Some aspects of gravitational quantum mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and free particle wave function. In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.     

The X<Superscript>−</Superscript>···benzohydrazide complexes: the interplay between anion-π and H-bond interactions

The compounds containing the benzohydrazide (BH) nucleus have a variety of biological activities because of various noncovalent intermolecular interactions. The interplay between anion-π and H-bond interactions, which can affect the activity of compounds, has been investigated in ten substituted BH exposed to the chloride ion using the quantum mechanical calculations. The total interaction energy is separated into the anion-π (ΔE _Aπ) and H-bond (ΔE _HB) contributions where both interactions are presented in the complexes. The electron-withdrawing substituents (EWSs) increase |ΔE _Aπ| and decrease |ΔE _HB|, while reversed changes are observed with the electron-donating substituents (EDSs). In addition, the total binding energy (ΔE) becomes more/less negative in the presence of EWSs/EDSs. The synergetic effects of mentioned interactions and substituent effects have also been investigated using the atoms in molecules (AIM), natural bond orbital (NBO) and molecular electrostatic potential (MEP) analyses. A good correlation is found between the energy data and the Hammett constants, the minimum of electrostatic potential (V _min) and the results of population analyses.     

Cholinesulfuric acid ionic liquid catalyzed an eco-friendly synthesis of 2,3-dihydroquinazolin-4(1H)-one in aqueous media

An efficient and straightforward approach to the synthesis of 2,3-dihydroquinazolin-4(1H)-one from 2-aminobenzamide and carbonyl compounds (aldehydes and ketones) using biocompatible choline sulfate-based acidic ionic liquid as a cheap and readily available catalyst in water has been developed. Various 2,3-dihydroquinazolin-4(1H)-one have been prepared using low-cost and environmental friendly solvent and catalyst in good to excellent yields in a shorter reaction time. The choline sulfate catalyst was prepared using a simple method from readily available starting material and was confirmed by ¹H NMR, FTIR, and TGA. The ease of the product separation without organic solvent and column chromatography and the reusability of the acidic ionic liquid catalyst makes this method economically affordable for large-scale synthesis.     

Highly efficient synthesis of dicoumarols and xanthene derivatives in presence of Brønsted–Lewis acidic ionic liquids catalyst

A series of metal chloride-based acidic ionic liquids have been prepared and used as an efficient catalyst in one-pot multicomponent synthesis of biscoumarins and substituted xanthenes derivatives under solvent-free conditions. Among the acidic ionic liquids, N-methylpyrrolidonium zinc chloride (Hnmp/ZnCl₃)-based Brønsted–Lewis acidic ionic liquids were found to be an effective and recyclable catalyst for a one-pot synthesis of biscoumarins through the domino Knoevenagel–Michael reaction of a variety of aldehydes with 4-hydroxycoumarin in short reaction times. The reactions which occur under relatively mild conditions afforded the biscoumarin derivatives employing a very low loading of catalyst in satisfactory isolated yields and high purity after simple work-up. The Brønsted–Lewis acidic ionic liquid catalyst was reused four times without any variation in yield.     

Magnetically nano core–shell Fe<Subscript>3</Subscript>O<Subscript>4</Subscript>@Cu(OH)<Subscript>x</Subscript>: a highly efficient and reusable catalyst for rapid and green reduction of nitro compounds

Magnetically separable nano core–shell Fe₃O₄@Cu(OH)_x with 22 % Cu content was prepared by the addition of sodium hydroxide to a mixture of CuCl₂·2H₂O and nano Fe₃O₄ in water. Characterization of the impregnated copper hydroxide was carried out by X-ray fluorescence (XRF), X-ray diffraction (XRD) atomic absorption spectroscopy (AAS), scanning electron microscopy (SEM), value stream mapping (VSM) and Brunauer–Emmett–Teller (BET) analysis. The core–shell nanocatalyst exhibited the excellent catalytic activity toward reduction of various nitro compounds to the corresponding amines with NaBH₄. All reactions were carried out in H₂O (55–60 °C) within 3–15 min to afford amines in high to excellent yields. Reusability of core–shell Cu(OH)_x catalyst was examined 9 times without significant loss of its catalytic activity.     

Efficient Multi‐component Synthesis of Highly Substituted Imidazoles Utilizing P2O5/SiO2 as a Reusable Catalyst

Phosphorus pentoxide supported on silica gel (P₂O₅/SiO₂) has been used as an efficient and reusable catalyst for the one‐pot pseudo four‐component synthesis of 2,4,5‐trisubstituted imidazoles from benzil or benzoin, aldehydes, and ammonium acetate. It was also used for four‐component preparation of 1,2,4,5‐tetrasubstituted imidazoles from benzil or benzoin, aldehydes, primary amine, and ammonium acetate under thermal solvent‐free conditions. The remarkable features of this new procedure are high conversions, cleaner reaction, simple experimental and work‐up procedures and also the catalyst can be easily separated from the reaction mixture and reused several times without any loss of its activity.     

A two-phase approach for setting targets in DEA with negative data

Conventional DEA models have been introduced to deal with non-negative data. In the real world, in some occasions, we have outputs and/or inputs, which can take negative data. In DEA literature some approaches have been presented for evaluating performance of units, which operate with negative data. In this paper, firstly, we give a brief review of these works, then we present a new additive based approach in this framework. The proposed model is designed to provide a target with non-negative value associated with negative components for each observed unit, failed by other methods. An empirical application in banking is then used to show the applicability of the proposed method and make a comparison with the other approaches in the literature.     

Experimental and Theoretical Assessment of Brittle Fracture in Engineering Components Containing a Sharp V-Notch

A criterion was proposed to predict brittle fracture in engineering components containing sharp V-shaped notches and subjected to mixed mode I/II loading. The criterion, called SV-MTS, was developed based on the maximum tangential stress (MTS) criterion proposed originally for analyzing crack problems. The curves which are obtained from the SV-MTS criterion could be used conveniently to predict the fracture resistance and also the notch bifurcation angle in sharp V-notched components under pure mode II and also mixed mode loading. To evaluate the validity of the proposed criterion, a set of fracture tests were conducted on a new test specimen, called sharp V-notched Brazilian disc (SV-BD), under mixed mode loading conditions. It is shown that the experimental results obtained from PMMA specimens are in very good agreement with the curves of SV-MTS criterion.     

Highly chemoselective reductive amination-coupling by one-pot reaction of aldehydes, HMDS and NaBH4

An efficient and highly chemoselective synthesis of symmetrical secondary amines via reductive amination of aldehydes with inexpensive and commercially available HMDS and sodium borohydride in high to quantitative yields is reported.     

Doppler-free two-photon spectroscopy of the 2ν3 band of SF6

The assignments of most of the observed Doppler-free two-photon spectra of the 2ν₃ band of SF₆ near the P(14)–P(20) lines of a 10-μm CO₂ waveguide laser are reported. The rovibrational and anharmonic constants for this band were obtained, along with ground state constants determined from observed “forbidden” transitions.