On the total mean curvature of a nonrigid surface

Using the Green’s theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field, which immediately yields the following well-known theorem: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.     

The complexity of recursive constraint satisfaction problems

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem.     

A two-parameter generalization of the complete elliptic integral of second kind

A two-parameter generalization of the complete elliptic integral of second kind is expressed in terms of the Appell function F ₄. This function is further reduced to a quite simple bilinear form in the complete elliptic integrals K and E. Some physical applications are briefly mentioned.     

On H. Weyl and J. Steiner Polynomials

The paper deals with root location problems for two classes of univariate polynomials both of geometric origin. The first class discussed, the class of Steiner polynomial, consists of polynomials, each associated with a compact convex set . A polynomial of this class describes the volume of the set V + tB ⁿ as a function of t, where t is a positive number and B ⁿ denotes the unit ball in . The second class, the class of Weyl polynomials, consists of polynomials, each associated with a Riemannian manifold , where is isometrically embedded with positive codimension in . A Weyl polynomial describes the volume of a tubular neighborhood of its associated as a function of the tube’s radius. These polynomials are calculated explicitly in a number of natural examples such as balls, cubes, squeezed cylinders. Furthermore, we examine how the above mentioned polynomials are related to one another and how they depend on the standard embedding of into for m > n. We find that in some cases the real part of any Steiner polynomial root will be negative. In certain other cases, a Steiner polynomial will have only real negative roots. In all of this cases, it can be shown that all of a Weyl polynomial’s roots are simple and, furthermore, that they lie on the imaginary axis. At the same time, in certain cases the above pattern does not hold.

Erasmus Darwin, the nephew of the great scientist Charles Darwin, believed that sometimes one should perform the most unusual experiments. They usually yield no results but when they do . . . . So once he played trumpet in front of tulips for the whole day. The experiment yielded no results.

Submitted: March 5, 2007., Revised: February 1, 2008., Accepted: February 2, 2008.     

Boron macrocycles having a calix-like shape. Synthesis, characterization, X-ray analysis, and inclusion properties

The syntheses, structure, and inclusion properties of trinuclear boron compounds having a calix-like shape are described. The compounds have been obtained via self-assembly reactions between salicylaldehyde derivatives and 3-aminophenylboronic acid, whereby the formation of three N --> B coordination bonds favored the oligomerization. The products have high melting points (>370 degrees C), are stable to moisture, and have good solubility in organic solvents; the latter property is useful for host-guest recognition experiments. The structural analysis by X-ray diffraction revealed that diverse conformations are possible because of the presence of two different units of aromatic rims. A cone-cone (double-cone) conformation is observed for three of these compounds, while the remaining one has a cone-partial cone conformation. An analysis of the molecular packing showed that the molecules are stacked in columns in two different orientations in relation to the organization of the macrocycles when referred to the N-B bonds. The inclusion properties toward primary amines and ammonium chlorides were analyzed by titration experiments and monitored by UV spectroscopy, whereby association constants on the order of 10(2)-10(3) M(-1) were determined.     

Molecular beam measurements and Monte Carlo simulations of the kinetics of N2O decomposition on Rh(111) single-crystal surfaces

The kinetics of N2O decomposition on Rh(111) single-crystal surfaces were investigated both experimentally by isothermal molecular beam measurements and theoretically using a Monte Carlo algorithm. The present work was directed to the understanding of two unusual observations derived from our previous work on this system, namely, (1) the lower rates for N2O decomposition seen at higher reaction temperatures, and (2) the lower total nitrogen yields and final oxygen surface coverages that accompany that behavior. Experimentally, it was determined here that after the rhodium surface is rendered inactive by N2O decomposition at high (520 K) temperatures, significant activity is still possible at lower (350 K) temperatures. The Monte Carlo simulations explain these observations by assuming that the surface sites required for the activation of adsorbed N2O increase in size with increasing reaction temperature.     

