On the perturbation of the observability equation in linear control systems

The aim of this paper is to investigate stability and sensitivity of the observability variable in linear control systems, (LCS) for short. We first present two results of Hölder continuity in the abstract framework of the ordinary differential equation initial-value problem x′(t) = f(t,x(t)),x(t ₀) = x ₀. Afterwards, we apply our results to automatic systems, providing henceforth the sharpest bounds for the parametric input-output relation in LCS.     

Quantum Group Structure of Lie Superalgebra osp (1/2)

We quantize the enveloping Lie superalgebraU(osp(1/2)) in the nonstandard simple root system withtwo odd simple roots. The quantum supergroup structureassociated with the nonstandard simple root system is also given.     

Ionene supported peroxodisulfates: Polymeric reagents for the oxidative deprotection of TMS and THP ethers and oxidative cleavage of the C=N bond in water

Oxidative deprotection of trimethylsilyl and tetrahydropyranyl ethers, and deprotection of phenylhydrazones, semicarbazones, and oximes to their corresponding carbonyl compounds carried out in water at reflux condition using ionene supported peroxodisulfates is reported. The reagents are recyclable and products are obtained in excellent yield under environmentally benign conditions without overoxidation to carboxylic acid.     

Dynamic mechanical relaxation behavior of block copolymers at high temperatures

We carried out dynamic mechanical measurements to investigate three different examples of block copolymers: styrene–isoprene diblock copolymers and styrene–butadiene–styrene and styrene–(styrene butadiene)–styrene triblock copolymers. Isochronal and isothermal measurements of the real and imaginary parts of the complex shear modulus were performed over wide ranges of temperature and frequency. The measurements showed the presence of an additional relaxation process appearing at temperatures higher than those of the glass relaxation of the polystyrene phase, which has been misinterpreted by some authors as an order–disorder transition. The frequency dependence revealed that this process was a relaxation process and did not belong to a first‐order transition. Moreover, the influence of crosslinking via dicumylperoxide was measured, and we constructed complete master curves to confirm the presence of two relaxation processes. The high‐temperature relaxation process was strongly suppressed by crosslinking. Therefore, it was possible to detect the glass relaxation process of the polystyrene phase in a precise manner. The results were compared with those of homopolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2198–2206, 2001     

Differential pulse adsorption stripping voltammetric determination of copper(II) with 2-mercaptobenzimidazol at a hanging mercury-drop electrode.

Copper(II) was selectively accumulated on a hanging mercury-drop electrode by using 2-mercaptobenzimidazole. Ensuing measurements were carried out by differential pulse adsorption stripping voltammetry. Factors affecting the accumulation, reduction, and stripping steps were investigated and a procedure was developed. The optimum conditions for the analysis of copper were pH 5.0, 5.33 x 10(-5) M 2-mercaptobenzimidazole and an accumulation potential of -0.10 V (vs. Av/AgCl). A linear range was obtained in the concentration range 0.2-100 ng/ml with a 90 s accumulation time and a scan rate of 16 mV/s. For ten successive determinations of 1.0, 20.0 and 70.0 ng/ml copper(II), relative standard deviations of 4.2, 3.5 and 2.8%, respectively, were obtained. The developed method was applied to the determination of copper in commercial salts and aluminium alloys.     

Sensitivity analysis for abstract equilibrium problems

We develop the general framework of sensitivity analysis for equilibrium problems in the setting of vector topological normed space. Our approach does not make any recourse to geometrical properties and the obtained result can be viewed as an extension and generalization of the well-known results (on variational inequalities) in the literature. Even though we have worked under arbitrary constraints Kλ with Hölder-property—that have been decisive in our treatment—we have obtained, in a similar spirit of Domokos [J. Math. Anal. Appl. 230 (1999) 382-389], the best lower bound for the continuity modulus despite of the properties of the boundary of Kλ.     

Gray Codes,Loopless Algorithm and Partitions

The generation of efficient Gray codes and combinatorial algorithms that list all the members of a combinatorial object has received a lot of attention in the last few years. Knuth gave a code for the set of all partitions of [n] = {1,2,...,n}. Ruskey presented a modified version of Knuth’s algorithm with distance 2. Ehrlich introduced a looplees algorithm for the set of the partitions of [n]; Ruskey and Savage generalized Ehrlich’s results and introduced two Gray codes for the set of partitions of [n]. In this paper, we give another combinatorial Gray code for the set of the partitions of [n] which differs from the aforementioned Gray codes. Also, we construct a different loopless algorithm for generating the set of all partitions of [n] which gives a constant time between successive partitions in the construction process.      

On the normal ordering of multi-mode boson operators

Combinatorial aspects of normal ordering for annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled, since otherwise the problem of normal ordering is reduced to the cooresponding problem of the single-mode case. To describe the normal ordering in the multi-mode case, for each mode, a color is introduced, and colored contractions are considered. A depiction for colored contractions via colored linear representations is given. By analogy with the single-mode case, associated colored Stirling numbers are defined as coefficients appearing in the process of normal ordering for powers of the number operators. Several properties of these colored Stirling numbers are discussed.     

Further extended Caputo fractional derivative operator and its applications

In this paper, our principle aim is to establish a new extension of the Caputo fractional derivative operator involving the generalized hypergeometric type function F _p (a, b; c; z; k), introduced by Lee et al. Some extensions of the generalized hypergeometric functions and their integral representations are also presented. Furthermore, linear and bilinear generating relations for the extended hypergeometric functions are obtained. We also present some properties of the extended fractional derivative operator.