Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise on the Gompertzian growth of tumours. Our results are obtained by solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study. We perform simulations to analyze various aspects, of the probability distribution, of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (τ) to the steady-state distribution as a function of (i) of the correlation strength (λ) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (α). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.     

Phase diagram of superconductivity and antiferromagnetism in high-Tc hole-doped cuprates

A phase diagram of superconductivity (SC) and antiferromagnetism (AFM) for hole-doped cuprate superconductors in presence of chemical potential (μ) by using a model Hamiltonian is reported here. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single particle Green functions. The expressions for appropriate single particle correlation function are derived. It is assumed that SC arises due to BCS pairing mechanism and AFM order is simulated by staggered magnetic field in lattices of Cu–O planes. The expressions for SC order parameter, AFM order parameter and dopant concentration are calculated analytically by using Green function technique of D.N. Zubarev. The value of SC gap (z), AFM gap (h) and chemical potential (μ) are solved self consistently for different dopant concentrations (x) by changing model parameters. It is found that a disordered phase appears after antiferromagnetism is destroyed in the range of very small doping. On further increase of the doping, the SC critical temperature first increases, attains a maximum value (?39 K) and then decreases which agrees well with experimental observations for hole-doped cuprates. Our theoretical findings suggest that the AFM coupling plays the vital role of the glue for the Cooper pairs.     

Oxygen atom transfer promoted nitrate to nitric oxide transformation: a step-wise reduction of nitrate → nitrite → nitric oxide

Nitrate reductases (NRs) are molybdoenzymes that reduce nitrate (NO₃⁻) to nitrite (NO₂⁻) in both mammals and plants. In mammals, the salival microbes take part in the generation of the NO₂⁻ from NO₃⁻, which further produces nitric oxide (NO) either in acid-induced NO₂⁻ reduction or in the presence of nitrite reductases (NiRs). Here, we report a new approach of VCl₃ (V³⁺ ion source) induced step-wise reduction of NO₃⁻ in a Co^II-nitrato complex, [(12-TMC)Co^II(NO₃⁻)]⁺ (2,{Co^II–NO₃⁻}), to a Co^III–nitrosyl complex, [(12-TMC)Co^III(NO)]²⁺ (4,{CoNO}⁸), bearing an N-tetramethylated cyclam (TMC) ligand. The VCl₃ inspired reduction of NO₃⁻ to NO is believed to occur in two consecutive oxygen atom transfer (OAT) reactions, i.e., OAT-1 = NO₃⁻ → NO₂⁻ (r₁) and OAT-2 = NO₂⁻ → NO (r₂). In these OAT reactions, VCl₃ functions as an O-atom abstracting species, and the reaction of 2 with VCl₃ produces a Co^III-nitrosyl ({CoNO}⁸) with V^V-Oxo ({V^V O}³⁺) species, via a proposed Co^II-nitrito (3, {Co^II–NO₂⁻}) intermediate species. Further, in a separate experiment, we explored the reaction of isolated complex 3 with VCl₃, which showed the generation of 4 with V^V-Oxo, validating our proposed reaction sequences of OAT reactions. We ensured and characterized 3 using VCl₃ as a limiting reagent, as the second-order rate constant of OAT-2 (k₂^/) is found to be ∼1420 times faster than that of the OAT-1 (k₂) reaction. Binding constant (K_b) calculations also support our proposition of NO₃⁻ to NO transformation in two successive OAT reactions, as K_{b(Co^II–NO2⁻)} is higher than K_{b(Co^II–NO3⁻)}, hence the reaction moves in the forward direction (OAT-1). However, K_{b(Co^II–NO2⁻)} is comparable to K_b{CoNO}⁸, and therefore sequenced the second OAT reaction (OAT-2). Mechanistic investigations of these reactions using ¹⁵N-labeled-¹⁵NO₃⁻ and ¹⁵NO₂⁻ revealed that the N-atom in the {CoNO}⁸ is derived from NO₃⁻ ligand. This work highlights the first-ever report of VCl₃ induced step-wise NO₃⁻ reduction (NRs activity) followed by the OAT induced NO₂⁻ reduction and then the generation of Co-nitrosyl species {CoNO}⁸.

Single metal-induced reduction of NO₃⁻ → {NO₂⁻} → NO via oxygen atom transfer reaction.     

A Zwitterionic Tetrastanna(II) Cyclic Crown

A 12-membered zwitterionic tetrastanna(II) cycle 1 having a crown ether-like topology has been isolated from the deprotonation of 1,1′-methylenediimidazole ( B ) with two equivalents of Sn[N(SiMe₃)₂]₂ ( A ). The solid-state structure and NMR analysis confirms the tetrastanna(II) cycle 1 to be comprised of two stannate(II) and two stannyliumylidene ion pairs in alternating positions of the heterocycle. Computational analysis shows greater nucleophilicity at the proximally located stannate(II) centers. Nonetheless, the tetrastanna(II) cycle 1 remains poorly reactive due to engagement of Sn^II lone pair electrons in intramolecular donor-acceptor interactions. Simple deprotonation reaction between Sn[N(SiMe₃)₂]₂ ( A ) and N-(diisopropylphenyl)imidazole ( C ) in equimolar ratio has led to a stannylene 2 , involving the formation of a Sn−C covalent bond with the anionic imidazol-2-yl carbon center along with the release of NH(SiMe₃)₂. Compound 2 exists as a dimer, where the unsubstituted ring nitrogen atom coordinated intermolecularly to the other stannylene center.     

