Existence of many ergodic absolutely continuous invariant measures for piecewise-expandingC 2 chaotic transformations in ℝ2 on a fixed number of partitions

Let Ω be a region in ℝⁿ and letp = P_i ) _i ^1m , be a partition ofΩ into a finite number of closed subsets having piecewise C² boundaries of finite(n - 1 )dimensional measure. Let τ:Ω→Ω be piecewise C² onP where, τ_i = τ|p_i is aC ² diffeomorphism onto its image, and expanding in the sense that there exists α > 1 such that for anyi = 1, 2,...,m ‖Dτ_i ^-1 ‖ < α^-1, where Dτ_i ^-1 is the derivative matrixτ _i ^- 1 and |‖·‖ is the Euclidean matrix norm. By means of an example, we will show that the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we will construct a piecewise expanding C² transformation on a fixed partition with a finite number of elements in ℝ², but which has an arbitrarily large number of ergodic, absolutely continuous invariant measures     

Microwave Assisted Deprotection of N,N-Dimethylhydrazones in Water Using Palladium Chloride–Tin Chloride as Catalyst

Summary.  N,N-Dimethylhydrazones of ketones and aldehydes undergo facile cleavage to the corresponding carbonyl compounds upon exposure to microwaves in water containing a catalytic amount of PdCl₂–SnCl₂ in high yields. Corresponding authors. E-mail: rahman@umz.ac.ir Received December 27, 2001. Accepted (revised) February 6, 2002     

Superabsorbent hydrogel composites

A new cost‐effective approach to enhance gel strength of superabsorbent hydrogels was invented. Superabsorbent hydrogel composites (SHCs) were prepared through an optimized rapid solution polymerization of concentrated partially neutralized acrylic acid in the presence of a crosslinking agent under normal atmospheric conditions. Kaolin was used as an inorganic component in the polymerization process to strengthen the hydrogel products. FT‐IR spectroscopy was used to confirm grafting of acrylic chains on to the surface of kaolin particles. Morphology of the products was studied by scanning electron microscopy (SEM). Compared with the kaolin‐free hydrogel (control), kaolin caused a reduced equilibrium swelling and swelling rate as low as 17–31% and 19–29%, respectively. Kaolin, however, resulted in enhanced gel strength as high as 21–35% compared to the control. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) were used to study thermal properties of the composites. The SHCs exhibited higher thermal stability than the control. Meanwhile, changes in certain thermal transitions reconfirmed the chemical interaction of the acrylic chain with kaolin. These thermostabilized strengthened superabsorbent hydrogels may be considered as good candidates for agricultural application to retain more water under soil pressure. Copyright © 2003 John Wiley & Sons, Ltd.     

Dielectrophoresis with 3D microelectrodes fabricated by surface tension assisted lithography

This paper demonstrates the utilization of 3D semispherical shaped microelectrodes for dielectrophoretic manipulation of yeast cells. The semispherical microelectrodes are capable of producing strong electric field gradients, and in turn dielectrophoretic forces across a large area of channel cross‐section. The semispherical shape of microelectrodes avoids the formation of undesired sharp electric fields along the structure and also minimizes the disturbance of the streamlines of nearby passing fluid. The advantage of semispherical microelectrodes over the planar microelectrodes is demonstrated in a series of numerical simulations and proof‐of‐concept experiments aimed toward immobilization of viable yeast cells.     

