Transition to superfluidity in strongly coupled fermion systems: low density limit

The rôle of interacting bound pairs in strongly coupled fermion systems is considered in connection with the transition to superfluidity. Model calculations are performed for finite-range separable interaction potentials. The results of a cluster-Hartree-Fock approximation are compared with recent approaches improving the Nozières and Schmitt-Rink theory. In the low-density strong coupling limit, a first order transition to the superfluid phase is obtained.     

Scanning capacitance microscopy and spectroscopy applied to local charge modifications and characterization of nitride-oxide-silicon heterostructures

We have combined a home-built capacitance sensor with a commercial scanning force microscope to obtain a Scanning Capacitance Microscope (SCM). The SCM has been used to study Nitride-Oxide-Silicon (NOS) heterostructures which offer potential applications in charge storage technology. Charge writing and reading on a submicrometer scale is demonstrated with our SCM setup. In addition, SCM appears to be very useful for the characterization of subsurface defects in semiconductor devices which are inaccessible by most of the other scanning probe microscopies. Finally, we introduce a novel spectroscopic mode of SCM operation which offers combined voltage-dependent and spatially resolved information about inhomogeneous charge distributions in semiconductor devices.     

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

Truncation error bounds for modified continued fractions with applications to special functions

Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a _n , 1;x ₁), with andnth approximant

Building of mathematical models of continuum media on the basis of the invariance principle

The system of differential equations which describes the motion of continuum media of gas, liquid, Reiner-Rievling-type liquid, etc., is considered.% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHbp% GCdaWgaaWcbaGaamiDaaqabaGccqGHRaWkcaqGKbGaaeyAaiaabAha% caqGOaGaeqyWdiNaaeyDaiaabMcacaqG9aGaaeimaiaabUdaaeaacq% aHbpGCcaGGBbGaaeyDamaaBaaaleaacaqG0baabeaakiabgUcaRiaa% cIcacaqG1bGaeyyXICTaey4bIeTaaiykaiaabwhacaGGDbGaeyOeI0% IaamizaiaadMgacaWG2bGaey4dIuTaaiikaiabgEGirlaabwhacaGG% PaGaey4kaSIaey4bIeTaamiCaiaacUdaaeaacaWGWbWaaSbaaSqaai% aadshaaeqaaOGaey4kaSIaaeyDaiabgwSixlabgEGirlaadchacqGH% RaWkcaWGhbGaaeizaiaabMgacaqG2bGaaeiiaiaabwhacqGHRaWkca% WGibGaeqOXdyMaeyypa0JaaGimaiaac6caaaaa!7268!\[\begin{gathered} \rho _t + {\text{div(}}\rho {\text{u) = 0;}} \hfill \\ \rho [{\text{u}}_{\text{t}} + ({\text{u}} \cdot \nabla ){\text{u}}] - div\prod (\nabla {\text{u}}) + \nabla p; \hfill \\ p_t + {\text{u}} \cdot \nabla p + G{\text{div u}} + H\phi = 0. \hfill \\ \end{gathered} \]Solving the problem of its group classification, we obtained all the state equations which lead to the expansion of the main group assumed by the initial equations under the arbitrary elements , G, H.     

Some remarks on derivations in Banach algebras and related results

Summary In the first section of this paper we consider some functional equations which are closely connected to derivations (i.e. additive mappings with the propertyD(ab) = aD(b) + D(a)b) on Banach algebras. IfD is a derivation on some algebraA, then the equationD(a) = – aD(a ^–1 )a holds for all invertible elementsa A. It seems natural to ask whether this functional equation characterizes derivations among all additive mappings. It is too much to expect an affirmative answer to this question in arbitrary algebras, since it may happen that even in normed algebras the group of all invertible elements contains only scalar multiples of the identity. We try to answer the question above in Banach algebras, since in Banach algebras invertible elements exist in abundance. In the second section of the paper we prove some results concerning representability of quadratic forms by bilinear forms.     

Structural and electrochemical studies of annealed LiNiVO4 thin films

We prepared stoichiometric lithium nickel vanadate amorphous thin films by using r.f. magnetron sputtering under controlled oxygen partial pressure. The amorphous films were heated at various temperatures, 300–600 °C, for 8 h. The as‐deposited and annealed thin films were characterized by Rutherford backscattering spectroscopy, nuclear reaction analysis, Auger electron spectroscopy, X‐ray diffraction, scanning electron microscopy and atomic force microscopy. The electrochemical behavior of the various films was studied by the galvanostatic method. The cells were tested in a liquid electrolyte at room temperature, with lithium metal used as the counter and reference electrode. The best electrochemical storage value was obtained with the thin film annealed at 300 °C, which showed superior capacity and small capacity loss during cycling. Copyright © 2007 John Wiley & Sons, Ltd.     

A Polarographic Study of ϵ-Caprolactam Complexes of Uranium and Tellurium

The polarographic behaviour of uranium and tellurium has been studied in the presence of increasing concentration of complex forming agent viz. ?-caprolactam at pH 4.4 for U(VI) and at pH 10.0 for Te(IV) at μ=0.1 M KNO₃. In both cases the waves have been found to be diffusion controlled and irreversible. The values of kinetic parameters (σπ_a and K°_f,h) have been calculated as a function of the ligand concentration. Method is suitable for the quantitative determination of these metals individually and simultaneously with the effect of diverse ions.     

Influence of target surface degradation on the properties of r.f. magnetron‐sputtered calcium phosphate coatings

This paper reports a detailed study of how repeated r.f. magnetron sputtering from a hydroxyapatite (HA) powder target affects the nature and reproducibility of a sequential series of thin‐film coatings deposited onto Ti6Al4V substrates. An evaluation of the effective lifespan of the HA sputter targets and the reproducibility of the calcium phosphate (CaP) coatings produced from them has been made from Fourier transform infrared spectroscopy, XPS and, as appropriate, atomic force microscopy and SEM/energy dispersive x‐ray analyses. The annulus region of the target surface, from which sputtering under r.f. magnetron conditions normally occurs, showed severe surface degradation after only one deposition run, as indicated by significant PO₄^3? and OH^? depletion. This deterioration continued after each subsequent deposition cycle but to a much lesser extent than that observed in the initial sputtering period. The layers produced from all of the sputter runs contained the expected Ca²⁺ and PO₄^3? species characteristic of a CaP system but were OH^? deficient in the as‐deposited state. However, the chemical and morphological properties of the coatings did not change significantly until after the third consecutive sputter cycle. Hence, these data indicate that, even though a significant level of degradation of the HA target occurs at the outset of the sputtering procedure, the general plasma conditions employed here have a dominant influence on the coating properties until a critical degradation condition is met. As such, the compacted HA powder targets of interest can have a life‐cycle greater than single usage without detriment to the chemistry and morphology of the coatings produced from them. Copyright © 2003 John Wiley & Sons, Ltd.     

An extremal problem related to probability

Summary We consider a walk from a stateA ₁ to a stateA _n+1 in which the probability of remaining atA _i isp _i , and the probability of progressing fromA _i toA _i+1 is 1 –p _i . The probabilityW _nk of reachingA _n+1 fromA ₁ in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp ₁,,p _n . We determine the maximum value ofW _nk and the (unique) choice (p ₁,,p _n ) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday