In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

A series of 5-aminoalkylpyrrolo[3,2-c]azepine derivatives was synthesized and their serotonin 2 (5-HT2) receptor antagonist and antiplatelet aggregation activities were evaluated. 5-HT2 receptor antagonist activity was largely determined by the nature of the substituent at the 8-position as well as the aminoalkyl group at the 5-position of the pyrrolo[3,2-c]azepine ring. Compound 18a, 5-[3-[4-(...

We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel...

The title compound, [Ni(C(14)H(16)N(5)O(3))(2)](n) or [Ni(ppa)(2)](n), where ppa is 8-ethyl-5-oxo-2-(piperazin-1-yl)-5,8-dihydro-pyrido[2,3-d]pyrimidine-6-carboxyl-ate, was synthesized under hydro-thermal conditions. The Ni(II) atom (site symmetry ) exhibits a distorted trans-NiN(2)O(4) octa-hedral geometry defined by two monodentate N-bonded and two bidentate O,O'-bonded ppa monoanions. The ex...

A series of new arylfluoroquinolones has been prepared. These derivatives are characterized by having fluorine atoms at the 6- and 8-positions, substituted amino groups at the 7-position, and substituted phenyl groups at the 1-position. The in vitro antibacterial potency is greatest when the 1-substituent is 2,4-difluorophenyl and the 7-substituent is a 3-amino-1-pyrrolidinyl group. 1-(4-Fluoro...

In the present paper, we describe proapoptotic activity of several heterocyclic compounds 9, 12, 18, 19 and 20 possessing succinimide (as well as succinimide related) moieties. The compounds properties were examined with the aid of flow cytometry on the promyelocytic leukemia cell line HL-60. The highest proapoptotic activity exhibited compound 12 (4-{4-[4-(2-methoxyphenyl)piperazin-1-yl]butyl}...

In the title compound, [CdCl(2)(C(13)H(19)N(3)O)], the Cd(II) ion is penta-coordinated with the N,N,O-tridentate Schiff base 2-{[2-(piperazin-4-ium-1-yl)eth-yl]imino-meth-yl}phenolate ligand and two Cl atoms in a highly distorted square-pyramidal geometry; the piperazine ring adopts a chair conformation. In the crystal structure, adjacent mol-ecules are linked together via N-H⋯O and N-H⋯Cl hydr...

In the title compound, C26H28N5O2+·Cl-·CH3OH {systematic name: 4-(2-carbamoyl-1-benzo-furan-5-yl)-1-[4-(5-cyano-1H-indol-3-yl)but-yl]piperazin-1-ium chloride methanol monosolvate}, the protonated piperazine ring adopts a chair conformation. The indole ring plane is nearly perpendicular to the benzo-furan ring system, with a dihedral angle of 85.77 (2)°. In the crystal, the organic cations, Cl- ...

The title compound, C(10)H(15)N(2) (+)·H(2)PO(4) (-), is built up from 4-phenyl-piperazin-1-ium cations and dihydrogen phosphate anions. The inter-connection between two adjacent anions is assured by two strong O-H⋯O hydrogen bonds, which lead to the formation of infinite wave-like chains which spread along the a axis. The organic cations connect these chains via N-H⋯O hydrogen bonds. The cryst...

We define the notions of unilateral metric derivatives and “metric derived numbers” in analogy with Dini derivatives (also referred to as “derived numbers”) and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not “metrically differentiable” (in a certain strong sense) is σsymmetrically porous ...