Some properties of Van Koch’s curves

We investigate the properties of an integral operator T with a Cauchy kernel. The operator acts from L ^∞(Γ, μ), where Γ is a Van Koch curve, to the space of functions ? → ?. We prove that the range of T is nontrivial and lies in the space AC(Γ) of functions continuous in ?, vanishing at ∞, and analytic outside Γ. We also show that T is injective and compact while satisfying some special functional equation. These results may be regarded as a natural continuation of our research on the problem of AC-removability of quasiconformal curves whose solution was announced in [1] for the first time and supplemented later with some other properties of Van Koch’s curves [2, 3]. In this paper the problem is discussed in a more general setting and, in particular, all important details lacking in [1] are given. Some open problems are formulated.     

Analysis of Amaryllidaceae alkaloids from Chlidanthus fragrans by GC-MS and their cholinesterase activity

The underivatized alkaloid mixture extracted from the bulbs of Chlidanthus fragrans Herb. was investigated by capillary GC/MS for the first time. Fifteen known Amaryllidaceae alkaloids of five structure types were identified. The main alkaloids were tazzetine (9, tazettine-type), chlidanthine (2, galanthamine-type), belladine (8, belladine-type) and lycorine (12, lycorine-type). The alkaloid extract from the bulbs showed promising human blood acetylcholinesterase (IC50 = 20.1 +/- 2.9 microg/mL) and human plasma butyrylcholinesterase (IC50 = 136.8 +/- 6.9 microg/mL) inhibitory activity.     

Discrete complex analysis on isoradial graphs

We study discrete complex analysis and potential theory on a large family of planar graphs, the so-called isoradial ones. Along with discrete analogues of several classical results, we prove uniform convergence of discrete harmonic measures, Green?s functions and Poisson kernels to their continuous counterparts. Among other applications, the results can be used to establish universality of the critical Ising and other lattice models.     

Interpretation of substituent effects on 13C and 15N NMR chemical shifts in 6-substituted purines

A range of purine derivatives modified at position 6 of the basic purine skeleton exhibit a variety of biological activities. Several derivatives are used or tested nowadays for pharmacological treatments. The present work aims to analyze the effects of substituents on the electron distribution in the purine core as reflected by NMR chemical shifts. We collected a comprehensive set of experimental NMR data for a variety of 6-substituted purines (-NH(2), -NHMe, -NMe(2), -OMe, -Me, -CCH, and -CN) and determined the molecular and crystal structures of three derivatives (-NHMe, -CCH, and -CN) by X-ray diffraction. The density-functional methods calibrated in our recent study (Phys. Chem. Chem. Phys., 2010, 12, 5126) have been employed to enable understanding of the substituent-induced changes in the NMR chemical shifts of the atoms in the purine skeleton. Analyses of the nuclear shielding using localized molecular orbitals (LMOs), specifically the natural LMOs (NLMOs) and Pipek-Mezey LMOs, were used to break down the values of the isotropic (13)C and (15)N NMR chemical shifts and the chemical shift tensors into the contributions of the individual LMOs. The experimental and calculated trends in the chemical shift of the N-3 atom correlate nicely with the Hammett constants (σ(para)) and the calculated natural charges on N-3, whereas the contributions of the LMOs to the N-1 and C-6 chemical shifts are found to be more complex.     

Charge carrier mobility in poly[methyl(phenyl)silylene] studied by time-resolved terahertz spectroscopy and molecular modelling

Time-resolved terahertz spectroscopy and combination of quantum chemistry modeling and molecular dynamics simulations were used for the determination of charge carrier mobility in poly[methyl(phenyl)silylene]. Using time-resolved THz spectroscopy we established the on-chain charge carrier drift mobility in PMPSi as 0.02 cm(2) V(-1) s(-1). This value is low due to the formation of polarons: the hole is self-trapped in a potential formed by local chain distortion and the transient THz conductivity spectra show signatures of its oscillations within this potential well. This view is supported by the agreement between experimental and calculated values of the on-chain charge carrier mobility.     

Note: Counterintuitive gauge-dependence of nuclear magnetic resonance shieldings for rare-gas dimers: does a natural gauge-origin for spherical atoms exist?

A counterintuitive gauge-dependence of NMR shieldings for rare-gas dimers is presented and analyzed. It is shown that common belief about the existence of a natural gauge-origin for spherical atoms with respect to NMR shielding calculations is wrong.     

Structural evolution and properties of solid solutions of hexagonal InMnO3 and InGaO3

