Velocity and ejector-jet assisted differential pumping: Novel design stages for environmental SEM

Velocity and ejection pumping are proposed as novel evacuation techniques to assist the static differential pumping already in use in the environmental scanning electron microscope. The gas velocity (or momentum) that accompanies the supersonic jet stream formed through the first pressure limiting aperture is used to initially force the gas out of the system by placing the second pressure limiting aperture at an optimum position in the gaseous jet. By this method, the gaseous particle thickness between the two apertures is minimised and the required pumping speed of the first evacuation stage is also reduced to an absolute minimum. A further improvement is achieved by inserting an appropriately shaped baffle between the two apertures, which shields the second aperture from the gas jet of the first and acts as an ejector-jet pump. The gas leak rate through the second aperture is maintained at an acceptable low level by both systems, even below the static leak rate level when the ejector-jet design is used, in particular. The result of either method has a double benefit, namely, the electron beam loss in the intermediate pumping stage is minimised together with a reduction of pump speed requirements. This translates to best instrument performance and minimal manufacturing costs.     

Stability of a cubic functional equation in intuitionistic random normed spaces

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.     

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.     

Solution of the Ulam Stability Problem for Euler–Lagrange Quadratic Mappings

In 1940 S. M. Ulam proposed at the University of Wisconsin theproblem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist.” In 1968 S. U. Ulam proposed the moregeneral problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?” In 1978 P. M. Gruber proposed theUlam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?” According to P. M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982–1996 we solved the above Ulam problem, or equivalently the Ulam type problem for linear mappings and established analogous stability problems. In this paper we first introduce newquadratic weighted meansandfundamental functional equationsand then solve theUlam stability problemfornon-linear Euler–Lagrange quadratic mappingsQ:X → Y, satisfying a mean equation and functional equation[formula]for all 2-dimensional vectors (x₁, x₂) X², withXa normed linear space (Y a real complete normed linear space), and any fixed pair (a₁, a₂) of realsa_iand any fixed pair (m₁, m₂) of positive realsm_i(i = 1, 2), [formula]     

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.

     

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.