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.     

Efficient Transformation of Furfuryl Alcohol Into Ethyl Levulinates via Alcoholysis Reaction Catalyzed by SnO2/H-Mordenite Catalyst

Catalysis Surveys from Asia - Catalytic production of ethyl levulinate by alcoholysis of furfuryl alcohol with ethanol was investigated over H-mordenite supported Sn catalyst under atmospheric N2...     

Liquid phase benzylation of toluene using benzyl alcohol over iron promoted sulfated zirconia

Concentrated (0.2 M) aqueous solutions of HP-acids, such as H_3+x+mPV^IV _mV^V _x-mMo_12-xO₄₀ and their analogues with an excess VO²⁺ cation, are oxidized by dioxygen at 343 K and atmospheric pressure through intermediate active complexes (IAC) [H_x+m-1PV^IV _mV^V _x-mMo_12-xO₄₀ ^{4 -}] · [VO²⁺]_y · O₂, where m + y ≥ 3. The electron transfer to the coordinated O₂ molecule inside AC is the limiting stage at high m. At low m, the formation of IAC becomes the limiting stage that results in a sharp decrease in the oxidation rate. This revised version was published online in August 2006 with corrections to the Cover Date.     

Photophysics of untethered ZnTPP-fullerene complexes in solution

The spectroscopy and dynamic behavior of the self-assembled, Soret-excited zinc tetraphenylporphyrin (ZnTPP) plus fullerene (C(60)) model system in solution has been examined using steady state fluorescence quenching, nanosecond time-correlated single photon counting, picosecond fluorescence upconversion, and picosecond transient absorption methods. Evidence of ground state complexation is presented. Steady-state quenching of the S(2) and S(1) fluorescence of ZnTPP by C(60) reveals that the quenching processes only occur in the excited complexes, are ultrafast, and proceed at different rates in the two states. Only uncomplexed ZnTPP is observed by fluorescence lifetime methods; the locally excited complexes are either dark or, more likely, rapidly relax to products that do not radiate strongly. Both short-range (Dexter) energy transfer and electron transfer relaxation mechanisms are evaluated. Picosecond transient absorption data obtained from the subtle differences between the spectra of Soret-excited ZnTPP with and without a large excess of added C(60) reveal the formation, on a subpicosecond time scale, of relatively long-lived charge-separated species. Soret excitation of ZnTPP···C(60) does not produce a quantitative yield of species in the lower S(1) excited state.     

Thermal characterisation of dye-intercalated K-10 montmorillonite ceramics using photoacoustic technique

Thermal diffusivity (TD) measurements were performed on some industrially important dyes – auramine O (AO), malachite green and methylene blue (MB) – adsorbed K-10 montmorillonites using photoacoustic method. The TD value for the dye-adsorbed clay mineral was observed to change with a variation in dye concentration. The contribution of the dye towards TD was also determined. The repeatedly adsorbed samples with MB and AO exhibited a lower TD than the single-adsorbed samples. TD values of sintered MB samples were also obtained experimentally. These sintered samples exhibit a higher TD, although they show a trend similar to that of non-sintered pellets. A variation in dye concentration and sintering temperature can be used for tuning the TD value of the clay mineral to the desired level.     

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.     

Leaching studies over immobilized a-amylase. importance of the nature of enzyme attachment

The enzyme α-amylase was immobilized on montmorillonite K-10 via adsorption and covalent bonding. These two modes of attachment play a vital role in the leaching of enzyme. Covalent bonding retains most of the enzyme even at high loadings. The significance of temperature has also been established. Higher temperatures lead to severe leaching in case of adsorbed enzyme. Covalent linkage, being of higher strength, does not yield to enzyme leaching even at high temperatures. This revised version was published online in June 2006 with corrections to the Cover Date.     

Surface electron properties and catalytic activity of Sr doped lanthana

The electron donating properties, surface acidity/basicity and catalytic activity of lanthana for various dopant concentrations of strontium are reported at two activation temperatures. The catalytic activity has been correlated with electron donating properties and surface acidity/basicity of the oxide.     

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.     

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.