Almost sure stochastic stability of a viscoelastic double-beam system

This paper investigates the dynamic stability of a viscoelastic double-beam system under parametric excitations. It is assumed that the two beams, made from Voigt–Kelvin material, are simply supported and continuously joined by a Winkler elastic layer. Each pair of axial forces consists of a constant part and a time-dependent stochastic function. In the case of “non-white” excitations, by using the direct Liapunov method, bounds of the almost sure stability of the double-beam system as a function of retardation time, bending stiffness, stiffness modulus of the Winkler layer, variances of the stochastic forces and the intensity of the deterministic components of axial loading are obtained. Numerical calculations are performed for the Gaussian process with a zero mean, as well as a harmonic process with a random phase. When the excitations are wideband noises, almost sure stability is obtained within the concept of the Liapunov exponent. White noise and Ornstein–Uhlenbeck processes are considered as models of wideband noises.     

Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading

Free transverse vibration and buckling of a double-beam continuously joined by a Winkler elastic layer under compressive axial loading with the influence of rotary inertia and shear are considered in this paper. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli?CFourier method. The boundary value and initial value problems are solved. The natural frequencies and associated amplitude ratios of an elastically connected double-beam complex system and the analytical solution of the critical buckling load are determined. The presented theoretical analysis is illustrated by a numerical example, in which the effect of physical parameters characterizing the vibrating system on the natural frequency, the associated amplitude ratios and the critical buckling load are discussed.     

On Dyakonov type theorems for harmonic quasiregular mappings

We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.     

Determination of diclofenac sodium in commercial pharmaceutical formulations and human control serum using a kinetic-spectrophotometric method

A kinetic method for the determination of micro quantities of diclofenac sodium (DS) is described in this paper. The method is based on a ligand-exchange reaction. The reaction was followed spectrophotometrically by monitoring the rate of appearance of the cobalt diclofenac complex at 376 nm. The optimum operating conditions regarding reagent concentrations and temperature were established. The optimized conditions yielded a theoretical detection limit of 1.29 microg ml(-1) based on the 3S(b) criterion. The interference effects of certain drugs, foreign ions and amino acids upon the reaction rate were studied in order to assess the selectivity of the method. The developed procedure was successfully applied to the rapid determination of diclofenac sodium in commercial pharmaceutical preparations and human control serum. The unique features of this procedure are that determination can be carried out at room temperature and the analysis time is short. The newly developed method is simple, inexpensive, and efficient for use in the analysis of a large number of samples.     

Development and validation of a SPE-GC-MS method for the determination of pesticides in surface water

A method for analysis of 20 commonly used pesticides in surface water based on solid-phase extraction and gas chromatography-mass spectrometry was proposed. During method development the key parameters that can affect SPE extraction and determination such as selection of efficient SPE sorbent, pH of water sample, type and volume of elution solvent, breakthrough volume and matrix effects were investigated. The method was validated using spring water spiked with appropriate concentration of pesticides. The obtained correlation coefficients were in range 0.9972–1.000, limits of detection (LOD) were 0.001–0.5?µg?L^?1 and the limits of quantification (LOQ) were 0.005–1?µg?L^?1 depending on a pesticide. Much higher LOD (20?µg?L^?1) and LOQ (50?µg?L^?1) values were obtained for bentazone. The influence of matrix was assessed using real water samples spiked with appropriate concentration of pesticide standards solution. Both signal enhancement and suppression were observed, depending on a pesticide, therefore standard addition method was used for pesticides determination. The developed method was applied on real water samples taken in close vicinity of agricultural fields. Many of the targeted pesticides were found in the samples and the results are presented in this article.     

Effect of preparation of sol-gel coatings on the strength of optical fibres

SiO₂, TiO₂, ZrO₂, and TiO₂-ZrO₂ thin coatings were applied by sol-gel method on quartz fibres during the fibre drawing. Durable layers with the thicknesses up to 0.7 m were obtained. The layer smoothness and thickness were determined using electron microprobe analyzer and electron or optical microscopy. In order to investigate a decrease in the strength of sol-gel coated fibres a novel method employing silica capillaries was developed. The fibre strength decrease was explained by the influence of water penetrating as a result of the coating process into the flaws on the fibre surface.     

Bismuth titanate thin films prepared by wet-chemical techniques: effect of sol ageing time

In this work, layered perovskite bismuth titanate (Bi₄Ti₃O₁₂) thin films were fabricated on α-alumina substrates by spin coating process. Precursor sol was prepared by sol–gel process from bismuth nitrate and titanium butoxide in concentrated acetic acid, with diethylamine as a stabilizer. Processes occurring in the precursor sol were followed in the ageing period of 20 days. Thin films prepared from the as-synthesized and aged sols are crack-free, with the thickness of ~1 μm, uniform surface texture and rounded grains having grain size in nanometer range. Sintering of thin films was performed at various temperatures, and sintered thin films exhibited dense structure, fully crystallized with typical Aurivillius phase and without any preferred orientation and impurity phase. The influence of ageing of the precursor sol on the microstructure of obtained thin films was also investigated. Direct relation between hydrodynamic diameter of precursor particles and the morphology and the grain size of the obtained films was observed.     

Stochastic stability of a rotating shaft

The stochastic stability problem of an elastic, balanced rotating shaft subjected to action of axial forces at the ends is studied. The shaft is of circular cross-section, it rotates at a constant rate about its longitudinal axis of symmetry. The effect of rotatory inertia of the shaft cross-section is included in the present formulation. Each force consists of a constant part and a time-dependent stochastic function. Closed form analytical solutions are obtained for simply supported boundary conditions. By using the direct Liapunov method almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, damping coefficient, damping ratio, angular velocity, mode number and geometric and physical parameters of the shaft. Numerical calculations are performed for the Gaussian process with a zero mean and as well as an harmonic process with random phase.     

Besov–Lipschitz and Mean Besov–Lipschitz Spaces of Holomorphic Functions on the Unit Ball

We give several characterizations of holomorphic mean Besov–Lipschitz spaces on the unit ball in ${\mathbb C^N} $ and appropriate Besov–Lipschitz spaces and prove the equivalences between them. Equivalent norms on the mean Besov–Lipschitz spaces involve different types of L ^p -moduli of continuity, while in characterizations of Hardy–Sobolev spaces we use not only the radial derivative but also the gradient. The characterization in terms of the best approximation by polynomials is also given.     

A modification of the DIRECT method for Lipschitz global optimization for a symmetric function

In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function. An efficient modification of the well-known DIRECT (DIviding RECTangles) method called SymDIRECT is proposed for solving this problem. The method is illustrated and tested on several standard test functions. The application of this method to solving complex center-based clustering problems for the data having only one feature is particularly presented.