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The novel heteronuclear complexes [{cis-PtCl (NH₃)(μ-pyrazine)ZnCl (terpy)}](ClO₄)₂ (Pt-L1-Zn) and [{cis-PtCl (NH₃)(μ-4,4′-bipyridyl)ZnCl (terpy)}](ClO₄)₂ (Pt-L2-Zn) (where terpy = 2,2′:6′,2′′-terpyridine, L1 = pyrazine, L2 = 4,4′-bipyridyl) were synthesized and characterized. The pK_a values were determined, and based on them it was established that the π-acceptor ability of the pyrazine bridging ligand is more affective on lower pK_a values. The kinetic measurements of the substitution reactions with biologically relevant ligands, such as guanosine-5′-monophosphate (5′-GMP), inosine-5′-monophosphate (5′-IMP) and glutathione (GSH), were studied at pH 7.4. The reactions were followed under pseudo-first-order conditions by UV–Vis spectrophotometry. The order of reactivity of the investigated biomolecules for the first reaction is 5′-GMP > 5′-IMP > GSH, while for the second is 5′-IMP > GSH. Pt-L1-Zn complex is more reactive than Pt-L2-Zn. The cytotoxic activity of heteronuclear Pt-L1-Zn and Pt-L2-Zn complexes was determined on human colorectal cancer cell line (HCT-116) and human breast cancer cell line (MDA-MB-231). Both complexes significantly reduced cell viability on tested cell lines and exerted significant cytotoxic effects, with better effect on HCT-116 cells than cisplatin, especially after 72 hr (IC₅₀ < 0.52 μM). The Pt-L2-Zn complex showed higher activity against human breast cancer cells (MDA-MB-231) than cisplatin after 72 hr. The higher reactivity toward DNA constituent and significant cytotoxic activity may be attributed to the different geometry, Lewis acidity of different metal centers, as well as, to choice of bridging ligands.     

Quantum dots as a promising agent to combat COVID-19

Approximately every 100 years, as witnessed in the last two centuries, we are facing an influenza pandemic, necessitating the need to combat a novel virus strain. As a result of the new coronavirus (severe acute respiratory syndrome coronavirus type 2 [SARS-CoV-2] outbreak in January 2020, many clinical studies are being carried out with the aim of combating or eradicating the disease altogether. However, so far, developing coronavirus disease 2019 (COVID-19) detection kits or vaccines has remained elusive. In this regard, the development of antiviral nanomaterials by surface engineering with enhanced specificity might prove valuable to combat this novel virus. Quantum dots (QDs) are multifaceted agents with the ability to fight against/inhibit the activity of COVID-19 virus. This article exclusively discusses the potential role of QDs as biosensors and antiviral agents for attenuation of viral infection.     

Lipophilicity and bio‐mimetic properties determination of phytoestrogens using ultra‐high‐performance liquid chromatography

This paper presents lipophilicity and bio‐mimetic property determination of 15 phytoestrogens, namely biochanin A, daidzein, formononetin, genistein, genistein‐4,7‐dimethylether, prunetin, 3,4,7‐trihydroxyisoflavon, 4,6,7‐trihydroxyisoflavon, 4,6,7‐trimethoxyisoflavon, daidzin, genistin, ononin, sissotrin, coumestrol and coumestrol dimethylether. High‐performance liquid chromatography with fast gradient elution and Caco‐2 cell line were used to determine the physicochemical properties of selected phytoestrogens. Lipophilicity was determined on octadecyl‐sylane stationary phase using pH 2.0 and pH 7.4 buffers. Immobilized artificial membrane chromatography was used for prediction of interaction with biological membranes. Protein binding was measured on human serum albumin and α‐1‐acid‐glycoprotein (AGP) stationary phases. Caco‐2 assay was used as a gold standard for assessing in vitro permeability. The obtained results differentiate phytoestrogens according to their structure where aglycones show significantly higher lipophilicity, immobilized artificial membrane partitioning, AGP binding and Caco‐2 permeability compared with glucosides. However, human serum albumin binding was very high for all investigated compounds. Furthermore, a good correlation between experimentally obtained chromatographic parameters and in silico prediction was obtained for lipophilicity and human serum albumin binding, while the somewhat greater difference was obtained for AGP binding and Caco‐2 permeability.     

Environmentally Stable Polymer Gels with Super Deformability and High Recoverability Enhanced by Sub‐5 nm Particles in the Nonvolatile Solvent

It remains challenging to satisfy the combined performances for hydrogels with excellent mechanical behavior, high deformability, and super recoverability under harsh environmental conditions. In this study, we first established a strong polymer network via the crosslinking of polymer chains on the surfaces of sub‐5‐nm calcium hydroxide nanospherulites in ethylene glycol solvent. The organic gel expressed excellent mechanical properties such as a recoverable compressive engineering stress of 249 MPa and an elongation stress of 402 KPa, which was attributed to the uniform nanosized crosslinking structure as characterized by SEM. Moreover, the nonvolatile solvent remained in the gel, meaning that the sample can resist a wide temperature range of ?56 to 100 °C without losing the elastic properties. This novel organic gel could provide promising routes to develop the ideal elastic carriers for wearable devices, smart skin sensors, and damping materials. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 713–721     

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

Markov shifts and topological entropy of families of homoclinic tangles

The existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.     

Stereoselective Insertion of Benzynes into Lawsones: Synthesis of Biologically Important Benzannulated Bicyclo[3.3.0]octanes

An ideal stereoselective insertion of in situ generated benzynes into lawsones through domino formal [2+2]-cycloaddition followed by rearrangement is disclosed. The reaction allowed for the preparation of biologically important benzannulated bicyclo[3.3.0]octanes in good yields and with excellent selectivities by using simple substrates and conditions.