On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences

We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the k-level has subquadratic (O(n^2-1/2s) complexity. This answers one of the main open problems from the author’s previous paper [DCG 29, 375-393 (2003)], which provided a weaker upper bound for a restricted class of curves only (graphs of degree-s polynomials). When combined with existing tools (cutting curves, sampling, etc.), the new idea generates a slew of improved k-level results for most of the curve families studied earlier, including a near-O(n^3/2 bound for parabolas.     

Least‐squares meshfree method for incompressible Navier–Stokes problems

A least‐squares meshfree method based on the first‐order velocity–pressure–vorticity formulation for two‐dimensional incompressible Navier–Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least‐squares method. Equal‐order moving least‐squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix‐free element‐by‐element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier–Stokes problem and the flow over a square obstacle for time‐dependent Navier–Stokes problem are investigated for the presented least‐squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright © 2004 John Wiley & Sons, Ltd.     

Behavior and surface energies of polybenzoxazines formed by polymerization with argon,oxygen, and hydrogen plasmas

Polybenzoxazine (PBZZ) thin films can be fabricated by the plasma‐polymerization technique with, as the energy source, plasmas of argon, oxygen, or hydrogen atoms and ions. When benzoxazine (BZZ) films are polymerized through the use of high‐energy argon atoms, electronegative oxygen atoms, or excited hydrogen atoms, the PBZZ films that form possess different properties and morphologies in their surfaces. High‐energy argon atoms provide a thermodynamic factor to initiate the ring‐opening polymerization of BZZ and result in the polymer surface having a grid‐like structure. The ring‐opening polymerization of the BZZ film that is initiated by cationic species such as oxygen atoms in plasma, is propagated around nodule structures to form the PBZZ. The excited hydrogen atom plasma initiates both polymerization and decomposition reactions simultaneously in the BZZ film and results in the formation of a porous structure on the PBZZ surface. We evaluated the surface energies of the PBZZ films polymerized by the action of these three plasmas by measuring the contact angles of diiodomethane and water droplets. The surface roughness of the films range from 0.5 to 26 nm, depending on the type of carrier gas and the plasma‐polymerization time. By estimating changes in thickness, we found that the PBZZ film synthesized by the oxygen plasma‐polymerization process undergoes the slowest rate of etching in CF₄ plasma. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4063–4074, 2004     

Recent advances in the analysis of steroid hormones and related drugs.

The development during the last 15 years and the state-of-the-art in the analysis of bulk steroid hormone drugs and hormone-like structures and pharmaceutical formulations made thereof are summarized. Other steroids (sterols, bile acids, cardiac glycosides, vitamins D) as well as biological-clinical aspects and pharmacokinetic and metabolic studies are excluded from this review. The state-of-the-art is summarized based on comparisons of monographs in the latest editions of the European Pharmacopoeia, United States Pharmacopoeia and the Japanese Pharmacopoeia. This is followed by sections dealing with new developments in the methodology for the fields of spectroscopic and spectrophotometric, chromatographic, electrophoretic and hyphenated techniques as well electroanalytical methods. The review is terminated by two problem-oriented sections: examples on impurity and degradation profiling as well as enantiomeric analysis.     

Electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols in aprotic media.

The electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols on graphite electrodes was studied using cyclic voltammetry, chronoamperometry, constant-potential coulometry and preparative constant-potential electrolysis techniques. The data revealed that the reduction on graphite was irreversible and followed an EC mechanism. The diffusion coefficients and the number of electrons transferred were determined using the chronoamperometric Cottrell slope and the ultramicro disc Pt-electrode steady-state current. The number of electrons was also determined by bulk electrolysis. The compounds were subjected to constant-potential preparative electrolysis and the electrolysis products were purified and identified by spectroscopic methods. Based on these findings, a mechanism for the electro-reduction process is proposed.     

Synthesis of paramagnetic BODIPY dyes as new double (spin and fluorescence) sensors

Paramagnetic pyrroline and 1,2,3,6-tetrahydropyridine derivatives of BODIPY and their diamagnetic analogs have been synthesized and characterized as novel redox double sensor and cation sensitive reagents.     

Optical bistability in an all-optical fiber nonlinear fabry-perot resonator with linear absorption

An all-optical fiber nonlinear Fabry-Perot resonator is proposed. The steady-state model for describing this resonator is developed. The transmission and refection bistabilities are shown numerically. Our results show that the bistability in this system is similar to that in a normal nonlinear Fabry-Perot etalon, except that the characteristics of the bistability can be changed not only by the cavity length but also by the phase shifts of the fiber loop mirrors.     

Effect of oxygen exposure on the magnetic properties of ultrathin Co/Ge(1 1 1) films

Influences of oxygen exposure on the magnetic properties of Co/Ge(1 1 1) ultrathin films have been investigated by surface magneto-optic Kerr effect technique. As the oxygen exposure increases on Co/Ge(1 1 1) films, their magnetic properties could be modified. As an example for 15 ML Co/Ge(1 1 1) films, the coercivity increases from 730 to 920 Oe and the remanence Kerr intensity is reduced for 500 Langmuir (L) of oxygen exposure. Corresponding compositions analyzed by Auger electron spectroscopy measurement shows that the amount of oxygen on the surface layers increases with increasing the oxygen exposure time. Oxygen distributes on the topmost layers of the film. The adsorbed oxygen influences the electronic density of states of Co and results in the changes of the magnetic properties. Besides, the appearance of O/Co/Ge interface could modify the stress anisotropy, and as a result the coercivity of ultrathin Co/Ge(1 1 1) film is enhanced.     

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.