An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Theoretical investigations of the gas phase reaction of limonene (C10H16) with OH radical

The rate coefficients of hydroxyl radical (OH) reaction with limonene were computed using canonical variational transition state theory with small-curvature tunnelling between 275 and 400 K. The geometries and frequencies of all the stationary points are calculated using hybrid density functional theory methods M06-2X and MPWB1K with 6-31+G(d,p), 6-311++G(d,p), and 6-311+G(2df,2p) basis sets. Both addition and abstraction channels of the title reaction were explored. The rate coefficients obtained over the temperature range of 275–400 K were used to derive the Arrhenius expressions: k(T) = 4.06×10^?34 T^7.07 exp[4515/T] and k(T) = 7.37×10^?25 T^3.9 exp[3169/T] cm³ molecule^?1 s^?1 at M06-2X/6-311+G(2df,2p) and MPWB1K/6-311+G(2df,2p) levels of theory, respectively. Kinetic study indicated that addition reactions are major contributors to the total reaction in the studied temperature range. The atmospheric lifetime (τ) of limonene due to its reactions with various tropospheric oxidants was calculated and concluded that limonene is lost in the atmosphere within a few hours after it is released. The ozone production potential of limonene was computed to be (14–18) ppm, which indicated that degradation of limonene would lead to a significant amount of ozone production in the troposphere.     

Optically-driven red blood cell rotor in linearly polarized laser tweezers

We have constructed a dual trap optical tweezers set-up around an inverted microscope where both the traps can be independently controlled and manipulated in all the three dimensions. Here we report our observations on rotation of red blood cells (RBCs) in a linearly polarized optical trap. Red blood cells deform and become twisted in hypertonic phosphate buffer saline and when trapped, experience an unbalanced radiation pressure force. The torque generated from the unbalanced force causes the trapped RBC to rotate. Addition of Ca⁺⁺ ions in the solution, keeping the osmolarity same, makes the cell membranes stiffer and the cells deform less. Thus the speed of rotation of the red blood cells can be controlled, as less deformation and in turn less asymmetry in shape produces less torque under the radiation pressure resulting in slower rotation at the same laser power     

A DFT‐based exploration augmented by X‐ray and NMR of the stereoselectivity in the 1,3‐dipolar cycloaddition of 1‐pyrroline‐1‐oxide to methyl cinnamate and benzylidene acetophenone

A B3LYP/6–31G* study was carried out for the reactions of 1‐pyrroline‐1‐oxide (N1) with methyl cinnamate (E1) and benzylidene acetophenone (E2) for getting a quantitative rationalization of the experimental findings. The product ratios were determined by NMR studies of the crude reaction mixtures. The conformation and stereochemistry of the isolated cycloadducts were finally confirmed by 2D NMR and X‐ray diffraction. The endo/exo‐selectivities were predicted through the computation of activation parameters on the basis of assumed concerted mechanism. The regioselectivity and reactivity were amply predicted by local and global electrophilicity indices and were found to be in good agreement with the experimental findings which were supportive of polar character and of the direction of charge transfer (CT) accompanying the cycloaddition. It was found that the cycloaddition involving methyl cinnamate was endo‐selective, while that with benzylidene acetophenone produced the exo‐isomer as the major adduct. Copyright © 2010 John Wiley & Sons, Ltd.     

A study of the deterministic character of optical damage by femtosecond laser pulses and applications to nanomachining

A remarkable feature of material damage induced by short-pulsed lasers is that the energy threshold becomes deterministic for sub-picosecond pulses. This effect, coupled with the advent of kHz and higher repetition rate chirped pulse amplification systems, has opened the field of femtosecond machining. Yet the mechanism of optical breakdown remains unclear. By examining the damage threshold as a function of polarization, we find that, contrary to established belief, multiphoton ionization plays an insignificant role in optical breakdown. The polarization independence, combined with the observed precise and uniform dielectric breakdown threshold even for nanometer-scale features, leads us to conclude that the fundamental mechanism is self-terminated Zener-impact ionization, and that the deterministic and uniform damage threshold throughout the sample threshold stems from the uniform valence-electron density found in good-quality optical materials. By systematically exploring optical breakdown near threshold, we find that we can consistently machine features as small as 20 nm, demonstrating great promise for applications ranging from Micro ElectroMechanical Systems (MEMS) construction and microelectronics, to targeted disruption of cellular structures and genetic material. PACS 32.80.Rm; 77.22.Jp; 81.16.-c     

Local operator products in gauge theories,II

We study the operator product expansion of two gauge-invariant currents. We discuss the operators that may appear in the expansion. We study the hadronic matrix elements of gauge-variant operators that may appear in the operator product expansion and show that in the physical applications contemplated so far their hadronic physical matrix elements either vanish or cannot be isolated from strong interactions. We also study the gauge dependence of the Green's functions of the product of two (weak or e.m.) currents and show that is corresponds to the gauge dependence of the additional renormalization counterterms due to weak and electromagnetic interactions.     

Steric effect on fluorescence quenching

In this communication we have reported the steric effect on the fluorescence quenching rate constants of the electron transfer (ET) process. We have done a comparative study using donor (D)-acceptor (A) systems with different exergonicity (-deltaG(f)). Different carbazole derivatives (CZ): 1,4-dicyanobenzene (DCB) systems (-deltaG(f) = 0.7-0.8 eV) were found to be among those limiting systems that show a clear-cut steric dominance in the process of fluorescence quenching. It is known that with increasing exergonicity the ET distance increases and hence steric dependence becomes insignificant. On the other hand, with decreasing exergonicity the ET distance decreases and a pronounced steric dominance should be observed. However, in the D-A systems having lower exergonicity compared to CZ-DCB systems, this steric dominance is observed only in polar medium. In non-polar medium due to exciplex formation the D-A distance effectively becomes much longer and therefore no steric dominance is observed.     

Molecules in an electric field: Some structural and spectroscopic consequences

It is theoretically shown that under the influence of an appropriately directed external electric field (ε) in H₂CO or a similar molecule (of the XYC = O type), the barrier to planar inversion in the ³n π* state decreases as the field strength increases. The molecule assumes a forced planar geometry in the ³n π* state rather abruptly when ε_(applied) > ε_(critical). This phenomenon of field-induced change of structure of an isolated molecule has the attributes of a first order phase transition. The effects should be spectroscopically detectable in the inversion spectrum. The existence of another critical field strength at which the molecule makes a more or less continuous transition from the normal convalent to a purely ionic structure is demonstrated and rationalized through a simple model.