Boundary measures of Markov chains

It is known that each Markov chain has associated with it a polytope and a family of Markov measures indexed by the interior points of the polytope. Measure-preserving factor maps between Markov chains must preserve the associated families. In the present paper, we augment this structure by identifying measures corresponding to points on the boundary of the polytope. These measures are also preserved by factor maps. We examine the data they provide and give examples to illustrate the use of this data in ruling out the existence of factor maps between Markov chains. E. Cawley was partially supported by the Modern Analysis joint NSF grant in Berkeley. S. Tuncel was partially supported by NSF Grant DMS-9303240.     

Molecular switch based on a cucurbit[6]uril containing bistable [3]rotaxane

A bistable CB6-based [3]rotaxane with two recognition sites has been prepared very efficiently in a high yield synthesis through CB6 catalyzed 1,3-dipolar cycloaddition; this rotaxane behaves as a reversible molecular switch and exhibits conformational changes caused by the movement of rings under base, acid and heat stimuli from one location to the other.     

Linear optical transmission measurements and computational study of linear polarizabilities, first hyperpolarizabilities of a dinuclear iron(III) complex

The optical transmission spectral study of a dinuclear metal complex [FeL(MeOH)Cl]2 (L=N-(5-methylphenyl)-3-methoxysalicylaldimine) has been carried out. The linear optical characterization shows that this molecule has transparency in the visible range. To understand linear optical and microscopic second-order nonlinear optical (NLO) behavior of the compound, we have computed the electric dipole moment (mu) and dispersion-free first hyperpolarizabilities (beta) using Finite Field second-order M?ller-Plesset perturbation (FF MP2) procedure; and also dispersion-free linear polarizabilities (alpha), frequency-dependent linear polarizabilities within the linear optical spectrum and first hyperpolarizabilities at lambda=730-1050 and 1000-1400 nm wavelength areas using time-dependent Hartree-Fock (TDHF) method. The ab-initio calculation results reveal that the examined complex might have linear optical and microscopic NLO behavior with non-zero values.     

Synthesis and X-ray crystal structure determination of N-p-methylphenyl-4-benzoyl-3,4-diphenyl-2-azetidinone

The title compound, C₂₉H₂₃NO₂, has been characterized by single-crystal X-ray diffraction at two different temperatures (303 K and 120 K) and wavelengths (MoK _α and CuK _α). The non-centrosymmetric hexagonal crystal structure contains four-membered planar β-lactam ring with an unusually long C-C bond. The β-lactam ring is almost planar.     

Optical and electronic properties of fluorene‐based copolymers and their sensory applications

A series of novel, fluorene‐based conjugated copolymers, poly[(9,9‐bis{propenyl}‐9H‐fluorene)‐co‐(9,9‐dihexyl‐9H‐fluorene)] ( P1 ), poly[(9,9‐bis{carboxymethylsulfonyl‐propyl}fluorenyl‐2,7‐diyl)‐co‐(9,9‐dihexyl‐9H‐fluorene)] ( P2 ) and poly[(9,9‐dihexylfluorene)‐co‐alt‐(9,9‐bis‐(6‐azidohexyl)fluorene)] ( P3 ), are synthesized by Suzuki coupling reactions and their electrochemical properties, in the form of films, are investigated using cyclic voltammetry. The results reveal that the polymer films exhibit electrochromic properties with a pseudo‐reversible redox behavior; transparent in the neutral state and dark violet in the oxidized state. Among the three polymers, P2 possesses the shortest response time and the highest coloration efficiency value. These polymers emit blue light with a band gap value of around 2.9 eV and have high fluorescent quantum yields. Their metal ion sensory abilities are also investigated by titrating them with a number of different transition metal ions; all of these polymers exhibit a higher selectivity toward Fe³⁺ ions than the other ions tested with Stern–Volmer constants of 4.41 × 10⁶M^?1, 3.28 × 10⁷M^?1, 1.25 × 10⁶M^?1, and 6.56 × 10⁶M^?1 for P1 , P2 , water soluble version of P2 ( P2S ) and P3 , respectively. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Polymethacrylate-based monolithic capillary column with weak cation exchange functionalities for capillary electrochromatography

Polymethacrylate-based monolith with weak cation exchange functionalities was prepared in capillary column (i.d. 100 μm, o.d. 375 μm) by in situ polymerization of butyl methacrylate, ethylene dimethacrylate and N-methacryloyl-L-glutamic acid in presence of porogens. The porogen mixture included N,N-dimethyl formamide and phosphate buffer. The preparation procedure of stationary phase contained the synthesis of monomer, silanization of capillary inner wall and in situ polymerization. The use of amino acid based monomer for the monolith synthesis is one of the originalities of this novel approach. N-methacryloyl-L-glutamic acid has two carboxyl functionalities. The separation of the solutes were performed at different acetonitrile/phosphate buffer and acetonitrile/sodium hydroxide contents. The applied voltage for the alkyl benzenes was changed between +5 and +30 kV. CEC separations of alkyl benzenes, acidic, basic, phenolic and some polycylic aromatic compounds were succesfully performed under capillary-electrochromatography mode with cathodic electroosmotic flow.