COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces.Presented theorems generalize recent results of Gordji et...     

Measurement of product concentration of two parallel reactive jets using digital image processing

The chemically sensitive LIF technique [9] is employed to study the mixing of two reactive axisymmetric jets, one of which carries fluorescein, in an ambient quiescent fluid. The degree of mixing depends on the jet spacing and the axial position downstream of the jets and power laws are found to hold for some concentration characteristics. Unlike the far velocity field of dual plane jets, self preservation laws are not found to hold in general for the concentration field.     

Synthesis of heterocyclic systems with carbohydrate fragment

The reactions of levoglucosenone with amides of several -nitrocarboxylic acids and acetoacetic acid result in tetra hydropyridones fused with a carbohydrate fragment. In the case of acetoacetic acid amides, mixtures of keto and enol tautomers were obtained. The stereochemistry of cyclization is discussed in detail.For Communication 1, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 409–414, February, 1996.     

Design and synthesis of novel 1,4-benzodiazepine surrogates as potential CCKA and CCKB antagonists via palladium-catalyzed three-component cascade reactions

Structurally diverse novel 1,4-benzodiazepine analogues related to selective CCKA antagonist MK-329, and CCKB antagonists L-365,260 and YM022 are prepared via palladium-catalyzed three component domino reactions involving allenylation-carbonylation-anion capture in one-pot cascade protocol in good to excellent yields.     

Synthesis and structure of azido-and amino-substituted dibenzoxazepinones

1,3-Dinitro[b, f][1,4]dibenzoxazepin-11(10H)-one enters nucleophilic substitution reactions with N-nucleophiles, azide ion preferably replacing the nitro group in position 3, whereas amines the one in position 1. Structures of the substitution products were confirmed by X-ray diffraction and ¹H NMR NOE spectroscopy. The selectivity observed in the reaction with amines was supposed to be caused by the stabilization of the intermediate σ-complex with the NH…O intramolecular hydrogen bond. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2018–2022, October, 2007.     

Reaction of Polynitrotoluenes with Phthalic Anhydride

2,4-Dinitro- and 2,4,6-trinitrotoluenes react with phthalic anhydride in boiling N,N-dimethylaniline to give nitro group reduction products.     

Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.     

A New Fourier Truncated Regularization Method for Semilinear Backward Parabolic Problems

We study the backward problem for non-linear (semilinear) parabolic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new Fourier truncated regularization method for stabilising the ill-posed problem. In comparison with previous studies on solving the nonlinear backward problem, our method shows a significant improvement.     

Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces

Let X be a non-empty set and F:X×X→X be a given mapping. An element (x,y)∈X×X is said to be a coupled fixed point of the mapping F if F(x,y)=x and F(y,x)=y. In this paper, we consider the case when X is a complete metric space endowed with a partial order. We define generalized Meir-Keeler type functions and we prove some coupled fixed point theorems under a generalized Meir-Keeler contractive condition. Some applications of our obtained results are given. The presented theorems extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393].     

On a new generalization of metric spaces

In this paper, we introduce the \({\mathcal {F}}\)-metric space concept, which generalizes the metric space notion. We define a natural topology \(\tau _{{\mathcal {F}}}\) in such spaces and we study their topological properties. Moreover, we establish a new version of the Banach contraction principle in the setting of \({\mathcal {F}}\)-metric spaces. Several examples are presented to illustrate our study.