Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms

The Ramanujan Journal - Recently, Andrews and Yee studied two-variable generalizations of two identities involving partition functions $$p_\omega (n)$$ and $$p_\nu (q)$$ introduced by Andrews,...     

Synthesis,structural characterization and DNA binding affinity of new bioactive nano‐sized transition metal complexes with sulfathiazole azo dye for therapeutic applications

The azo dye ligand 4‐(5‐chloro‐2‐hydroxyphenylazo)‐N‐thiazol‐2‐ylbenzenesulfonamide (H₂L) formed by the coupling reaction of sulfathiazole and p‐chlorophenol was synthesized and characterized using elemental analysis and Fourier transform infrared (FT‐IR) as well as UV–visible spectra. Nano‐sized divalent Cu, Co, Ni, Mn and Zn complexes of the synthesized azo dye ligand were prepared and investigated using various spectroscopic and analytical techniques. Elemental and thermal analyses indicated the formation of the Cu(II), Ni(II) and Mn(II) complexes in a molar ratio of 1:2 (L:M) while Co(II) and Zn(II) complexes exhibited a 1:1 (M:L) ratio. FT‐IR spectral studies confirmed the coordination of the ligand to the metal ions through the phenolic hydroxyl oxygen, azo nitrogen, sulfonamide oxygen and/or thiazole nitrogen. The geometric arrangements around the central metal ions were investigated applying UV–visible and electron spin resonance spectra, thermogravimetric analysis and molar conductance measurements. X‐ray diffraction patterns revealed crystalline nature of H₂L and amorphous nature of all synthesized complexes. Transmission electron microscopy images confirmed nano‐sized particles and their homogeneous distribution over the complex surface. Antibacterial, antifungal and antitumour activities of the investigated complexes were screened compared with familiar standard drugs to confirm their potential therapeutic applications. The Cu(II) complex showed IC₅₀ of 3.47 μg ml^?1 (5.53 μM) against hepatocellular carcinoma cells, which means that it is a more potent anticancer drug compared with the standard cisplatin (IC₅₀ = 3.67 μg ml^?1 (12.23 μM)). Furthermore, the Co(II), Ni(II), Cu(II) and Zn(II) complexes displayed IC₅₀ greater than that of an applied standard anticancer agent (5‐flurouracil) towards breast carcinoma cells. Hence, these complexes can be considered as promising anticancer drugs. The mode of binding of the complexes with salmon serum DNA was determined through electronic absorption titration and viscosity studies.     

Spectral decomposition of the cubic Casimir operator associated with Jacobi group

The Ramanujan Journal - By means of the Hermite-theta function, we study the spectral resolution of the cubic Casimir operator on a fundamental domain of the Jacobi group.     

On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems

Numerical Algorithms - The problem of shifted linear systems is an important and challenging issue in a number of research applications. Krylov subspace methods are effective techniques for...     

Solving the incompressible fluid flows by a high-order mesh-free approach

In this paper, we propose for the first time to extend the application field of the high-order mesh-free approach to the stationary incompressible Navier-Stokes equations. This approach is based on a high-order algorithm, which combines a Taylor series expansion, a continuation technique, and a moving least squares (MLS) method. The Taylor series expansion permits to transform the nonlinear problem into a succession of continuous linear ones with the same tangent operator. The MLS method is used to transform the succession of continuous linear problems into discrete ones. The continuation technique allows to compute step-by-step the whole solution of the discrete problems. This mesh-free approach is tested on three examples: a flow around a cylindrical obstacle, a flow in a sudden expansion, and the standard benchmark lid-driven cavity flow. A comparison of the obtained results with those computed by the Newton-Raphson method with MLS, the high-order continuation with finite element method, and those of literature is presented.     

Descent Perry conjugate gradient methods for systems of monotone nonlinear equations

Numerical Algorithms - In this paper, we present a family of Perry conjugate gradient methods for solving large-scale systems of monotone nonlinear equations. The methods are developed by combining...     

Spectroscopic investigation,DFT, fluorescence,molecular docking and biological studies of divalent and trivalent binuclear complexes prepared from benzoyl thiosemicarbazide derivative of 2‐benzylmalonohydrazide

The binuclear Cr (III), Mn (II) and Fe (III) complexes of N,N′‐(2,2′‐(2‐benzylmalonyl)bis (hydrazine‐1‐carbonothioyl))dibenzamide (H₄BPCD), which derived from the combination of 2‐benzylmalonohydrazide suspension with benzoyl‐isothiocyanate, have been isolated and investigated by the necessary analytical and spectroscopic techniques. The IR studies show that H₄BPCD dispose as a mono‐negative hexadentate ligand (NOS)₂ towards Mn (II) ion and tetra‐negative hexadentate (NOS)₂ towards both Cr (III) and Fe (III) ions. The values of molar conductance in DMSO suggested the non‐electrolytic nature for all complexes. The magnetic measurements and the electronic transitions data confirmed the hexa‐coordinate geometry of complexes. The DFT geometry optimization of all compounds and IR comparative study of both theoretical and experimental of H₄BPCD were carried out. Moreover, the H₄BPCD and its Cr (III) complex displayed intra ligand (π → π*) fluorescence emission spectra which corroborate their photoactive nature. The coordinated and crystalline water molecules have been investigated by (TG/DTG) studies. The kinetic and thermodynamic parameters were computed using Horowitz‐ Metzger, Coats‐Redfern and Broido methods. Biological studies of DNA binding, minimum inhibitory concentration, in vitro determination of SOD‐like activity and MTT‐cytotoxicity assay as well as molecular docking studies were tested for the ligand and its complexes.     

Synthesis and Inhibitory Effect of Some Indole-Pyrimidine Based Hybrid Heterocycles on α-Glucosidase and α-Amylase as Potential Hypoglycemic Agents

The Michael addition reaction of barbituric acid with chalcones incorporating the indole scaffold was achieved by using a highly efficient bimetallic Iron–palladium catalyst in the presence of acetylacetone (acac). This catalytic approach produced the desired products in a simple operation and low catalyst loading with acceptable yield of the new hybrids. All tested compounds were subjected for biological activity on α-glucosidase and α-amylase. The results revealed that all synthesized compounds exhibited very good activity against both enzymes when compared to positive control (acarbose). Moreover, compound 5o showed the best activity whereas its IC₅₀ (μM) are 13.02+0.01 and 21.71+0.82 for α-glucosidase and α-amylase respectively. Both compounds 5o and 5l exhibited high similarity in binding mode and pose with amylase protein (4UAC). The obtained data may be used for developing potential hypoglycemic agents.     

Serum Zinc Measurement,Total Antioxidant Capacity,and Lipid Peroxide Among Acute Coronary Syndrome Patients With and Without ST Elevation

Applied Biochemistry and Biotechnology - Despite advances in the management of cardiovascular diseases, acute coronary syndrome (ACS) remains the leading cause of death worldwide. ACS is associated...