A reliable synthesis of 2- and 6-amino-β-cyclodextrin and permethylated-β-cyclodextrin

A new, reliable method for the introduction of an amine group at positions 2 or 6 of β-cyclodextrin and permethyl-β-cyclodextrin is described. It involves selective tosylation followed by azide substitution and almost quantitative reduction with triphenylphosphine followed by hydrolysis of the phosphinimine intermediate.     

Stability of streaming layer in an unbounded self-gravitational fluid

The stability of a streaming layer of incompressible, inviscid, self-gravitational fluid bounded in an infinite similar medium is investigated. The critical wave numbers are found when the layer has a linear streaming velocity profile.     

Nonseparable graphs with a given number of cycles

G. Ringel conjectured that for every positive integer n other than 2, 4, 5, 8, 9, and 16, there exists a nonseparable graph with n cycles. It is proved here that the conjecture is true even with the restriction to planar and hamiltonian graphs.     

On the chiral connection between the ferromagnet,the axisymmetric gravitational problem and the SU(2) vacuum gauge field

A single chiral structure is shown to underly several three-dimensional field equations of physics, e.g., the ferromagnet, the stationary axi-symmetric gravitational problem, and the vacuum SU(2) gauge field in the Coulomb gauge. This connection invites cross-fertilization of exact solutions. As illustrations, exact finite energy solutions are obtained for the ferromagnet via the corresponding Weyl, Kerr, and Tominatsu-Sato solutions of Einstein's gravitational equations. Comments are made on the “local gauge invariance” of the ferromagnet and the gravitational field.     

The effect of gravitational waves from a spinning rod on its rigidity

The energy and angular momentum flux carried by gravitational waves from a spinning rod are calculated exactly in the weak field limit of general relativity. It is shown that contrary to common belief, the energy and angular momentum flux are not proportional and the energy and angular momentum equations governing the evolution of the rod are not identical. The spinning rod does not remain rigid: Its length increases. Both the angular deceleration and the rate of change of length are dependent on the nature of the material of the rod, and these rates are small, as expected.     

Self-complementary magic squares of doubly even orders

A magic square $M$ in which the entries consist of consecutive integers from $1,2,\dots ,n^2$ is said to be self-complementary of order$n$ if the resulting square obtained from $M$ by replacing each entry $i$ by $n^2+1?i$ is equivalent to $M$ (under rotation or reflection). We present a new construction for self-complementary magic squares of order $n$ for each $n\ge 4$, where $n$ is a multiple of $4$.     

The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadings

Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth‐order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r → 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz‐type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Modeling complexity in musical rhythm

This article constructs a tree structure for the music rhythm using the L‐system. It models the structure as an automata and derives its complexity. It also solves the complexity for the L‐system. This complexity can resolve the similarity between trees. This complexity serves as a measure of psychological complexity for rhythms. It resolves the music complexity of various compositions including the Mozart effect K488. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

ChemInform Abstract: Theoretical Study on the Assembly and Stabilization of a Magic Cluster Al4N‐

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Metal–Organic‐Framework‐Derived Hollow N‐Doped Porous Carbon with Ultrahigh Concentrations of Single Zn Atoms for Efficient Carbon Dioxide Conversion

The development of efficient and low energy‐consumption catalysts for CO₂ conversion is desired, yet remains a great challenge. Herein, a class of novel hollow porous carbons (HPC), featuring well dispersed dopants of nitrogen and single Zn atoms, have been fabricated, based on the templated growth of a hollow metal–organic framework precursor, followed by pyrolysis. The optimized HPC‐800 achieves efficient catalytic CO₂ cycloaddition with epoxides, under light irradiation, at ambient temperature, by taking advantage of an ultrahigh loading of (11.3 wt %) single‐atom Zn and uniform N active sites, high‐efficiency photothermal conversion as well as the hierarchical pores in the carbon shell. As far as we know, this is the first report on the integration of the photothermal effect of carbon‐based materials with single metal atoms for catalytic CO₂ fixation.