In vitro anti‐proliferative and in silico docking studies of heteroleptic copper(II) complexes of pyridazine‐based ligands and ciprofloxacin

Three heteroleptic copper(II) complexes of the type [Cu(L^1–3)(cf)(ClO₄)] ( 1 – 3 ), where cf = ciprofloxacin, have been synthesized using pyridazine‐based ligands 3‐chloro‐6‐(salicylidenehydrazinyl)pyridazine (HL¹), 3‐chloro‐6‐(4‐diethylaminosalicylidenehydrazinyl)pyridazine (HL²) and 3‐chloro‐6‐(5‐bromosalicylidenehydrazinyl)pyridazine (HL³). Electronic spectral data and magnetic moment values suggest octahedral geometry for the synthesized copper(II) complexes. Electrochemical data of the copper(II) complexes present an irreversible one‐electron reduction wave in the cathodic potential region (E_pc) between ?0.631 and ?0.670 V. Frontier molecular orbital calculations were carried out, and the obtained low‐energy gap supports the bio‐efficacy of the complexes. All the complexes were screened for their in vitro cytotoxicity activity against three human cancerous (breast adenocarcinoma (MCF‐7), hepatoma (HepG‐2) and cervical (HeLa)) and one non‐cancerous (non‐tumorigenic human dermal fibroblast (NHDF)) cell lines using MTT assay, in which complex 2 exhibited higher activity. The apoptosis induction by the complexes was analysed using the Hoechst dye staining method with MCF‐7 cell line, which indicates higher apoptotic activity of complex 2 . A molecular docking study was carried out to ascertain the binding affinity of the synthesized heteroleptic copper(II) complexes with phosphoinositide 3‐kinase gamma (PI3Kγ) receptor.     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

The Riemann–Hilbert analysis to the Pollaczek–Jacobi type orthogonal polynomials

In this paper, we study polynomials orthogonal with respect to a Pollaczek–Jacobi type weight The uniform asymptotic expansions for the monic orthogonal polynomials on the interval (0,1) and outside this interval are obtained. Moreover, near , the uniform asymptotic expansion involves Airy function as , and Bessel function of order α as in the neighborhood of , the uniform asymptotic expansion is associated with Bessel function of order β as . The recurrence coefficients and leading coefficient of the orthogonal polynomials are expressed in terms of a particular Painlevé III transcendent. We also obtain the limit of the kernel in the bulk of the spectrum. The double scaled logarithmic derivative of the Hankel determinant satisfies a σ‐form Painlevé III equation. The asymptotic analysis is based on the Deift and Zhou's steepest descent method.     

Resonances in bounded media: Nonlinear and boundary effects

We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.     

Modification of an implicit approach based on nonstandard rules for structural dynamics analysis

The present study aims to modify a recently suggested implicit approach consisted of the approximate Euler method and closed-form exponential mapping (herein referred to as the Liu scheme) for the dynamic analysis of structures. Such modification has been developed based upon nonstandard rules. The equation of motion is formulated in the augmented dynamic space to apply the exponential mapping as a group preserving scheme. The formulation of the proposed method involves the hyperbolic sine and cosine functions. The method is therefore prone to divergence due to the behavior of the hyperbolic functions in structures with a high ratio of stiffness to mass. In the present study, to consider the properties of the structural equation into the formulation of the time step size and thereby avoid the divergence, a parameter, known as stability parameter, is thus derived from the exact solution of the equation of motion based on nonstandard rules. Embedding this parameter into the proposed method improves its stability. Afterward, for evaluating the performance of the proposed method, it is applied to several structures with different loading patterns while implemented in programing environment of the Matlab software. The results are compared to those of several commonly used numerical methods in structural applications. It is found that the proposed method has acceptable convergence and accuracy, and low time consumption compared to several commonly used methods. Furthermore, its stability is guaranteed by embedding the stability parameter into the proposed method.     

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

Preparation and Characterization of Activated Carbon from Microwave and Conventional Heated Almond Shells Using Phosphoric Acid Activation

Activated carbon production from almond shells using phosphoric acid activation agent was achieved by applying both conventional heating and microwave heating in succession. The morphology and surface properties of activated carbon were studied using thermogravimetric and differential gravimetric analysis, Fourier-transform infrared spectroscopy, scanning electron microscopy, and Brunauer–Emmett–Teller analysis. A surface area of 1128 m²/g was achieved by optimizing the microwave power (500?W), microwave application time (15?minutes), conventional heating time (45?minutes), conventional heating temperature (500?°C), and the phosphoric acid:sample ratio (0.7:1). An adsorption capacity of methylene blue of 148?mg/g and an iodine value of 791?mg/g was obtained for the prepared activated carbon.     

Atomic-Scale Insights into Electrode Surface Dynamics by High-Speed Scanning Probe Microscopy

Atomic-scale processes at electrode surfaces in liquid electrolytes are central elemental steps of electrochemical reactions. Detailed insights into the structure of these interfaces can be obtained with in situ scanning tunnelling and atomic force microscopy. By increasing the time resolution of these methods into the millisecond range, highly dynamic processes at electrode surfaces become directly observable. This review gives an overview of in situ studies with video-rate scanning probe microscopy techniques. Firstly, quantitative investigations into the dynamic behaviour of individual adsorbed atoms and molecules are described. These reveal a complex dependence of adsorbate surface diffusion on potential and co-adsorbed species and provide data on adsorbate–adsorbate and adsorbate–substrate interactions in a liquid environment. Secondly, results on collective dynamic phenomena are discussed, such as molecular self-assembly, the dynamics of nanoscale structures, nucleation and growth, and surface restructuring due to phase-formation processes.