A procedure to construct exact solutions of nonlinear evolution equations

In this paper, we implemented the functional variable method for the exact solutions of the Zakharov?CKuznetsov-modified equal-width (ZK-MEW), the modified Benjamin?CBona?CMahony (mBBM) and the modified KdV?CKadomtsev?CPetviashvili (KdV?CKP) equations. By using this scheme, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider applicability for handling nonlinear wave equations.     

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.     

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...     

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.     

Perfume alcohols supported to sulfochlorinated poly(styrene-co-divinyl benzene) beads

Perfume alcohols such as 2-phenyl ethanol and eugenol were supported to sulfochlorinated poly(styrene-co-divinyl benzene) beads in the presence of base such as triethyl amine, pyridine, and sodium bicarbonate and their hydrolysis at different temperature was studied.     

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.     

Synthesis of four new vic-dioximes and their nickel(II), cobalt(II), copper(II) and cadmium(II) complexes

Four unsymmetrical vic-dioximes: [L¹H₂] N-(4-butylphenyl)amino-amphi-glyoxime, [L²H₂] N-(4-butylphenyl)amino-anti-glyoxime, [L³H₂] N-(4-phenylazophenyl)amino-amphi-glyoxime and [L⁴H₂] N-(4-phenylazophenyl)amino-anti-glyoxime have been prepared from amphi-chloroglyoxime, anti-chloroglyoxime, 4-butylaniline and 4-(phenylazo)aniline respectively. The complexes of these vic-dioximes with Ni^II, Co^II, Cu^II and Cd^II ions have been investigated. All are insoluble in common solvents. Their i.r. spectra and elemental analyses are given, together with mass and ¹H-n.m.r. spectra of the ligands.