The effect of hydrostatic pressure on the ferroelectric phase transition in [NH2(CH3)2]3[Sb2Cl9]

The effect of hydrostatic pressure on the ferroelectric phase transition temperature in [NH₂(CH₃)₂]₃[Sb₂Cl₉] (DMACA) has been studied by electric permittivity measurements at pressures up to 400 MPa. The pressure-temperature phase diagram is given. The phase transition temperature (T_c) increases with increasing pressure up to 150 MPa, passes through a maximum and then decreases with a further increase of pressure. The unexpected nonlinear decrease in T_c with pressure increasing above 150 MPa suggests that the mechanism of ferroelectric phase transition in DMACA is different from hitherto assumed.     

On norms of composition operators acting on Bergman spaces

For arbitrary composition operators acting on a general Bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of D.G. Pokorny and J.E. Shapiro. Next, we obtain a geometric formula for the norms of composition operators with linear fractional symbols, thus extending a result of C. Cowen and P. Hurst and revealing the meaning of their computation. Finally, we obtain a lower bound for essential norm of an arbitrary composition operator related to the well-known criterion of B. MacCluer and J.H. Shapiro. As a corollary, norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol.     

A study on the applications of the acoustic design sensitivity analysis of vibrating bodies

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters predicting these characteristics is a necessary and important step of the acoustic design and optimization process. Acoustic design sensitivity analysis includes the computation and evaluation of the sensitivity information required for this procedure. In this study, a boundary element code performing the sensitivity analysis of the acoustic pressure by using the matrix sensitivities with respect to different design variables has been developed. The effect of the precision of boundary element discretization on the acoustic pressure sensitivity is examined via this code. The formulation is applied to a multi-source system and the dimension sensitivity analysis of near field pressures of two-dilating-spherical source is performed. The last application is devoted to a real sound source: a washing machine sitting on the floor. Sensitivity of the field pressures to the machine’s dimensions (size), surface velocity and frequency is examined on the bases of the boundary element model of the machine and half-space condition. The impacts of these variables are compared; and a limiting speed for the machine responding both the acoustical and operational requirements is determined.     

Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

Simultaneous determination of cloramphenicol, salicylic acid and resorcinol by capillary zone electrophoresis and its application to pharmaceutical dosage forms

This study demonstrates the separation of active ingredients in acne formulations (salicylic acid, cloramphenicol and resorcinol in presence of azulene) by capillary zone electrophoresis. Factors affecting their separations were the buffer pH and concentration, applied voltage, sample preparation, and presence of additives. Optimun results were obtained with a 50 mM sodium tetraborate-50 mM sodium phosphate, pH 9.0. The carrier electrolyte gave baseline separation with good resolution, short migration times (<6 min), great reproducibility and accuracy. Calibration plots were linear over at least three orders of magnitude of analyte concentrations, the lower limits of detection being within the range 0.39-1.25 μg ml⁻¹. The procedure was fast and reliable and commercial pharmaceuticals could be analysed without prior sample clean-up procedure.     

On existence and asymptotic stability of solutions of a nonlinear integral equation

We prove an existence theorem for a nonlinear integral equation being a Volterra counterpart of an integral equation arising in the traffic theory. The method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.