Asymptotic Normality of a Combined Regression Estimator

In this paper, we propose a combined regression estimator by using a parametric estimator and a nonparametric estimator of the regression function. The asymptotic distribution of this estimator is obtained for cases where the parametric regression model is correct, incorrect, and approximately correct. These distributional results imply that the combined estimator is superior to the kernel estimator in the sense that it can never do worse than the kernel estimator in terms of convergence rate and it has the same convergence rate as the parametric estimator in the case where the parametric model is correct. Unlike the parametric estimator, the combined estimator is robust to model misspecification. In addition, we also establish the asymptotic distribution of the estimator of the weight given to the parametric estimator in constructing the combined estimator. This can be used to construct consistent tests for the parametric regression model used to form the combined estimator.     

Density and Correlations in Large One and Three Dimensional Systems of Fermions

The density and correlations are studied for a system of fermions moving in an average harmonic oscillator potential in one and three dimensions when the number of fermions are large. The technique is based on the use of Mehler's formula for the product of two Hermite functions and con-. tour integrations. Wigner transform is then calculated using this technique. It is shown that it becomes a step function when number of fermions become large. By integrating out momenta, an expression for the density of fermions is derived. Two-particle correlation function is studied in detail. Dyson's type of correlations for a system of nucleons is studied. The connection between one dimensional system of fermions and eigenvalues of a random Hermitean Hamiltonian is shown. The Coulomb energy difference of isobars is studied using nucleon density and correlations.     

Modification of the spectra of correlated charm-anticharm quark pairs in the quark-gluon plasma

Heavy quarks play an important role in probing the properties of strongly interacting quark-gluon plasma(QGP)created in ultra-relativistic heavy-ion collisions.We study the interactions of single heavy(charm)quarks and correlated charm and anticharm(ccˉ)quark pairs with the medium constituents of QGP by performing fireball+Langevin simulations of the pertinent Brownian motion with elastic collisions.Besides studying the traditional observables,the nuclear modification factor and the elliptic flow of single heavy quarks in QGP for different thermal relaxation rates,we also study the broadening of the azimuthal correlations of charm and anticharm quark pairs in the QGP medium for different relaxation rates and transverse momenta classes.We quantified the smearing of ccˉpair azimuthal correlations with an increasing thermal relaxation rate:while the(nearly)back-to-back correlations among ccˉpairs are almost completely washed out at low transverse momentum(pT),these correlations at high pT largely survive the pair diffusion.This provides a novel observable for diagnosing the properties of QGP.     

Significance of activation energy and Wu's slip features in Cross nanofluid with motile microorganisms

The current article investigates the impact of the bioconvection in an unsteady flow of magnetized Cross nanofluid with gyrotactic microorganisms and activation energy over a linearly stretched configuration. The analysis has been performed by utilizing the realistic Wu's slip boundary and zero mass flux conditions. The effects of nonlinear thermal radiation and the activation energy are also addressed. The governing flow equations are deduced to a dimensionless form by considering suitable transformations which are numerically targeted via a shooting algorithm. The physical visualization of each physical parameter governing the flow problem has been displayed graphically for distribution of velocity, temperature, concentration and motile microorganisms. The numerical treatment for the variation of skin friction coefficient, local Nusselt number, local Sherwood number and motile density number is performed in tabular forms.     

Thermoelectricity Generation and Electron–Magnon Scattering in a Natural Chalcopyrite Mineral from a Deep‐Sea Hydrothermal Vent

Current high‐performance thermoelectric materials require elaborate doping and synthesis procedures, particularly in regard to the artificial structure, and the underlying thermoelectric mechanisms are still poorly understood. Here, we report that a natural chalcopyrite mineral, Cu_1+xFe_1?xS₂, obtained from a deep‐sea hydrothermal vent can directly generate thermoelectricity. The resistivity displayed an excellent semiconducting character, and a large thermoelectric power and high power factor were found in the low x region. Notably, electron–magnon scattering and a large effective mass was detected in this region, thus suggesting that the strong coupling of doped carriers and antiferromagnetic spins resulted in the natural enhancement of thermoelectric properties during mineralization reactions. The present findings demonstrate the feasibility of thermoelectric energy generation and electron/hole carrier modulation with natural materials that are abundant in the Earth’s crust.     

Synthesis of 7-hydroxy-6H-benzo[c]chromen-6-ones based on a ‘[3+3] cyclization/domino retro-Michael-aldol-lactonization’ strategy

The TiCl₄-mediated [3+3] cyclization of 2,4-bis(trimethylsilyloxy)penta-1,3-diene with 3-silyloxyalk-2-en-1-ones afforded 2-acetylphenols, which were transformed into functionalized chromones. The Me₃SiOTf-mediated condensation of the latter with 1,3-bis(silyl enol ethers) and subsequent domino ‘retro-Michael-aldol-lactonization’ reaction afforded 7-hydroxy-6H-benzo[c]chromen-6-ones.     

Reply to the comment on ‘Modified perturbation series for the anharmonic oscillator using linearization technique’

It is pointed out that the value of the perturbed energy calculated in the comment by Rath and Pattnayak, is incorrect. When the coupling parameter has the value unity, the energy up to second order of perturbation theory is 0.801 compared to its exact value of 0.804. The suggested split of the Hamiltonian into an unperturbed and perturbed part does not seem to be of any use as the unperturbed part contains anharmonic terms.     

In vitro enzyme inhibition activities of crude ethanolic extracts derived from medicinal plants of Pakistan

Twenty two crude ethanolic extracts from 14 indigenous medicinal plants were subjected to enzyme inhibition screening against acetylcholinesterase (AChE), butyrylcholinesterase (BChE) and lipoxygenase enzymes (LO). Three extracts showed activity against AChE, nine extracts were found to be active against BChE and four extracts inhibited the enzyme LO. The most significant inhibition activities (> or =50%) were found in extracts derived from Aloe vera (leaves), Alpinia galanga (rhizome), Curcuma longa (rhizome), Cymbopogon citratus (leaves), Ocimum americanum (leaves), Ocimum americanum (stem) and Withania somnifera (roots).     

Free-Standing CoO-POM Janus-like Ultrathin Nanosheets

A single-step solution-based strategy is used to obtain 2D Janus-like free-standing ultrathin nanosheets build from two structurally unrelated species, that is, polyoxomolybdate (POM) and CoO. A controlled 2D-to-1D morphological transition was achieved by judiciously adjusting the solvent choice. These POM-CoO heterostructures can behave as an ideal catalyst for the epoxidation of styrene. Benefiting from their amphiphilic nature, these 2D POM-CoO nanosheets have also been used as surfactant to emulsify immiscible solvents. It is anticipated that structurally diverse polyoxometalates will offer promise as design elements for variety of structurally and compositionally tunable van der Waals integrated heteromaterials having a broad range applications.