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.     

A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.     

Simultaneous adsorption and dechlorination of carbon tetrachloride using copper nanoparticles@graphene oxide composites

Cu nanoparticles@graphene oxide composites (CGC) were synthesized by a simplistic and effective chemical reduction method. The resulting CGC composites were characterized by X-ray diffraction, scanning electron microscopy with energy dispersive X-ray analysis, transmission electron microscopy, Fourier transform infrared spectroscopy and thermogravimetric analysis. The performance of the CGC composites for dechlorination of carbon tetrachloride was evaluated. The batch investigations indicated that carbon tetrachloride could be almost completely removed by CGC after 75 min. The adsorption isotherm was also discussed. The high removal capacities of CGC with respect to the bare nanoscale zerovalent copper owe to the increased adsorption sites in the composites that are resulted from aggregation inhibition, which leads to the reduced Cu nanoparticles size.     

Synthesis of new water soluble diorganotin(IV) complexes with hydrazones derived from Girard-T reagent as antibacterial and anticancer agents

Three new water-soluble organotin complexes R₂Sn(5-BrSalGT)Cl [R = Ph, Me] and Ph₂Sn(2-OHNaphGT)Cl have been synthesized by the reaction of R₂SnCl₂ (R = Ph or Me) with Schiff bases derived from condensation of Girard-T reagent with 5-bromosalicylaldehyde and 2-naphthaldehyde, (5-BrH₂SalGT)Cl (1) and (2-OHH₂NaphGT)Cl (2). The synthesized compounds have been investigated by elemental analysis, conductometric measurements, IR, ¹H NMR, and ¹¹⁹Sn NMR spectroscopy. These data show that the deporotonated ligand is coordinated to Sn(IV) via ONO atoms and six-coordinate zwitterionic complexes are formed. The ligands and their complexes were investigated for their in vitro toxicity against Gram-positive (Bacillus subtilis and Staphylococcus aureus) and Gram-negative (Escherichia coli and Pseudomonas aeruginosa) bacteria. The results show remarkable antibacterial activity against the studied bacteria. All complexes exhibit more inhibitory effects than the parent ligand. The anticancer activity of all compounds were also performed on HN5 cell line and (2-OHH₂NaphGT)Cl with concentration of 1 mg mL^?1 was found to show higher anticancer activity than other compounds.     

Preparation,characterization and application of 1,4-disulfopiperazine-1,4-diium chloride ([Piper-(SO<Subscript>3</Subscript>H)<Subscript>2</Subscript>]·2Cl) as an efficient dicationic ionic catalyst for the <Emphasis Type="Italic">N</Emphasis>-Boc protection of amines

In this work, 1,4-disulfopiperazine-1,4-diium chloride ([Piper-(SO₃H)₂]·2Cl), as a novel Brönsted acidic ionic catalyst is synthesized and characterized using a series of techniques including FT-IR, TGA, DTA, SEM, pH analysis and Hammett acidity function. This substance can significantly catalyze the N-Boc protection of amines without solvent interference at room temperature. The advantages of this manner are chemoselectivity, short reaction times, suitable yields, excellent yields of the products, without solvent interference and ease of preparation as well as reusability of the catalyst.     

Inhibitory effect of safranal and crocin,two principle compounds of <Emphasis Type="Italic">Crocus sativus</Emphasis>, on fibrillation of lysozyme

A key feature in more than twenty amyloid-related diseases is the aggregation of intra-and/or extracellular misfolded proteins as amyloid fibrils. Therefore, preventing or reversing amyloid aggregation by using of small molecules is considered as useful approaches to the treatment of these diseases. We have evaluated the ability of safranal and crocin, to inhibit amyloid self-assembly of hen egg white lysozyme (HEWL), as an in vitro model system. Structural properties of HEWL in the presence of these compounds were investigated individually using thioflavin T, anilinonaphthalene-8-sulfonic acid fluorescence assays, far-UV circular dichroism and scanning electron microscopy as well as docking method. Our results showed that incubation of HEWL with either crocin or safranal at various concentrations leads a significant inhibition in the rate of amyloid formation. Docking analysis revealed crocin and safranal interact with the central hydrophobic region of lysozyme through van der Waals interaction. Hydroxyl group in crocin through hydrogen bonds connected to the several hydrophilic amino acids of lysozyme, while in safranal there are just one aldehyde group that through hydrogen bonds connected to aspartic acid in lysozyme. It can be concluded that both hydrophobic and hydrophilic groups contribute to lower lysozyme fibril accumulation.     

On the Auslander–Reiten conjecture for Cohen–Macaulay rings and path algebras

In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of d-th syzygy of R-modules of finite length, provided R is an isolated singularity. Based on this result, it is shown that under a mild assumption on the base ring R, satisfying the Auslander–Reiten conjecture behaves well under completion and reduction modulo regular elements. In addition, it will turn out that, if R is a commutative Noetherian ring and 𝒬 a finite acyclic quiver, then the Auslander–Reiten conjecture holds true for the path algebra R𝒬, whenever so does R. Using this result, examples of algebras satisfying the Auslander–Reiten conjecture are presented.     

Determination of brilliant green from fish pond water using carbon nanotube assisted pseudo-stir bar solid/liquid microextraction combined with UV-vis spectroscopy-diode array detection

This paper describes the development of a new design of hollow fiber solid/liquid phase microextraction (HF-SLPME) for determination of brilliant green (BG) residues in water fish ponds. This method consists of an aqueous donor phase and carbon nanotube reinforced organic solvent (acceptor phase) operated in direct immersion sampling mode. The multi-walled carbon nanotube dispersed in the organic solvent is held in the pores and lumen of a porous polypropylene hollow fiber. It is in contact directly with the aqueous donor phase. In this method the solid/liquid extractor phase is supported using a polypropylene hollow fiber membrane. Both ends of the hollow fiber segment are sealed with magnetic stoppers. This device is placed inside the donor solution and plays the rule of a pseudo-stir bar. It is disposable, so single use of the fiber reduces the risk of carry-over problems. Brilliant green (BG) after extraction from the aqueous samples with mentioned HF-SLPME device was determined by ultraviolet-visible spectroscopy with diode array detection (UV-vis/DAD). The absorption wavelength was set to 625 nm (λ(max)). The effect of different variables on the extraction was evaluated and optimized to enhance the sensitivity and extraction efficiency of the proposed method. The calibration curve was linear in the range of 1.00-10,000 μg L(-1) of BG in the initial solution with R(2)=0.979. Detection limit, based on three times the standard deviation of the blank, was 0.55 μg L(-1). All experiments were carried out at room temperature (25±0.5°C).