Entropy of random chaotic interval map with noise which causes coarse-graining

A random chaotic interval map with noise which causes coarse-graining induces a finite-state Markov chain. For a map topologically conjugate to a piecewise-linear map with the Lebesgue measure being ergodic, we prove that the Shannon entropy for the induced Markov chain possesses a finite limit as the noise level tends to zero. In most cases, the limit turns out to be strictly greater than the Lyapunov exponent of the original map without noise.     

Acyldesilylation of 5-Trimethylsilyl-2-furancarboxaldehyde

5－Acyl－2－furancarboxaldehydes2arelmpol－tantIntermedlateslforsynthesizingnaturallyoccuTTingfuranoldfattyacidswhichhaveantloxldanteffectsandantlneoplastlcactlvltlesInbiologicalsystems－．Nakayamaela尸reportedsuccessfulhalodesllylatlonofethyls－trlm...     

Solvent‐dependent formation of inclusion complexes between methylated cyclodextrins and biodegradable polymers

The inclusion complexes (ICs) of unmodified natural and methylated α‐cyclodextrins (CDs) with biodegradable polymers, polyethylene glycol and poly(ε‐caprolactone), were prepared by two methods, that is, the one using water and the other using chloroform as the solvent for the respective CDs. The ICs obtained were characterized by IR, WAXD, DSC, and ¹³C CP/MAS NMR. It was found that the possibility and the phenomena of IC formation could be varied with the degree of methyl substitution of CD as well as the type of solvents used. Methylated α‐CDs showed the prominent characteristics of IC formation with polymers in the case where chloroform was used than in the case where water was used as the solvent for CDs, while vice versa in the case of native α‐CD. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 879–891, 2008     

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases is described. We have achieved a total synthesis and revised the structure of plakevulin A. Several analogues including untenone A, manzamenone A, and optically active plakevulin A, were prepared and tested with an enzyme inhibition assay for mammalian DNA polymerases. The effect of the methyl ester moiety, and the substituents at the 1- and 4-positions of plakevulin A on DNA polymerase activities are discussed.     

Two Non-closure Properties on the Class of Subexponential Densities

Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.     

Cage-shaped borate esters with tris(2-oxyphenyl)methane or -silane system frameworks bearing multiple tuning factors: geometric and substituent effects on their Lewis acid properties

Boron complexes that contain new tridentate ligands, tris(o‐oxyaryl)methanes and ‐silanes, were prepared. These complexes had a cage‐shaped structure around a boron center and showed higher Lewis acidity and catalytic activity than open‐shaped boron compounds. The cage‐shaped ligands determined the properties of the borates by altering the geometry and were consistently bound to the metal center by chelation. The synthesized compounds were L?B(OC₆H₄)₃CH, L?B(OC₆H₄)₃SiMe, and its derivatives (L=THF or pyridine as an external ligand). Theoretical calculations suggested that the cage‐shaped borates had a large dihedral angle (C_ipso‐O‐B‐O) compared with open‐shaped borates. The geometric effect due to the dihedral angle means that compared with open‐shaped, the cage‐shaped borates have a greater Lewis acidity. The introduction of electron‐withdrawing groups on the aryl moieties in the cage‐shaped framework increased the Lewis acidity. Substitution of a bridgehead Si for a bridgehead C decreased the Lewis acidity of the boron complexes because the large silicon atom reduces the dihedral angle of C_ipso‐O‐B‐O. The ligand‐exchange rates of the para‐fluoro‐substituted compound B(OC₆H₃F)₃CH and the ortho‐phenyl‐substituted compound B(OC₆H₃Ph)₃CH were less than that of the unsubstituted borate B(OC₆H₄)₃CH. The ligand‐exchange rate of B(OC₆H₄)₃SiMe was much faster than that of B(OC₆H₄)₃CH. A hetero Diels–Alder reaction and Mukaiyama‐type aldol reactions were more effectively catalyzed by cage‐shaped borates than by the open‐shaped borate B(OPh)₃ or by the strong Lewis acid BF₃?OEt₂. The cage‐shaped borates with the bulky substituents at the ortho‐positions selectively catalyzed the reaction with less sterically hindered substrates, while the unsubstituted borate showed no selectivity.     

Synthesis of oxosumanenes through benzylic oxidation

Oxosumanenes were synthesized through benzylic oxidation. The electronic and redox properties were revealed to exhibit the expanded π-conjugation compared to sumanene. Single-crystal X-ray analysis of monooxosumanene showed columnar π-stacking in a concave-convex fashion. Stereoselective trimethylation of the trioxo derivative was performed via 1,2-addition to the carbonyl groups.     

Polymorphism of 4-Fluorophenylpyruvic Acid Studied by X-Ray Crystallography and Vibrational Spectroscopy

Two polymorphic forms (I and II) of 4-fluorophenylpyruvic acid (F-PPA) were obtained by crystallization from different solvents, showing a melting point at 163.2 and 171.0 °C. Crystal structures of polymorphs I and II were determined by X-ray crystallography. IR and Raman spectra of the two polymorphs were measured and the spectral characteristics were compared with those of phenylpyruvic acid. the two polymorphs show similar molecular and crystal structures to each other, except for the molecular geometries of the enol and the carboxylic acid moieties. Distinct IR spectral differences which result from the crystal field splitting were observed between the two polymorphs.     

Highly resolved scanning tunneling microscopy study of Si(0 0 1) surfaces flattened in aqueous environment

A surface preparation method with fine SiO₂ particles in water is developed to flatten Si(0 0 1) surfaces on the nanometer scale. The flattening performance of Si(0 0 1) surfaces after the surface preparation method is investigated by scanning tunneling microscopy. The observed surface is so flat that 95% of the view area (100 × 100 nm²) is composed of only three atomic layers, namely, one dominant layer occupying 50% of the entire area and two adjacent layers. Furthermore, a magnified image shows the outermost Si atoms regularly distributed along the 〈1 1 0〉 direction on terraces.     

Enzymatic resolution of flavanone oximes

The optically active (R)- and (S)-flavanones were prepared by an enzymatically enantioselective hydrolysis of (±)-flavanone oxime O-acylates employing lipases, followed by hydrolysis with acid.