Cooling,identification and spectroscopy of super-heavy element ions

We briefly discuss some possibilities for cooling, identification and spectroscopy of super-heavy element (SHE) ions based on recent results obtained from studies of atomic and molecular ions in linear rf traps. Since these investigations only relied on the charge and the mass of the ion of interest, we believe it should be straight forward to adopt most of the techniques for SHE ion research.     

Bounds for the cup-length of Poincaré spaces and their applications

Our main result offers a new (quite systematic) way of deriving bounds for the cup-length of Poincaré spaces over fields; we outline a general research program based on this result. For the oriented Grassmann manifolds, already a limited realization of the program leads, in many cases, to the exact values of the cup-length and to interesting information on the Lyusternik-Shnirel'man category.     

Reservoir operations optimization via fuzzy criterion decision processes

In this paper, we propose the treatment of complex reservoir operation problems via our newly developed tool of fuzzy criterion decision processes. This novel approach has been shown to be a more flexible and useful analysis tool especially when it is desirable to incorporate an expert’s knowledge into the decision models. Additionally, it has been demonstrated that this form of decision models will usually result in an optimal solution, which guarantees the highest satisfactory degree. We provide a practical exemplification procedure for the models presented as well as an application example.     

Effect of the pore surface modification of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes

We have investigated the effect of the surface state and surface treatment of the pores of an inorganic substrate on the plasma‐grafting behavior of pore‐filling‐type organic/inorganic composite membranes. Shirasu porous glass (SPG) was used as the inorganic substrate, and methyl acrylate was used as the grafting monomer. The grafting rate increased as the density of silanol on the SPG substrate increased. This result suggests that radicals are generated mainly at the silanol groups on the pore surface by plasma irradiation. The SPG substrates were treated with silane coupling agents used to control the mass of organic material bonded to the pore surface. The thickness of the grafted layer became thinner as the mass of organic material bonded to the pore surface of SPG increased. This decrease in the thickness of the grafted layer could be explained by the decrease in the penetration depth of vacuum ultraviolet rays contained in plasma having a wavelength of less than 160 nm that generated radicals in the pores of the substrate. The thickness of the grafted layer inside the SPG substrates could be controlled through the control of the mass of organic material bonded to the pore surface of the SPG substrate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 846–856, 2006     

On the multi-attribute stopping problem with general value functions

We examine a sequential selection problem in which a single option must be selected. Each option's value is a function of its attributes, whose precise values can be ascertained at a given cost. We prove the optimality of a threshold stopping rule for a general class of objective functions.     

Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

There is no upper bound of small transfinite compactness degree in metrizable spaces

In [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993], Aarts and Nishiura investigated several types of dimensions modulo a class P of spaces. These dimension functions have natural transfinite extensions. The small transfinite compactness degree trcmp is such transfinite dimension function extending the small compactness degree cmp. We shall prove that there is no upper bound for trcmp in the class of metrizable spaces, i.e. for each ordinal number α there exists a metrizable space Xα such that trcmpXα=α. We also give a characterization of the dimension dim of a separable (compact) metrizable space in terms of the function cmp of the product of this space with a nowhere locally compact zero-dimensional factor.     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Radiation induced synthesis and swelling characterization of thermo-responsive N-isopropylacrylamide-co-ionic hydrogels

Two-component thermo-responsive hydrogels poly(N-isopropylacrylamide)-co-vinylbenzyltrimethylammonium chloride (NIPA-co-VBT) and poly(N-isopropylacrylamide)-co-p-sodium styrene sulphonate (NIPA-co-SSS) were prepared by using high energy gamma radiation. The gels were characterized by Fourier transformed infrared spectroscopy (FTIR), scanning electron microscopy (SEM) and sol-gel analysis. The presence of ionic monomers in NIPA leads to lower gel content. Introduction of ionic components in the matrix enhanced swelling extent but caused slower volume transition. The swelling studies in alcohol indicated that swelling extent was function of polarity of the swelling medium and all gels followed the order water > methanol > ethanol > iso-propanol. In mixed co-solvents (water-alcohol), they exhibit complex reentrant behavior. The co-polymer gels containing VBT swelled faster and to higher extent than those containing SSS. The dynamic swelling studies indicated that diffusion of water in PNIPA gel shifts from Fickian for PNIPA to anomalous for NIPA-co-ionic gels also the mean swelling time (MST) decreases for gels containing ionic monomers.