One-loop effective potential in N=12 generic chiral superfield model

We obtain the one-loop quantum corrections to the Kählerian and superpotentials in the generic chiral superfield model on the nonanticommutative superspace. Unlike all previous works, we use a method which does not require to rewrite a star-product of superfields in terms of ordinary products. In the Kählerian potential sector the one-loop contributions are analogous to ones in the undeformed theory while in the chiral potential sector the quantum corrections contain a deformation parameter.     

Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.     

Magnetic and transport properties of double distorted perovskites CaCuMn6O12 and CaCu2Mn5O12

Magnetic and transport properties of double distorted perovskites CaCuMn₆O₁₂ and CaCu₂Mn₅O₁₂ are studied in a range 2–300 K. The leading role in magnetism of these compounds belongs to antiferromagnetic exchange interaction of Cu²⁺ in square coordination with Mn³⁺/Mn⁴⁺ in octahedral coordination. The values of saturation magnetization indicate that Mn³⁺ ions in square coordination are coupled ferromagnetically with Mn³⁺/Mn⁴⁺ in octahedral coordination. The colossal magnetoresistance in the pellet samples is due assumingly to intergranular spin-polarized tunneling of current carriers.     

Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames

It has been described earlier that imaging measurements of laser-induced fluorescence (LIF) in flames can be calibrated to number densities with an integrated absorption measurement provided the integrated absorption is small. In this paper a method is presented that extends the technique to flames with substantial absorption, improves the number density determination and allows the experimental parameters to be chosen more freely. The method is based on an iterative computer procedure that reconstructs the 1-D spatially resolved absorption profile from laser measurements of the 1-D spatially resolved LIF and the integrated absorption of the laser beam. The technique is experimentally demonstrated by measurements of OH number densities in atmospheric flames. It is potentially a single-pulse method. Other applications of the iterative procedure are mentioned.     

The construction of discontinuous controls for non-linear dynamical system with uncertainties

The properties of the solutions of a family of non-linear parametric problems are investigated in the neighbourhood of regular and irregular values of the parameter. Rules are proposed for constructing feedback-type controlling for non-linear dynamical systems with perturbations. An example is presented.     

L-functions of second-order cusp forms

We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we investigate the effect of adding an assumption of periodicity to this criterion. 2000 Mathematics Subject Classification Primary—11F12, 11F66 G. Mason: Research supported in part by NSF Grant DMS 0245225. C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34.     

Stereochemistry of seven-membered heterocycles: XLV. Highly diastereoselective addition of dimethyl 1,2,4,5-tetrazine-3,6-dicarboxylate to 2-substituted 1,3-dithiacyclohept-5-enes

Conformationally heterogeneous 2-substituted 1,3-dithiacyclohept-5-enes (R = Ph, Me, t-Bu), which exist in solution as chair and boat conformers, react with dimethyl 1,2,4,5-tetrazine-3,6-dicarboxylate with high exo-diastereoselectivity: only the chair conformer is involved. The steric structure of 4-methyl-3,5-dithia-9,10-diazabicyclo[5.4.0]undeca-7,10-diene was determined by X-ray analysis. Its crystal packing and supramolecular structure were also analyzed.     

Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients

For about thirty years, time series models with time-dependent coefficients have sometimes been considered as an alternative to models with constant coefficients or non-linear models. Analysis based on models with time-dependent models has long suffered from the absence of an asymptotic theory except in very special cases. The purpose of this paper is to provide such a theory without using a locally stationary spectral representation and time rescaling. We consider autoregressive-moving average (ARMA) models with time-dependent coefficients and a heteroscedastic innovation process. The coefficients and the innovation variance are deterministic functions of time which depend on a finite number of parameters. These parameters are estimated by maximising the Gaussian likelihood function. Deriving conditions for consistency and asymptotic normality and obtaining the asymptotic covariance matrix are done using some assumptions on the functions of time in order to attenuate non-stationarity, mild assumptions for the distribution of the innovations, and also a kind of mixing condition. Theorems from the theory of martingales and mixtingales are used. Some simulation results are given and both theoretical and practical examples are treated. Received 2004; Final version 23 December 2004