Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp has been investigated. It is known that a laser beam shows an oscillatory self-focusing and defocusing behavior with the propagation distance. To overcome the defocusing, localized upward plasma density ramp is introduced, so that the laser beam attains a minimum spot size and maintains it with only a mild ripple. The density ramp could be important for the self-focusing of a Hermite–Gaussian laser by choosing the laser and plasma parameters appropriately. Self-focusing becomes stronger as the propagation distance increases. The behavior of beam-width parameters with the distance of propagation is presented graphically.     

Linear and nonlinear nonlocal boundary value problems for differential-operator equations

This study focuses on nonlocal boundary value problems (BVPs) for linear and nonlinear elliptic differential-operator equations (DOEs) that are defined in Banach-valued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal L_p -regularity and Fredholmness of linear BVPs, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness and maximal smoothness of solutions of nonlocal BVPs for nonlinear DOEs are shown. These results are applied to nonlocal BVPs for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties.     

Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.     

On the growth and approximation of entire functions represented by Laplace–Stieltjes’ transformation

In the present paper, we obtain the characterization of various growth parameters of an entire function F(s) represented by Laplace–Stieltjes transformation in terms of the rate of decrease of \(E_n ( {F,\beta } ),\)where \(E_n ( {F,\beta } )\) represents the error in approximating the function F(s) by exponential polynomials.     

Biomolecular docking,antimicrobial and cytotoxic studies on new bidentate schiff base ligand derived metal (II) complexes

Three new metal complexes [Cu(L)₂] (1), [Co(L)₂] (2) and [Zn(L)₂] (3) have been prepared by the reaction of hydrated salts of metal (II) acetate with new Schiff base ligand HL, [2‐((4‐(dimethylamino)phenylimino)methyl)‐4,6‐di‐t‐butylphenol] and characterized by different physico‐chemical analyses such as elemental analysis, single XRD, ¹H NMR, FTIR and UV–Vis spectroscopic techniques. Their biomolecular docking, antimicrobial and cytotoxicity studies have also been demonstrated. The proposed structure of Schiff base ligand HL and complex 2 are confirmed by Single crystal X‐ray crystallography study. This analysis revealed that metal (II) complexes remain in distorted tetrahedral coordination environments. The electronic properties such as HOMO and LUMO energies are carried out by gaseous phase DFT/B3LYP calculations using Gaussian 09 program. Complex 1 showed a good binding propensity to the DNA and HSA, during the assessment of docking studies. Schiff base ligand HL and its metal (II) complexes, 1–3 screened for their in vitro antimicrobial activities using the disc diffusion method against selected microbes. Complex 1 shows higher antimicrobial activity than complexes 2, 3 and Schiff base ligand HL. According to the results obtained from the cytotoxic studies, Schiff base ligand HL and its metal (II) complexes 1–3 have better cytotoxicity against MCF‐7 cell lines with potency higher than the currently used chemotherapeutic agent cyclophosphamide.     

Methods and approaches for determination and enantioseparation of (RS)‐propranolol

Propranolol, a β‐adrenergic receptor antagonist, is a chiral compound that is marketed as a racemate, but only the (S)‐(?)‐enantiomer is responsible for the β‐adrenoceptor blocking activity. Different chromatographic methods have been applied for separation and determination of enantiomers of (RS)‐propranolol. In this article a review is presented on different liquid chromatographic methods used for enantioseparation of (RS)‐propranolol, using both HPLC and TLC. In addition, some aspects of enantioseparation under achiral phases of liquid chromatography have been briefly mentioned.     

Comparative evaluation of antibacterial potentials of nano cobalt oxide with standard antimicrobials

Development of suitable potent antimicrobial is the urgent need of modern era to cope up the problem of antimicrobial resistance. The applications of nanotechnology in metal oxides have shown favorable effects to some extent in this area. Thus, the present study was investigated to evaluate the antibacterial properties of cobalt oxide (Co₃O₄) nanoparticles at different concentrations and their comparison with standard antimicrobials i.e. tetracycline and gentamicin. Nanoparticles were synthesized and characterized by standard techniques. The antibacterial potentials of Co₃O₄ nanoparticles against S. aureus and E. coli were determined at various concentrations. The maximum zone of inhibitions of Co₃O₄ nanoparticles against S. aureus and E. coli at 500 μg/ml were 21.17 mm and 24.00 mm, respectively. The Co₃O₄ nanoparticles seemed more effective than gentamicin against S. aureus and E. coli. The nanoparticles with respect to tetracycline showed higher than 1 activity index at ≥ 125 μg/ml for E. coli and ≥31.25 μg/ml for S. aureus. It was also higher than 1 at all compared concentrations with respect to gentamicin against both bacteria. In conclusion, Co₃O₄ nanoparticles seemed to have potent antibacterial potential and these might be very helpful to replace the conventional antimicrobials to solve the problem of antibacterial resistance.     

Synthesis and computational studies of potent antimicrobial and anticancer indolone scaffolds with spiro cyclopropyl moiety as a novel design element

The indolones nucleus is the central core to develop new effective anticancer agents and its substitution at the 3-position can affect antitumor activity, 3-spirocyclopropyl-2-oxindoles have attracted the scientist's community to design and develop expedition's strategies towards their construction and explore the potential of this useful scaffold with their newer derivatives in medicinal world. The present paper describes the synthesis of 3-spirocyclopropyl-2-indolone derivatives in three steps via synthesis of ylide leading to methylene-indolinones followed by the formation of the final product spirocyclopropyl oxindole derivatives with improved yields. In this milieu we considered motivating to advance exploration the biological potencies and computational studies of our newly synthesized molecules. The aimed target molecules were screened for antimicrobial and anticancer activities where they exhibited substantial effective antimicrobial activities. Amongst them, potent compound, bromospirocyclopropyl indolone, 6d displayed encouraging MIC ranging from 0.007 to 0.49 μg/mL for gram positive microbes and also substantial anticancer activity with an IC₅₀ of 11.5 μg/mL. Finally, the computational modelling studies were performed to explore structure-activity relationship analysis. Active site of receptor protein shows docking scores of these molecules as - 5.78 kcal/mol and ?5.097 kcal/mol for the docked target proteins. The binding energy of the best score is found to be ?41.67 kcal/mol to ?44.67 kcal/mol. Thus, the present paper efficaciously validated spirocyclopropyl indolone framework for drug candidates as potent anticancer as well as antimicrobial compounds.