Martin Boundary of a Fine Domain and a Fatou-Naïm-Doob Theorem for Finely Superharmonic Functions

Let Γ be a graph with the doubling property for the volume of balls and P a reversible random walk on Γ. We introduce H¹ Hardy spaces of functions and 1-forms adapted to P and prove various characterizations of these spaces. We also characterize the dual space of H¹ as a BMO-type space adapted to P. As an application, we establish H¹ and H¹- L¹ boundedness of the Riesz transform.     

Platelet-12 lipoxygenase targeting via a newly synthesized curcumin derivative radiolabeled with technetium-99m

Background

One of the most popular techniques for cancer detection is the nuclear medicine technique. The present research focuses on Platelet-12-lipoxygenase (P-12-LOX) as a promising target for treating and radio-imaging tumor tissues. Curcumin was reported to inhibit this enzyme via binding to its active site.

Results

A novel curcumin derivative was successfully synthesized and characterized with yield of 74%. It was radiolabeled with the diagnostic radioisotope technetium-99m with 84% radiochemical yield and in vitro stability up to 6 h. The biodistribution studies in tumor bearing mice confirmed the high affinity predicted by the docking results with a free binding energy value of (ΔG ?50.10 kcal/mol) and affinity (13.64 pki) showing high accumulation in solid tumor with target/non-target ratio >6.

Conclusion

The newly synthesized curcumin derivative, as a result of a computational study on platelet-12 lipoxygenase, showed its excellent free binding energy (?G ?50.10 kcal/mol) and high affinity (13.64 pKi). It could be an excellent radio-imaging agent that targeting tumor cells via targeting of P-12-LOX.

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Graphical abstract This novel curcumin derivative was successfully synthesized and radiolabeled with technetium-99m and biologically evaluated in tumor bearing mice that showed high accumulation in solid tumor with target/non-target ratio >6 confirming the affinity predicted by the docking results. Predicted binding mode of a new curcumin derivative in complex with 12-LOX active site. b Curcumin itself in the 12-LOX active site biological distribution of ^99mTc-curcumin derivative complex in solid tumor bearing Albino mice

     

Hereditary triangular matrix comonads

We recognize Harada’s generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with comodules over comonads. With this conceptual tool at hand, we obtain several of the Harada results with simpler proofs, some of them under more general hypothesis, besides with a characterization of the normal triangular matrix comonads that are hereditary, that is, of homological dimension less than or equal to 1. Our methods rest on a matrix representation of additive functors and natural transformations, which allows us to adapt typical algebraic manipulations from Linear Algebra to the additive categorical setting.     

Characterizing optimal wages in principal-agent problems without using the first-order approach

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA.     

An implementation of a reduced subgradient method via Luenberger-Mokhtar variant

We present an implementable algorithm for minimizing a convex function which is not necessarily differentiable subject to linear equality constraints and to nonnegativity bounds on the variables. The algorithm is based on extending the variant proposed by Luenberger to the nondifferentiable case and using the bundle techniques introduced by Lemaréchal to approximate the subdifferential of the objective function. In particular, at each iteration, we compute a search direction by solving a quadratic subproblem, and an inexact line search along this direction yields a decrease in the objective value. Under some assumptions, the convergence of the proposed algorithm is analysed. Finally, some numerical results are presented, which show that the algorithm performs efficiently.     

Analysis of a meshless method for the time fractional diffusion-wave equation

In this paper a numerical technique is proposed for solving the time fractional diffusion-wave equation. We obtain a time discrete scheme based on finite difference formula. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method and the convergence order of the time discrete scheme is \(\mathcal {O}(\tau ^{3-\alpha })\). Firstly, we change the main problem based on Dirichlet boundary condition to a new problem based on Robin boundary condition and then, we consider a semi-discrete scheme with Robin boundary condition and show when \(\beta \rightarrow +\infty \) solution of the main semi-discrete problem with Dirichlet boundary condition is convergent to the solution of the new semi-discrete problem with Robin boundary condition. We consider the new semi-discrete problem with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that convergence order of the numerical scheme based on Galekin meshless is \(\mathcal {O}(h)\). In the considered method the appeared integrals are approximated using Gauss Legendre quadrature formula. The main aim of the current paper is to obtain an error estimate for the meshless Galerkin method based on the radial basis functions. Numerical examples confirm the efficiency and accuracy of the proposed scheme.     

