A Positive Doubly Power Bounded Operator with a Nonpositive Inverse Exists on any Infinite-dimensional AL-Space

In this paper we construct a positive doubly power bounded operator with a nonpositive inverse on an AL-space.     

A characterization of an order ideal in Riesz spaces

In this paper we give a characterization of order ideals in Riesz spaces.

     

Un théorème de type Beurling–Lax dans la boule unitéA Beurling–Lax type theorem in the unit ball

We prove a Beurling–Lax theorem for a family of reproducing kernel Hilbert spaces of functions analytic in an open subset of the unit ball containing the origin. The spaces under consideration are characterized by functions called Schur multipliers. Using the theory of linear relations in Pontryagin spaces we also give coisometric realizations of Schur multipliers. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 349–354.     

Structural stability and energetics of C,Si, and Ge microclusters: empirical many-body potential energy function calculation

The structural stability and energetics of carbon, silicon, and germanium microclusters containing 3?7 atoms have been investigated by using a recently developed empirical many-body potential energy function (PEF), which comprises two- and three-body atomic interactions. The PEF satisfies both bulk cohesive energy per atom and bulk stability exactly. It has been found that the most stable C_3?4 microclusters are linear withD _∞h symmetry but C_5?7 microclusters are planar withD _nh symmetry. Silicon and germanium microclusters show similar structural stability. TheX _n (X=Si, Ge;n=3?7) microclusters are found to be most stable in the following forms:X ₃ is triangular withD _3h symmetry,X ₄ is tetragonal withT _d symmetry,X ₅ is square pyramidal withD _4h symmetry,X ₆ is bipyramidal square withO _h symmetry, and finallyX ₇ is square pyramidal having two atoms underneath withD _2h symmetry.     

Determination of trace elements in Na-bentonitic clay by INAA in Turkey

Instrumental neutron activation analysis was applied to the determination of trace elements in a Na-bentonitic clay. The irradiation was done in the Triga Mark II type reactor of ITU Nuclear Energy Institute. The sample was irradiated in two steps for short- and long- lived isotopes. After irradiation, spectra were taken using a germanium detector, multichannel analyzer Canberra System 100 and a fitting program called Sampo 90. The spectra of short-lived isotopes were analyzed to determine Al, Mg, Na, K, Ca, Ti elements and Mn, V trace elements. The spectra of long-lived isotopes were analyzed to determine Sc, Br, Sb, Cs, La, Ce, Sm, Yb, Hf, Pa, Np trace elements.     

Kinetic study of the crystallization processes of some decorative ceramic glazes

A kinetic study of the crystallization processes was performed for some decorative ceramic glazes in the PbO-SiO₂-Na₂O-K₂O-CaO(BaO)-Al₂O₃-B₂O₃ system with addition of 10% TiO₂ and ZnO. The crystallization kinetics has been studied in non-isothermal conditions using DTA technique. The apparent activation energies of the crystallization processes were calculated using the Kissinger method. The main crystalline phase, which provides the decorative effect, is rutile. This has been identified by X-ray diffraction and it is clearly visible in the optical microscopy images taken in transmitted light, as needle-like or even prismatic crystals arranged in radial-fibrous aggregates.     

Pure uterine lipoma

Lipomatous tumors of the uterus are unusual, benign neoplasms seen in postmenopausal women. Although many of the mixed-type cases such as lipoleiomyoma and fibrolipoma have been reported, pure uterine lipomas are extremely rare. In the literature, a few cases with pure uterine lipoma have been reported. We first present the advanced magnetic resonance findings of pure uterine lipoma, followed by those of ultrasonography (US) and computed tomography (CT). We markedly detected lipid peaks on the magnetic resonance spectroscopy (MRS) and the apparent diffusion coefficient value to be 0.00 due to chemical-shift effects with diffusion-weighted imaging (DWI). Although pelvic lipomatous tumors can be diagnosed with US and CT, in some cases, further workup may be required to localize the lesion. MRI may yield more valuable data for differential diagnosis. MRS and DWI findings provide additional clues on the nature of the lesion.     

Chemical composition,antimicrobial, and lipase enzyme activity of essential oil and solvent extracts from Serapias orientalis subsp. orientalis

The volatile components of essential oil (EO), SPME, and SPME of solvent extracts ( n -hexane, methanol, and water) obtained from fresh Serapias orientalis subsp. orientalis ( Soo ) were analyzed by GC-FID/MS. EO of Soo gave 11 compounds in the percentage of 99.97%; capronaldehyde (37.01%), 2-( E )-hexenal (23.19%), and n -nonanal (19.05%) were found to be major constituents. SPME GC-FID/MS analyses of fresh plant and solvent extracts of Soo revealed 7, 12, 7, and 4 compounds within the range of 99.7% to 99.9%. Limonene (76.5%, 41.7%, and 61.3%) was the major compound in SPMEs of the n -hexane and methanol extracts. α -Methoxy- p -cresol (52.9%) was the main component in its water extract. The antimicrobial activity of EO and the solvent extracts of Soo were screened against 9microorganisms. EO showed the best activity against Mycobacterium smegmatis , with 79.5 µg/mL MIC value. The n -hexane, methanol, and water extracts were the most active against the Staphylococcus aureus within the range of 81.25–125.0 µg/mL (MIC). IC ₅₀ values for the lipase enzyme inhibitory activity of EO and solvent extracts ( n -hexane, methanol, and water) were determined to be 59.87 µg/mL, 64.03 µg/mL, 101.91 µg/mL, and 121.24 µg/mL, respectively.     

On the Loewner problem in the class

Loewner's theorem on boundary interpolation of functions is proved under rather general conditions. In particular, the hypothesis of Alpay and Rovnyak (1999) that the function , which is to be extended to an function, is defined and continuously differentiable on a nonempty open subset of the real line, is replaced by the hypothesis that the set on which is defined contains an accumulation point at which satisfies some kind of differentiability condition. The proof of the theorem in this note uses the representation of functions in terms of selfadjoint relations in Pontryagin spaces and the extension theory of symmetric relations in Pontryagin spaces.

     

On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series

For a rational formal power series in N non-commuting indeterminates, with matrix coefficients, we establish the formula which relates the intersection of the null spaces of coefficients to the intersection of the null spaces of values of this series at N-tuples of $n\times n$ matrices, for n large enough. As an application, we formulate the criteria of observability, controllability, and minimality for a recognizable formal power series representation in terms of matrix substitutions. To cite this article: D. Alpay, D.S. Kalyuzhny??-Verbovetzki??, C. R. Acad. Sci. Paris, Ser. I 339 (2004).