On the generalized weighted Sobolev inequality

Let $\Omega$ be an open subset of $\mathbb{R}^N.$ We identify various classes of Young functions $\Phi,\,\Psi$, and weight functions $g\in L^1_\text{loc}(\Omega)$ so that the following generalized weighted Sobolev inequality holds: \begin{equation*}\label{ineq:Orlicz} \Psi^{-1}\left(\int_{\Omega}|g(x)|\Psi( |u(x)| )dx \right)\leq C\Phi^{-1}\left(\int_{\Omega}\Phi(|\nabla u(x)|) dx \right),\,\,\,\forall\,u\in \mathcal{C}^1_c(\Omega), \end{equation*} for some $C>0$. As an application, we study the existence of non-negative solutions for certain nonlinear weighted eigenvalue problems.Comment: 27 page

Constraints on the Parameterized Deceleration Parameter in FRW Universe

Confirmation of accelerated expansion of the universe probed the concept of dark energy theory, and since then, numerous models have been introduced to explain its origin and nature. The present work is based on reconstructing dark energy by parametrization of the deceleration parameter in the FRW universe filled with radiation, dark matter, and dark energy. We have chosen some well-motivated parametrized models 1-3 in an attempt to investigate the energy density in terms of deceleration parameters by estimating the cosmological parameters with the help of different observational datasets. Also, we have introduced a new model 4 for the parametrization of the deceleration parameter. Then we analyzed the cosmography parameters using the best-fit values of the parameters. Using the information criteria, we have examined the viability of the models

Origin of Ferroelectricity in Orthorhombic LuFeO3_3

We demonstrate that small but finite ferroelectric polarization ($\sim$0.01 $\mu$C/cm$^2$) emerges in orthorhombic LuFeO$_3$ ($Pnma$) at $T_N$ ($\sim$600 K) because of commensurate (k = 0) and collinear magnetic structure. The synchrotron x-ray and neutron diffraction data suggest that the polarization could originate from enhanced bond covalency together with subtle contribution from lattice. The theoretical calculations indicate enhancement of bond covalency as well as the possibility of structural transition to the polar $Pna2_1$ phase below $T_N$. The $Pna2_1$ phase, in fact, is found to be energetically favorable below $T_N$ in orthorhombic LuFeO$_3$ ($albeit$ with very small energy difference) than in isostructural and nonferroelectric LaFeO$_3$ or NdFeO$_3$. Application of electric field induces finite piezostriction in LuFeO$_3$ via electrostriction resulting in clear domain contrast images in piezoresponse force microscopy.Comment: 12 pages, 8 figure

Reactivity of electrochemically synthesised zinc nanofiber in facile reduction of nitro and azide compounds

1076-1083Electrochemistry is used in generation of metallic nano zinc wire from aqueous zinc chloride. For this electrochemical process we have designed a unit galvanic cell. During the electrochemical process both aliphatic and aromatic nitro and azide compounds undergo facile reduction to the corresponding amines. ZnCl2 is used as stoichiometric reagent and causes electrochemical deposition of zinc in cathode. During the process wire shaped nano zinc architecture has been formed in cathode which is supposed to be the active reagent for reduction. The cathode deposited material has been characterised by powder XRD, XPS, FESEM, HRTEM, EDX, SQUID etc. The corresponding amines are prepared in good yields. Both zinc salts and aqueous solution can be recycled

Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet

Collective spin-wave excitations-magnons-in a quantum Hall ferromagnet are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. Detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if these signals are equal the magnon detection remains elusive. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is generated by equilibration (partial or full, depending on the bias voltage) between edge channels and propagating magnons. Our model, which agrees with experimental observations, also allows us to pinpoint the regime of ballistic magnon transport in our device

"The fruits of independence": Satyajit Ray, Indian nationhood and the spectre of empire

Challenging the longstanding consensus that Satyajit Ray's work is largely free of ideological concerns and notable only for its humanistic richness, this article shows with reference to representations of British colonialism and Indian nationhood that Ray's films and stories are marked deeply and consistently by a distinctively Bengali variety of liberalism. Drawn from an ongoing biographical project, it commences with an overview of the nationalist milieu in which Ray grew up and emphasizes the preoccupation with colonialism and nationalism that marked his earliest unfilmed scripts. It then shows with case studies of Kanchanjangha (1962), Charulata (1964), First Class Kamra (First-Class Compartment, 1981), Pratidwandi (The Adversary, 1970), Shatranj ke Khilari (The Chess Players, 1977), Agantuk (The Stranger, 1991) and Robertsoner Ruby (Robertson's Ruby, 1992) how Ray's mature work continued to combine a strongly anti-colonial viewpoint with a shifting perspective on Indian nationhood and an unequivocal commitment to cultural cosmopolitanism. Analysing how Ray articulated his ideological positions through the quintessentially liberal device of complexly staged debates that were apparently free, but in fact closed by the scenarist/director on ideologically specific notes, this article concludes that Ray's reputation as an all-forgiving, ‘everybody-has-his-reasons’ humanist is based on simplistic or even tendentious readings of his work

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Reactivity of Electrochemically Synthesised Nano Zinc Wire in Facile Reduction of Nitro and Azide Compounds

Electrochemistry is used in generation of metallic nano zinc wire from aqueous zinc chloride. For this electrochemical process we designed a unit galvanic cell. During the electrochemical process both aliphatic and aromatic nitro and azide compounds undergo facile reduction to the corresponding amines. ZnCl2 is used as stoichiometric reagent and causes electrochemical deposition of zinc in cathode. During the process wire shaped nano zinc architecture has been formed in cathode which is supposed to be the active reagent for reduction. The cathode deposited material has been characterised by powder XRD, XPS, FESEM, HRTEM, EDX, SQUID etc. The corresponding amines are prepared in good yields. Both zinc salts and aqueous solution can be recycled

Making and breaking of Sn-C and In-C bonds in situ: the cases of allyltins and allylindiums

This article does not have an abstract

Pd<SUP>0</SUP>/Sn<SUP>II</SUP> promoted Barbier-type allylation and crotylation of sulfonimines

A one-pot Barbier protocol is described for the facile formation of homoallyl sulfonamides from sulfonimines and allyl or crotyl bromide in the presence of SnCl2, and catalytic Pd2(dba)3&#183;CHCl3 at room temperature