Preparation of Silica-Bonded S-Sulfonic Acid: A Recyclable Catalyst for the Synthesis of Bis-Indolylmethanes

Silica bonded S-sulfonic acid (SBSSA) was prepared by the reaction of 3-mercaptopropylsilica (MPS) and chlorosulfonic acid in chloroform. Silica-bonded S-sulfonic acid, as a reusable solid acid catalyst, was used for the condensation reactions of indole with carbonyl compounds at ambient temperature. Tetra-(indolyl)methanes were also obtained by the condensation reaction of indole with dialdehyde compounds. Silica bonded S-sulfonic acid was recovered and reused.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Detectability conditions for output-only subspace identification

ABSTRACT

The scope of output-only/blind identification is restricted to stochastic/statistical processes, but for the first time in this study, the detectability conditions for general output-only subspace identification are investigated. This aids the range of input sources to be extended in a much realistic manner, beyond the only stochastic inputs. For this purpose, the subspace framework is assigned to make a connection between the output signal contents and the LTI system order. A few substantial hypotheses and algebraic statements are propounded affirming the sufficiency of the genuine output sequences for the identification purpose. This can be perceived as the cornerstone of state-space model reconstruction. In order to consolidate the notions according to reality, several examples are studied and examined for different input classes with stochastic disturbance.     

The Different,but Interesting Behaviors of Benzyl Systems in the Willgerodt-Kindler Reaction under Solvent-Free Conditions

On the benzyl system, bearing various functional groups, have been carried out the Willgerodt-Kindler reaction to obtain thiobenzmorpholide ( 1 ). The reactions, under solvent-free conditions, were performed in both classical (reflux, room temperature) and nonclassical (microwave) conditions to attempt our elucidation of the reactions pathways. Unlike benzylamine and benzyl mercaptan, benzyl halides give poor result due to the type of amine. The experimental results suggest that the proposed reaction pathway involves the oxidation coupling of benzylic substrates, followed by a thiolation step and an attack of the amine on the thiolated product to give ( 1 ).     

Amplified Electrochemical DNA Sensor Based on Polyaniline Film and Gold Nanoparticles

In this work, an electrochemical DNA biosensor, based on a dual signal amplified strategy by employing a polyaniline film and gold nanoparticles as a sensor platform and enzyme‐linked as a label, for sensitive detection is presented. Firstly, polyaniline film and gold nanoparticles were progressively grown on graphite screen‐printed electrode surface via electropolymerization and electrochemical deposition, respectively. The sensor was characterized by scanning electron microscopy (SEM), cyclic voltammetry and impedance measurements. The polyaniline‐gold nanocomposite modified electrodes were firstly modified with a mixed monolayer of a 17‐mer thiol‐tethered DNA probe and a spacer thiol, 6‐mercapto‐1‐hexanol (MCH). An enzyme‐amplified detection scheme, based on the coupling of a streptavidin‐alkaline phosphatase conjugate and biotinylated target sequences was then applied. The enzyme catalyzed the hydrolysis of the electroinactive α‐naphthyl phosphate to α‐naphthol; this product is electroactive and has been detected by means of differential pulse voltammetry. In this way, the sensor coupled the unique electrical properties of polyaniline and gold nanoparticles (high surface area, fast heterogeneous electron transfer, chemical stability, and ease of miniaturisation) and enzymatic amplification. A linear response was obtained over a concentration range (0.2–10 nM). A detection limit of 0.1 nM was achieved.     

Synthesis of 2‐Aryl‐5‐oxo‐4‐[2‐(phenylmethylidene)hydrazino]‐2,5‐dihydro‐1H‐pyrrole‐3‐carboxylates by the Reaction between Hydrazones,Acetylenedicarboxylates, and 1‐Aryl‐N,N′‐bis(arylmethylidene)methanediamines

An efficient approach for the preparation of functionalized 2‐aryl‐2,5‐dihydro‐5‐oxo‐4‐[2‐(phenylmethylidene)hydrazino]‐1H‐pyrroles is described. The four‐component reaction between aldehydes, NH₂NH₂?H₂O, dialkyl acetylenedicarboxylates, and 1‐aryl‐N,N′‐bis(arylmethylidene)methanediamines proceeds in EtOH under reflux in good‐to‐excellent yields (Scheme 1). The structures of 4 were corroborated spectroscopically (IR, ¹H‐ and ¹³C‐NMR, and EI‐MS, and, in the case of 4f , by X‐ray crystallography). A plausible mechanism for this type of reaction is proposed (Scheme 2).