Generalized Derivations with Engel Conditions on One-Sided Ideals

Let R be a noncommutative prime ring and I a nonzero left ideal of R. Let g be a generalized derivation of R such that [g(r ^k ), r ^k ] _n  = 0 for all r ∈ I, where k, n are fixed positive integers. Then there exists c ∈ U, the left Utumi quotient ring of R, such that g(x) = xc and I(c ? α) = 0 for a suitable α ∈ C. In particular we have that g(x) = α x, for all x ∈ I.     

On Defining Sets of Full Designs with Block Size Three

A defining set of a t-(v, k, λ) design is a subcollection of its blocks which is contained in no other t-design with the given parameters, on the same point set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. We show that if a t-(v, k, λ) design D is contained in a design F, then for every minimal defining set d _D of D there exists a minimal defining set d _F of F such that \({d_D = d_F\cap D}\). The unique simple design with parameters \({{\left(v,k, {v-2\choose k-2}\right)}}\) is said to be the full design on v elements; it comprises all possible k-tuples on a v set. Every simple t-(v, k, λ) design is contained in a full design, so studying minimal defining sets of full designs gives valuable information about the minimal defining sets of all t-(v, k, λ) designs. This paper studies the minimal defining sets of full designs when t = 2 and k = 3. Several families of non-isomorphic minimal defining sets of these designs are found. For given v, a lower bound on the size of the smallest and an upper bound on the size of the largest minimal defining set are given. The existence of a continuous section of the spectrum comprising approximately v values is shown, where just two values were known previously.     

One‐pot three‐component synthesis of novel 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carboxylic acid derivatives

A simple and easy synthesis of 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carboxylic acid ( 3 ) has been successfully developed through a one‐pot three‐component condensation reaction of (2‐amino‐phenyl)‐oxo‐acetic acid sodium salt ( 1 ) obtained from the hydrolysis of isatin with ammonium acetate and 3‐nitrobenzaldehyde. Some novel quinazoline‐ester derivatives 4‐7 were then obtained by the reaction between the new compound 3 and various alcohols. Then, quinazoline‐amide derivatives 10‐14 were synthesized from the reaction of various amines and 2‐(3‐nitro‐phenyl)‐quinazoline‐4‐carbonyl chloride ( 8 ), obtained by the reaction of compound 3 with SOCl₂. Finally, some novel quinazoline‐azo derivatives 17‐19 were synthesized by the coupling reaction between β‐dicarbonyl compounds and the novel amino‐quinazoline derivative compound 15 , obtained by reduction of nitro‐quinazoline derivative compound 11 . Thus, a new series of quinazoline‐4‐carboxylic acid, ester, amide, and azo derivatives was synthesized and fully characterized by ¹H NMR, ¹³C NMR, IR, and mass spectrometry analysis.     

Ruthenium(II)-NHC-catalyzed (NHC = perhydrobenzimidazol-2-ylidene) alkylation of amines using the hydrogen borrowing methodology under solvent-free conditions

Transition Metal Chemistry - New ruthenium(II) complexes with N-heterocyclic carbene ligand were synthesized by transmetalation reactions between silver(I) N-heterocyclic carbene complexes and...     

A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm

Swarm intelligence is a research branch that models the population of interacting agents or swarms that are able to self-organize. An ant colony, a flock of birds or an immune system is a typical example of a swarm system. Bees’ swarming around their hive is another example of swarm intelligence. Artificial Bee Colony (ABC) Algorithm is an optimization algorithm based on the intelligent behaviour of honey bee swarm. In this work, ABC algorithm is used for optimizing multivariable functions and the results produced by ABC, Genetic Algorithm (GA), Particle Swarm Algorithm (PSO) and Particle Swarm Inspired Evolutionary Algorithm (PS-EA) have been compared. The results showed that ABC outperforms the other algorithms.     

Development of Kinetic Mechanism for the Esterification of Acrylic Acid with Hexanol Catalyzed by Ion‐Exchange Resin

The heterogeneous esterification reaction of acrylic acid with hexanol over three different cation‐exchange resins, Amberlyst 131, Amberlyst 15, and Dowex 50Wx‐400, was investigated. Surface area, pore volume, average pore diameter, and acid capacity analyses were carried out for these three catalysts. Amberlyst 131 gave the highest conversion, and therefore, further experiments were performed catalyzed by Amberlyst 131. The absence of external and internal mass transfer resistances was investigated for the esterification of acrylic acid with hexanol. Experiments showed that the reaction is controlled by chemical step rather than external and internal mass transfer steps. The effects of temperature, catalyst loading, and alcohol to acid molar ratio on the conversion of acrylic acid were determined. The activation energy and kinetic and adsorption constants were determined according to the Langmuir–Hinshelwood–Hougen–Watson mechanism.     

Synthesis of N'-[4'-Benzo(15-Crown-5)]-4-Tolylaminoglyoxime and N'-[4'-Benzo(15-Crown-5)]-4-Chlorophenylaminoglyoxime and Their Complexes with Copper (II), Nickel (II) and Cobalt (II)

N'-[4'-benzo(15-crown-5)]-4-tolylaminoglyoxime (H₂L¹),the sodium chloride salt of H₂L¹ (H₂L¹...NaCl),N'-[4'-benzo(15-crown-5)]-4-chlorophenylaminoglyoxime(H₂L²) and the sodium chloride salt of H₂L² (H₂L²...NaCl)have been prepared from p-chlorophenylchloroglyoxime,p-tolylchloroglyoxime, 4'-aminobenzo[15-crown-5] and sodiumbicarbonate or sodium bicarbonate and sodium chloride. Nickel (II),cobalt (II) and copper (II) complexes of H₂L and H₂L...NaClhave a metal-ligand ratio of 1 : 2 and the ligand coordinatesthrough the two N atoms, as do most of the vic-dioximes. Their IR spectra and elemental analyses are given, together with¹H NMR spectra of the ligands.