One-step synthesis of oxazoline and dihydrooxazine libraries

The reactions of 1,2- and 1,3-hydroxyalkyl azides and aldehydes in the presence of Lewis acid result in the one-step construction of oxazolines and dihydrooxazines, respectively. The reaction was adapted to parallel synthesis using a polymer-bound phosphine to scavenge excess hydroxyalkyl azide. Thus, a 60-member library of various disubstituted oxazolines and di- and trisubstituted dihydrooxazines was generated.     

Theoretical insights into the augmented-neural-network approach for combinatorial optimization

The augmented-neural-network (AugNN) approach has been applied lately to some NP-Hard combinatorial problems, such as task scheduling, open-shop scheduling and resource-constraint project scheduling. In this approach the problem of search in the solution-space is transformed to a search in a weight-matrix space, much like in a neural-network approach. Some weight adjustment strategies are then used to converge to a good set of weights for a locally optimal solution. While empirical results have demonstrated the effectiveness of the AugNN approach vis-à-vis a few other metaheuristics, little theoretical insights exist which justify this approach and explain the effectiveness thereof. This paper provides some theoretical insights and justification for the AugNN approach through some basic theorems and also describes the algorithm and the formulation with the help of examples.     

Paramagnetic 19F chemical shift probes that respond selectively to calcium or citrate levels and signal ester hydrolysis

Paramagnetic magnetic resonance chemical shift probes containing a proximal CF(3) group have been characterised. Different systems have been created that report reversible changes in calcium ion concentrations in the millimolar regime, signal the presence of citrate selectively in competitive aqueous media and allow the monitoring of remote ester/amide hydrolysis in relayed, irreversible transformations. Chemical shift non-equivalence is amplified by the presence of the proximate lanthanide ion, with a mean separation between the CF(3) group and the metal ion of 6.4 ? found for a thulium complex, in an X-ray structure of the metal complex aqua adduct. The enhanced rate of longitudinal relaxation of the (19)F nucleus allows faster data acquisition.     

Galois extensions,plus closure,and maps on local cohomology

Given a local domain $(R,\mathfrak{m})$ of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain S such that the induced map on local cohomology modules $H_{\mathfrak{m}}^i(R)\to H_{\mathfrak{m}}^i(S)$ is zero for each $i<\dim R$. We prove that the extension S may be chosen to be generically Galois, and analyze the Galois groups that arise.     

Effect of Cr doping on the ac electrical properties of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles

Magnesium aluminate nanoparticles with different chromium concentration (0–12%) have been synthesized by a citrate–nitrate sol–gel route. X-ray diffraction studies confirmed the formation of single-phase cubic spinel structure excluding the presence of any secondary phase. Crystallite size of the synthesized nanoparticles was found to increase from 8.5 to 19.8 nm with the increase in Cr concentration. Fourier transformed infrared spectroscopic studies confirmed the presence of AlO₆ group which led to the formation of MgAl₂O₄ spinel structure. Surface morphology of the sintered pellets was investigated with the help of a field emission scanning electron microscope which revealed the existence of both grain and grain boundary along with their aggregates. The dielectric constant, dielectric loss and ac conductivity were studied as a function of frequency of the applied electric field for different composition and their nature of variation with frequency has been elucidated on the basis of Maxwell–Wagner interfacial model. Impedance spectroscopy technique has been used to study the effect of grain and grain boundary on the electrical properties of this spinel oxide. All the electrical parameters showed strong dependence on the nanostructural properties and were found to vary consistently with the increase of doping concentration.     

Superposition of Quantum Confinement Energy (SQCE) model for estimating shell thickness in core-shell quantum dots: validation and comparison

A novel theoretical model based on superposition of core and shell band-gaps, termed as SQCE model, is developed and reported here, which enables one to estimate the shell thickness in a core-shell quantum dot (QD), which is critically important in deciding its optical and electronic properties. We apply the model to two experimental core-shell QD systems, CdSe-CdS and CdSe-ZnS, which we synthesize by microemulsion method. We synthesize and study two series of samples, R and S to study the optical properties. The core size is varied in the R-series (by varying water-to-surfactant ratio, R) whereas the shell thickness is varied in the S-series (by varying the shell-to-core precursor molar ratio, S). The core and core-shell QDs from R-series and S-series are characterized for particle size, shape and crystallographic information. The shell thickness for all core-shell QD samples is estimated by SQCE model, and experimentally measured with TEM and SAXS. A close match is observed between experimental values and model predictions, thus validating the model. Further, the optimum shell thickness (corresponding to maximum quantum yield) values for CdS and ZnS over a 4.26 nm CdSe core have been estimated as 0.585 nm and 0.689 nm, respectively, from the SQCE model. The SQCE model developed in this work is applicable to other core-shell quantum dots also, such as CdTe-CdS, CdTe-CdSe and CdS-ZnS, and will serve as a useful complement to experimental measurement.     

