A new algorithm for nonlinear least squares

A new algorithm for the nonlinear least-squares problems is introduced and illustrated in this article. It is shown that the new algorithm is relatively more efficient compared to the other algorithms in current use and it works for problems where other methods fail. The new method is illustrated by solving a number of classical test problems. In light of the present method, improvements for some other methods in current use are also suggested in this article. Bibliography: 22 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 207, pp. 143–157, 1993.     

On the Nuclear Energy Generation Rate in a Simple Analytic Stellar Model

This paper is concerned with the hydrostatic equilibrium of a purely gaseous star generating energy at a rate . By the common technique of integration theory of special functions the total net rate of nuclear energy generation is evaluated analytically for a linear density distribution function assumed for a simple stellar model.     

Some studies on thallium oxalates — IV

Thallium(III) was precipitated with oxalic acid in the presence of 0.025M RbNO₃ (or 0.0125M Rb₂SO₄) in 0.1M HNO₃ (or 0.05M H₂SO₄). Chemical analysis of the solid obtained corresponds to the formula Rb[Tl^III(C₂O₄)₂]·4 H₂O. Thermal studies (TG, DTG and DTA) indicated the dehydration and redox decomposition of the thallic salt to the thallous salt, and finally to a mixture of rubidium carbonate and oxides of thallium(I) and thallium(III). Infrared absorption spectra, microscopic observations and X-ray diffraction data were used to characterize the original salt, as well as the intermediates formed during the thermal decomposition of the salt. On the basis of these results, the salt may be represented as: Rb[Tl^III(C₂O₄)₂(H₂O)₂]·2 H₂O.

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Zusammenfassung Thallium (III) wurde mit Oxalsäure in Gegenwart von 0.025M RbNO₃ (oder 0.0125M Rb₂SO₄) in 0.1M HNO₃ (oder 0.05M H₂SO₄) gefällt. Die chemische Analyse der erhaltenen Festsubstanz entspricht der Formel Rb[Tl^III(C₂O₄)₂]·4H₂O. Thermische Untersuchungen (TG, DTG und DTA) zeigen die Dehydratisierung und Redoxzersetzung vom Thallitsalz zum Thallitsalz und schließlich zu einem Gemisch von Rubidiumcarbonat und Oxiden der Thallium(I) und Thallium(III). Infrarot-Absorptionsspektren, mikroskopische Beobachtungen und Röntgendiffraktionsdaten werden zur Charakterisierung des ursprünglichen Salzes sowie der während der thermischen Zersetzung des Salzes entstandenen Zwischenprodukte angewandt. Durch diese Ergebnisse kann das Salz wie folgt beschrieben werden: Rb[Tl^III(C₂O₄)₂(H₂O)₂]·2H₂O.

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() 0.025M RbNO₃ ( 0.0125M Rb₂SO₄) 0.1M HNO₃ ( 0.05M H₂SO₄) , Rb[Tl¹¹¹(C₂O₄)₂]. 4₂. (, ) - (). , , , . , Rb[Tl¹¹¹(C₂O₄)₂(H₂O)₂·2₂O.

     

Dichromate titration of thallium(I)

The formal redox potentials of the thallium(III)-thallium(I) couple in different acids of varying strengths are reported. The minimum concentration of hydrochloric acid required for a direct titration of thallium(I) with potassium dichromate is 5M. Thallium(I) can be titrated directly with the primary standard oxidant, potassium dichromate, at room temperature, with ferroin as indicator, in 6M hydrochloric acid. Atmospheric oxygen must be excluded.     

The three-component reaction of dicarbomethoxycarbene, aldehydes, and beta-nitrostyrenes: a stereoselective synthesis of substituted tetrahydrofurans

The Rh(II)-catalyzed reaction of dimethyl diazomalonate with aryl aldehydes and beta-nitrostyrenes results in the formation of highly substituted tetrahydrofurans. The reaction may be considered to involve the Huisgen dipolar cycloaddition of the carbonyl ylide, generated from the dicarbomethoxycarbene and the aldehyde, to the beta-nitrostyrene. The diastereoselectivity of the reaction may be attributed to the concerted nature of the carbonyl ylide cycloaddition.     

Protonated nitro group as a gas-phase electrophile: Experimental and theoretical study of the cyclization of <Emphasis Type="Italic">o</Emphasis>-nitrodiphenyl ethers,amines, and sulfides

A novel gas-phase electrophilic cyclization, initiated by the protonation of a nitro group, occurs for 2-nitrophenyl phenyl ether and for the analogous sulfide and amine, leading to heterocyclic intermediates in each case. Subsequently, the cyclic intermediates dissociate via two pathways: (1) unusual step-wise eliminations of two OH radicals to afford heterocyclic cations, [phenoxazine - H](+), [phenothiazine - H](+), and [phenazine + H](+), and (2) expulsion of H(2)O, to yield a heterocyclic ketone, followed by loss of CO. The proposed structures of the gas-phase product ions and reaction mechanisms are supported by chemical substitution, deuterium labeling, accurate mass measurements at high mass resolving power, product-ion mass spectra obtained by tandem mass spectrometry, mass spectra of reference compounds, and molecular orbital calculations. Using a mass spectrometer as a reaction vessel, we demonstrate that, upon protonation, a nitro group becomes an electrophile and participates in cyclization reactions in the gas phase.     

Homogeneity of a ZrF4-based glass at the nano-scale

A glass of composition 53ZrF₄–20BaF₂–4LaF₃–3AlF₃–20NaF (T_g=260°C) was prepared by careful crucible melting. High-resolution atomic force microscopy of fracture surfaces displayed the presence of nano-pores with diameters of 20–50 nm, being 4–10 nm deep, in all glasses. It was further found that only glasses without annealing and glasses with an annealing step considerably below T_g showed a distinct pattern, i.e. ripples of ≈20 nm in diameter and an rms roughness of ≈0.6 nm. Glasses annealed either near T_g or at the temperatures of maximum nucleation or maximum crystal growth rates showed both regions with the ripple pattern and regions with nano-hillocks, growing in size with increasing annealing temperature and time. Thus these hillocks nearly reach micro-dimensions of ≈270 nm in diameter and ≈65 nm in height following a 90 min annealing step at 343°C, the temperature of maximum crystal growth. These findings give evidence that the glass system, which is thought to be one of the most suitable for fiber drawing, is much less stable against nucleation and crystallization than anticipated.     

Polyvalent Interactions in Biological Systems: Implications for Design and Use of Multivalent Ligands and Inhibitors

Found throughout biology , polyvalent interactions are characterized by the simultaneous binding of multiple ligands on one biological entity to multiple receptors on another (top part of the illustration) and have a number of characteristics that monovalent interactions do not (bottom). In particular, polyvalent interactions can be collectively much stronger than corresponding monovalent interactions, and they can provide the basis for mechanisms of both agonizing and antagonizing biological interactions that are fundamentally different from those available in monovalent systems.