Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness

In this paper we consider interpolatory quadrature formulae with multiple nodes, which have the maximal trigonometric degree of exactness. Our approach is based on a procedure given by Ghizzeti and Ossicini (Quadrature formulae, Academie-Verlag, Berlin, 1970). We introduce and consider the so-called σ-orthogonal trigonometric polynomials of semi-integer degree and give a numerical method for their construction. Also, some numerical examples are included. The authors were supported in part by the Serbian Ministry of Science and Technological Development (Project: Orthogonal Systems and Applications, grant number #144004) and the Swiss National Science Foundation (SCOPES Joint Research Project No. IB7320-111079 “New Methods for Quadrature”).     

Synthesis,characterization and biological activity of copper(II) complexes with ligands derived from β-amino acids

Transition Metal Chemistry - Two copper(II) complexes with ligands derived from β-amino acids, 2-(1-aminocyclohexyl)acetic acid L1 and 2-(1-amino-4-(tert-butyl)cyclohexyl)acetic acid L2, were...     

On discrete inequalities of Wirtinger's type

Discrete inequalities of Wirtinger's type are considered. Constants in the obtained inequalities are the best ones. In the special case the inequalities (1) and (2) are obtained. They are proved by K. Fan, O. Taussky, and J. Todd: Discrete analogs of inequalities of Wirtinger, Montash. Math.59 (1955), 73–79.     

Spectrophotometric and potentiometric determination of acidic constants of oxo-phenyl pyridinium monoxime and dioxime

The UV absorption spectra of 1-(1-hydroxyimino-2-oxo-2-phenyl) pyridinium chloride (compound I) and 1-(1-hydroxyimino-2-oxo-2-phenyl)-4-hydroxyiminomethyl pyridinium chloride (compound II) in water solution at differentpH values have been measured. The spectral changes, with changingpH, in aqueous solutions are attributed to the dissociation of individual functional groups of the compounds. The mixed acidic constants (pKa) of the investigated monoxime and dioxime, have been determined spectrophotometrically in the series ofBritton-Robinson's buffer solutions in thepH range 3.0–5.19 and 7.70–9.90 (t=25±0.5°C,I=0.2). The followingpKa values have been obtained for monoximepKa ₁=4.30 and for dioximepKa ₁=4.28,pKa ₂=8.36.Thermodynamic acidic constants (pKa) have been determined on the basis of potentiometric titrations and they have been found to bepKa ₁=4.32 for compound I andpKa ₁=4.27,pKa ₂=8.51 for compound II. The values obtained by transferringpKa intopKa are in good agreement with the values obtained potentiometrically.

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Spektrophotometrische und potentiometrische Bestimmung der Aciditätskonstanten von Oxo-Phenyl-Pyridinium-Monooxim und -Dioxim

Zusammenfassung Die UV-Absorptionsspektren von 1-(1-Hydroxyimino-2-oxo-2-phenyl)-pyridiniumchlorid (Verbindung I) und 1-(1-Hydroxyimino-2-oxo-2-phenyl)-4-hydroxyiminomethylpyridiniumchlorid (Verbindung II) wurden in wäßrigen Lösungen bei verschiedenenpH-Werten aufgenommen. Die Änderungen in den Spektren, die in wäßrigen Lösungen mit derpH-Änderung entstehen, können der Dissoziation der einzelnen funktionellen Gruppen der untersuchten Verbindungen zugeschrieben werden. Die Mischaciditätskonstanten (pKa) des untersuchten Monooxims und Dioxims wurden spektrophotometrisch in einer Reihe vonBritton-Robinson-Pufferlösungen inpH-Intervallen 3.0–5.19 und 7.70–9.90 (t=25±0.5°C;I=0.2) bestimmt: für das MonooximpKa ₁=4.30 und für DioximpKa ₁=4.28 undpKa ₂=8.36. Die thermodynamischen Aciditätskonstanten (pKa) wurden aufgrund der potentiometrischen Titration berechnet:pKa ₁=4.32 für die Verbindung I undpKa ₁=4.27 undpKa ₂=8.51 für die Verbindung II. Die durch ÜbertragungpKa inpKa erhaltenen Werte sind mit den über die potentiometrische Methode erhaltenen Werten in guter Übereinstimmung.

     

Spline approximations to spherically symmetric distributions

Summary We discuss the problem of approximating a functionf of the radial distancer in ^d on 0r< by a spline function of degreem withn (variable) knots. The spline is to be constructed so as to match the first 2n moments off. We show that if a solution exists, it can be obtained from ann-point Gauss-Christoffel quadrature formula relative to an appropriate moment functional or, iff is suitably restricted, relative to a measure, both depending onf. The moment functional and the measure may or may not be positive definite. Pointwise convergence is discussed asn. Examples are given including distributions from statistical mechanics.The work of the first author was supported in part by the National Science Foundation under grant DCR-8320561.     

Fractality and self‐organization in the orthodox iconography

The authors consider the Orthodox iconography of Byzantine style aimed at examining the existence of complex behavior and fractal patterns. It has been demonstrated that fractality in icons is manifested as two types—descending and ascending, where the former one corresponds to the apparent information and the latter one to the hidden causal information defining the spatiality of icon. Self‐organization, recognized as the increase of the causal information in temporal domain, corresponds to contextualization of the observer's personage position. The results presented in the forms of plots and tables confirm the adequacy of the model being the completion of visual perception. © 2015 Wiley Periodicals, Inc. Complexity 21: 55–68, 2016     

A method for efficient computation of integrals with oscillatory and singular integrand

Numerical Algorithms - A method based on modification of numerical steepest descent method to efficiently compute highly oscillatory integrals having endpoint singularities of algebraic and...     

Convergence of a Finite Difference Scheme for a Parabolic Transmission Problem in Disjoint Domains

In this paper we investigate a parabolic transmission problem in disjoint domains. An a priori estimate for its weak solution in appropriate Sobolev-like space is proved. The convergence of a finite difference scheme (FDS) approximating this problem is analyzed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)