Solid solutions InMn(1-x)Ga(x)O(3) (0 ≤ x ≤ 1) have been investigated using magnetic, dielectric, specific heat, differential scanning calorimetry (DSC), and high-temperature powder synchrotron X-ray diffraction (HT-SXRD) measurements. It was found that samples with 0.5 ≤ x ≤ 1 crystallize in space group P6(3)/mmc with a ~ 3.32 ? and c ~ 11.9 ?, and samples with 0.0 ≤ x ≤ 0.4 crystallize in space group P6(3)cm with a ~ 5.8 ? and c ~ 11.6 ? at room temperature. HT-SXRD data revealed the existence of a P6(3)cm-to-P6(3)/mmc phase transition at about 480 K in InMn(0.6)Ga(0.4)O(3) and at 950 K in InMn(0.7)Ga(0.3)O(3). However, no dielectric, phonon, second-harmonic-generation, or DSC anomalies were found to be associated with these phase transitions. The phase transition should be improper ferroelectric from the symmetry point of view, but the above-mentioned experimental facts, together with the absence of ferroelectric hysteresis loops, revealed no evidence for ferroelectricity in the low-temperature P6(3)cm structure. We suggest that InMn(1-x)Ga(x)O(3) corresponds to a nonferroelectric phase of hexagonal RMnO(3) with P6(3)cm symmetry. The antiferromagnetic phase-transition temperature decreases from 118 K for x = 0 to 105 K for x = 0.1 and 73 K for x = 0.2, and no long-range magnetic ordering could be found for x ≥ 0.3. Specific heat anomalies associated with short-range magnetic ordering were observed for 0.0 ≤ x ≤ 0.5. InMn(1-x)Ga(x)O(3) with small Mn contents (0.8 ≤ x ≤ 0.98) has a bright-blue color.     

Relativistic four-component DFT calculations of 1H NMR chemical shifts in transition-metal hydride complexes: unusual high-field shifts beyond the Buckingham-Stephens model

State-of-the-art relativistic four-component DFT-GIAO-based calculations of (1)H NMR chemical shifts of a series of 3d, 4d, and 5d transition-metal hydrides have revealed significant spin-orbit-induced heavy atom effects on the hydride shifts, in particular for several 4d and 5d complexes. The spin-orbit (SO) effects provide substantial, in some cases even the dominant, contributions to the well-known characteristic high-field hydride shifts of complexes with a partially filled d-shell, and thereby augment the Buckingham-Stephens model of off-center paramagnetic ring currents. In contrast, complexes with a 4d(10) and 5d(10) configuration exhibit large deshielding SO effects on their hydride (1)H NMR shifts. The differences between the two classes of complexes are attributed to the dominance of π-type d-orbitals for the true transition-metal systems compared to σ-type orbitals for the d(10) systems.     

Phototriggering electron flow through Re(I)-modified Pseudomonas aeruginosa azurins

The [Re(I)(CO)(3)(4,7-dimethyl-1,10-phenanthroline)(histidine-124)(tryptophan-122)] complex, denoted [Re(I)(dmp)(W122)], of Pseudomonas aeruginosa azurin behaves as a single photoactive unit that triggers very fast electron transfer (ET) from a distant (2 nm) Cu(I) center in the protein. Analysis of time-resolved (ps-μs) IR spectroscopic and kinetics data collected on [Re(I)(dmp)(W122)AzM] (in which M=Zn(II), Cu(II), Cu(I); Az=azurin) and position-122 tyrosine (Y), phenylalanine (F), and lysine (K) mutants, together with excited-state DFT/time-dependent (TD)DFT calculations and X-ray structural characterization, reveal the character, energetics, and dynamics of the relevant electronic states of the [Re(I)(dmp)(W122)] unit and a cascade of photoinduced ET and relaxation steps in the corresponding Re-azurins. Optical population of [Re(I)(imidazole-H124)(CO)(3)]→dmp (1)CT states (CT=charge transfer) is followed by around 110 fs intersystem crossing and about 600 ps structural relaxation to a (3)CT state. The IR spectrum indicates a mixed Re(I)(CO)(3),A→dmp/π→π(*)(dmp) character for aromatic amino acids A122 (A=W, Y, F) and Re(I)(CO)(3)→dmp metal-ligand charge transfer (MLCT) for [Re(I)(dmp)(K122)AzCu(II)]. In a few ns, the (3)CT state of [Re(I)(dmp)(W122)AzM] establishes an equilibrium with the [Re(I)(dmp(.-))(W122(.+))AzM] charge-separated state, (3)CS, whereas the (3)CT state of the other Y, F, and K122 proteins decays to the ground state. In addition to this main pathway, (3)CS is populated by fs- and ps-W(indole)→Re(II) ET from (1)CT and the initially "hot" (3)CT states, respectively. The (3)CS state undergoes a tens-of-ns dmp(.-)→W122(.+) ET recombination leading to the ground state or, in the case of the Cu(I) azurin, a competitively fast (≈30 ns over 1.12?nm) Cu(I)→W(.+) ET, to give [Re(I)(dmp(.-))(W122)AzCu(II)]. The overall photoinduced Cu(I)→Re(dmp) ET through [Re(I)(dmp)(W122)AzCu(I)] occurs over a 2 nm distance in <50 ns after excitation, with the intervening fast (3)CT-(3)CS equilibrium being the principal accelerating factor. No reaction was observed for the three Y, F, and K122 analogues. Although the presence of [Re(dmp)(W122)AzCu(II)] oligomers in solution was documented by mass spectrometry and phosphorescence anisotropy, the kinetics data do not indicate any significant interference from the intermolecular ET steps. The ground-state dmp-indole π-π interaction together with well-matched W/W(.+) and excited-state [Re(II)(CO)(3)(dmp(.-))]/[Re(I)(CO)(3)(dmp(.-))] potentials that result in very rapid electron interchange and (3)CT-(3)CS energetic proximity, are the main factors responsible for the unique ET behavior of [Re(I)(dmp)(W122)]-containing azurins.