On operators with the same local spectra

Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. We consider operators T ₁, T ₂ B(X) satisfying the relation for any vector x X, where _T (x) denotes the local spectrum of T B(X) at the point x X. We say then that T ₁ and T ₂ have the same local spectra. We prove that then, under some conditions, T ₁ – T ₂ is a quasinilpotent operator, that is as n . Without these conditions, we describe the operators with the same local spectra only in some particular cases.     

A Sagnac-Michelson fibre optic interferometer: Signal processing for disturbance localization

We present numerical and experimental results on a new generation fibre optic perimeter sensor based on a Sagnac and Michelson interferometers configuration. In particular, an original signal processing scheme is presented. The sensor can detect a potential intruder and determine its position along a protected zone. We propose a localization method that offers the inherent properties of both interferometers. After demodulation of the signals from both interferometers, the obtained amplitude characteristic of the Sagnac interferometer depends on a position of a disturbance along the interferometer, while amplitude characteristic of the Michelson interferometer does not depend on this position. So, quotient of both demodulated characteristics makes it possible to localize the disturbance. During investigations of a laboratory model of the sensor, it was possible to detect the position of the disturbance with a resolution of about 40 m along the 6-km-long sensor.     

Optimization of a flow injection system with amperometric detection for arsenic determination.

A selective and sensitive analytical procedure for rapid arsenic determination by gas-diffusion flow injection analysis with amperometric detection was developed. The method is based on the arsenite reduction by NaBH(4). Derived arsine diffuses through a PTF membrane into the acceptor flow stream and is amperometrically determined on a platinum working electrode. The limit of detection (3 sigma) at room temperature was 5 microg/dm(3) of As(III). The relative standard deviation for a 1 mg/dm(3) As(III) standard was 1.96% for six repetitive injections. Arsenic(V) was determined after its prereduction with potassium iodide. Arsenic determination was not interferred with by 1 mg/dm(3) Sb(III), 5 mg/dm(3) Sn(II), 10 mg/dm(3) Se(IV), 1 mg/dm(3) As(V), 1 mg/dm(3) hydrasine, 1 mg/dm(3) Fe(II) or 0.5 mg/dm(3) Fe(III) solution. The throughput of this method was 60 analyses per hour. This method was successfully applied to arsenic determination in some power plant waste water samples.     

Fluid flow through a helical pipe

In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→ 0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved.     

Fluid flow through a helical pipe

In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→ 0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved.     

A combined LDA and flow-visualization study on flue organ pipes

Temporally resolved schlieren flow visualization and Laser-Doppler Anemometry (LDA) measurements have been performed on real flue organ pipes during the stationary state as well as during the attack transient. The techniques prove highly efficient in providing information on the details of the flow. The measurements reveal several details of the flow and demonstrate its importance in the sound formation. The spatial development of harmonics as well as the influence of nicks is also studied. It turns out that the jet instability wave behaves differently when the jet moves inward and outward of the pipe.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Spectroscopic research on infrared emittance of coal ash deposits

This paper deals with thermal radiation characteristics of ash deposits on a pulverized coal combustion boiler of an electric power plant. Normal emittance spectra in the near to medium infrared (2.5–25 μm) region and total normal emittances were measured on four kinds of ground ash deposits. Measurements were conducted in the 570–1460 K temperature range which is common for boiler furnaces, by both heating and cooling the ash samples, with the aim to study the effect of their thermal history. Dependence of emittance on wavelength, temperature and chemical composition was studied, too. Samples were tested for transparency (opacity) to verify the accuracy of results. It was determined that the thicknesses used for the ash powders are opaque for infrared radiation for thicknesses in the order of a millimeter. Tests have shown that spectral emittance increases with an increase of wavelength with a characteristic pattern common for all samples. Spectral normal emittance increases strongly with temperature at shorter wavelengths and remains high and unchanged at longer ones. Emittance spectra are not very sensitive to chemical composition of ashes especially beyond λ ≈ 5 μm. With an increase of temperature, total emittance of the powdered sample decreases to a minimum value around 1200 K. Further temperature rise induces an increase of total emittance due to sintering in the ash. On cooling, the emittance increases monotonically following the hysteresis. Quantitative directions for evaluating thermal radiation characteristics of ash deposits for the merits of the safety design of boiler furnaces were proposed. That comprises correlating the experimentally obtained emittance spectra with curves of simple analytical form, i.e., a continuous function of minimum emittance vs. wavelength. The proposed method can be extended to other specimens from the same furnace and used to determine correlations for thermal calculation of old and design of new furnaces – with similar geometry and combusting similar coal. The method is potentially applicable to completely different boiler furnaces combusting different coal, and the authors recommend running the tests with new deposit samples. The data will then be applicable to the thermal design of a whole new class of furnaces, having similar geometry and combusting similar coal. This is expected to greatly enhance the accuracy and precision of thermal calculation as well as the efficiency of thermal design of steam boilers.     

The brachistochronic motion of a wheeled vehicle

The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin’s maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin’s maximum principle and singular optimal control theory.     

Efficient Direct Nitrosylation of α-Diimine Rhenium Tricarbonyl Complexes to Structurally Nearly Identical Higher Charge Congeners Activable towards Photo-CO Release

The reaction of rhenium α-diimine (N-N) tricarbonyl complexes with nitrosonium tetrafluoroborate yields the corresponding dicarbonyl-nitrosyl [Re(CO)₂(NO)(N-N)X]⁺ species (where X = halide). The complexes, accessible in a single step in good yield, are structurally nearly identical higher charge congeners of the tricarbonyl molecules. Substitution chemistry aimed at the realization of equivalent dicationic species (intended for applications as potential antimicrobial agents), revealed that the reactivity of metal ion in [Re(CO)₂(NO)(N-N)X]⁺ is that of a hard Re acid, probably due to the stronger π-acceptor properties of NO⁺ as compared to those of CO. The metal ion thus shows great affinity for π-basic ligands, which are consequently difficult to replace by, e.g., σ-donor or weak π-acids like pyridine. Attempts of direct nitrosylation of α-diimine fac-[Re(CO)₃]⁺ complexes bearing π-basic OR-type ligands gave the [Re(CO)₂(NO)(N-N)(BF₄)][BF₄] salt as the only product in good yield, featuring a stable Re-FBF₃ bond. The solid state crystal structure of nearly all molecules presented could be elucidated. A fundamental consequence of the chemistry of [Re(CO)₂(NO)(N-N)X]⁺ complexes, it that the same can be photo-activated towards CO release and represent an entirely new class of photoCORMs.     

Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

This paper reports an analytical investigation of non-isothermal fluid flow in a thin (or long) vertical pipe filled with porous medium via asymptotic analysis. We assume that the fluid inside the pipe is cooled (or heated) by the surrounding medium and that the flow is governed by the prescribed pressure drop between pipe’s ends. Starting from the dimensionless Darcy–Brinkman–Boussinesq system, we formally derive a macroscopic model describing the effective flow at small Brinkman–Darcy number. The asymptotic approximation is given by the explicit formulae for the velocity, pressure and temperature clearly acknowledging the effects of the cooling (heating) and porous structure. The theoretical error analysis is carried out to indicate the order of accuracy and to provide a rigorous justification of the effective model.