A new approach to the exact and approximate anharmonic vibrational partition function of diatomic and polyatomic molecules utilizing Morse and Rosen–Morse oscillators

Exact closed forms of the equilibrium partition functions in terms Jacobi elliptic functions are derived for a particle in a box and Rosen–Morse (Poschl–Teller) oscillator (perfect for modeling bending vibrational modes). An exact form of the equilibrium partition function of Morse oscillator is reported. Three other approximate forms of Morse partition function are presented. Having an exact closed‐form for the vibrational partition function can be very helpful in evaluating thermodynamic state functions, e.g., entropy, internal energy, enthalpy, and heat capacity. Moreover, the herein presented closed forms of the vibrational partition function can be used for obtaining spectroscopic and dynamical information through evaluating the two‐ and four‐point dipole moment time correlation functions in anharmonic media. Finally, a closed exact form of the rotational partition function of a particle on a ring in terms of the first kind of complete elliptic integral is derived. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Rational redesign of Candida antarctica lipase B for the ring opening polymerization of D,D-lactide

Based on molecular modelling, the enzyme Candida antarctica lipase B was redesigned as a catalyst for the ring opening polymerization of D,D-lactide. Two mutants with 90-fold increased activity as compared to the wild-type enzyme were created. In a preparative synthesis of poly(D,D-lactide) the mutants greatly improved the rate and the degree of polymerization.     

The use of umbelliferone in the synthesis of new heterocyclic compounds

New coumarin derivatives, namely 7-[(5-amino-1,3,4-thiadiazol-2-yl)methoxy]-2H-chromen-2-one, 5-[(2-oxo-2H-chromen-7-yloxy)methyl]-1,3,4-thiadiazol-2(3H)-one, 2-[2-(2-oxo-2H-chromen-7-yloxy)acetyl]-N-phenylhydrazinecarbothioamide, 7-[(5-(phenylamino)-1,3,4-thiadiazol-2-yl)methoxy]-2H-chromen-2-one and 7-[(5-mercapto-4-phenyl-4H-1,2,4-triazol-3-yl)methoxy]-2H-chromen-2-one were prepared starting from the natural compound umbelliferone. The newly synthesized compounds were characterized by elemental analysis and spectral studies (IR, 1H-NMR and 13C-NMR).     

On the stability of the solitary waves to the rotation Benjamin‐Ono equation

In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin‐Ono equation. By solving a minimization problem on the line, we construct a family of even travelling waves ψ_c,γ. We then prove the uniqueness of even ground states associated with large speed and their orbital stability. Note that this improves the results in Esfahani and Levandosky, where only the stability of the set of ground states is proven.     

Effect of NH4I and I2 concentration on agar gel polymer electrolyte properties for a dye-sensitized solar cell

Gel polymer electrolytes were prepared using agar polymer host, NH₄I, and I₂ salts. The sample of agar paste with 1.0 M of NH₄I and 0.2 μM of I₂ exhibits the highest conductivity and lowest viscosity values at room temperature of (2.64?±?0.19)?×?10^?3?S?cm^?1 and 1.17?±?0.29 Pa?s, respectively. All of the gel polymer electrolytes display Arrhenian behavior, and the optimum agar paste gave the lowest activation energy of 0.25 eV. It also had a good physical appearance compared with the other samples. This gel polymer electrolyte had a good potential and was applicable to a role as electrolyte in ITO-ZnO (N719 dye)/agar paste?+?1.0 M NH₄I?+?0.2 μM I₂/Au-Pd-ITO dye-sensitized solar cell.     

Convergence Dynamics of Delayed Hopfield-Type Neural Networks Under Almost Periodic Stimuli

Convergence dynamics of Hopfield-type neural networks subjected to almost periodic external stimuli are investigated. In this article, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures. By employing Halanay inequalities, we obtain delay independent sufficient conditions for the networks to converge exponentially toward encoded patterns associated with the external stimuli. The networks are guaranteed to have exponentially hetero-associative stable encoding of the external stimuli.     

Microchip electrophoresis for specific gene detection of the pathogenic bacteria V. cholerae by circle-to-circle amplification.

We have developed a new method for a fast and precise analysis of circle-to-circle amplification (C2CA) product for specific gene detection by microchip electrophoresis. In this method, we have added a new enzymatic step to the C2CA reaction, which could be carried out isothermally at 37 degrees C. Compared to the original single-stranded DNA, the double-stranded DNA that is produced by this enzymatic reaction is more reliable for analysis by microchip electrophoresis. C2CA product was detected within 55 s with high reproducibility by this method which was successfully applied to the detection of 10-ng genomic DNA of the pathogenic bacteria Vibrio. cholerae within 110 s. Purification was found to be an indispensable step for the analysis of the C2CA product of genomic DNA samples.     

Free‐radical‐promoted cationic photopolymerization under visible light in aerated media: New and highly efficient silane‐containing initiating systems

New systems for the visible‐light‐induced polymerization of cationic resins working through a free‐radical‐promoted process are presented. They are based on a photoinitiator (camphorquinone, isopropylthioxanthone, Eosin), a silane, and a diphenyl iodonium salt, the new compound being the silane. The overall efficiency is strongly affected by the silane structure. The rates of polymerization and final percent conversion are noticeably higher than those obtained in the presence of already studied reference systems. Moreover, contrary to previously investigated free‐radical‐promoted cationic polymerizations, oxygen does not inhibit the process and an unusual enhancement of the polymerization kinetics is found in aerated conditions: such an observation seems to have never been reported so far. The excited state processes and the role of oxygen as revealed by laser flash photolysis are discussed. The particular behavior of the silyl radicals is outlined. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2008–2014, 2008     

On the Filling Invariants at Infinity of Hadamard Manifolds

We study the filling invariants at infinity div _k for Hadamard manifolds defined by Brady and Farb [ Trans. Am. Math. Soc. 350(8) (1998), 3393–3405]. Among other results, we give a positive answer to the question they posed: whether these invariants can be used to detect the rank of a symmetric space of noncompact type.     

Acoustic emission from domain wall motion in ferroelectric lead germanate

Simultaneous visual observation and monitoring of the ultrasonic signals show that acoustic emission (AE) produced as Pb₅Ge₃O₁₁c-plate crystals undergo the ferroelectric hysteresis cycle results from domain wall nucleation and collapse. AE activity takes place predominantly at applied electric fields large enough to bring a crystal substantially towards its saturation polarisation. A notable feature observed in Pb₅Ge₃O₁₁ and Pb_5?xBa_xGe₃O₁₁ alloys is the existence of an abrupt threshold electric field, denoted by E_∞ in the high gain limit, for production of AE: as the electric field is increased beyond the threshold value, the amount of AE observed increases by several orders of magnitude. E_∞ depends linearly on the inverse of the c-plate sample thickness (1/d) and also upon sample temperature—falling to a minimum at about 70°C for Pb₅Ge₃O₁₁ and then rising steeply as the Curie temperature (178°C) is approached. E_∞ is also dependent on the rate of change of the applied electric field and as this is increased extrapolates to the high frequency limit of the coercive field. Measurements of crystal polarisation indicate a one-to-one correspondence between AE and the electrical Barkhausen pulses which occur during polarisation reversal—further evidence for domain nucleation and collapse as the source of AE. Optical and AE studies made simultaneously on gadolinium molybdate add confirmation that these particular processes are responsible for the AE produced by ferroelectric crystals.