A structural investigation of the alkali metal site distribution within bioactive glass using neutron diffraction and multinuclear solid state NMR

The atomic-scale structure of Bioglass and the effect of substituting lithium for sodium within these glasses have been investigated using neutron diffraction and solid state magic angle spinning (MAS) NMR. Applying an effective isomorphic substitution difference function to the neutron diffraction data has enabled the Na-O and Li-O nearest-neighbour correlations to be isolated from the overlapping Ca-O, O-(P)-O and O-(Si)-O correlations. These results reveal that Na and Li behave in a similar manner within the glassy matrix and do not disrupt the short range order of the network former. Residual differences are attributed solely to the variation in ionic radius between the two species. Successful simplification of the 2

Towards a web-based progressive handwriting recognition environment for mathematical problem solving

The emergence of pen-based mobile devices such as PDAs and tablet PCs provides a new way to input mathematical expressions to computer by using handwriting which is much more natural and efficient for entering mathematics. This paper proposes a web-based handwriting mathematics system, called WebMath, for supporting mathematical problem solving. The proposed WebMath system is based on client-server architecture. It comprises four major components: a standard web server, handwriting mathematical expression editor, computation engine and web browser with Ajax-based communicator. The handwriting mathematical expression editor adopts a progressive recognition approach for dynamic recognition of handwritten mathematical expressions. The computation engine supports mathematical functions such as algebraic simplification and factorization, and integration and differentiation. The web browser provides a user-friendly interface for accessing the system using advanced Ajax-based communication. In this paper, we describe the different components of the WebMath system and its performance analysis.

Structural characterisation of hypoxia-mimicking bioactive glasses

Nickel and cobalt are both known to stimulate the hypoxia-inducible factor-1 (HIF-1a), thus significantly improving blood vessel formation in tissue engineering applications. We have manufactured nickel and cobalt doped bioactive glasses to act as a controlled delivery mechanism of these ions. The resultant structural consequences have been investigated using the methods of isotopic and isomorphic substitution applied to neutron diffraction. The structural sites present will be intimately related to their release properties in physiological fluids such as plasma and saliva, and hence the bioactivity of the material. Detailed structural knowledge is therefore a prerequisite for optimising material design. Results show that nickel and cobalt adopt a mixed structural role within these bioactive glasses occupying both network-forming (tetrahedral) and network-modifying (5-fold) geometries. Two thirds of the Ni (or Co) occupies a five-fold geometry with the remaining third in a tetrahedral environment. A direct comparison of the primary structural correlations (e.g. Si-O, Ca-O, Na-O and O-Si-O) between the archetypal 45S5 Bioglass® and the Ni and Co glasses studied here reveal no significant differences. This indicates that the addition of Ni (or Co) will have no adverse effects on the existing structure, and thus on in vitro/in vivo dissolution rates and therefore bioactivity of these glasses.

Structure of rare-earth phosphate glasses by neutron diffraction

Neutron diffraction was used to measure the structure of the phosphate glasses RAl0.30P3.05O9.62, where R denotes Dy or Ho, and RAl0.34P3.20O10.04, where R denotes La or Ce. For each glass, isomorphic structures were assumed and difference function methods were employed to separate, essentially, those correlations involving the rare-earth ion, R3+, from the remainder. The ratio of bridging oxygen, OB, to terminal oxygen, OT, atoms in the PO4 tetrahedra was quantified and in both materials R3+ and Al3+ are found to act as network modifying cations which bind to the OT. The R–OT coordination number is 6.7(1) and 7.5(2) for the Dy/Ho and La/Ce glasses respectively.

Identification of the relative distribution of rare-earth ions in phosphate glasses

The relative distribution of rare-earth ions R3+ (Dy3+ or Ho3+) in the phosphate glass RAl0.30P3.05O9.62 was measured by employing the method of isomorphic substitution in neutron diffraction. It is found that 7.9(7) R-R nearest neighbors reside at 5.62(6) Angstrom in a network made from interlinked PO4 tetrahedra. Provided that the role of Al is explicitly considered, a self-consistent account of the local matrix atom correlations can be developed in which there are 1.68(9) bridging and 2.32(9) terminal oxygen atoms per phosphorus.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

An Example Concerning Valdivia Compact Spaces

∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998

Co-Connected Spaces

∗ Financial support of the Grant Agency of the Czech Republic under the grant no 201/96/0119 and of the Grant Agency of the Charles University under the grant GAUK 149 is gratefully acknowledged.

Operators Factoring through Banach Lattices and Ideal Norms

A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

A Characterization of Weakly Lindelöf Determined Banach Spaces

2000 Mathematics Subject Classification: 46B26, 46B03, 46B04.

Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)

2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

On the Algebraic Properties of Convex Bodies

AMS subject classification: 52A01, 13C99.