Study of the asymptotic Cramér–Rao Bound for the COLD uniform linear array

In this paper, we study the Cocentered Orthogonal Loop and Dipole pairs Uniform Linear Array (COLD-ULA) which is sensitive to the source polarization in the context of the localization of time-varying narrow-band far-field sources. We derive and analyze nonmatrix expressions of the deterministic Cramér–Rao Bound (${\text{CRB}}^{\mathrm{(COLD)}}$) for the direction and the polarization parameters under the assumption that all the sources are lying in the azimuthal plane. We denote this bound by ${\text{ACRB}}^{\mathrm{(COLD)}}$, where the “A” stands for Asymptotic, meaning that the presented results are derived under the assumption that the number of sensors is sufficiently large. While, to our knowledge, closed-form (nonmatrix) expressions of the ${\text{CRB}}^{\mathrm{(COLD)}}$ for multiple time-varying polarized sources signal do not exist in the literature, we show that the ${\text{ACRB}}^{\mathrm{(COLD)}}$ takes a closed-form (nonmatrix) expression in this context and is a good approximation of the ${\text{CRB}}^{\mathrm{(COLD)}}$ even if the number of sensor is moderate (about ten), if the source signals are not spatially too close. Our approach has two important advantages: (i) the computational complexity of the proposed closed-form of the bound is very low, compared to the brute force computation of a matrix-based deterministic CRB in case of time-varying model parameters and (ii) useful informations can be deduced from the closed-form expression on the behavior of the bound. In particular, we prove that the ${\text{ACRB}}^{\mathrm{(COLD)}}$ for the direction parameter is not affected by the knowledge or the lack of it concerning the polarization parameters. Another conclusion is that with a COLD-ULA, more model parameters can be estimated than for the uniformly polarized ULA without degrading the estimation accuracy of the localization parameter. Finally, we also study the ${\text{ACRB}}^{\mathrm{(COLD)}}$ for a priori known complex amplitudes.     

Inertia theorems for matrix polynomials

The Lyapunov method for determining the inertia of a matrix in terms of inertia of solutions of a certain linear matrix equation is extended to matrix polynomials.Generalization of well-known inertia theorems are obtained using the recently developed concept of Bezoutian for several matrix polynomials.     

Chemical composition of bioactive pressurized extracts of Romanian aromatic plants

In this contribution, pressurized liquid extraction (PLE) has been employed to isolate bioactive compounds from three native Romanian plants, oregano (Origanum vulgare), tarragon (Artemisia dracunculus) and wild thyme (Thymus serpyllum). Different PLE conditions have been tested including extraction with water, ethanol and their mixtures in a wide range of extraction temperatures (50-200°C), and the antioxidant capacity of the extracts was measured using different assays (DPPH radical scavenging, TEAC assay and Folin-Ciocalteau assay to measure total phenols). Moreover, a complete chemical characterization by using LC-MS/MS was carried out to be able to correlate the bioactivity with the particular chemical composition of each extract and plant. The use of PLE with water as a solvent at the highest temperature tested (200°C) always provided the highest extraction yields for the three studied plants, being maximum for oregano (>60%). Besides, oregano's pressurized water extracts at lower temperatures (50°C) presented the highest content on total phenols (184.9 mg gallic acid/g extract) and the best antioxidant activities (EC(50) 6.98 μg/ml). In general, oregano extracts were the most active, followed by wild thyme extracts. The antioxidant capacity measured by DPPH assay was highly correlated with the amount of total phenols. Moreover, the use of a LC-MS/MS method allowed the identification of 30 different phenolic compounds in the different extracts, including phenolic acids, flavones, flavanones and flavonols, which have an important influence on the total antioxidant capacity of the different extracts.     

Automorphic Invariant Isometric Operators

We consider isometric operators with finite defect numbers that are unitarily equivalent to their M?bius transformations. A functional characterization of such isometries is given in terms of their characteristic operator-functions. We show that any such isometry admits a contractive extension that is also unitarily equivalent to its M?bius transformation and a unitary extension in a larger space that has the same property. Examples of automorphic invariant operators are considered.     

Immobilization of protein on aldehyde-containing gels—I. Activation of hydrazide gel with glutaraldehyde

Several carriers containing aldehyde groups are described. The carriers were prepared through spacers containing hydrazide groups, followed by glutaraldehyde. Trypsin was coupled to all the carriers, and the influence of temperature, urea, and organic solvents on activity, as well as kinetic parameters of the bound enzyme, were studied. Since all the carriers were prepared similarly, and the same enzyme was coupled to them, similar behaviors were obtained, e.g., two maxima of activity for temperature and organic solvents. Even though all carriers show similar properties for the immobilized enzyme, their preparation and behavior is not always predictable.     

Sur un type de problème bilocal pour les équations aux dérivées partielles

Résumé L'auteur détermine pour l'équation (1), dans la bande 0≦t≦δ, avec l'hypothèse (2) concernant le second membre, la solution prenant sur les droites t=0, t=δ, des valeurs données. Cette solution est nnique. Elle vérifie la même condition (2) que le second membre de (1). à Giovanni Sansone pour son 70^me anniversaire     

New biheterocyclic spiro system — Spiro-[1,4-benzodioxin-2 (3H),2′(3′H)-benzothiazole]

A convenient preparative method has been developed for obtaining 3-methylspiro[1,4-benzodioxin-2 (3H),2(3H)-benzothiazole], the first representative of biheterocyclic spiro compounds of a new type.Institute of Organic Chemistry, National Academy of Sciences of the Ukraine, Kiev 253660; e-mail: iochkiev@sovam.com Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1568–1570, November, 1999.