Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

Studies in the field of polyethylene—V. Correlations between compressibility,crystallinity and molecular weight of high pressure natural polyethylenes

The P-V-T relations of high pressure polyethylene free of additives have been studied in a modified universal testing machine. These polymers show a rapid compression at the melting point of the crystalline phase.     

On the generators of semisimple lie algebras

It will be shown that given any element X in a simple Lie algebra $\text{Q}$ over C, there exists a Y ∈ $\text{Q}$ such that the Lie algebra generated by X and Y is $\text{Q}$. The result is extended to the real semisimple Lie algebras. In some sense the main theorem of this paper can be regarded as an extension of Morozov-Jacobson theorem concerning three dimensional simple Lie algebras (see the remark at the end of Sec. 4). A new property of a special class of regular elements, known as the cyclic elements, is given.     

Restes des formules de quadrature de Gauss et de Turán

Sans résumé Présenté par P. Turán     

Studies on terbium activated yttrium based tantalate phosphors

Terbium activated yttrium niobium tantalate phosphors were prepared by solid-state reaction and were characterized by photoluminescence measurements, X-ray diffraction and scanning electron microscopy. Photoluminescence (PL) of Y_0.95Tb_0.05Ta_1?xNb_xO₄ phosphors (x = 0–1) are influenced by the host-lattice composition, degree of crystalline order and particle morphology and size. The effect of the morpho-structural properties on PL characteristics of Y(Ta,Nb)O₄:Tb powders is reported.     

Electronic spectroscopy of the A1A' <-- X1A' system of CDF

To further investigate the Renner-Teller (RT) effect and barriers to linearity and dissociation in the simplest singlet carbene, we recorded fluorescence excitation spectra of bands involving the pure bending levels 2(n)(0) with n = 0-9 and the combination states 1(1)(0)2(n)(0) with n = 1-8 and 2(n)(0)3(1)(0) with n = 0-5 in the A(1)A'<-- X(1)A' system of CDF, in addition to some weak hot bands. The spectra were measured under jet-cooled conditions using a pulsed discharge source, and rotationally analyzed to yield precise values for the band origins and rotational constants; fluorescence lifetimes were also measured to probe for lifetime lengthening effects due to the RT interaction. The derived A state parameters are compared with previous results for CHF and with predictions of ab initio electronic structure theory. The approach to linearity in the A state is evidenced in a sharp increase in the A rotational constant with bending excitation, and a minimum in the vibrational intervals near 2(9). A fit of the vibrational intervals for the pure bending levels yields an A state barrier to linearity in good agreement both with that previously derived for CHF and ab initio predictions. From the spectra and lifetime measurements, the onset of extensive RT perturbations is found to occur at a higher energy than in CHF, consistent with the smaller A constant.     

Retention and selectivity tests of silica-based and metal-oxide bonded stationary phases for RP-HPLC

Chromatographic properties of silica-, zirconia- and alumina-based columns with octadecyl-, polyethylene glycol- and pentafluorophenylpropyl-bonded stationary phases were tested. Selectivities of nine columns for LC were characterized using chromatographic methods including Walters, Engelhardt, Tanaka and Galushko hydrophobicity and silanol activity tests, measurements of methylene selectivity in various aqueous-methanol and aqueous-acetonitrile mobile phases and of gradient lipophilic capacity as a measure of the effect of the sample hydrophobicity on gradient-elution separations. A semi-empirical interaction indices model, assuming a predominant role of the solvophobic interactions of test compounds with different polarities, was compared with the linear free energy relationships approach taking into account selective polar interactions. The interaction indices model was applied to both non-polar stationary phases bonded on silica, alumina and zirconia supports, and to the non-modified adsorbents in the normal-phase LC. The retention data of isomeric naphthalene disulfonic acids were used to compare the attractive and repulsive ionic interactions of the columns in purely aqueous mobile phases. The results of the hydrophobicity and polarity tests were consistent, and allowed column characterization and classification. Silanol activity was important with octadecyl silica columns, but was relatively insignificant with bonded polyethylene glycol and pentafluorophenylpropyl phases on silica gel support. Polar interactions with the alumina and zirconia support materials significantly affect the retention.     

A new algorithm that generates the image of the attractor of a generalized iterated function system

Numerical Algorithms - We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space...