Comment on Fermionic and Bosonic Pair-creation in an External Electric Field at Finite Temperature

We show that contrary to the claim made by Hallin and Liljenberg in Phys. Rev. D52 1150,(1995), (hep-th/9412188) the thermal correction to the thermal decay or pair production rate for a system placed in a heat bath in the presence of an external electric field, is always nonzero in the finite as well as infinite time limit. Using the formalism outlined there, we reestimate the decay rate for different values of temperature, mass and time.We also try to identify the parameter ranges where the quantity of interest agrees with that computed previously, at high temperature (in the infinite time limit), from the imaginary part of the effective action using imaginary time and real time formalism of thermal field theory. We also point out that in the strictly infinite time limit, the correct decay rate as obtained from the work of Hallin et. al. tends to diverge

Stereospecific synthesis of the aglycone of pseudopterosin E

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Emergence of a non-scaling degree distribution in bipartite networks: a numerical and analytical study

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We derive the exact analytical expression for the degree-distribution of all these different types of attachments while assuming that edges are incorporated sequentially, i.e., a single edge is added to the growing network in a time step. We also provide an approximate expression for the case when more than one edge are added in a time step. We show that depending on the relative weight between random and preferential attachment, the degree-distribution of this type of network falls into one of four possible regimes which range from a binomial distribution for pure random attachment to an u-shaped distribution for dominant preferential attachment

Synthesis, Characterization and Performance Study of Phosphosilicate Gel-Sulfonated Poly (Ether Ether Ketone) Nanocomposite Membrane for Fuel Cell Application

Phosphosilicate gel – SPEEK (Sulfonated Poly Ether Ether Ketone) hybrid nanocomposite membranes are proposed for performance enhancement of polymer electrolyte fuel cell. The nanocomposite membranes are synthesized and characterized at 50 and 60 weight percent of inorganic loading. Phosphosilicate gel particles of varying size (sub micro to nanometer) are synthesized using sol gel approach followed by grinding using planetary ball mill for different time. Transmission Electron Microscopy (TEM) reveals less than 10 nm particle size for 20 hr grinding. Nano composite membrane having inorganic particles of size less than 10 nm exhibits higher values of proton conductivity, ion exchange capacity and water uptake compared to composite membrane comprising of larger (400 nm and above) inorganic particles. The membrane is assembled with the electrode in the unit cell and the polarization characteristics are measured at different operating temperatures. Performance study reveals that between 70 to 80 C the membrane offers best performance in terms of peak power generation and of allowable load current. For the same conditions 40-50 % nano-enhancement of peak power generation is achieved by reducing the average gel particle size from sub micro to less than 10 nm. At medium temperature (between 70 to 80 C) the nanocomposite membrane offers more than 100 enhancement of peak power generation compared to that generated by SPEEK membrane. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2491

Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry

Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner Hamiltonians may be exploited to obtain a simple shape-invariant condition. Indeed a novel relation between potential and mass functions is derived, which leads to a class of exactly solvable model. As an illustration of our procedure, two examples are given for which one obtains whole spectra algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like or singular-oscillator-like spectra depending on the values of the shape-invariant parameter.Comment: 16 pages, 5 figs; Present e-mail of AG: [email protected]