Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula

By using an explicit representation for the horizontal lift of the Brownian motion on the Poincaré upper half-plane H², we show an expression for the heat kernel for the de Rham-Kodaira Laplacian on H². We apply the result to a study on the Selberg trace formula.     

Microparticles of poly(methacrylic acid)–gadolinium ion complex and their magnetic force microscopic images

Modified poly(methacrylic acid) microparticles complexed with gadolinium(III) (Gd³⁺) ions were prepared in 100 nm. The emulsion terpolymerization of methacrylic acid, ethyl acrylate, and allyl methacrylate and the following complexation with Gd³⁺ ions yielded the polymer particles with different Gd³⁺ ion contents. Potentiometric titration of the complexation of the particle with Gd³⁺ ions indicated the formation of a very stable tris‐carboxylate coordinate complex with the Gd³⁺ ion. Electron spin resonance and IR spectra of the complexed particles were dependent on the Gd³⁺ ion content and the coordination environment in each particle. The microparticles dispersed on a mica substrate were subjected to atomic force microscopy (AFM), followed by magnetic force microscopy (MFM). AFM showed 100‐nm‐sized and monodispersed spherical images. The following MFM clearly provided strong magnetic responses exactly on the same particle positions, of which the images were also dependent on the Gd³⁺ ion content in the particle. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1912–1918, 2004     

Effect of cadmium on the accumulation of arsenic in a marine green alga,Dunaliellasp.

To investigate the effect of cadmium on the accumulation of arsenic by Dunaliella sp., the arsenic accumulated in the alga was determined as a function of time for coexistence of the algae with arsenic and cadmium, with batch methodology. Growth of Dunaliella sp. was affected by addition of arsenic (Na₂HAsO₄.7H₂O) and cadmium (CdCl.2.5H₂O). Growth inhibition of Dunaliella sp. was accelerated by coexistence of arsenic and cadmium. The content of arsenic in Dunaliella sp. became a maximum at 15 h after exposure. The arsenic content in the cells was influenced by addition of cadmium to the solution; the arsenic content in the alga derived from growth in a 10 mg As dm ^?3 solution decreased from 2.7 mg g^?1 in the absence of cadmium to 0.35 mg g^?1 for the addition of 100 mg Cd dm^?3. Dunaliella sp. accumulated cadmium in large quantities but, in conditions of coexistence with arsenic and cadmium, the cadmium content in cells decreased with an increase in the concentration of arsenic in the growth medium Cadmium accumulation by Dunaliella sp. was observed in dead cells although arsenic accumulation was not observed. About 85% of arsenic in the cells was in the water-soluble fraction. On the other hand, about 42% of cadmium in the cells was in the water-soluble fraction, and about 55% was in a fraction soluble in cold trichloroacetic acid.     

Direct measurement of electron transport features in cytochrome c via V–I characteristics of STM currents

The morphology of and electron tunneling through single and cluster cytochrome c molecules deposited on self-assembled dodecanthiol monolayer film on a gold substrate have been studied experimentally using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy. STM images of a single cytochrome c molecule revealed a globular structure with a diameter of 4 nm and height of 1.5 nm. A spectroscopic study obtained by recording tunneling current–bias voltage (V–I) curves revealed that the STM current increases stepwise at asymmetric threshold sample bias voltages of +100 mV and –200 mV.     

Quantum tunneling of magnetization via well-defined Dy–Cu exchange coupling in a ferrimagnetic high-spin [Dy4Cu] single-molecule magnet

A centrosymmetric rectangular complex [Dy₄Cu] was prepared from dysprosium(III) 1,1,1,5,5,5-hexafluoropentane-2,4-dionate and copper(II) dimethylglyoximate. From magnetic studies, the Dy magnetic moments are all aligned parallel at the ground state via antiferromagnetic superexchange interaction with the central Cu spin. In pulsed-field magnetization measurements at 0.5 K, complex [Dy₄Cu] exhibited magnetization steps with hysteresis, which is typical of a single-molecule magnet. This behavior is explained in terms of a simple Ising model together with well-defined Dy–Cu exchange coupling (−0.64 K).     

Investigation for the cyclization efficiency of linear tetrapeptides: Synthesis of tentoxin B and dihydrotentoxin

Investigation of the cyclization efficiency of N-methyl linear tetrapeptides using a molecular modeling study and chemical synthesis is described. The linear peptide with two N-methyl groups, MeAla-Leu-MePhe-Gly, forms γ-turn like conformation with the amine at N-terminus and the carbonyl at C-terminus in closer proximity to give the desired cyclic tetrapeptide, dihydrotentoxin. In addition, synthesis of tentoxin B by the combination of Fmoc solid-phase peptide synthesis and cyclization in solution phase has been reported. An unusual amino acid, an L-N-methyl-β-hydroxyphenylalanine derivative, which was assembled on solid support, was prepared from ethyl cinnamate. Cyclic tetrapeptide formation and cleavage of benzyl ether were optimized with DIPCI/HOBt/DIPEA and Et₃SiH/Pd(OH)₂, respectively.     

Fluctuating Carbonaceous Networks with a Persistent Molecular Shape: A Saddle‐Shaped Geodesic Framework of 1,3,5‐Trisubstituted Benzene (Phenine)

A saddle‐shaped macromolecule has been synthesized. The molecule was designed as a geodesic saddle with 1,3,5‐trisubstituted benzene (named phenine) as the fundamental unit. The phenines were woven into a polygonal framework that was composed of 168 sp²‐hybridized carbon atoms. The saddle‐shaped structure with unique symmetry showed atypical conformational changes. The biaryl linkages in this molecule had a small energy barrier for rotation, and these structural fluctuations resulted in seven ¹H NMR resonances representing 84 aromatic hydrogen atoms. Nevertheless, the overall saddle shape of the molecule was persistent, and the “up” and “down” orientations of phenine moieties circulated to give average ¹H resonances. The structural characteristics of this molecule, including the anomalous entropy‐driven dimerization, may deepen our understanding of defect‐rich graphitic sheets.