The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.     

Path to achieving molecular dispersion in a dense reactive mixture

A uniform dispersion of reactants is necessary to achieve a complete reaction involving multicomponents. In this study, we have examined the role of plasticizer in the reaction of two seemingly unlikely reactants: a highly crystalline hexamethylenetetramine (HMTA) and a strongly hydrogen bonded phenol formaldehyde resin. By combining information from NMR, infrared spectroscopy and differential scanning calorimetry, we were able to determine the role of specific intermolecular interactions necessary for the plasticizer to dissolve the highly crystalline HMTA and to plasticize the phenol formaldehyde resin in this crosslinking reaction. The presence of the plasticizer increased the segmental mobility, disrupted the hydrogen bonded matrix, and freed the hydroxyl units, which further increased the solubility of the HMTA. Both the endothermic and exothermic transitions are accounted for in the calorimetric data obtained. For the first time, it is possible to obtain the effective molar ratio of each component needed to complete the crosslinking reaction efficiently. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1519–1526     

Amphiphilic block copolymer self‐assemblies of poly(NVP)‐b‐poly(MDO‐co‐vinyl esters): Tunable dimensions and functionalities

Functional, degradable polymers were synthesized via the copolymerization of vinyl acetate (VAc) and 2‐methylene‐1,3‐dioxepane (MDO) using a macro‐xanthate CTA, poly(N‐vinylpyrrolidone), resulting in the formation of amphiphilic block copolymers of poly(NVP)‐b‐poly(MDO‐co‐VAc). The behavior of the block copolymers in water was investigated and resulted in the formation of self‐assembled nanoparticles containing a hydrophobic core and a hydrophilic corona. The size of the resultant nanoparticles was able to be tuned with variation of the hydrophilic and hydrophobic segments of the core and corona by changing the incorporation of the macro‐CTA as well as the monomer composition in the copolymers, as observed by Dynamic Light Scattering, Static Light Scattering, and Transmission Electron Microscopy analyses. The concept was further applied to a VAc derivative monomer, vinyl bromobutanoate, to incorporate further functionalities such as fluorescent dithiomaleimide groups throughout the polymer backbone using azidation and “click” chemistry as postpolymerization tools to create fluorescently labeled nanoparticles. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2699–2710     

T1Effects in Sequential Dynamic Susceptibility Contrast Experiments

Residual effects of an initial bolus of gadolinium contrast agent have been previously demonstrated in sequential dynamic susceptibility contrast MR experiments. While these residual effects quickly reach a saturation steady state, their etiology is uncertain, and they can lead to spurious estimates of hemodynamic parameters in activation experiments. The possible influence ofT₁effects is now investigated with experiments in whichT₁weighting is varied as well as with serial regionalT₁measurements. Little evidence for significant residualT₁effects is found, suggesting instead that susceptibility effects underlie these observations. An initial saturation dose of contrast agent minimizes this effect.     

Sonogashira alkynylation of unprotected 8-brominated adenosines and guanosines: fluorescence properties of compact conjugated acetylenes containing a purine ring

A practical Sonogashira alkynylation protocol for the preparation of 8-alkynylated adenosines and guanosines has been developed. Protection of the sugar hydroxyl substituents is not required; protection hinders the purification of these products. A preliminary fluorescent study is reported, which shows that the presence of a substituent on the phenylene ring influences the fluorescent properties considerably, an outcome that could be utilized in biological applications.     

A rigid subspace of the real line whose square is a homogeneous subspace of the plane

Working in ZFC, we give an example as indicated in the title.

     

Experiences in Expert Systems

This paper describes some work carried out in the Scientific Research and Development Branch (SRDB) of the Home Office, intended to contribute to an overall aim of building up internal expertise in the field of expert systems. This was done by carrying out a number of pilot and demonstrator projects, two of which are described in some detail. The plan, which proved successful, was to build as far as possible on the relevant skills already possessed by an OR group in the branch. The lessons learned from these are summarized in the hope that they will be of use to other groups who wish to become involved in this important area.