Central and Functional Central Limit Theorems for a Class of Urn Models

We consider an approach based on tails to certain central limit and functional central limit theorems for a class of two color urn models. In particular, some of the results are derived from an associated Ornstein–Uhlenbeck process, and for another result we give an alternative proof based on martingale tails.      

Investigation of a non-linear system under partially prescribed random excitation

The problem of non-linear systems excited by random forces with known power spectral density functions and unspecified probability structure is considered. Sufficient, but not necessary, conditions on the input under which the response can be a Gaussian process are investigated. The approach is illustrated by investigating the hardening spring cubic oscillator under wide and narrow band excitations. The non-Gaussian probability density of the input that leads to Gaussian response is determined.     

Diisopropyl azodicarboxylate mediated selective dehydrogenation of 2-amino-3-cyano 4H-chromenes

Selective dehydrogenation of 2-amino-3-cyano 4H-chromenes to the corresponding 2-iminochromenes mediated by diisopropyl azodicarboxylate under neutral conditions is reported. The dehydrogenation reaction is compatible with phenolic hydroxyl group and generates iminochromene in high yields. The methodology provides an easy access to coumarin and N-tosyl 2-amino-3-cyano-4-aryl 4H-chromenes.     

Quantitative structure-activity relationship studies of boron-containing dipeptide proteasome inhibitors using calculated mathematical descriptors

Topological indices (TIs) and atom pairs (APs) were used to develop quantitative structure-activity relationship (QSAR) models of a set of 58 dipeptide boronic acids which are potent inhibitors of proteasome and have found applications in the treatment of various types of cancers. Of the three linear regression methods used for QSAR development, viz., principal components regression (PCR), partial least square (PLS), and ridge regression (RR), the last method gave the most satisfactory models whereas the remaining two methods yielded poor models. RR results obtained in this paper using TIs and APs are comparable to the CoMFA and CoMSIA results reported in the literature with the same set of compounds.     

Reactivity of conformationally constrained bispropargyl sulfones: complete preference for 6π-electrocyclization process

The reactivity of a series of conformationally constrained bispropargyl sulfones with an ortho alkenyl moiety was studied. Under basic condition, these molecules underwent isomerization, first to monoallene followed by 6π-electrocyclization (6π-EC). Another cycle of isomerization and 6π-EC gave the bis naphthyl sulfones. No Garratt–Braverman (GB) Cyclization product could be isolated even on easing up the strain. Computations with DFT (at BP86-D3/def2-SVP level) indicated that, it is energetically more favorable for the initially formed monoallenic intermediate to undergo electrocyclization rather than isomerize to bisallene. This is in contrast to the acyclic unconstrained counterpart, where isomerization to bisallene is preferred and competing GBC/6π-EC of bisallenes results in mixture of products.     

Poly (methyl methacrylate)-graphene oxide supported palladium catalyst: A ligand free protocol for Suzuki and Heck coupling reaction in water medium

A green and efficient approach for the ligand free Suzuki–Miyaura and Mizoroki–Heck C–C cross coupling reaction using low palladium loaded Graphene oxide-polymer composite catalyst has been described. High yields, easy work-up, easy availability and handling, eco-friendly and reusability of the catalysts are the main aspects of the present method. The simplicity of the entire sequence has made the protocol meritorious as a reasonable contribution to the existing methods in the field of substituted biphenyls and olefins. The supported heterogeneous catalyst was characterized using HRTEM, ICP-AES, PXRD, XPS, TGA, and FT-IR spectroscopy.     

Significant modifications in the electrical properties of poly(methyl methacrylate) thin films upon dispersion of silver nanoparticles

Electrical conductivity of thin solid films of PMMA with dispersed silver nanoparticles, synthesized by a novel method, was studied in dark conditions by changing the applied voltage and temperature and also under photoexcitation (by a mercury lamp, 125 W) at room temperature. Anomalous hysteresis in current-temperature characteristics during heating and cooling cycles was observed. The hysteresis-like behaviour was explained on the basis of the movements of molecules associated with different parts of a PMMA matrix and diffusion of silver nanoparticles in the PMMA matrix. Dark current in the PMMA films with dispersed silver nanoparticles has been observed to be higher than the corresponding current in the PMMA films without silver nanoparticles due to the creation of conduction paths by the silver nanoparticles/nanoclusters. The photoresponse in the thin solid films of PMMA with dispersed silver nanoparticles was the reverse of that observed in thin solid films of PMMA without silver nanoparticles. A decrease in photocurrent under illumination of light was observed due to the destruction of conduction paths by the illumination of light.