On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

Highly polarized dithiafulvenes: synthesis and nonlinear optical properties

Push-pull dithiafulvenes with reduced bond length alternation (BLA) and high optical nonlinearities have been prepared. The interplay between the proaromaticity of the donor and the structural and optical properties of these merocyanines is discussed. The donor ability of dithiafulvenes can reach that of ferrocene or dialkylaminophenyl groups.     

Dual frames in connected with generalized sampling in shift-invariant spaces

The aim of this article is to derive stable generalized sampling in a shift-invariant space by using some special dual frames in L²(0,1). These sampling formulas involve samples of filtered versions of the functions in the shift-invariant space. The involved samples are expressed as the frame coefficients of an appropriate function in L²(0,1) with respect to some particular frame in L²(0,1). Since any shift-invariant space with stable generator is the image of L²(0,1) by means of a bounded invertible operator, our generalized sampling is derived from some dual frame expansions in L²(0,1).     

Toward phenanthridin-2-ylidene: electrophilicity versus acidity in planar-constrained C-aryl iminium salts

A phenanthridinium salt was prepared in four steps, including an intramolecular CH-arylation and a hydride abstraction reaction. Treatment with sterically demanding bases does not lead to the corresponding carbene, but rather to addition products: the planar-constrained geometry significantly enhances the electrophilicity over the acidity of C-aryl iminium salts.     

Order Embeddings with Irrational Codomain: Debreu Properties of Real Subsets

The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-valued strictly isotone function (semicontinuous or not) also admits a representation by means of a lower (respectively, upper) semicontinuous strictly isotone function that takes values in the set of irrational numbers. These results are obtained by means of a direct construction. Moreover, they can be related to Cantor’s characterization of the real line to obtain much more general results on the semicontinuous Debreu properties of a wide family of subsets of the real line.      

Extremal positive and self-adjoint extensions of suboperators

This work is supported in part by the fund OTKA (No. 5-134).     

Preparation of activated carbons from cherry stones by activation with potassium hydroxide

Using cherry stones, the preparation of activated carbon has been undertaken in the present study by chemical activation with potassium hydroxide. A series of KOH-activated products was prepared by varying the carbonisation temperature in the 400-900 °C range. Such products were characterised texturally by gas adsorption (N₂, −196 °C), mercury porosimetry, and helium and mercury density measurements. FT-IR spectroscopy was also applied. The carbons prepared as a rule are microporous and macroporous solids. The degree of development of surface area and porosity increases with increasing carbonisation temperature. For the carbon heated at 900 °C the specific surface area (BET) is 1624 m² g⁻¹, the micropore volume is 0.67 cm³ g⁻¹, the mesopore volume is 0.28 cm³ g⁻¹, and the macropore volume is 1.84 cm³ g⁻¹.     

A proof of Parrott's theorem on quotient norms

We prove, as an application of our positive extension argument, a theorem of Parrott concerning the quotient norm with respect to spaces of Hilbert space operators.     

Microperforated insertion units: An alternative strategy to design microperforated panels

Microperforated panels (MPPs) coupled to a rigid wall have been proposed recently as an alternative to porous absorbers in situations having concerns with bacterial contamination and small particles discharge, like food, pharmaceutical and microelectronic industries. There exists also an increasing interest for MPP absorbers in the transportation industry and civil engineering. In general, an optimally designed MPP with good broadband absorption requires many submillimetric holes distributed over a panel of also submillimetric thickness. Such thin plates or foils become so fragile that they need to be protected from mechanical damage. In this paper, an alternative strategy is investigated which allows the design of MPPs with panels of millimetric thickness while maintaining their acoustic performance. These absorbers, named microperforated insertion units (MIUs), avoid the structural problems of the classical MPPs. An assessment of the sound absorption properties of these structures is presented. Comparisons between calculations and measurements are also made under two experimental conditions: plane waves at normal incidence (impedance tube) and free field (anechoic room).     

Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or Arc

Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product <formula> \langle f, g \rangle = ∈t_{E} f(ξ) \overline{g(ξ)} ρ(ξ) |d ξ|+ f(Z) A g(Z)^H, </formula> where E is a rectifiable Jordan curve or arc in the complex plane f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)), A is an M \times M Hermitian matrix, M l ₁ + ⋅s + l _m + m , |d ξ| denotes the arc length measure, ρ is a nonnegative function on E , and z _i ∈Ω, i=1,2,\ldots,m , where Ω is the exterior region to E . July 23, 1999. Dates revised: September 11, 2000 and February 16, 2001. Date accepted: February 26, 2001.