Investigation of intramolecular proton migration in a series of model, metal-cationized tripeptides using in situ generation of an isotope label

In this study we used an isotope label, generated in situ, to investigate intramolecular proton migration or scrambling during formation of [b(2)+17+Li](+) products by collision-induced dissociation (CID) of Li(+)-cationized tripeptides. To generate the isotope label, we used a McLafferty-type rearrangement of N-terminally acetylated, C-terminal peptide tert-butyl esters in which all amide positions were exchanged with deuterium. Using a set of small, model peptides, we show that intramolecular proton scrambling occurs during CID, particularly amongst adjacent sites along a peptide backbone, on the time scales employed for low-energy collisional activation in an ion-trap mass spectrometer.     

Comparison of various detection limit estimates for volatile sulphur compounds by gas chromatography with pulsed flame photometric detection

This paper addresses the variations that presently exist regarding the definition, determination, and reporting of detection limits for volatile sulphur compounds by gas chromatography with pulsed flame photometric detection (GC-PFPD). Gas standards containing hydrogen sulphide (H(2)S), carbonyl sulphide (COS), sulphur dioxide (SO(2)), methyl mercaptan (CH(3)SH), dimethyl sulphide (DMS), carbon disulphide (CS(2)), and dimethyl disulphide (DMDS) in concentrations varying from 0.36ppb (v/v) up to 1.5ppm (v/v) in nitrogen were prepared with permeation tubes and introduced in the gas chromatograph using a 0.25-ml gas sampling loop. After measuring the PFPD response versus concentration, the method detection limit (MDL), the Hubaux-Vos detection limit (x(D)), the absolute instrument sensitivity (AIS), and the sulphur detectivity (D(s)) were determined for each sulphur compound. The results show that the MDL determined by the US Environmental Protection Agency procedure consistently underestimates the minimum concentrations of volatile sulphur compounds that can be practically distinguished from the background noise with the PFPD. The Hubaux-Vos detection limits and the AIS values are several times higher than the MDL, and provide more conservative estimates of the lowest concentrations that can be reliably detected. Sulphur detectivities are well correlated with AIS values but only poorly correlated with MDL values. The AIS is recommended as a reliable and cost-effective measure of detection limit for volatile sulphur compounds by GC-PFPD, since the AIS is easier and faster to determine than the MDL and the Hubaux-Vos detection limit. In addition, this study confirmed that the PFPD response is nearly quadratic with respect to concentration for all volatile sulphur compounds.     

Modeling of ligation-induced helix/loop displacements in myoglobin: toward an understanding of hemoglobin allostery

Combining quantum and molecular mechanics (QM/MM) methods and protein structure prediction algorithms, helix and loop movements are computed along the pathway of CO dissociation from myoglobin (Mb). The results are compared with high-resolution crystallographic data using sequence-displacement graphs. These graphs provide an unbiased method for evaluating main-chain segmental motions; they resolve an apparent disagreement between two sets of high-resolution crystal structures for MbCO and deoxyMb. The QM/MM modeling of the CO deligation reproduces the experimentally observed spin states and photodissociated crystal structure. The principal effect of CO dissociation is shown to be a concerted rotation of the E and F helices, which hold the heme like a clamshell. The rotation is a response to deligation forces, which impel the F helix away from the heme because of the Fe spin conversion, and which allow the E helix to collapse toward the heme as nonbonded contacts on the distal side are relieved. Additional helix and loop displacements stem from these primary events. In particular, the CD loop is found to be repositioned as a result of steric interactions with the water molecule that becomes H-bonded to the distal histidine in deoxyMb. A similar EF rotation and CD loop displacement are proposed to be the first steps along the allosteric pathway from the R to the T state in hemoglobin.     

Synthesis of silica-gold nanocomposites and their porous nanoparticles by an in-situ approach

We demonstrate the one-step synthesis of a silica-gold nanocomposite by simultaneous hydrolysis and reduction of gold chloride. The aminophenyl group was used as a reducing agent, and the trimethoxy silane group acts a precursor for the formation of silica. The porous gold nanoparticles were formed by etching out the silica-gold nanocomposite by hydrofluoric acid. The electron diffraction of porous gold nanoparticles showed that the particle are polycrystalline with FCC structure. The silica-gold nanocomposite exhibited nonlinear current-voltage behavior, and the porous gold nanoparticles displayed linear current-voltage behavior.