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.     

Experimental Investigations on the Thermal Diffusion Characteristics and Photoluminescence in Multiphase Micro Fluids Containing ZnO Micro Tubes and Fluorescein Dye

Optics and Spectroscopy - Scattering of light by disordered structures is normally detrimental to their applicability in many optoelectronic devices. However, some micro and nanostructures are...     

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     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.     

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.