Determination of Esomeprazole on an Electropolymerized L‐arginine and β‐cyclodextrin Modified Screen Printed Carbon Electrode

The formation of an inclusion complex of the proton‐pump inhibitor (PPI) drug esomeprazole (ESO) with ß‐cyclodextrin (ß‐CD) has been investigated and proven by cyclic voltammetry (CV). The formation constant of the complex was determined. Thereafter, an electropolymerized β‐CD and L‐arginine (L‐arg) modified screen printed carbon electrode (P‐β‐CD‐L‐arg/SPCE) was developed for the determination of ESO using differential pulse adsorptive stripping voltammetry (DPAdSV). A significant enhancement of the peak current was observed when applying an accumulation step due to the effect of adsorption. Electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV) further indicated that the polymer of β‐CD and L‐arg efficiently improved the electron transfer kinetic between analyte and electrode surface. Under the optimized conditions, the oxidation peak current was linearly proportional to the concentration of the drug in the range of 1.0×10^?8 to 1.0×10^?5 M. The DPAdSV method was successfully used to determine the concentrations of the drug in spiked human serum samples.     

Correlation between Electrochemical Impedance and Spectroscopic Measurements in Adsorbing Paraquat on Silver: Application in Underground Water Samples

The electrochemical impedance spectroscopy (EIS) has been used to study the interaction between paraquat and carbon modified by silver (Ag? CPE) and silver particles‐impregnated natural phosphate (Ag/NPh? CPE). This study was developed using spectrophotometry (UV? Vis) and infrared spectroscopy. The resulting interaction was controlled by adsorption at lower concentration (≤1.0×10^?5 mol L^?1) and by diffusion in the opposite case. Both electrodes are used to determining paraquat with a low detection limit (<1.0×10^?12 mol L^?1). The precision expressed as relative standard deviation RSD for the concentration level 1.0×10^?5 mol L^?1 of paraquat, (n=8) were 0.93 % and 1.1 % for Ag/NPh? CPE and Ag? CPE respectively.     

Computational Design,Synthesis and Application of a New Selective Molecularly Imprinted Polymer for Electrochemical Detection

A computational approach was developed to find a suitable functional monomer to design a new molecularly imprinted polymer (MIP), based on which methacyrlic acid (MAA) was selected as a functional monomer to synthesize the molecular imprinted and non‐imprinted polymers. All calculations were carried out using Gaussian 03 software based on the application of Hartree?Fock (HF) method with 6‐31G (d) basis set. The performance of the MIPs prepared with different ratios of MAA was then evaluated using equilibrium rebinding assays. The MIP with the highest binding capacity was chosen as recognition material for the fabrication of new PVC sensors and their responses were compared with each other and with previously reported modifiers in literature. The addition of the ionic surfactant (TFPB) was found to have a synergistic effect on the response mechanism of the electrodes. The results of the MIP modified sensors show that they provide an improved electrode slope, wider pH range and a highly extended life time reaching 7 months compared to 2–4 weeks in case of traditional ion‐exchangers reported in literature, besides, being successfully applied for measurements in biological samples.     

Synthesis and some transformations of 1-methyl-2-(thiophen-3-yl)-1<Emphasis Type="Italic">H</Emphasis>-benzimidazole

1-Methyl-2-(thiophen-3-yl)-1H-benzimidazole was synthesized by the Weidenhagen reaction, followed by N-methylation. Electrophilic substitution reactions of the title compound, in particular nitration, bromination, sulfonation, formylation, and acylation, were studied. The formylation and acylation in polyphosphoric acid afforded mixtures of 2- and 5-substituted isomers at the thiophene ring. The nitration of 1-methyl-2-(thiophen-3-yl)-1H-benzimidazole involved the thiophene ring or both thiophene and benzene fragments, depending on the conditions. Steric arrangement of the heterocycles in the 1-methyl-2-(thiophen-3-yl)-1H-benzimidazole molecule was analyzed by quantum chemical calculations.