Truncated Trust Region Methods Based on Preconditioned Iterative Subalgorithms for Large Sparse Systems of Nonlinear Equations

This paper is devoted to globally convergent methods for solving large sparse systems of nonlinear equations with an inexact approximation of the Jacobian matrix. These methods include difference versions of the Newton method and various quasi-Newton methods. We propose a class of trust region methods together with a proof of their global convergence and describe an implementable globally convergent algorithm which can be used as a realization of these methods. Considerable attention is concentrated on the application of conjugate gradient-type iterative methods to the solution of linear subproblems. We prove that both the GMRES and the smoothed COS well-preconditioned methods can be used for the construction of globally convergent trust region methods. The efficiency of our algorithm is demonstrated computationally by using a large collection of sparse test problems.     

Decompositions of measures on orthoalgebras and difference posets

We present a general decomposition theorem for elements of an ordered group with respect to a cone. This result enables us to obtain decompositions of finitely additive measures defined on quantum logics, orthoalgebras, or, more generally, on difference posets with values in Dedekind complete lattice ordered groups, with respect to a given cone of measures. In particular, we gain Yosida-Hewitt-type and Lebesgue-type decompositions.     

Value distribution of the Lerch zeta-function with algebraic irrational parameter. IV

We obtain a joint limit theorem in the space of analytic functions for Lerch zeta-functions with algebraic irrational parameter. The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-81/09.     

Maximal dominated operator semigroups

Maximal operator semigroups, bounded in a certain sense, on real or complex vector spaces are studied. For any maximal semigroup \MM dominated by a certain pair of homogeneous functions there is an operator quasinorm for which \MM is exactly the semigroup of contractions in this quasinorm. Applications to Riesz spaces are given. In particular, maximal semigroups of matrices dominated by a given positive matrix are characterized. We thus answer the question implicitly posed in [2]. November 20, 1998     

Simple Explicit Formulas for the Frame-Stewart Numbers

Several different approaches to the multi-peg Tower of Hanoi problem are equivalent. One of them is Stewart's recursive formula ¶¶ S (n, p) = min {2S (n₁, p) + S (n-n₁, p-1) | n₁, n-n₁ ? \mathbbZ⁺}. S (n, p) = min \{2S (n_1, p) + S (n-n_1, p-1)\mid n_1, n-n_1 \in \mathbb{Z}^+\}. ¶¶In the present paper we significantly simplify the explicit calculation of the Frame-Stewart's numbers S(n, p) and give a short proof of the domain theorem that describes the set of all pairs (n, n₁), such that the above minima are achieved at n₁.     

π‐Expanded α,β‐Unsaturated Ketones: Synthesis,Optical Properties,and Two‐Photon‐Induced Polymerization

A library of π‐expanded α,β‐unsaturated ketones was designed and synthesized. They were prepared by a combination of Wittig reaction, Sonogashira reaction, and aldol condensation. It was further demonstrated that the double aldol condensation can be performed effectively for highly polarized styrene‐ and diphenylacetylene‐derived aldehydes. The strategic placement of two dialkylamino groups at the periphery of D ‐π‐A‐π‐D molecules resulted in dyes with excellent solubility. These ketones absorb light in the region 400–550 nm. Many of them display strong solvatochromism so that the emission ranges from 530–580 nm in toluene to the near‐IR region in benzonitrile. Ketones based on cyclobutanone as central moieties display very high fluorescence quantum yields in nonpolar solvents, which decrease drastically in polar media. Photophysical studies of these new functional dyes revealed that they possess an enhanced two‐photon absorption cross section when compared with simpler ketone derivatives. Due to strong polarization of the resulting dyes, values of two‐photon absorption cross sections on the level of 200–300 GM at 800 nm were achieved, and thanks to that as well as the presence of the keto group, these new two‐photon initiators display excellent performance so that the operating region is 5–75 mW in some cases.     

Characterization of Diamond Nanoparticles by High-Speed Micro-Thermal Field-Flow Fractionation

Micro-thermal field-flow fractionation was used to characterize the particle size distribution of nanometer-sized diamond nanoparticles. Although the experimental conditions were chosen to perform high-speed separation, and, consequently, the resolution achieved experimentally was not very high, the application of the original correction method for the zone spreading allowed for obtaining of very good calculated particle size distribution or, explicitly, a true polydispersity index of the diamond nanoparticle sample. The future use of several samples of diamond nanoparticles of different average sizes and different surface chemistries should allow deeper insight into the effect of these particulate characteristics on the retention in micro-thermal field-flow fractionation.     

Electrochemical Activity of Wedelolactone and Probing its Interaction with DNA Using Voltammetry at a Carbon Electrode

Wedelolactone (WLA) is a polyphenolic coumestan derivative found in extracts of plants used in traditional medicine. Due to its cytostatic activity, WLA is one of natural compounds tested as potential anticancer drugs. In this work we for the first time studied electrochemical properties of WLA using cyclic (CV) and square‐wave (SWV) voltammetry at the basal‐plane pyrolytic graphite electrode. A reversible pair of peaks, corresponding to catechol/o‐benzoquinone redox system, was observed using CV around 0.275 V vs. Ag|AgCl|3 M KCl reference electrode. Measurements of SWV signal of WLA in the presence of single‐ or double‐stranded DNA suggested a weak interaction without evident preference for double‐stranded DNA. An indirect assay, employing electroactive DNA intercalator doxorubicin as competitor, confirmed absence of intercalative DNA binding of WLA.     

Determination of the specific heat using laser flash apparatus

Journal of Thermal Analysis and Calorimetry - The main aim of this article was to describe the methodology for the measurement of specific heat using the laser flash apparatus. The obtained values...