Resolvability in circulant graphs

A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u, v ∈ V (G) there is a vertex w ∈ W such that d(u, w) ≠ d(v, w). A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G, denoted by dim(G). For a vertex u of G and a subset S of V (G), the distance between u and S is the number min s∈S d(u, s). A k-partition Π = {S 1 , S 2 , . . . , S k } of V (G) is called a resolving partition if for every two distinct vertices u, v ∈ V (G) there is a set S i in Π such that d(u, Si )≠ d(v, Si ). The minimum k for which there is a resolving k-partition of V (G) is called the partition dimension of G, denoted by pd(G). The circulant graph is a graph with vertex set Zn , an additive group of integers modulo n, and two vertices labeled i and j adjacent if and only if i-j (mod n) ∈ C , where CZn has the property that C =-C and 0 ■ C. The circulant graph is denoted by Xn, Δ where Δ = |C|. In this paper, we study the metric dimension of a family of circulant graphs Xn, 3 with connection set C = {1, n/2 , n-1} and prove that dim(Xn, 3 ) is independent of choice of n by showing that dim(Xn, 3 ) ={3 for all n ≡ 0 (mod 4), 4 for all n ≡ 2 (mod 4). We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C = {±1, ±2} and prove that pd(Xn, 4 ) is independent of choice of n and show that pd(X5,4 ) = 5 and pd(Xn,4 ) ={3 for all odd n ≥ 9, 4 for all even n ≥ 6 and n = 7.     

Line broadening studies in low energy plasma focus

Optical emission spectroscopic studies were carried out to characterise the plasma leading to the estimation of two plasma parameters, electron density and temperature. These experiments were conducted on a 2 kJ plasma device which is equipped with squirrel cage electrode configuration enclosed in a glass vacuum chamber filled with hydrogen at a pressure of 5 mbar. Spectral emissions obtained from each flash were photographed in the region of 4000–6000 Å using one metre Czerny-Turner spectrograph cum monochromator. Detailed examination of the observed features showed that theH _β andH _λ lines of hydrogen showed significant broadening of the order of 35 Å FWHM which is due to Stark effect expected in high density plasmas. Further several atomic lines of Cu and Zn from the electrode material (brass) showed broadening which was due to quadratic Stark effect. A comparative study of the broadening of lines obtained in DC arc, hollow cathode and plasma focus was made. Electron density from Stark broadened hydrogen lines and quadratic Stark Coefficient C₄ for the CuI and ZnI lines were evaluated. The excitation temperature was determined from the line intensity ratio method using CuI lines.     

A note on some relations in the queue Glx/M/c

Closed-form relations are derived for the probabilities and performance measures observed at random/arrival/departure epochs in a multi-server queue with group arrivals.     

Superconductivity with transition temperature up to 80 K for TbSr2Cu2.7Mo0.3O7+δ

A Tb-123 phase with the composition, TbSr₂Cu_2.7Mo_0.3O_7+δ, has been synthesized in single-phase form by the solid-state reaction route. Its phase purity has been confirmed from neutron powder diffraction studies. The as-synthesized Tb-123 sample does not show superconductivity down to 5 K. On the other hand, an unusually high antiferromagnetic ordering temperature (T_N) of around 7 K is seen for the Tb moments. After 120-atm-O₂ post-annealing, bulk superconductivity is achieved in this compound with a superconducting transition temperature (T_c) of about 30 K, without any significant effect on T_N. To achieve higher oxygen content and higher T_c, the as-synthesized sample was subjected to high-pressure oxygenation, carried out in a closed cell, at 5 GPa and 400 °C in the presence of AgO as an excess-oxygen source. This sample exhibited superconductivity onset at around 80 K with a Meissner fraction larger than 10% at 5 K. Our observation of superconductivity at 80 K is the highest T_c to-date for the Tb-123 type compounds.