Determining radii of meromorphy via orthogonal polynomials on the unit circle

Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szeg functions.     

Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

Dihalodimethyltin(IV) complexes of 2‐(pyrazol‐1‐ylmethyl)pyridine

Reaction of dichloro‐ and dibromodimethyltin(IV) with 2‐(pyrazol‐1‐ylmethyl)pyridine (PMP) afforded [SnMe₂Cl₂(PMP)] and [SnMe₂Br₂(PMP)] respectively. The new complexes were characterized by elemental analysis and mass spectrometry and by IR, Raman and NMR (¹H, ¹³C) spectroscopies. Structural studies by X‐ray diffraction techniques show that the compounds consist of discrete units with the tin atom octahedrally coordinated to the carbon atoms of the two methyl groups in a trans disposition (Sn? C = 2.097(5), 2.120(5) Å and 2.110(6), 2.121(6) Å in the chloro and in the bromo compounds respectively), two cis halogen atoms (Sn? Cl = 2.4908(16), 2.5447(17) Å; Sn? Br = 2.6875(11), 2.7464(9) Å) and the two donor atoms of the ligand (Sn? N = 2.407(4), 2.471(4) Å and 2.360(5), 2.455(5) Å). In both cases, the Sn? N(pyridine) bond length is markedly longer than the Sn? N(pyrazole) distance. Copyright © 2003 John Wiley & Sons, Ltd.     

Diagramme polythermique du systeme ternaire H2O—Al(NO3)3—Mg(NO3)2

The solid—liquid equilibria of the ternary system H₂O—Al(NO₃)₃—Mg(NO₃)₂ were studied at –30, –20, –10 and 0°C by using a synthetic method which allows to detemine all the characteristic points of isothermal sections. The stable solid phases which appear are respectively: ice, Al(NO₃)₃·9H₂O, Mg(NO₃)₂·9H₂O and Mg(NO₃)₂·6H₂O. Neither double salts nor mixed crystals are observed in the temperature and composition field studied. Polytherm diagram layout show two invariant transformations correspond with an eutectic point and a peritectic point.This revised version was published online in November 2005 with corrections to the Cover Date.     

Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: A full nonlinear analysis

In this paper, the planar dynamics of a nonlinearly constrained pipe conveying fluid is examined numerically, by considering the full nonlinear equation of motions and a refined trilinear-spring model for the impact constraints—completing the circle of several studies on the subject. The effect of varying system parameters is investigated for the two-degree-of-freedom (N=2) model of the system, followed by less extensive similar investigations forN=3 and 4. Phase portraits, bifurcation diagrams, power spectra and Lyapunov exponents are presented for a selected set of system parameters, showing some rather interesting, and sometimes unexpected, results. The numerical results are compared with experimental ones obtained previously. It is found that in the parameter space that includesN, there exists a subspace wherein excellent qualitative, and reasonably good (N=2) to excellent (N=4) quantitative agreement with experiment. In the latter case, excellent agreement is not only obtained in the threshold flow velocities (u) for the key bifurcations, but the inclusion of the nonlinear terms improves agreement with experiment in terms of amplitudes of motion and by capturing features of behaviour not hitherto predicted by theory.     

[VS_4Cu_6(Py)_8I_3]的合成和晶体结构

在(NH4)3VS4/CuI/Py反应体系中合成了新化合物 [VS4Cu6(Py)8I3]并测定其晶体结构。该化合物(C40H40N8Cu6I3S4V)属正交晶系, 空间群为Fdd2, 晶胞参数为: a = 29.924(6), b = 13.475(3), c = 25.853(5) , V = 10425(4) ?, Dc = 2.006 g/cm3, Mr = 1573.92, Z = 8, (MoK) = 4.546 mm-1, F(000) = 6048。结构由直接法解出, 用全矩阵最小二乘法修正, 最终偏离因子R = 0.023, wR = 0.069。簇合物分子是由6个带端基配体的Cu沿着四面体单元VS4的6条SS边配位而成, 6个Cu排列成了1个八面体, V基本位于八面体的中心, 整个分子具有C2对称性。     

Magnetic calorimeter for registration of small energy release

A scheme of magnetic calorimeter for registration of rare events characterized by small energy release (cosmic rays, WIMPs, solitary X-ray quanta) is proposed. The calorimeter is brought to operation by adiabatic demagnetization, and its magnetic response is measured by a quantum interferometer (SQUID, A. Barone and G. Paterno, Physics and applications of Josephson Effect). Special consideration is given to the specific features of calorimeter operation in the ferromagnetic transition region. The trigger registration of ultrasmall energy release by a ferromagnetic system in the metastable state is described.