On the asymptoticity aspect of Hyers-Ulam stability of mappings

The object of the present paper is to prove an asymptotic analogue of Th.M. Rassias' theorem obtained in 1978 for the Hyers-Ulam stability of mappings.

     

Controllable Synthesis of Mesoporous Iron Oxide Nanoparticle Assemblies for Chemoselective Catalytic Reduction of Nitroarenes

Iron(III) oxide is a low‐cost material with applications ranging from electronics to magnetism, and catalysis. Recent efforts have targeted new nanostructured forms of Fe₂O₃ with high surface area‐to‐volume ratio and large pore volume. Herein, the synthesis of 3D mesoporous networks consisting of 4–5 nm γ‐Fe₂O₃ nanoparticles by a polymer‐assisted aggregating self‐assembly method is reported. Iron oxide assemblies obtained from the hybrid networks after heat treatment have an open‐pore structure with high surface area (up to 167 m² g^?1) and uniform pores (ca. 6.3 nm). The constituent iron oxide nanocrystals can undergo controllable phase transition from γ‐Fe₂O₃ to α‐Fe₂O₃ and to Fe₃O₄ under different annealing conditions while maintaining the 3D structure and open porosity. These new ensemble structures exhibit high catalytic activity and stability for the selective reduction of aryl and alkyl nitro compounds to the corresponding aryl amines and oximes, even in large‐scale synthesis.     

Microporous polystyrene particles for selective carbon dioxide capture

This study presents the synthesis of microporous polystyrene particles and the potential use of these materials in CO(2) capture for biogas purification. Highly cross-linked polystyrene particles are synthesized by the emulsion copolymerization of styrene (St) and divinylbenzene (DVB) in water. The cross-link density of the polymer is varied by altering the St/DVB molar ratio. The size and the morphology of the particles are characterized by scanning and transmission electron microscopy. Following supercritical point drying with carbon dioxide or lyophilization from benzene, the polystyrene nanoparticles exhibit a significant surface area and permanent microporosity. The dried particles comprising 35 mol % St and 65 mol % DVB possess the largest surface area, ～205 m(2)/g measured by Brunauer-Emmett-Teller and ～185 m(2)/g measured by the Dubinin-Radushkevich method, and a total pore volume of 1.10 cm(3)/g. Low pressure measurements suggest that the microporous polystyrene particles exhibit a good separation performance of CO(2) over CH(4), with separation factors in the range of ～7-13 (268 K, CO(2)/CH(4) = 5/95 gas mixture), which renders them attractive candidates for use in gas separation processes.     

Approximations of ternary Jordan homomorphisms and derivations in multi-C ? ternary algebras

Using fixed point methods, we prove the generalized Hyers–Ulam stability of homomorphisms in multi-C ^? ternary algebras and of derivations on multi-C ^? ternary algebras for the additive functional equation $$\sum_{i=1}^{m}f \bigg(mx_i+\sum_{j=1,\ j\ne i}^{m}x_j\bigg)+ f\bigg(\sum_{i=1}^{m}x_i\bigg)= 2f\bigg(\sum_{i=1}^{m}mx_i\bigg) \quad (m\in {\mathbb{N}},\ m\geqq2).$$      

Easily characterized systems of C60 grafted on SiO2

Fullerenes grafted on silica with cleavable anchors give materials that can be easily characterized after thermal/chemical treatment or use as catalysts. Transesterification of an ester linkage leads to detachment of the fullerene moiety from the silica and permits study with standard spectroscopic methods. In particular, UV-vis spectroscopy was proved to be a valuable tool permitting structure analysis and quantitative determination at the same time.     

Zinc(II) binding ability of tri-, tetra- and penta-peptides containing two or three histidyl residues

Macroscopic and microscopic protonation processes and zinc(II) complexes of a series of multihistidine peptides (Ac-HGH-OH, Ac-HGH-NHMe, Ac-HHGH-OH, Ac-HHGH-NHMe, Ac-HVGDH-NH(2), Ac-HHVGD-NH(2), Ac-HVHAH-NH(2), Ac-HAHVH-NH(2), Ac-HPHAH-NH(2) and Ac-HAHPH-NH(2)) were studied by potentiometric, NMR and ESI-MS spectroscopic techniques. Protonations of histidyl imidazole-N donor functions were not much affected by the number and location of histidyl residues, but the presence of C-terminal carboxylate groups had a significant impact on the basicities of the neighbouring histidyl sites. The formation of 2N(im) and 3N(im) macrochelates with the stoichiometry of [ZnL] was the major process in the complexation reactions of all peptides followed by the formation of hydroxo or amide bonded species. Thermodynamic stabilities of the zinc(II) complexes were primarily determined by the number of histidyl residues, but the presence of C-terminal carboxylate functions has also a significant contribution to metal binding. The stabilizing effect of the aspartyl beta-carboxylate group was also observed, but its extent is much weaker than that of the C-terminal carboxylate with a neighbouring histidyl residue. Zinc(II) promoted peptide amide deprotonation and co-ordination was observed only in the zinc(II)-Ac-HHVGD-NH(2) system above pH 8.     

On approximation of approximately linear mappings by linear mappings

Assume A is a normed linear space, B is a Banach space, and f: A → B is a mapping “approximately linear.” We solve the following Ulam problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist.”