Crystal structure of bis-N,N′-p-chlorosalicylideneamine-1,2-diaminobenzene

The crystal structure of the title compound, C₂₀H₁₄N₂O₂Cl₂, has been determined by single crystal X-ray diffraction techniques. It crystallizes in the orthorhombic system witha=7.532(3)Å,b=18.563(2)Å,c=25.089(3)Å, space groupPbca,V=3507.9(3)ų,Z=8,F(000)=1584.D _x =1.459 g cm^–3,M=385.3 a. m. u., (MoK)=0.7107 Å, =3.35 cm^–1,T=297°K,R=0.086,R _w =0.049 for 2119 unique diffractometer data. The molecules are linked by van der Waals forces.     

Structure of N-(2-thiophenyl)-salicylaldimino-diethylamino nickel(II) complex

N-(2-thiophenyl)-salicylaldimino-diethylamino nickel(II) complex crystallizes in the orthorhombic crystal system witha=19.089(4),b=14.268(7),c=12.091(4) Å, space group Pbca,Z=8, andD _x =1.449 g cm^–3. The central nickel atom is coordinated with S, O, and N atoms. The coordination plane is nearly planar and nearly perpendicular to the diethylamine plane which consist of N(2), C(14), C(15), C(16), and C(17).     

The crystal structure of a N-(2-thiophenyl)-salicylaldiminopiperidino nickel(II) complex

The crystal and molecular structure of the title complex, C₁₈H₁₉N₂OSNi, has been determined by direct methods. The compound crystallizes in monoclinic crystal system witha=11.968(1),b=12.182(1),c=12.399(1) Å, =115.23(1)°, space group P2₁/n. Nickel is in a slightly distorted square-planar environment of two nitrogens [1.881(2) and 1.952(2) Å] and one oxygen [1.856(3) Å] and one sulphur [2.138(2) Å] atom. Ni is 0.005 Å out of the plane of its ligands.     

Crystal structure of tris-(2,2′,2″)-triaminoethylamino-salicylidene iron(III) complex

Tris-(2,2,2)-triaminoethylamino-salicylidene iron(III) crystallizes in the monoclinic crystal system witha=7.766(2),b=25.423(5),c=13.318(5) Å, =118.04(3)°, space group P2₁/c,V=2320.8(6) ų,Z=4, andD _x=1.464 g cm^–3. The center of the axially distorted octahedron is occupied by the Fe atom which is coordinated by six donor nitrogen and oxygen atoms infac positions. The planes of coordinated atoms (N and O) with the Fe(III) atom are almost planar and the maximum elevated atom from these planes is O(1) (–0.1065 Å).     

A Proof of a Conjecture on the Convolution of Harmonic Mappings and Some Related Problems

Ukrainian Mathematical Journal - Recently, Kumar, et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They verified this...     

Synthesis,spectroscopic characterization,crystal structure,density functional theory studies and biological properties of coordination complex Ni(II) 2-fluorobenzoate with 3-hydroxypyridine

A novel Ni(II) complex containing 2-fluorobenzoate and 3-hydroxypyridine ligands was synthesized and characterized using elemental analysis, Fourier transform infrared (FT-IR) spectroscopy and single-crystal X-ray diffraction. FT-IR peaks show that the carboxylate group from 2-fluorobenzoate has a monodentate coordination mode. The coordination environment around the Ni²⁺ ion is of distorted octahedral geometry. The octahedral geometry consists of a total of four oxygen atoms from two carboxylate groups of two fluorobenzoate anions, two water molecules and two nitrogen atoms from two 3-hydroxypyridine ligands. The complex shows excellent inhibitory effects against some metabolic enzymes. K_i values for the complex were found as 108.17 ± 25.63, 124.88 ± 36.20, 28.11 ± 2.87, 20.95 ± 5.65 and 32.63 ± 9.67 μM against human carbonic anhydrase I, human carbonic anhydrase II, α-glycosidase, acetylcholinesterase and butyrylcholinesterase, respectively. In addition, geometry optimization and vibration frequencies were calculated, and single point energy was studied based on optimization. Experimental and theoretical data were compared. The B3LYP/6-31G(d,p) basis set was used for all calculations.     

Fusion systems and constructing free actions on products of spheres

We show that every rank two p-group acts freely and smoothly on a product of two spheres. This follows from a more general construction: given a smooth action of a finite group G on a manifold M, we construct a smooth free action on ${M \times \mathbb S^{n_1}\times \dots \times \mathbb S^{n_k}}$ when the set of isotropy subgroups of the G-action on M can be associated to a fusion system satisfying certain properties. Another consequence of this construction is that if G is an (almost) extra-special p-group of rank r, then it acts freely and smoothly on a product of r spheres.     

A Generalized Univariate Newton Method Motivated by Proximal Regularization

We devise a new generalized univariate Newton method for solving nonlinear equations, motivated by Bregman distances and proximal regularization of optimization problems. We prove quadratic convergence of the new method, a special instance of which is the classical Newton method. We illustrate the possible benefits of the new method over the classical Newton method by means of test problems involving the Lambert W function, Kullback?CLeibler distance, and a polynomial. These test problems provide insight as to which instance of the generalized method could be chosen for a given nonlinear equation. Finally, we derive a closed-form expression for the asymptotic error constant of the generalized method and make further comparisons involving this constant.     

Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems

In this work, by using weak conjugate maps given in (Azimov and Gasimov, in Int J Appl Math 1:171–192, 1999), weak Fenchel conjugate dual problem, ${(D_F^w)}$ , and weak Fenchel Lagrange conjugate dual problem ${(D_{FL}^w)}$ are constructed. Necessary and sufficient conditions for strong duality for the ${(D_F^w)}$ , ${(D_{FL}^w)}$ and primal problem are given. Furthermore, relations among the optimal objective values of dual problem constructed by using Augmented Lagrangian in (Azimov and Gasimov, in Int J Appl Math 1:171–192, 1999), ${(D_F^w)}$ , ${(D_{FL}^w)}$ dual problems and primal problem are examined. Lastly, necessary and sufficient optimality conditions for the primal and the dual problems ${(D_F^w)}$ and ${(D_{FL}^w)}$ are established.     

Determination of Chemical Effect on the Kβ1/Kα, Kβ2/Kα, Kβ2/Kβ1 and Kβ/Kα X-Ray Intensity Ratios of 4d Transition Metals

It is clear that detailed studies performed under identical experimental conditions are desirable to determine the effect of the chemical environment on the value of intensity ratios. To better understand this effect, we conducted measurements on Kβ₁/Kα, Kβ₂/Kα, Kβ₂/Kβ₁ and Kβ/Kα x-ray intensity ratios. The Kα and Kβ_1,2 emission spectra for compounds of 4d transition metals Y, Zr, Nb, and Mo were measured using a Si(Li) solid-state detector. The samples were excited by 22.69 keV x-rays emitted from a ¹⁰⁹Cd radioisotopes source. The experimental results for pure elements are compared with the other experimental and theoretical values.