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 $4$.     

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     

One‐Pot Bioconversion of l‐Arabinose to l‐Ribulose in an Enzymatic Cascade

This work reports the one‐pot enzymatic cascade that completely converts l ‐arabinose to l ‐ribulose using four reactions catalyzed by pyranose 2‐oxidase (P2O), xylose reductase, formate dehydrogenase, and catalase. As wild‐type P2O is specific for the oxidation of six‐carbon sugars, a pool of P2O variants was generated based on rational design to change the specificity of the enzyme towards the oxidation of l ‐arabinose at the C2‐position. The variant T169G was identified as the best candidate, and this had an approximately 40‐fold higher rate constant for the flavin reduction (sugar oxidation) step, as compared to the wild‐type enzyme. Computational calculations using quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) showed that this improvement is due to a decrease in the steric effects at the axial C4‐OH of l ‐arabinose, which allows a reduction in the distance between the C2‐H and flavin N5, facilitating hydride transfer and enabling flavin reduction.     

Coupling between an optical phonon and the Kondo effect

We explore the ultrafast optical response of Yb14MnSb11, providing further evidence that this compound is the first d-electron, ferromagnetic, underscreened Kondo lattice. These results also provide the first demonstration of coupling between an optical phonon mode and the Kondo effect.     

Conductivity and FTIR studies on PEO-LiX [X: CF3SO3(-), SO4(2-)] polymer electrolytes

Polymer electrolytes based on poly(ethylene oxide)-lithium triflate (PEO-LiCF3SO3) and poly(ethylene oxide)-lithium sulphate (PEO-Li2S4) were prepared by using solution casting method. Measurements of conductivity and dielectric were carried out on these films as a function of frequency at various temperatures. It was observed that PEO-LiCF3SO3 polymer electrolytes have higher conductivity. The interaction between PEO and Li salts were studied by Fourier transform infrared (FTIR).