A proposed method for generating and receiving narrow beams of ultrasound in the Fast Reactor liquid sodium environment

In the liquid sodium coolant of the Fast Reactor there are several measurements which may be performed using ultrasonic techniques. This paper gives a brief outline of one such measurement and then describes the design of an ultrasonic waveguide for the generation and detection of ultrasound in this hostile situation. The successful laboratory tests of the device are also reported.     

Bilinear Hilbert Transform on Measure Spaces

In this article we obtain the boundedness of the periodic, discrete and ergodic bilinear Hilbert transform, from , where 1$, and $p_3\ge 1$" align="middle" border="0"> . The main techniques are a bilinear version of the transference method of Coifman and Weiss and certain discretization of bilinear operators. In the periodic case, we also obtain the boundedness for      

New synthesis of substituted 3-aryl-1-naphthaldehydes

A general, unequivocal procedure for the preparation of specifically substituted 3-aryl-1-naphthaldehydes was developed. Benzylmagnesium bromides with 5-aryl-2, 2-dimethyl-4-pentene-3-ones (12) gave exclusively 1,4-addition products, 5,6-diaryl-2,2-dimethyl-3-hexanones (13). The hexanones on oxidation with peracetic acid gave 3,4-diarylbutanoic acids (14), which were cyclized to tetralones (15). The tetralones on treatment with MeMgI followed by dehydration and dehydrogenation gave 3-aryl-1-methylnaphthalenes (10), which were converted into corresponding aldehydes (11). When benzylmagnesium bromides were added to 4-aryl-3-butene-2-ones (1), mixtures of 1,2 and 1,4-addition products were formed. Further treatment of these mixtures also yielded the desired methylnaphthalenes along with various identified side products.     

Ouroboros: Heterocycles closed by dative σ bonds and stabilized by π delocalization

Heteroarenes such as (aza and oxa)borines are increasingly important as synthetic targets and reagents. We map the intramolecular cyclization of saturated heterocyclic chains through dative bonding. A related set of planar unsaturated aza-, oxa-, and fluora-rings that feature dative σ bonding enhanced by π delocalization are identified. The systems have, in general, the formulae A′(CH₂)_mD′ and A′(CH)_mD′, where m?=?3 and 4, and A′ and D′ are acceptor and donor sites, respectively. In each case, the ring isomers, achievable via A′←D' internal coordination (in the manner of Kekulé’s ouroboros), are more stable than chains. Unsaturated aromatic rings examined herein include a oxadiborine with a hypervalent oxygen center and a dioxadiborine. They are isoelectronic with an azaborine, which was synthesized more recently, and benzene.     

Diagonally neighbour transitive codes and frequency permutation arrays

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication, while at the same time maintaining a constant power output. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family.     

Gilbert N. Lewis and the chemical bond: the electron pair and the octet rule from 1916 to the present day

We describe the development of Lewis's ideas concerning the chemical bond and in particular the concept of the electron pair bond and the octet rule. We show that the concept of the electron pair bond has endured to the present day and is now understood to be a consequence of the Pauli principle. In contrast the octet rule is now regarded as much less important than was originally generally believed, although Lewis himself knew several exceptions and regarded it as less important than what he called the rule of two (the electron pair). The octet rule was more strongly promoted by Langmuir who is also responsible for the term covalent bond. However, many more exceptions to the octet rules than were known to Lewis are now known and the terms hypervalent and hypovalent used to describe such molecules are no longer particularly useful. Today it is realized that bonding electron pairs in many molecules are not as well localized as Lewis believed, nevertheless resonance structures, i.e., plausible alternative Lewis structures, are still often used to describe such molecules. Moreover electrons are not always found in pairs, as for example in linear molecules, which can, however, be satisfactorily described by Linnett's double quartet theory. The electron density distribution in a molecule can now be analyzed using the ELF and other functions of the electron density to show where electron pairs are most probably to be found in a molecule.     

Characterization of high molecular weight polyethylenes using high temperature asymmetrical flow field-flow fractionation with on-line infrared, light scattering, and viscometry detection

High temperature asymmetrical flow field-flow fractionation (HTAF4) coupled to infrared (IR), multi-angle light scattering (MALS), and viscometry (Visc) detection is introduced as a tool for the characterization of high molecular weight polyethylenes. The high molecular weight fraction strongly affects the rheological behaviour and processability of polyethylene materials and can often not be accurately resolved by current technology such as high temperature size-exclusion chromatography (HTSEC). Molecular weight (M), radius of gyration (Rg), and intrinsic viscosity [eta] of linear high density polyethylene (HDPE) and branched low density polyethylene (LDPE) samples are studied in detail by HTAF4 and are compared to HTSEC. HTAF4 showed a better separation and mass recovery than HTSEC for very high molecular weight fractions in HDPE and LDPE samples. As no stationary phase is present in an HTAF4 channel, the technique does not show the typical drawbacks associated with HTSEC analysis of high molecular weight polyethylenes, such as, exclusion effects, shear degradation, and anomalous late elution of highly branched material. HTAF4 is applied to study the relation between the molecular weight and the zero shear viscosity eta0 for high molecular weight HDPE. It was found that the zero shear viscosity values predicted from HTAF4 results are in good qualitative agreement with measured values obtained from dynamic mechanical spectroscopy (DMS) experiments, whereas eta0 values predicted from HTSEC do not show a strong correlation. The low molecular weight cutoff of HTAF4 is approximately 5x10(4) as a result of relatively large pores in the HTAF4 channel membrane. HTAF4 is, therefore, currently not suited to analyze low molecular weight materials.     

Mean2-Bounded Operators on Hilbert Space and Weight Sequences of Positive Operators

We introduce and study the class of mean₂-bounded operators on Hilbert space. These operators, which are characterized by a uniform boundedness condition on the 'quadratic averages' of their powers, are intimately related to operator-valued weight sequences and weighted norm inequalities. Mean₂-bounded operators exhibit a lively interplay with the discrete Hilbert transform in an array of settings. Under appropriate circumstances, mean₂-bounded operators have a rich spectral theory leading to powerful transference properties.