Solving Linear Systems Whose Elements Are Nonlinear Functions of Intervals

The paper addresses the problem of solving linear algebraic systems the elements of which are, in the general case, nonlinear functions of a given set of independent parameters taking on their values within prescribed intervals. Three kinds of solutions are considered: (i) outer solution, (ii) interval hull solution, and (iii) inner solution. A simple direct method for computing a tight outer solution to such systems is suggested. It reduces, essentially, to inverting a real matrix and solving a system of real linear equations whose size n is the size of the original system. The interval hull solution (which is a NP-hard problem) can be easily determined if certain monotonicity conditions are fulfilled. The resulting method involves solving n+1 interval outer solution problems as well as 2n real linear systems of size n. A simple iterative method for computing an inner solution is also given. A numerical example illustrating the applicability of the methods suggested is solved.     

Study of absorption spectra of Er<Superscript>3+</Superscript> in KTaO<Subscript>3</Subscript> crystals

The first results of the study of optical absorption spectra of KTaO₃: Er³⁺ crystals are presented. In the 350–660-nm region, lines are observed deriving from intraconfigurational electronic transitions from the ⁴ I _15/2 ground state to levels of the ⁴ F _9/2, ⁴ S _3/2, ² H _11/2, ⁴ F _7/2, ⁴ F _5/2(⁴ F _3/2), ² G _9/2, and ⁴ G _11/2 excited states of the Er³⁺ ions. A comprehensive study of transitions to the ⁴ F _9/2, ⁴ S _3/2, ² H _11/2, and ⁴ F _7/2 levels at 77 K is carried out. The number of lines observed for the above transitions fits the theoretically possible number for ?-? electronic transitions in Er³⁺ ions in the cubic crystal field. In the case of a differently charged substituted ion, this situation occurs only under nonlocal impurity charge compensation. The energies of the excited state levels for the transitions under study are determined.     

Photoconductivity and the structural phase transition in SrTiO3

Detailed photoconductivity measurements have been performed in nominally pure SrTiO₃ in order to elucidate the effect of the antiferrodistorsive cubic-tetragonal phase transition. Small features in the photoconductivity’s temperature dependence in the phase transition region were found using low intensity interband UV or 514 nm light illumination. Such features are associated with a transformation of the defect system controlling the photoconductivity. At the same time, the temperature behavior of the photoconductivity spectral maximum reveals a rather unusual feature which is connected with changes in the absorption band edge structure in the phase transition region.     

Simple,Rapid and Sensitive Electrochemical Method for the Determination of the Triketone Herbicide Sulcotrione in River Water Using a Glassy Carbon Electrode

We report a novel, simple, rapid and sensitive electrochemical method for the determination of sulcotrione, a member of the relatively new class of triketone herbicides, using differential pulse voltammetry on a glassy carbon electrode. Its electrochemical behavior including influences of electrolyte composition, pH and scan rate was studied to select optimal experimental parameters for its determination. In Britton? Robinson buffer at pH 3 sulcotrione provided a well‐defined reduction peak at ?0.84 V (vs. Ag/AgCl electrode), with good repeatability (relative standard deviation of 2.3 % for 8 measurements at 10 µM concentration level). With optimized parameters differential pulse voltammetry rendered two linear concentration ranges from 0.2 to 2 µM and from 2 to 50 µM with a detection limit of 0.05 µM. The proposed procedure was successfully applied to the determination of sulcotrione in spiked river water samples with satisfactory recoveries (93–109 %). The developed method may represent a simple, rapid and sensitive alternative to highly toxic mercury electrodes and chromatographic methods.     

Simultaneous production and purification ofBacillus subtilis α-amylase

Production of α-amylase withB. subtilis CCM 2722 in an aqueous two-phase polyethylene glycol/dextran system integrated with product purification by affinity chromatography on crosslinked starch during cultivation was studied. The medium was drawn from the bioreactor to the external settler during fermentation. After phase separation in the settler the dextran-rich bottom phase with cells was returned to the bioreactor. The PEG-rich top phase was pumped to the column with crosslinked starch and returned to the bioreactor after α-amylase adsorption. The same volumetric productivities, 0.53 U/mL/h, were reached in both batch and described process, but total productivity of the latter method was much higher owing to shortening upstream and downstream processing time. The enzyme of 98% homogenity in 95% yield was obtained after its elution from the column.     

Exact solution to a parametric linear programming problem

In this paper, we present a cubically convergent method for finding the largest eigenvalue of a nonnegative irreducible tensor. A cubically convergent method is used to solve an equivalent system of nonlinear equations which is transformed by the tensor eigenvalue problem. Due to particular structure of tensor, Chebyshev’s direction is added to the method with a few extra computation. Two rules are designed such that the descendant property of the search directions is ensured. The global convergence is proved by using the line search technique. Numerical results indicate that the proposed method is competitive and efficient on some test problems.     

Li and Nb codoping in dielectric properties and phase transitions of KTaO3: Reentrant dipolar glass and long-range dipole ordering

Abstract

The highly polarizable perovskite-type oxide, KTaO₃ doped simultaneously with Li⁺ and Nb⁵⁺ (K_1?xLi_xTa_1?yNb_yO₃, KLTN), reveals unexpected properties and ordering effects. Studies of the dielectric permittivity ?'(T, f) (10—300K, 100Hz-1 MHz) for x = 0.0014 and y = 0.024 show collective dipolar ordering effects with a transition from paraelectric into a mixed phase (coexisting dipole-glass-like and long-range ordered ferroelectric phases) taking place near 39 K. At 15 K another phase transition into a reentrant dipolar glass-like state is observed. Such a sequence of transitions and the existence of a reentrant glass state are unknown for electrical dipolar systems.     

On shape-preserving wavelet estimators of cumulative distribution functions and densities

In a previous paper we introduced a general class of shapepreserving wavelet approximating operators (approximators) which transform cumulative distribution functions (cdf) and densities into functions of the same type. Empirical versions of these operators are used in this paper to introduce, in an unified way, shape- preserving wavelet estimators of cdf and densities, with a priori prescribed smoothness properties. We evaluate their risk for a variety of loss functions and analyze their asymptotic behavior. We study the convergence rates depending on minimal additional assumptions about the cdf/ density. These assumptions are in terms of the function belonging to certain homogeneous Besov or Triebel- Lizorkin spaces and others. As a main evaluation tool the integral p-modulus of smoothness is used     

Petrov modules and zeros of Abelian integrals

We prove that the Petrov module _f associated to an arbitrary semiweighted homogeneous polynomial f? C[x,y] is free and finitely generated. We compute its generators and use this to obtain a lower bound for the maximal number of zeros of complete Abelian integrals.