Selective oxidation of ethylbenzene to acetophenone over Cr(III) Schiff base complex intercalated into layered double hydroxide

A new heterogeneous catalyst, Cr(III) Schiff base‐containing layered double hydroxide, was synthesized using the intercalation method. The Cr(III) Schiff base complex derived from 2‐hydroxy‐1‐naphthaldehyde and 4‐aminobenzoic acid was intercalated into the layered double hydroxide. The synthesized materials were characterized using inductively coupled plasma atomic emission spectrometry, energy‐dispersive X‐ray analysis, scanning electron microscopy, X‐ray diffraction, Brunauer–Emmett–Teller surface area measurement, Fourier transform infrared spectroscopy, thermogravimetric analysis, diffuse reflectance UV–visible spectroscopy and electron paramagnetic resonance spectroscopy. The catalytic activity was investigated for the oxidation of ethylbenzene with tert‐butylhydroperoxide as an oxidant under solvent‐free conditions as well as with lower chromium concentrations. In the oxidation reaction, ethylbenzene was oxidized to acetophenone and benzaldehyde. The catalyst was recycled ten times without significant loss of catalytic activity. Leaching studies performed with hot filtration experiments showed that the chromium catalyst was heterogeneous in nature and stable under the reaction conditions.     

A self-consistent approach to soft mode analysis in size driven ferroelectricity

The polarization distribution in a finite size system obtained through Landau phenomenology is shown to contain unphysical oscillatory parts [P. Khare, D. Sa, Solid State Commun. 150 (2010) 172]. Self-consistency in the solution has been used to remove such difficulty and the issue of soft mode in such system has been addressed. The temperature as well as the size dependence of the soft mode frequency is calculated and compared with the experiment. The extrapolation length for the size driven ferroelectricity is argued to behave in a way similar to that of correlation length in phase transition in bulk system.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Structure of Vimose

Abstract

The structure of vimose, a novel tetrasaccharide isolated from the dried twigs of Orthenthera viminea (Family: Asclepiadaceae) has been established as O-β-L-diginopyranosyl-(1 →4)-O-β-L-diginopyranosyl-(1 →4)-O-β-L-diginopyranosyl-(1 → 4)-α-L-diginopyranose 1 on the basis of spectral and chemical evidence.     

Uncertainty Quantification for Modern High-Dimensional Regression via Scalable Bayesian Methods

Tremendous progress has been made in the last two decades in the area of high-dimensional regression, especially in the “large p, small n” setting. Such sample starved settings inevitably lead to models which are potentially very unstable and hence quite unreliable. To this end, Bayesian shrinkage methods have generated a lot of recent interest in the modern high-dimensional regression and model selection context. Such methods span the wide spectrum of modern regression approaches and include among others, spike-and-slab priors, the Bayesian lasso, ridge regression, and global-local shrinkage priors such as the Horseshoe prior and the Dirichlet–Laplace prior. These methods naturally facilitate tractable uncertainty quantification and have thus been used extensively across diverse applications. A common unifying feature of these models is that the corresponding priors on the regression coefficients can be expressed as a scale mixture of normals. This property has been leveraged extensively to develop various three-step Gibbs samplers to explore the corresponding intractable posteriors. The convergence of such samplers however is very slow in high dimensions settings, making them disconnected to the very setting that they are intended to work in. To address this challenge, we propose a comprehensive and unifying framework to draw from the same family of posteriors via a class of tractable and scalable two-step blocked Gibbs samplers. We demonstrate that our proposed class of two-step blocked samplers exhibits vastly superior convergence behavior compared to the original three-step sampler in high-dimensional regimes on simulated data as well as data from a variety of applications including gene expression data, infrared spectroscopy data, and socio-economic/law enforcement data. We also provide a detailed theoretical underpinning to the new method by deriving explicit upper bounds for the (geometric) rate of convergence, and by proving that the proposed two-step sampler has superior spectral properties. Supplementary material for this article is available online.     

Supersymmetry breaking in quantum mechanics

We study the restoration of rotational symmetry of the heavy quark potential obtained from elongated planar and off-axis Wilson loops measured on a 16⁴ lattice at β=5.4 and 5.7. While the rotational symmetry is still distorted at β=5.4 the potential is consistent with rotational symmetry at β=5.7. If we were in the asymptotic scaling region the linear slope would correspond at β=5.7 to a string tension Λ_L/?σ = 0.0074±0.0002.     

Weakly tight functions, their Jordan type decomposition and total variation in effect algebras

In the present paper, we have studied envelopes of a function m defined on a subfamily E (containing 0 and 1) of an effect algebra L. The notion of a weakly tight function is introduced and its relation to tight functions is investigated; examples and counterexamples are constructed for illustration. A Jordan type decomposition theorem for a locally bounded real-valued weakly tight function m defined on E is established. The notions of total variation |m| on the subfamily E and m-atoms on a sub-effect algebra E (along with a few examples of m-atoms for null-additive as well as non null-additive functions) are introduced and studied. Finally, it is proved for a real-valued additive function m on a sub-effect algebra E that, m is non-atomic if and only if its total variation |m| is non-atomic.     

Supersymmetric quantum mechanics in one,two and three dimensions

We discuss a few supersymmetric quantum mechanical models in one, two and three dimensions. In the case of one particle in both two and three dimensions we present some examples where supersymmetry is unbroken and the ground state is many-fold degenerate. Further, we consider the supersymmetric generalization of the nearest neighbour XY model and show that supersymmetry remains unbroken in this case.     

Summability of Laguerre series at the pointx=0

In this paper, the authors prove a theorem on matrix summability of Laguerre series at the point x=0. Various results on Casàro, Nörlund and generalized Nörlund summability method have been deduced.