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.     

Decorations of graphene oxide with cisplatin toward investigation of fluorescence quencher on regulatory sequence of BRCA1 and BRCA2

Journal of the Iranian Chemical Society - Herein, we investigated the interaction of cisplatin loaded on GO (GO@CDDP) with two regulatory sequences, BRCA1 and BRCA2, synthesized from ssDNA based on...     

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 ).     

One‐Pot Synthesis of Dialkyl 2‐(Alkyl or aryl)‐6‐(pyrimidin‐2‐ylthio)‐4‐thioxo‐5,6‐dihydro‐4H‐1,3‐oxazine‐5,6‐dicarboxylate Derivatives via a Four‐Component Reaction

A number of new dialkyl 2‐(alkyl or aryl)‐6‐(pyrimidin‐2‐ylthio)‐4‐thioxo‐5,6‐dihydro‐4H‐1,3‐oxazine‐5,6‐dicarboxylate have been prepared in good yield from the multicomponent reaction between 2‐mercaptopyrimidines and acetylenic diesters with acetyl or benzoyl isothiocyanate.