Determination of impurities and counterions of pharmaceuticals by capillary electromigration methods

The review presents a survey of recent applications of high‐performance capillary electromigration methods—capillary zone electrophoresis, nonaqueous capillary electrophoresis, capillary isotachophoresis, micellar electrokinetic chromatography, microemulsion electrokinetic chromatography and capillary electrochromatography—for the determination of impurities of pharmaceuticals, including chiral impurities, for the period 2007–2013. In addition, due to the missing evaluation of the determination of counterions of pharmaceuticals by capillary electromigration methods in the last 20 years, the publications dealing with this topic since 1995 are included in this review. General aspects of both these types of applications of capillary electromigration methods in pharmaceutical analysis are discussed, and detailed experimental conditions used for determination of various chemical impurities and counterions of many particular drugs are described.     

Nonlinear vibrations of a sandwich piezo-beam system under piezoelectric actuation

The paper describes the use of active structures technology for deformation and nonlinear free vibrations control of a simply supported curved beam with upper and lower surface-bonded piezoelectric layers, when the curvature is a result of the electric field application. Each of the active layers behaves as a single actuator, but simultaneously the whole system may be treated as a piezoelectric composite bender. Controlled application of the voltage across piezoelectric layers leads to elongation of one layer and to shortening of another one, which results in the beam deflection. Both the Euler–Bernoulli and von Karman moderately large deformation theories are the basis for derivation of the nonlinear equations of motion. Approximate analytical solutions are found by using the Lindstedt–Poincaré method which belongs to perturbation techniques. The method makes possible to decompose the governing equations into a pair of differential equations for the static deflection and a set of differential equations for the transversal vibration of the beam. The static response of the system under the electric field is investigated initially. Then, the free vibrations of such deformed sandwich beams are studied to prove that statically pre-stressed beams have higher natural frequencies in regard to the straight ones and that this effect is stronger for the lower eigenfrequencies. The numerical analysis provides also a spectrum of the amplitude-dependent nonlinear frequencies and mode shapes for different geometrical configurations. It is demonstrated that the amplitude–frequency relation, which is of the hardening type for straight beams, may change from hard to soft for deformed beams, as it happens for the symmetric vibration modes. The hardening-type nonlinear behaviour is exhibited for the antisymmetric vibration modes, independently from the system stiffness and dimensions.

     

On the existence of a stable periodic solution of an impacting oscillator with damping

A system that consists of an impacting oscillator with damping has been considered in this paper. In the first part a method of analytical determination of the existence of periodic solutions to the equations of motion and a method of analysis of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples. In the second part of the paper, the results of some numerical investigations have been presented. The goal of these studies was to determine, in which regions of parameters characterizing the system, the motion of the oscillator is periodic and stable.     

Controlling grafting density and side chain length in poly(n‐butyl acrylate) by ATRP copolymerization of macromonomers

Atom transfer radical polymerization (ATRP) was used for the preparation and subsequent copolymerization of two acryloyl‐terminated poly(n‐butyl acrylate) macromonomers with different degrees of polymerization (DP_nBA = 25 and 42). Homopolymerization of the higher molecular weight macromonomer ( MM1 ; PnBA₄₂‐A, M_n = 5600, DP_MM = 42, M_w/M_n = 1.18) resulted in preparation of a densely grafted polymer with a narrow molecular weight distribution (M_w/M_n = 1.14), but with the limited degree of polymerization DP = 12. The ultimate degree of homopolymerization for the lower molecular weight macromonomer ( MM2 ; PnBA₂₅‐A, M_n = 3400, DP_MM = 25, M_w/M_n = 1.20) was higher, and DP increased from 12 to 22. The limited DP could be because of progressively increasing steric congestion for macromonomers in approaching the growing chain ends of densely grafted polymers. When MMs were copolymerized with nBA, the reactivity of MM was nearly the same as that of nBA monomer irrespective of the differences in the degree of polymerization of the MMs and the initial molar ratio of nBA to MM. Well‐defined graft polymers with different lengths of backbone and side chains, and different graft density were successfully prepared by “grafting through” ATRP. Tadpole‐shaped and dumbbell‐shaped graft polymers were also synthesized by ATRP. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5454–5467, 2006     

Strong and conditional invariance principles for samples attracted to stable laws

Summary. We prove almost sure convergence of a representation of normalized partial sum processes of a sequence of i.i.d. random variables from the domain of attraction of an α-stable law, α<2. We obtain an explicit form of the limit in terms of the LePage series representation of stable laws. One consequence of these results is a conditional invariance principle having applications to option pricing as well as to resampling by signs and permutations. Received: 11 April 1994 / In revised form: 5 November 1996     

Invited paperFourier-transform heterodyne spectroscopy of liquid and solid surfaces

Fourier-transform heterodyne spectroscopy is a simple but powerful technique to study narrow line shapes and small frequency shifts. We review the technique and its application to the study of hydrodynamic fluctuations. We introduce a simple scheme for obtaining the full spectrum of light scattered from liquid and solid surfaces. Using this scheme we obtained a spectral resolution of 200 Hz. Two applications of the technique, one involving the detection of counter-propagating capillary waves, the other measurement of the epitaxial crystal-growth speed of a crystalline silicon interface, are presented. Received: 21 August 1996     

A Way To Discover Maxwell's Equations Theoretically

The Coulomb force, established in the rest frame of a source-charge Q, when transformed to a new frame moving with a velocity V has a form F = q E + q v × B, where E = E′_∥ + γE′_⊥ and B = (1/c ²)v × E and E′ is the electric field in the rest frame of the source. The quantities E and B are then manifestly interdependent. We prove that they are determined by Maxwell's equations, so they represent the electric and magnetic fields in the new frame and the force F is the well known from experiments Lorentz force. In this way Maxwell's equations may be discovered theoretically for this particular situation of uniformly moving sources. The general solutions of the discovered Maxwell's equations lead us to fields produced by accelerating sources.