Infrared and Raman spectra, ab initio calculations, conformational stability and vibrational assignment of 1-bromo-1-silacyclopentane

Infrared and Raman spectra (3500-60 cm(-1)) of gas and/or liquid and solid 1-bromo-1-silacyclopentane (c-C4H8SiBrH) have been recorded and the vibrational data indicate the presence of a single conformer with no symmetry which is consistent with the twisted form. Ab initio calculations with a variety of basis sets up to MP2(full)/6-311+G(2df,2pd) predict the envelope-axial and envelope-equatorial conformers to be saddle points with nearly the same energies but approximately 900 cm(-1) (5.98 kJ/mol) lower in energy than the planar conformer. Density functional theory calculations by the B3LYP method predict slightly lower energies for the two envelope forms and considerably lower energy for the planar form compared to the MP2 predictions. By utilizing the MP2(full)/6-31G(d) calculations the force constants, frequencies, infrared intensities, band contours, Raman activities, and depolarization values have been obtained to support the vibrational assignment. Estimated r0 structural parameters have been obtained from adjusted MP2(full)/6-311+G(d,p) calculations. These experimental and theoretical results are compared to the corresponding quantities of some other five-membered rings.     

On the homology of elementary Abelian groups as modules over the Steenrod algebra

We examine the dual of the so-called “hit problem”, the latter being the problem of determining a minimal generating set for the cohomology of products of infinite projective spaces as a module over the Steenrod Algebra A at the prime 2. The dual problem is to determine the set of A-annihilated elements in homology. The set of A-annihilateds has been shown by David Anick to be a free associative algebra. In this note we prove that, for each k≥0, the set of kpartiallyA-annihilateds, the set of elements that are annihilated by Sqⁱ for each i≤2^k, itself forms a free associative algebra.     

Factorizations that Involve Ramanujan＇s Function k（q） = r（q）r2（q2）

In the “lost notebook”, Ramanujan recorded infinite product expansions for

Scientists and mathematicians collaborating to build quantitative skills in undergraduate science

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum.     

Generalizing inplace multiplicity identities for integer compositions

In a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities. Since then, we asked whether one could generalize one of these results even further by considering compositions in which certain parts could come from t kinds (rather than just two kinds, which was the crux of the original result). In this paper, we provide such a generalization. A straightforward bijective proof is given and generating functions are provided for each of the types of compositions which arise. We close by briefly mentioning some arithmetic properties satisfied by the functions which count such compositions.     

Congruences modulo powers of 2 for a certain partition function

We study the divisibility properties of the coefficients c(n) defined by

$\prod_{n=1}^\infty\frac{1}{(1-q^n)^2(1-q^{3n})^2}=\sum _{n=0}^\infty c(n)q^n.$

An analogue of Ramanujan’s partition congruences is obtained for certain coefficients c(n) modulo powers of 2. Furthermore, an analogue of the identity that Hardy regarded as Ramanujan’s most beautiful is proved.

     

Aharonov-Bohm excitons at elevated temperatures in type-II ZnTe/ZnSe quantum dots

Optical emission from type-II ZnTe/ZnSe quantum dots demonstrates large and persistent oscillations in both the peak energy and intensity indicating the formation of coherently rotating states. Furthermore, these Aharonov-Bohm oscillations are shown to be remarkably robust and persist until 180 K. This is at least one order of magnitude greater than the typical temperatures in lithographically defined rings. To our knowledge, this is the highest temperature at which the AB effect has been observed in solid-state and molecular nanostructures.     

Synthesis and photophysics of a linear non-covalently linked porphyrin-fullerene dyad

The synthesis and characterization of a new pyridinofullerene ligand capable of forming axially symmetric complexes with ZnTPP is reported; molecular modelling studies, 1H NMR, UV-Vis spectroscopy and fluorescence quenching data support formation of a strong complex between the new ligand and ZnTPP.     

Renaissance of Topotactic Ion-Exchange for Functional Solids with Close Packed Structures

Recently, many new, complex, functional oxides have been discovered with the surprising use of topotactic ion-exchange reactions on close-packed structures, such as found for wurtzite, rutile, perovskite, and other structure types. Despite a lack of apparent cation-diffusion pathways in these structure types, synthetic low-temperature transformations are possible with the interdiffusion and exchange of functional cations possessing ns² stereoactive lone pairs (e. g., Sn(II)) or unpaired nd^x electrons (e. g., Co(II)), targeting new and favorable modulations of their electronic, magnetic, or catalytic properties. This enables a synergistic blending of new functionality to an underlying three-dimensional connectivity, i. e., [-M−O-M-O-]_n, that is maintained during the transformation. In many cases, this tactic represents the only known pathway to prepare thermodynamically unstable solids that otherwise would commonly decompose by phase segregation, such as that recently applied to the discovery of many new small bandgap semiconductors.     

Pd(II)-Mediated C−H Activation for Cysteine Bioconjugation

Selective bioconjugation remains a significant challenge for the synthetic chemist due to the stringent reaction conditions required by biomolecules coupled with their high degree of functionality. The current trailblazer of transition-metal mediated bioconjugation chemistry involves the use of Pd(II) complexes prepared via an oxidative addition process. Herein, the preparation of Pd(II) complexes for cysteine bioconjugation via a facile C−H activation process is reported. These complexes show bioconjugation efficiency competitive with what is seen in the current literature, with a user-friendly synthesis, common Pd(II) sources, and a more cost-effective ligand. Furthermore, these complexes need not be isolated, and still achieve high conversion efficiency and selectivity of a model peptide. These complexes also demonstrate the ability to selectively arylate a single surface cysteine residue on a model protein substrate, further demonstrating their utility.