Addition of aluminium,zinc and magnesium hydrides to rhodium(iii)

We report the addition of M–H bonds (M = Al, Zn, Mg) to a Rh(iii) intermediate generated from the reductive elimination of triethylsilane from [Cp*Rh(H)₂(SiEt₃)₂]. A series of new heterobimetallic complexes possessing Rh–M bonds have been isolated and characterised by a number of spectroscopic (¹H, ²⁹Si, ¹³C, ¹⁰³Rh NMR, infrared, and X-ray diffraction) and computational techniques (NBO and QTAIM analysis). Experimental and computational data are consistent with cleavage of the M–H bond upon addition to rhodium with formation of new Rh–M and Rh–H bonds. Upon photolysis the Al analogue of this series undergoes a further elimination reaction producing triethylsilane and a highly unusual Rh₂Al₂H₄ containing cluster proposed to contain an Al(i) bridging ligand.     

Analytical examples of diffusive waves generated by a traveling wave

We construct analytical solutions for a system composed of a reaction–diffusion equation coupled with a purely diffusive equation. The question is to know if the traveling wave solutions of the reaction–diffusion equation can generate a traveling wave for the diffusion equation. Our motivation comes from the calcic wave, generated after fertilization within the egg cell endoplasmic reticulum, and propagating within the egg cell. We consider both the monostable (Fisher–KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails whose exponents are roots of second-, third-, or fourth-order polynomials. These raise conditions on the coefficients for existence of a traveling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered.     

Gaseous flow measurements in an internal combustion engine assembly using molecular tagging velocimetry

A molecular tagging velocimetry (MTV) system was applied for mapping in-cylinder flows in an internal combustion engine. The images were captured inside an optical engine assembly that reproduces operation of a 2.2 L four stroke gasoline engine. A recently developed algorithm to process MTV images is based on a fast-normalized spatial correlation approach implemented using MATLAB software. The code allows accurate detection of the MTV grid nodes displacements. It processes simultaneously velocity vector and circulation fields for individual cycles, and ensemble averages of those over a few hundred sequential cycles to obtain mean and standard deviation values. Then probability density functions are reconstructed to quantify cycle-to-cycle variability of the in-cylinder flow.     

The use of precision castings in the three-dimensional photoelastic analysis of threaded tubular connections

A new, room-temperature formulated, epoxy-resin system with superior stress-freezing photoelastic properties is presented. The ease of producing relatively large, high-quality, precision castings is discussed. Stress-optical, rheological, and mechanical properties are given. Cylindrical tubes joined by integrally cast Stub Acme and American Standard rolled thread profiles with typical geometric parameters are loaded in tension and analyzed using the stressfreezing method. Results are presented for surface axial stress distributions for the wall surfaces opposite the threaded profiles. Additionally, the fillet stress distribution for the first engaged thread as a function of the distance along the thread helix from the location of initial contact is presented. Comparison with a finite-element analysis is given. Paper was presented at the 1983 SEM Spring Conference on Experimental Mechanics held in Cleveland, OH on May 15–19.     

Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

One‐Pot Synthesis of Pomegranate‐Structured Fe3O4/Carbon Nanospheres‐Doped Graphene Aerogel for High‐Rate Lithium Ion Batteries

A unique hierarchically nanostructured composite of iron oxide/carbon (Fe₃O₄/C) nanospheres‐doped three‐dimensional (3D) graphene aerogel has been fabricated by a one‐pot hydrothermal strategy. In this novel nanostructured composite aerogel, uniform Fe₃O₄ nanocrystals (5–10 nm) are individually embedded in carbon nanospheres (ca. 50 nm) forming a pomegranate‐like structure. The carbon matrix suppresses the aggregation of Fe₃O₄ nanocrystals, avoids direct exposure of the encapsulated Fe₃O₄ to the electrolyte, and buffers the volume expansion. Meanwhile, the interconnected 3D graphene aerogel further serves to reinforce the structure of the Fe₃O₄/C nanospheres and enhances the electrical conductivity of the overall electrode. Therefore, the carbon matrix and the interconnected graphene network entrap the Fe₃O₄ nanocrystals such that their electrochemical function is retained even after fracture. This novel hierarchical aerogel structure delivers a long‐term stability of 634 mA h g^?1 over 1000 cycles at a high current density of 6 A g^?1 (7 C), and an excellent rate capability of 413 mA h g^?1 at 10 A g^?1 (11 C), thus exhibiting great potential as an anode composite structure for durable high‐rate lithium‐ion batteries.     

Double Bruhat Cells in Kac–Moody Groups and Integrable Systems

We construct a family of integrable Hamiltonian systems generalizing the relativistic periodic Toda lattice, which is recovered as a special case. The phase spaces of these systems are double Bruhat cells corresponding to pairs of Coxeter elements in the affine Weyl group. In the process we extend various results on double Bruhat cells in simple algebraic groups to the setting of Kac–Moody groups. We also generalize some fundamental results in Poisson–Lie theory to the setting of ind-algebraic groups, which is of interest beyond our immediate applications to integrable systems.     

Orbital nature in the electronic states of cyclopropene

Self-consistent field results for the excited electronic states of cyclopropene, with regard to the spatial extent of the π* orbital in the lowest energy ¹(π, π*) state, are found to be identical with that for ethylene. Due to the forced planarity of the ring structure, dihedrally twisted conformers of the upper electronic state cannot contribute significantly to the oscillator strength which must therefore receive a substantial contribution from the vertical transition; this conclusion is contrary to the self-consistent field results. For a proper theoretical treatment of the problem the importance of a multi-configuration approach in an extended basis with ¹(σ, σ*)-type states is emphasized.     

N-Acetylneuraminic Acid: Neoglycoproteins and Pseudopolysaccharides

Abstract

A simplified procedure for the synthesis of acetochloroneuraminic acid is described starting from the methyl ester. N-acetyl neuraminic acid α-allyl glycoside was prepared in high yield using silver salicylate as catalyst. Reductive ozonolysis of the allyl group, followed by direct reductive ami nation to protein carriers, gave immunogenic neoglycoproteins. Copolymerization of the α-allyl glycoside with acrylamide produced a water-soluble pseudopolysaccharide useful for the EL ISA technique.     

The Conversion of 1,3-Cyclooctadiene to 1-Vinylcyclohexene

Meroquinene (1), a key degradation product of quinine and an important intermediate in the preparation of the cinchona and other alkaloids,¹ has only recently been synthesized ² even though attempts were made at its preparation for over thirty years. These early attempts were frustrated primarily by the difficulty encountered in the introduction of a potential vinyl group onto a piperidine ring. Alkylation of 3-car-bethoxy-N-benzoyl-4-piperidone (2) with either phenoxyethyl chloride³ or dimethylaminoethyl chloride (3)⁴ resulted in exclusive formation of the O-alkylated product, even though alkylation of the presumably analogous 2-carbethoxycyclohexanone with 3 gave nearly equal amounts of C- and O- alkylated materials.⁴ The use of other piperidone derivatives in this reaction was precluded by the report that attempts to alkylate 3-car-bethoxy-N-alkyl-4-piperidones gave only the quaternary nitrogen product.⁵