Solution and structural studies of the Cd(II) – Aconitate system

The complexing ability of the binary system trans-aconitic acid (H₃L) with regard to Cd(II) and the crystal structures of the binary system Cd(II)–(H₃L), [Cd₃L₂(H₂O)₆] n(1) and ternary systems of Cd(II)–(H₃L)–Lewis base [Lewis base = 1,10-phenanthroline (2) and 2,2′-bipyridine (3)] have been determined. Compound 1 is a rare binodal four-connected three-dimensional (3D) metal-organic framework possessing a moganite (mog) topology. Compounds 2 and 3 represent infinite one-dimensional (1D) chains forming three-dimensional metal-supramolecular structures through H-bond and π–π stacking interactions. All compounds have been characterized by spectroscopic and thermogravimetric techniques.     

Amino cyclodextrin per-O-methylation: Synthesis of 3-monoamino-permethylated derivatives

A method for the per-O-methylation of amino-cyclodextrins is described. The tert-butyloxycarbonyl protecting group was used for protection of the amino group since it is stable to the alkaline conditions necessary for the permethylation step and can be removed under mildly acidic conditions that leave the cyclodextrin skeleton intact. 3-Monoamino-α-permethylated cyclodextrin and 3-monoamino-β-permethylated cyclodextrin were synthesized based on the above method.     

Quadratic functional equations in a set of Lebesgue measure zero

Let R$\mathbb{R}$ be the set of real numbers, Y   a Banach space and f:R→Y$f:\mathbb{R}\to Y$. We prove the Hyers–Ulam stability theorem for the quadratic functional inequality

‖f(x+y)+f(x−y)−2f(x)−2f(y)‖≤?$\Vert f(x+y)+f(x-y)-2f(x)-2f(y)\Vert \le ?$

for all (x,y)∈Ω$(x,y)\in \Omega$, where Ω⊂R²$\Omega \subset {\mathbb{R}}^2$ is of Lebesgue measure 0. Using the same method we dealt with the stability of two more functional equations in a set of Lebesgue measure 0.     

Approximation of a General Cubic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces

In this paper, we investigate the generalized Hyers–Ulam stability of a general cubic functional equation in Felbin’s type fuzzy normed linear spaces and some applications of our results in the stability of general cubic functional equation from a linear space to a Banach space will be exhibited.     

A new characterization of Möbius transformations by use of Apollonius hexagons

The purpose of this paper is to give a new characterization of Möbius transformations from the standpoint of conformal mappings. To this end a new concept of Apollonius hexagons on the complex plane is used.

     

Contents to Volume 62

Volume Contents

Contents to Volume 62     

Hyers–Ulam–Rassias Stability of Derivations in Proper JCQ*–triples

In this paper, we investigate stability of derivations in proper JCQ*–triples associated to the following Pexiderized functional equation $$f(x + y + z) = f_{0}(x) + f_{1}(y) + f_{2}(z)$$ .     

Inertial projection and contraction algorithms for variational inequalities

In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.     

The Size of a Maximum Subgraph of the Random Graph with a Given Number of Edges

Doklady Mathematics - We have proven that the maximum size k of an induced subgraph of the binomial random graph $$G(n,p)$$ with a given number of edges $$e(k)$$ (under certain conditions on this...