Infinite Dimensional Bicomplex Spectral Decomposition Theorem

This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex Hilbert spaces are introduced and treated in relation with the classical Hilbert space M′ imbedded in any bicomplex Hilbert space M.     

Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces

This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities x ₁ , ..., x _n locally modelled on specialLagrangian cones C ₁, ..., C _n in ^m with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space _X of deformations of X in M, and construct a natural topology on it. Then we show that _X is locally homeomorphic to the zeroes of a smooth map : _{X X} between finite-dimensional vector spaces.Here the infinitesimal deformation space _X depends only on the topology of X, and the obstruction space _X only on the cones C ₁, ..., C _n at x ₁, ..., x _n . If the cones C _i are stable then _X is zero, and _X is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.     

Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

Stability properties of a nonstandard finite difference scheme for a hantavirus epidemic model

This paper studies the stability properties of a nonstandard finite difference (NSFD) scheme used to simulate the dynamics of a mouse population model in hantavirus epidemics. It is shown that this difference scheme and the underlying system of differential equations have the same dynamics. The proof uses the fact that the total population obeys the logistic equation, as well as techniques from calculus, graphical analysis, and dynamical systems.     

Stability and fragmentation of organic silicon functionalizations studied by laser desorption mass spectrometry

A method is introduced to investigate organic functionalizations on silicon by laser-induced thermal desorption (LITD), where well-ordered Si(1 1 1)-(1 × 1):H(D) surfaces are used to determine the desorption temperature as a function of laser fluence. To demonstrate the potential of this technique silicon surfaces with ultrathin oxide layers were functionalized with organic end groups. The species desorbed with focused XeCl laser pulses were monitored at an oblique angle and their time-of-flight (TOF) distributions were measured with a quadrupole mass analyzer after electron impact ionization. By assuming a negligible contribution of the oxide and organic layers to the heating effect, the TOF temperatures measured for Si(1 1 1)-(1 × 1):H(D) could be used to determine the mass of the desorbed species. Detailed results are presented for dimethylsilyl (DMS), bromomethyldimethylsilyl (BMDMS), and chloromethyldimethylsilyl (CMDMS) terminated surfaces which were prepared by silanization with suitable chloro and disilazane compounds. While for the DMS termination dimethylsilanol (76 u) is desorbed as a single species, clearly identifying the terminating group, in the case of BMDMS and CMDMS further fragmentation of the end group occurs at the surface.     

A new class of indolosesquiterpene alkaloids from polyathia suaveolens

Three new alkaloids, polyavolensin, polyavolensinol and polyavolensinone, isolated from the stem of Polyathia suaveolens are shown to belong to a new class of indolosesquiterpenes with structures 4, 5, 6 respectively by PMR, CMR and mass spectrometry. They have also been interrelated by chemical reactions.