On dihedrants admitting arc-regular group actions

We consider Cayley graphs Γ over dihedral groups, dihedrants for short, which admit an automorphism group G acting regularly on the arc set of Γ. We prove that, if D _2n ≤G≤Aut(Γ) is a regular dihedral subgroup of G of order 2n such that any of its index 2 cyclic subgroups is core-free in G, then Γ belongs to the family of graphs of the form \((K_{n_{1}}\otimes\cdots\otimes K_{n_{\ell}})[K_{m}^{\mathrm{c}}]\), where 2n=n ₁???n _? m, and the numbers n _i are pairwise coprime. Applications to 1-regular dihedrants and Cayley maps on dihedral groups are also given.     

Efficiency of Monte Carlo computations in very high dimensional spaces

A standard measure for comparing different Monte Carlo estimators is the efficiency, which generally thought to be declining with increasing the number of dimensions. Here we give some numerical examples, ranging from one-hundred to one-thousand dimensional integration problems, that contradict this belief. Monte Carlo integrations carried out in one-thousand dimensional spaces is the other nontrivial result reported here. The examples concern the computation of the probabilities of convex sets (polyhedra and hyperellipsoids) in case of multidimensional normal probabilities.     

Structural Insights into the Trp‐Cage Folding Intermediate Formation

The 20 residue long Trp‐cage is the smallest protein known, and thus has been the subject of several in vitro and in silico folding studies. Here, we report the multistate folding scenario of the miniprotein in atomic detail. We detected and characterized different intermediate states by temperature dependent NMR measurements of the ¹⁵N and ¹³C/¹⁵N labeled protein, both at neutral and acidic pH values. We developed a deconvolution technique to characterize the invisible—fully folded, unfolded and intermediate—fast exchanging states. Using nonlinear fitting methods we can obtain both the thermodynamic parameters (ΔH^F–I, T_m^F–I, ΔC_p^F–I and ΔH^I–U, T_m^I–U, ΔC_p^I–U) and the NMR chemical shifts of the conformers of the multistate unfolding process. During the unfolding of Trp‐cage distinct intermediates evolve: a fast‐exchanging intermediate is present under neutral conditions, whereas a slow‐exchanging intermediate‐pair emerges at acidic pH. The fast‐exchanging intermediate has a native‐like structure with a short α‐helix in the G¹¹–G¹⁵ segment, whereas the slow‐exchanging intermediate‐pair presents elevated dynamics, with no detectable native‐like residue contacts in which the G¹¹? P¹² peptide bond has either cis or trans conformation. Heteronuclear relaxation studies combined with MD simulations revealed the source of backbone mobility and the nature of structural rearrangements during these transitions. The ability to detect structural and dynamic information about folding intermediates in vitro provides an excellent opportunity to gain new insights into the energetic aspects of the energy landscape of protein folding. Our new experimental data offer exceptional testing ground for further computational simulations.     

Multi-arm Star Polyisobutylenes. V. Characterization of Multi-arm Polyisobutylene Stars by Viscometry,Pour Points,Electron Microscopy,and Ultrasonic Shear Degradation

Abstract

Structure/property relationship of multi-arm star polyisobutylenes [?-(PIB) _n s] were characterized by a variety of techniques, including vis-cometry, pour points, electron microscopy, and ultrasonic degradation. The intrinsic viscosity of ?-(PIB) _n s changes very little with temperature in the 30 to 100°C range, whereas that of linear PIBs of the same molecular weight increases strongly with temperature. Kinematic viscosity measurements of select ?-(PIB) _n s gave viscosity indices in excess of 130. The viscosity of ?-(PIB) _n s is mainly determined by the molecular weight of the arms and much less by the number of arms or overall molecular weights. Electron microscopy of ?-(PIB) _n s indicates a compact spherical morphology, a conclusion that was substantiated by radius of gyration measurements. Pour points of ?-(PIB) _n s are ?27°C. Ultrasonic studies gave insight into the mechanism of shear degradation of ?-(PIB) _n s. These characteristics render ?-(PIB) _n s of interest as rheology control additives for motor oils.     

The Effect of the Electron Density Distribution of Guest on the Entropy Change During Complex Formation of Calix[6]arene Hexasulfonate Host with ortho- and para-cresols as Guests

The π–π interaction-based inclusion complexation of calix[6 Danil de Namor, A. F., Cleverly, R. M. and Zapata-Ormachea, M. L. 1998. Chem. Rev., 98: 2495[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]arene hexasulfonate as host with neutral aromatic guest molecules was studied in aqueous media. To vary the distribution of electron density on the guest's aromatic rings, the phenol parent compound was substituted in the para- or ortho- positions with CH₃ group. To study the interaction between calixarene and the guests, PL, DSC and quantum-chemical methods were used. The results indicate 1:1 stoichiometry of the formed host-guest complexes. Although the enthalpy change during complex formation of calixarene with p- or o-cresol are the same, the Gibbs free energy change is significantly higher in the case of calixarene—o-cresol complexes. This property is due to the unexpected entropy change during the complex formation. Using molecular dynamic calculations, a guest-induced redistribution of the electron density on the calixarene rings, followed by the restructuring of the solvent molecules was identified as a background of this unexpected entropy change at molecular level.     

