New classes of second order difference equations solvable by factorization method

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.     

Biological and catalytic evaluation of Ru(II)‐p‐cymene complexes of Schiff base ligands: Impact of ligand appended moiety on photo‐induced DNA and protein cleavage,cytotoxicity and C‐H activation

Two organometallic Ru(II)‐p‐cymene complexes of the type [Ru(η⁶‐p‐cymene)(L)Cl]PF₆ 1 and 2 , where L is N,N‐bis(4‐isopropylbenzylidene)ethane‐1,2‐diamine (bien, L1 ) or N,N‐bis (pyren‐2‐ylmethylene)ethane‐1,2‐diamine (bpen, L2 ) have been prepared and characterized well. Because of appended pyrenyl groups in coordinated bpen ligand, the complex 2 exhibits higher DNA and protein binding than complex 1 in which isopropylbenzyl groups are incorporated. Interestingly, the luminescent characteristic complex 2 is unique in displaying DNA cleavage after light activation by UVA light at 365 nm through oxygen dependent mechanism. AFM analysis attests the photo‐induced DNA fragmentation ability of complex 2 . Also, the complex 2 cleaves the protein after light exposure in a non‐specific manner suggesting that it can act as a protein photo cleaving agent. In contrast to the trend of DNA and protein interaction of complexes, the complex 1 exhibits cytotoxic activity against human breast carcinoma ( MCF‐7 ) and liver carcinoma ( HepG2 ) with potency higher than that of complex 2 due to enhanced hydrophobicity of isopropyl groups present in p‐cymene and bien ligands. Indeed, complex 2 is inactive against MCF‐7 and HepG2 cancer cell lines even up to 200 μM concentration. The AO/EB staining assay reveals that the complex 1 is able to induce late apoptotic mode of cell death in breast cancer cells, which is further confirmed by inter‐nucleosomal DNA cleavage. Furthermore, the complexes 1 and 2 are evaluated for their catalytic activities and found to be working well for the β‐carboline directed C–H arylation to afford the desired products in good yield (40–47%).     

Ab initio simulations of liquid electrolytes for energy conversion and storage

Understanding physicochemical properties of liquid electrolytes is essential for predicting and optimizing device performance for a wide variety of emerging energy technologies, including photoelectrochemical water splitting, supercapacitors, and batteries. In this work, we review recent progress and open challenges in predicting structural, dynamical, and electronic properties of the liquids using first-principles approaches. We briefly summarize the basic concepts of first-principles molecular dynamics (FPMD), and we discuss how FPMD methods have enriched our understanding of a number of liquids, including aqueous solutions, organic electrolytes and ionic liquids. We also discuss technical challenges in extending FPMD simulations to the study of liquid electrolytes in more complex environments, including the interface between electrolytes and electrodes, which is a key component in many energy storage and conversion systems.     

Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Elasticity and stability of shape-shifting structures

As we enter the age of designer matter — where objects can morph and change shape on command — what tools do we need to create shape-shifting structures? At the heart of an elastic deformation is the combination of dilation and distortion or stretching and bending. The competition between the latter can cause elastic instabilities, and over the last fifteen years, these instabilities have provided a multitude of ways to prescribe and control shape change. Buckling, wrinkling, folding, creasing, and snapping have become mechanisms that when harmoniously combined enable mechanical metamaterials, self-folding origami, ultralight and ultrathin kirigami, and structures that appear to grow from one shape to another. In this review, I aim to connect the fundamentals of elastic instabilities to the advanced functionality currently found within mechanical metamaterials.     

On the swelling behavior of poly(N-Isopropylacrylamide) hydrogels exposed to perfluoroalkyl acids

Per- and polyfluoroalkyl substances (PFAS) have rapidly accumulated in the environment due to their widespread use prior to commercial discussion in the early 21st century, and their slow degradation has magnified concerns of their potential toxicity. Monitoring their distribution is, therefore, necessary to evaluate and control their impact on the health of exposed populations. This investigation evaluates the capability of a simple polymeric detection scheme for PFAS based on crosslinked, thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) hydrogels. Surveying swelling perturbations induced by several hydrotropes and comparable hydrocarbon analogs, tetraethylammonium perfluorooctane sulfonate (TPFOS) showed a significantly higher swelling ratio on a mass basis (65.5 ± 8.8 at 15°C) than any of the other analytes tested. Combining swelling with the fluorimetric response of a solvachromatic dye, nile red, revealed the fluorosurfactant to initiate observable aggregation (i.e., its critical aggregation concentration) at 0.05 mM and reach saturation (i.e., its charge neutralization concentration) at 0.5 mM. The fluorosurfactant was found to homogeneously distribute throughout the polymer matrix with energy dispersive X-ray spectroscopy, marking the swelling response as a peculiar nexus of fluorinated interfacial positioning and delocalized electrostatic repulsion. Results from the current study hold promise for exploiting the physiochemical response of PNIPAM to assess TPFOS's concentration.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

Highly sensitive perylene tetra-(alkoxycarbonyl) based colorimetric and ratiometric probes for fluorine detection

Fluoride anion (F^?) affects environmental, biological, and chemical processes significantly. Therefore, its detection has received increasing attention, and sensitive, effective, and convenient probes for F^? detection need to be developed urgently. In this work, two perylene tetra-(alkoxycarbonyl) (PTAC) based colorimetric and ratiometric probes, P1 and P2, were developed for the detection of F^?. The interactions between F^? and these two probes were investigated by absorption, electrochemistry, ¹H NMR, and density functional methods. Both the two probes were complexed with F^? with a ratio of 1:1. The detection limits of P1 and P2 were 0.22 μM and 0.87 μM, respectively. It was worth noting that the absorption peak of P1 showed a 190 nm red shift when sensing F^?, and P1 is the largest red shift value reported in F^? probes based on PTAC derivatives. This phenomenon was resulted from the unique configuration and deprotonation of P1 that can promote the intramolecular charge transfer (ICT). This strategy provides an example for the development of other ion probes based on D-A type ICT mechanism.