Some open categorical problems inTop

In this paper, a pendant to a recent survey paper, the authors discuss several open problems in categorical topology. The emphasis is on topology-oriented problems rather than on more general category-oriented ones. In fact, most problems deal with full subconstructs or superconstructs of the constructTop of topological spaces and continuous maps.     

On the Interpretation of Optimal Dual Solutions in Convex Programming

The relationships between multiple optimal dual solutions of a convex programming problem and the corresponding primal optimal value function are established by straightforward arguments on known results in duality theory. The subsequent discussion includes a demonstration that one-sided shadow prices can be found by solving a linear programming problem, conditions for the uniqueness and validity of the classical shadow price interpretation and a specialization of the results to the linear programming case.     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

Generating Metallic Amorphous Core–Shell Nanoparticles by a Solid‐State Amorphization Process

Metallic crystalline/amorphous core–shell nanoparticles consisting of a crystalline Pd core (c‐Pd) surrounded by an amorphous Fe₂₅Sc₇₅ shell (a‐FeSc) are prepared by inert‐gas condensation. A phase transformation of the c‐Pd by a solid‐state diffusion process resulting in an amorphous core (a‐PdSc) surrounded by an amorphous FeSc shell is observed if the core–shell structure is irradiated at ambient temperature with 300 keV electrons. The amorphization process seems to involve the diffusion of irradiation‐induced defects and is presumably driven by the large negative heat of mixing of Pd and Sc, as well as by the excess enthalpy of the interfaces between the c‐Pd regions and the surrounding a‐FeSc. The structural transformation reported here opens a new way to producing metallic amorphous core–shell nanoparticles of different chemical compositions and probably novel properties.     

A note on adapting methods for continuous global optimization to the discrete case

In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a concave function over the integers contained in a compact polyhedron. Computational experience with this algorithm is reported.     

Reaction of N-acylthioureas with electrophilic reagents : Synthesis of 1,3,5-oxadiazinium salts, 1,3,5-thiadiazinium salts, 1,2,4-dithiazolium salts and benzothiazoles

N-Acylthioureas 1 can be easily transformed into 2,4-diamino-6-aryl-1,3,5-oxadiazinium salts 12, 2,4-diamino-6-aryl-1,3,5-thiadiazinium salts 13,3-amino-5-aryl-1,2,4-dithiazolium salts 19 and 2-acylimino-benzothiazolines 22, respectively by reaction with different electrophiles. The structure of the compounds prepared is confirmed by analytical data as well as by chemical transformations.     

Characterization and quantification of Sm(III)/ and Cm(III)/clay mineral outer-sphere species by TRLFS in D2O and EXAFS studies

In order to assess the long-term safety of deep radioactive waste repositories, a precise characterization of the different sorption processes on a molecular basis and the exact definition of geochemical boundary conditions for their relevance are of immense importance. Through sorption on various minerals the migration of radionuclides will be hindered and their retention will be ensured. Using time-resolved laser fluorescence spectroscopy (TRLFS) and extended X-ray absorption fine structure (EXAFS) spectroscopy, it was possible to identify outer-sphere sorbed trivalent lanthanides and actinides onto different montmorillonites and illite. Furthermore, the quantification of Cm(III)/clay outer-sphere sorption in D(2)O at different ionic strengths was shown. The results were confirmed by ion exchange model calculations. Finally, the structural parameters of a Sm(III)/clay outer-sphere complex were obtained by EXAFS measurements.