A Luminescent Zinc(II) Coordination Polymer for Selective Detection of Fe3+ and Cr2O72− in Water and Catalytic CO2 Fixation

Fluorescence-based detection technique using coordination polymer has been considered an attractive alternative over conventional approaches. Herein, a new luminescent zinc(II) coordination polymer, [Zn(4-ABPT)(NIPA)(H₂O)], SSICG-5 , is synthesized by using a Lewis acidic Zn(II) ion, aromatic nitro group containing ligand 5-nitroisophthalic acid (H₂NIPA), and basic −NH₂ rich ligand 3,5-di(pyridine-4-yl)-4H-1,2,4-triazol-4-amine (4-ABPT). SSICG-5 can detect Fe³⁺ and Cr₂O₇²⁻ selectively with a LOD of 0.16 μM and 1.94 μM, respectively. Additionally, carbon dioxide (CO₂) fixation via one-pot CO₂ cycloaddition reaction has significant importance for reduced waste formation, minimizing reaction time and lowering chemical usage. Zn metal centre of SSICG-5 possesses a replaceable coordinated water molecule. The active metal sites combined with the Lewis acidic and basic sites of the ligands make SSICG-5 an ideal bifunctional heterogeneous catalyst for efficient CO₂ cycloaddition reaction under room temperature (RT), solvent-free conditions. Notably, SSICG-5 exhibits near quantitative conversion (turnover number (TON) of 198) of propylene oxide to its carbonate compound under mild reaction conditions.     

Facile soft solution synthesis of delafossite structured Cu(Cr1-xFex)O2 (x = 0, 0.5, and 1) materials and their supercapacitor application

Journal of Solid State Electrochemistry - The investigation of metal oxides with delafossite-type crystal structure for electrochemical energy storage applications is an emerging area....     

Compact stars admitting Finch-Skea symmetry in the presence of various matter fields

In the present study, we investigate the anisotropic stellar solutions admitting Finch-Skea symmetry (viable and non-singular metric potentials) in the presence of some exotic matter fields, such as Bose-Einstein Condensate (BEC) dark matter, the Kalb-Ramond fully anisotropic rank-2 tensor field from the low-energy string theory effective action, and the gauge field imposing \begin{document}$ U(1) $\end{document} symmetry. Interior spacetime is matched with both Schwarzchild and Reissner-N?rdstrom vacuum spacetimes for BEC, KB, and gauge fields. In addition, we study the energy conditions, Equation of State (EoS), radial derivatives of energy density and anisotropic pressures, Tolman-Oppenheimer-Volkoff equilibrium condition, relativistic adiabatic index, sound speed, and surface redshift. Most of the aforementioned conditions are satisfied. Therefore, the solutions derived in the current study lie in the physically acceptable regime.     

Three Component syn-1,2-Arylmethylation of Internal Alkynes**

A Pd-catalyzed three-component syn-1,2-arylmethylation of internal alkynes (ynamides/yne-acetates/alkynes) is described. The readily available and bench stable coupling partners iodo-arenes, and methyl boronic acid are successfully used in this coupling strategy to access the methyl-containing tetra-substituted olefins; the scope is broad showing excellent functional-group tolerance. Notably, the transformation is regio- as well as stereoselective. The biologically relevant motifs (BRM) bearing iodo-arenes and ynamides are also used for the late-stage syn-1,2-arylmethylation of alkynes. Aryl-alkylation, aryl-trideuteriomethylation, alkynyl-methylation, and alkenyl-methylation of ynamides are also presented. The Me-substituted alkenes are further transformed into synthetically important β-amino-indenones and α-fluoro-α′-methyl ketones.     

Harnessing Deep Neural Networks to Analyze Multi-Channel Anion Sensing Characteristics of a Ru(II)-Pyrazolyl-Bis(Benzimidazole) Complex

In this work, the anion-responsive conduct of a Ru(II)-bipyridine complex incorporating pyrazolyl-bis (benzimidazole) ligand is thoroughly investigated in acetonitrile and water via absorption and emission spectroscopy as well as by square-wave voltammetry (SWV). Substantial alteration of the photo-redox behavior of the complex is observed in the presence of the selected anions. The free form of the complex exhibits emission indicating the “on-state”, while inclusion of anions leads to quenching of emission and represents the “off-state”. The restoration of the initial state of the complex is feasible in the presence of acid and the process is reversible and can be recycled. In essence, the complex functions as anion- and acid-responsive molecular switches. Additionally, we applied herein neural network based deep learning methodologies, viz. Artificial Neural Networks (ANNs) and Adaptive Neuro-Fuzzy Inference System (ANFIS)} for thorough analysis and fully understand the multi-channel anion sensing behavior of the complex.