld‐atom refinement (Acta Crystallogr. Sect. A­ 2008 , 64, 383–393; IUCrJ. 2014 , 1,61–79), but it relies on tabulated invariom scattering factors (Acta Crystallogr. Sect. B­ 2013 , 69, 91–104) and the Hansen/Coppens multipole model; disordered structures can be handled as well. Five linear‐coordinate 3d metal complexes, for which the wrong element is found if standard independent‐atom model scattering factors are relied upon, are studied, and it is shown that only aspherical‐atom scattering factors allow a reliable assignment. The influence of anomalous dispersion in identifying the correct element is investigated and discussed.