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.     

借助数轴透析金属与盐溶液的反应进程

借助数轴透析“一种金属与溶液中多种盐反应”和“多种金属与溶液中一种盐反应”中溶质与滤渣的组成,直观地将反应进程和结果展现其中,建立思维模型,化难为易,有利于学生掌握与应用。     

BSDE approach to utility maximization with square-root factor processes

We consider the utility-based portfolio selection problem in a continuous-time setting. We assume the market price of risk depends on a stochastic factor that satisfies an affine-form, square-root, Markovian model. This financial market framework includes the classical geometric Brownian motion, CEV model, and Heston’s model as special cases. Adopting the BSDE approach, we obtain closed-form solutions for the optimal portfolio strategies and value functions for the logarithmic, power, and exponential utility functions.     

Single crystal X-ray of 1-[(1,2,4-triazole-4-yl)imino]diacetyl monoxime (L) as a novel triazole and the characterization and biological studies of its chelates of Co2+, Pd2+, and Fe3+

A novel and efficient synthesis of 1-[(1,2,4-triazole-4-yl)imino]diacetyl monoxime ( L ) is described. The advantages of this method are that it is inexpensive, the starting reactants are readily available, and it has good yield and short reaction times. The hull of the product was suggested by elemental analyses, spectral and single crystal X-ray. Novel Co ²⁺ , Pd²⁺, and Fe ³⁺ chelates derived from L were characterized by Fourier transform infrared spectroscopy, suggesting that L acts as bidentate via the two azomethine groups. Tetrahedral geometry for Fe³⁺ and Co²⁺ and square-planar geometry around the Pd²⁺ chelate were suggested depending on the spectral and magnetic data. The results of density functional theory were applied to illustrate the geometry of L towards the metal ions. Coats–Redfern and Horowitz–Metzger methods were applied to investigate the kinetic and thermodynamic parameters of the chelates. Cyclic voltammetry was carried out to study the stability of the Co²⁺ and Fe³⁺ chelates. L and its complexes were tested against three types of cancer cells, antibacterial and antifungal.     

An insight into the potent antioxidant activity of a dithiocarbohydrazone appended cis-dioxidomolybdenum (VI) complexes

In search of antioxidants with enriched potency, the present study focus on the design and synthesis of a dithiocarbohydrazone, H₃TCL derived from thiocarbohydrazide and 3-ethoxysalicylaldehyde and its coordination complexes with molybdenum, viz, [MoO₂(HTCL)D] ( 1 – 2 ) (where D = methanol ( 1 ), DMSO ( 2 )) and [MoO₂(HTCL)D]·DMF (where D = H₂O ( 3 )). The synthesized compounds were characterised by elemental analysis, spectroscopic techniques (FT-IR, UV–vis and ¹H-NMR), conductivity measurements and cyclic voltammetry. Moreover the solid state structures of all the three complexes were established by single crystal X-ray diffraction analysis as mononuclear neutral species in which the molybdenum centre assumes a distorted octahedral geometry. The dithiocarbohydrazone binds to the molybdenum centre through its phenolate oxygen, O(1), azomethine nitrogen, N(1) and thioenolate sulfur, S(1) in a dianionic tridentate mode. The assessment of intermolecular contacts in the crystal arrangement was quantified using Hirshfeld surface analysis. Further the antioxidant potential of the dithiocarbohydrazone, H₃TCL and its molybdenum complexes 1 – 3 were evaluated using 1,1-diphenyl-2-picrylhydrazyl(DPPH), 2,2′-azinobis-3-ethylbenzothiazoline-6-sulfonic acid (ABTS) and total antioxidant assays. The antioxidant activities were then compared with standard antioxidant, L-ascorbic acid. The antioxidant potential of the synthesized compounds were then validated by molecular docking studies. Molecular modelling study was achieved to evaluate the recognition of target compound at the binding pocket of the human antioxidant enzyme, 3MNG. The docking results showed that the complexes selectively bond to the vital amino acids present in the binding pocket of the target enzyme, 3MNG.     

Phytochemical Differentiation of Saffron (Crocus sativus L.) by High Resolution Mass Spectrometry Metabolomic Studies

The metabolite profiling of saffron (Crocus sativus L.) from several countries was measured by using ultra-performance liquid chromatography combined with high resolution mass spectrometry (UPLC-HR MS). Multivariate statistical analysis was employed to distinguish among the several samples of C. sativus L. from Greece, Italy, Morocco, Iran, India, Afghanistan and Kashmir. The results of this study showed that the phytochemical content in the samples of C. sativus L. were obviously diverse in the different countries of origin. The metabolomics approach was deemed to be the most suitable in order to evaluate the enormous array of putative metabolites among the saffron samples studied, and was able to provide a comparative phytochemical screening of these samples. Several markers have been identified that aided the differentiation of a group from its counterparts. This can be important for the selection of the appropriate saffron sample, in view of its health-promoting effect which occurs through the modulation of various biological and physiological processes.