Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

Arithmetic tests forA-stability,A[α]-stability,and stiff-stability

Arithmetic tests forA-stability,A[]-stability, and stiff-stability are presented as special cases of a general stability test for numerical integration methods. The test evolves from extracted properties of the characteristic polynomial (in two variables) of the numerical method applied to the prototype scalar ordinary differential equation , Re {q}<0. The several steps of the test impose root clustering conditions — such as being Hurwitz — on a polynomial of one variable.Research sponsored in part by a special grant of the Syracuse University Senate Research Committee to the first author and by the National Science Foundation under Grant ENG76-21816 to the second author.The research reported herein was completed while the first author was on sabbatical leave in the Department of Electrical Engineering and Computer Sciences at the University of California in Berkeley, California.     

Nevanlinna–Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna–Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.     

Novel trialkylsilyl(germyl)-substituted thienyl- and furylbenzimidazoles and their N-substituted derivatives – synthesis,structure and cytotoxic activity

The reaction of 1,2-phenylenediamine with a variety of silicon- or germanium-containing 2-furaldehydes or 2-thienylcarbaldehydes in DMFA gave the corresponding benzimidazole derivatives in moderate yields (36–49%) in the presence of sodium hydrogen sulfite. As a result, a new series of silyl, germyl substituted hetarylbenzimidazoles were synthesized and their in vitro cytotoxicity was studied. The quaternisation of N-substituted benzimidazoles by heating with various alkyl, allyl and propargyl chlorides and bromides leads to the formation of benzimidazolinium salts. Potential cytotoxic activity of synthesized new benzimidazoles and benzimidazolinium salts was tested in vitro on two monolayer tumour cell lines: MG-22A (mouse hepatoma), HT-1080 (human fibrosarcoma) and normal mouse fibroblasts (NIH 3T3) and compared with corresponding benzimidazoles.     

Co3O4−CeO2 Nanocomposites for Low-Temperature CO Oxidation

In an effort to combine the favorable catalytic properties of Co₃O₄ and CeO₂, nanocomposites with different phase distribution and Co₃O₄ loading were prepared and employed for CO oxidation. Synthesizing Co₃O₄-modified CeO₂ via three different sol-gel based routes, each with 10.4 wt % Co₃O₄ loading, yielded three different nanocomposite morphologies: CeO₂-supported Co₃O₄ layers, intermixed oxides, and homogeneously dispersed Co. The reactivity of the resulting surface oxygen species towards CO were examined by temperature programmed reduction (CO-TPR) and flow reactor kinetic tests. The first morphology exhibited the best performance due to its active Co₃O₄ surface layer, reducing the light-off temperature of CeO₂ by about 200 °C. In contrast, intermixed oxides and Co-doped CeO₂ suffered from lower dispersion and organic residues, respectively. The performance of Co₃O₄-CeO₂ nanocomposites was optimized by varying the Co₃O₄ loading, characterized by X-ray diffraction (XRD) and N₂ sorption (BET). The 16–65 wt % Co₃O₄−CeO₂ catalysts approached the conversion of 1 wt % Pt/CeO₂, rendering them interesting candidates for low-temperature CO oxidation.     

Synthesis and Cytotoxic Activity of 1‐{3‐[1‐(5‐Organylsilylfuran‐2‐yl)silinan‐1‐yl]propyl}amines and Some Trimethylgermyl Analogues

New highly cytotoxic 1‐{3‐[1‐(5‐organylsilyl‐furan‐2‐yl)silinan‐1‐yl]propyl}amines and some trimethylgermyl analogues (IC₅₀ 1–7 μg mL^?1) have been synthesized by a hydrosilylation reaction of aliphatic and heterocyclic N‐allylamines in the presence of Speier’s catalyst. The effects of the silacycle, the element‐organic substituent in position 5 of the furan ring, and the structure of the amine on the cytotoxicity of the new compounds have been studied.     

Pricing caps with HJM models: The benefits of humped volatility

In this paper we compare different multifactor HJM models with humped volatility structures, to each other and to models with strictly decreasing volatility. All the models are estimated on Euribor and swap rates panel data maximizing the quasi-likelihood function obtained from the Kalman filter. We develop the analysis in two steps: first we study the in-sample properties of the estimated models, then we test the pricing performance on caps. We find the humped volatility specification to greatly improve the model estimation and to provide sufficiently accurate cap prices, although the models has been calibrated on interest rates data and not on cap prices. Moreover, we find the two-factor humped volatility model to outperform the three-factor models in pricing caps.     

The spectrochemical determination of total strontium in bone,milk and vegetation

Samples of bone ash are mixed with anhydrous copper sulphate and graphite and pelleted A d c. arc is used to excite the spectra which are then evaluated by microphotometry The effective concentration range is 50 – 350 p p. m of strontium in the ash and the coefficient of variation is 6% for single exposures at the 90 p p m levelIn the case of milk and vegetation, strontium and calcium are separated as insoluble oxalates and the strontium content of this fraction determined by a method similar to that used for bones, with a similar range and accuracy. An alternative flame photometric method is described for the determination of strontium in the calcium-strontium oxalate fraction, thc coefficient of variation of the whole analytical operation being 5% per determination