Stepanov ergodic perturbations for some neutral partial functional differential equations

In this work, we give sufficient conditions for the existence and uniqueness of μ?pseudo almost periodic integral solutions for some neutral partial functional differential equations with Stepanov μ?pseudo almost periodic forcing functions. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main results, we give applications to a neutral model arising in physical systems, as well as an application to heat equations with discrete and continuous delay. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis and characterization of (E)- and (Z)-3-mercapto-2-propenenitrile. Microwave spectrum of the Z-isomer

The kinetically unstable compound 3-mercapto-2-propenenitrile (HS-CH=CH-C[triple bond]N) has been prepared for the first time by flash vacuum pyrolysis at 800 degrees C of 3-(tert-butylthio)-2-propenenitrile with a yield of 77% and a Z:E ratio of 8:1. Several deuterium and 15N isotopologues were also prepared using isotopically enriched compounds. Quantum chemical calculations of the structural and conformational properties of the Z- and E-isomers were undertaken at the B3LYP/6-311++G(3df,2pd), MP2/6-311++G(3df,2pd), MP2/aug-cc-pVTZ, and G3 levels of theory. These methods all predict that the Z- and the E-forms each have two "stable" planar rotameric forms with the H-S-C=C link of atoms in either a synperiplanar or an antiperiplanar conformation, with the synperiplanar form of the Z-isomer as the global minimum. The Z-isomer has been investigated by means of Stark-modulation microwave spectroscopy. Spectra attributable to the parent and three deuterium-substituted isotopologues of a single conformer were recorded and assigned. Additionally, the spectrum belonging to the first excited state of the lowest bending vibration was assigned. The ground-state rotational constants obtained by the least-squares analysis of these transitions were found to be in excellent agreement with the corresponding approximate equilibrium values generated by the MP2/aug-cc-pVTZ calculations. The preferred conformer of this molecule was found to have a synperiplanar arrangement of the H-S-C=C chain of atoms and a planar or nearly planar geometry, with a stabilizing intramolecular hydrogen bond formed between the H atom of the thiol group and pi-electron density associated with the C[triple bond]N triple bond. The possible astrochemical/astrobiological significance of this compound is discussed.     

Bio-smart materials: kinetics of immobilized enzymes in p(HEMA)/p(pyrrole) hydrogels in amperometric biosensors

Various strategies are being pursued to confer the highly specific molecular recognition properties of bioactive molecules to the transducer action of inherently conductive polymers. We have successfully integrated inherently conductive polypyrrole within electrode-supported, UV cross-linked hydroxyethyl methacrylate (HEMA)-based hydrogels. These electroactive composites were used as matrixes for the physical immobilization of several oxidase enzymes to fabricate clinically important biosensors. Measurements were made of the amperometric responses via H₂O₂ oxidation for each biosensor. Apparent Michaelis constants, K_m(app), for glucose oxidase immobilized in p(HEMA) membranes and in p(HEMA)/p(Pyrrole) composite membranes were 13.8 and 43.7 mM respectively compared to 33 mM in solution. The inclusion of polypyrrole in the hydrogel network increased the thermal stability of the immobilized enzyme at 60°C by 30% and 40% compared to p(HEMA) membranes and solution phase respectively. The composite also yielded larger I_max values (19 μA/cm⁻²) for glucose biosensors compared to similar glucose biosensors fabricated without the conducting polymer (15 μA). K_m(app) values for cholesterol oxidase immobilized in the same composite films were ca. three orders of magnitude higher than the K_m for the soluble enzyme. The polypyrrole component is shown to reduce diffusive transport but to confer thermal stability to these biosensors.     

Theoretical study of the electronic structure of LiNa and LiNa<Superscript>+</Superscript> molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in ^1,3Σ, ^1,3Π, and ^1,3Δ symmetries are presented. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiNa⁺ dissociating into Li (2s, 2p, 3s, and 3p) + Na⁺ and Li⁺  + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and Na (1s²2s²2p⁶) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and LiNa⁺ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺Na and LiNa⁺.     

Multiferroics by rational design: implementing ferroelectricity in molecule-based magnets

Multiferroic materials: A novel class of multiferroics based on organic-inorganic hybrid materials is synthesized. The ferromagnetic properties originate from the coordination network, whereas the ferroelectricity results from the polar organic ions (see picture, M=magnetization and P=polarization).     

Novel complex phenomena in ferroelectric nanocomposites

A first-principles-based effective Hamiltonian is used to investigate finite-temperature properties of ferroelectric nanocomposites made of periodic arrays of ferroelectric nanowires embedded in a matrix formed by another ferroelectric material. Novel transitions and features related to flux-closure configurations are found. Examples include (i)?a vortex core transition, that is characterized by the change of the vortex cores from being axisymmetric to exhibiting a 'broken symmetry'; (ii)?translational mode of the vortex cores; (iii)?striking zigzag dipolar chains along the vortex core axis; and (iv)?phase-locking of ferroelectric vortices accompanied by ferroelectric antivortices. These complex phenomena are all found to coexist with a spontaneous electrical polarization aligned along the normal of the plane containing the vortices.     

Constraint programming for stochastic inventory systems under shortage cost

One of the most important policies adopted in inventory control is the replenishment cycle policy. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a constraint programming approach able to compute optimal replenishment cycle policy parameters under non-stationary stochastic demand, ordering, holding and shortage costs. We show how in our model it is possible to exploit the convexity of the cost-function during the search to dynamically compute bounds and perform cost-based filtering. Our computational experience show the effectiveness of our approach. Furthermore, we use the optimal solutions to analyze the quality of the solutions provided by an existing approximate mixed integer programming approach that exploits a piecewise linear approximation for the cost function.