On series Σc k f(kx) and Khinchin’s conjecture

We prove the optimality of a criterion of Koksma (1953) in Khinchin’s conjecture on strong uniform distribution. This verifies a claim of Bourgain (1988) and leads also to a near optimal a.e. convergence condition for series Σ _k=1 ^∞ c _k f(kx) with f ∈ L ². Finally, we show that under mild regularity conditions on the Fourier coefficients of f, the Khinchin conjecture is valid assuming only f ∈ L ².     

Preparation of hydroxypropyl cellulose microfibers by high-speed rotary spinning and prediction of the fiber-forming properties of hydroxypropyl cellulose gels by texture analysis

Water-soluble, nonionic cellulose-based fibers were prepared from aqueous hydroxypropyl cellulose gels of 5–13-μm diameter by using a high-speed rotary spinning technique. A combination of texture analysis and viscosity measurement was applied to determine the optimum concentration of hydroxypropyl cellulose gels for fiber formation. The examined concentration range of hydroxypropyl cellulose gels was 38–52 % w/w. The textural properties including the adhesiveness of gels of different concentrations were determined based on the load-distance and load-time curves, while the obtained fiber formation was visually observed with an optical microscope. The texture analysis method enabled the determination of the optimum gel concentration from the point of fiber formation. An unequivocal correlation was determined between the adhesiveness of gels and their fiber-forming ability. The adhesiveness has a local minimum where the productivity of the fiber formation process and the micromorphology of the emitted fibers are optimal. Statistical analysis of the distribution of fiber diameters confirmed that in case of the optimum concentration, the distribution approaches normality. Mechanical properties of the prepared fibers were also evaluated using texture analysis, which indicated that the fibers made of gels of the suggested optimum concentration had the most desirable elastic behavior. An optimum concentration range of hydroxypropyl cellulose exists that enables fiber formation with the required characteristics from the point of further pharmaceutical formulation processing.     

Studies on the Chemistry of Tetraamminezinc(II) Dipermanganate ([Zn(NH3)4](MnO4)2): Low‐Temperature Synthesis of the Manganese Zinc Oxide (ZnMn2O4) Catalyst Precursor

Tetraamminezinc(II) dipermanganate ([Zn(NH₃)₄](MnO₄)₂; 1 ) was prepared, and its structure was elucidated with XRD‐Rietveld‐refinement and vibrational‐spectroscopy methods. Compound 1 has a cubic lattice consisting of a 3D H‐bound network built from blocks formed by four MnO anions and four [Zn(NH₃)₄]²⁺ cations. The other four MnO anions are located in a crystallographically different environment, namely in the cavities formed by the attachment of the building blocks. A low‐temperature quasi‐intramolecular redox reaction producing NH₄NO₃ and amorphous ZnMn₂O₄ could be established occurring even at 100°. Due to H‐bonds between the [Zn(NH₃)₄]²⁺ cation and the MnO anion, a redox reaction took place between the NH₃ and the anion; thus, thermal deammoniation of compound 1 cannot be used to prepare [Zn(NH₃)₂](MnO₄)₂ (contrary to the behavior of the analogous perrhenate (ReO ) complex). In solution‐phase deammoniation, a temperature‐dependent hydrolysis process leading to the formation of Zn(OH)₂ and NH₄MnO₄ was observed. Refluxing 1 in toluene offering the heat convecting medium, followed by the removal of NH₄NO₃ by washing with H₂O, proved to be an easy and convenient technique for the synthesis of the amorphous ZnMn₂O₄.     

Equilibria of 3-pyridylmethanol with copper(II). A comparative electron spin resonance study by the decomposition of spectra in liquid and frozen solutions

The copper(II)-3-pyridylmethanol (L) system was investigated in aqueous solution by two-dimensional ESR evaluation at 298 K, and computer simulation of the individual anisotropic spectra at 77 K. The data revealed that the paramagnetic copper(II) complexes [CuL] (2+), [CuL 2] (2+), [CuL 3] (2+), and [CuL 4] (2+) are formed up to pH approximately 7 at a moderate or high excess of ligand. As compared with chelating ligands, two differences were observed for the complexation of 3-pyridylmethanol with copper(II): (1) In contrast with the well-resolved spectra in frozen solution, considerable line-broadening and distortion of the spectral shapes were seen at 298 K, which was interpreted in terms of isomeric equilibria and the medium-rate interconversion of various complexes on the ESR time-scale. (2) At low temperature, there were dramatic changes in the concentration distribution, the minor complexes with higher numbers of coordinating ligands ([CuL 3] (2+) and in particular [CuL 4] (2+)) becoming strongly favored. This phenomenon is explained by the significant differences in the formation enthalpy values of various species, shifting the equilibria according to the van't Hoff equation, and a significant undercooling in the course of fast freezing of the solution, which enhances the changes of the concentration distribution.