Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints. This joint estimation problem is framed in the original context of semiparametric models allowing us to handle the (generally unknown) density generator as an infinite-dimensional nuisance parameter. In the first part of the paper, a computationally efficient and memory saving implementation of the robust and semiparmaetric efficient R-estimator for shape matrices is derived. Building upon this result, in the second part, a joint estimator, relying on the Tyler’s M-estimator of location and on the R-estimator of shape matrix, is proposed and its Mean Squared Error (MSE) performance compared with the Semiparametric Cramér-Rao Bound (SCRB).

     

A Construction of the Level 3 Modules for the Affine Lie Algebra and a New Combinatorial Identity of the Rogers-Ramanujan Type

We obtain a vertex operator construction of level 3 standard representations for the affine Lie algebra . As a corollary, we also get new conbinatorial identities.

     

On the extreme spectral properties of Toeplitz matrices generated byL 1 functions with several minima/maxima

In this paper we are concerned with the asymptotic behavior of the smallest eigenvalue ₁ ⁽ⁿ⁾ of symmetric (Hermitian)n ×n Toeplitz matricesT _n (f) generated by an integrable functionf defined in [–, ]. In [7, 8, 11] it is shown that ₁ ⁽ⁿ⁾ tends to essinff =m _f in the following way: ₁ ⁽ⁿ⁾ –m _f 1/n ^2k . These authors use three assumptions:A1)f –m _f has a zero inx =x ₀ of order 2k.A2)f is continuous and at leastC ^2k in a neighborhood ofx ₀.A3)x =x ₀ is the unique global minimum off in [–, ]. In [10] we have proved that the hypothesis of smoothnessA2 is not necessary and that the same result holds under the weaker assumption thatf L ¹[–, ]. In this paper we further extend this theory to the case of a functionf L ¹[–, ] having several global minima by suppressing the hypothesisA3 and by showing that the maximal order 2k of the zeros off –m _f is the only parameter which characterizes the rate of convergence of ₁ ⁽ⁿ⁾ tom _f .     

Minimum blocking configurations

Some results on configurations realizing minimum blocking sets of a finite projective plane are obtained by introducing a suitable attraction property.Dedicated to Professor M. Scafati Tallini on the occasion of her 65th birthday     

Formation and stability of pyrophosphate complexes with aliphatic amines in aqueous solution

The complex formation between pyrophosphate (P(2)O(7)(4-)) and protonated methylamine, ethylenediamine, diethylenetriamine, triethylenetetramine, tetraethylenepentamine and pentaethylenehexamine, has been studied potentiometrically, in aqueous solution, at 25 degrees C. It was found that the species ALH(q)(A = amine, L = P(2)O(7)(4-)) are formed with q = 1 ... n(n = 3, 5, 6, 7, 7 and 8 for the above amines respectively). Mono- and di-amines form species A(p)LH(q) too. The stability of these species is quite high [e.g. H(4)A(4+) + HL(3-)ALH(5)(+): log K = 8.1 (A = pentaethylenehexamine)] and depends strictly on the charges involved in the formation reaction. Charges of reactants being equal, the stability trend is penten > tetren > trien > dien > en > meta and cationic mixed species are more stable than anionic ones. These results are discussed in relation to speciation problems in natural and biological fluids.     

Copper(II) complexes of N-(phosphonomethyl)glycine in aqueous solution: a thermodynamic and spectrophotometric study

Copper(II) complexes with the herbicide N-(phosphonomethyl)glycine (glyphosate) have been investigated in aqueous solution by means of pH-metric measurements at different temperatures, 5 相似文献   

Synthesis and X-Ray Analysis of a Nickel Triphenyl-Cyclopropenyl Complex. A mo-interpretation of the geometry and bonding in the (C3H3)ML3-type of complexes

The reaction of [(C₃Ph₃)Ni(PPh₃)₂]ClO₄ with P(CH₂CH₂PPh₂)₃(pp₃) and NaBPh₄ yields the [(C₃Ph₃)Ni(pp₃)]BPh₄-complex. After long exposure of the solution of this compound in acetone/butanol to the air a new derivative [(C₃Ph₃)-Ni(pp₂po)]BPh₄· 0.5 C₄H₉OH, where pp₂po is (Ph₂PCH₂CH₂)₂P(CH₂ CH₂POPh₂), is obtained. Complete X-ray analysis has been carried out for the latter complex: a=18.303 (5); b=29.445 (6), c=13.305 (5) Å, β=112.70 (9)°; space group monoclinic, P2₁/a, Z=4. Disorder problems were encountered in the refinement of the structure. The best R is 0.093. One of the arms of the parent pp₃-molecule, not coordinated to the metal, undergoes oxidation. The Ni-atom, coordinated by the three remaining P-atoms of the ligand, is also linked in a roughly η³-mode to the cyclopropenium ligand. The geometry of the molecule is examined in detail. Extended HMO-calculations were performed to interpret how the variation of P? Ni? P angles affects the bonding between the NiP₃- and C₃H₃-fragments. The conclusion is that the overall energy of the complex may be lowered in spite of a weakening of the Ni-cyclopropenium linkage. Extensions are made to other systems containing a linkage between a metal and a X₃-ring (X=P,As).     

The magnetic behaviour of [NnBu4]4[Ni16Pd16(CO)40]: an even-electron homoleptic carbonyl-metal cluster anion displaying a J = 2 ground state

The magnetic behaviour of the even-electron [Ni16Pd16(CO)40]4- cluster, in its [NnBu4]+ salt, has been investigated by magnetometry and muon spin rotation/relaxation (muSR) spectroscopy. The susceptibility measurements show an exceptionally high magnetic moment corresponding to a total spin value J=2. This suggests a Hund filling of a quadruplet ground state, quite unique in carbonyl-metal clusters. SQUID magnetometry shows a departure from the Curie-Weiss law, for T>150 K, and strong deviation from a Brillouin behaviour of the magnetisation curves. muSR spectroscopy in zero applied field shows a temperature independent decay of the muon spin polarisation, similar to that of a purely paramagnetic system. The observed muon spin repolarisation in a moderate external longitudinal field, however, invalidates this simple picture and suggests the presence of a local anisotropy field acting on the cluster's magnetic moment. A consistent interpretation of magnetometry and muSR results implies the occurrence of an additional interaction of the cluster spin with an effective crystalline field. The inclusion of this interaction in a model Hamiltonian allows us to successfully reproduce both the susceptibility and magnetisation data.