Database transformations consist of queries and updates which are two fundamental types of computations in any databases the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. In the theoretical studies of database transformations, considerable effort has been directed towards exploiting the close ties betwe...

Four selfreciprocal integral transformations of Hankel type are defined through I,Cy) fo’,Cx),,,Cxy)Cx, ’ where 1,2,3, 4; Ix 0; ct(x) x /, g,(x) x-J(x), J(x) being the Bessel function of the first kind oforder Ix; th(x) x1-2, g2,(x) (-1)x2gt,,(x); tx3(x) x--2, ,qx,(x) x /,q,,(x), and ct,(x) x 2, g4,(x)(-1)xgLa(x). The simultaneous use of transformations Y/’I, and /’z, (which are denoted by allo...

In this article we discuss an approach to database optimisation in which a conceptual schema is optimised by applying a sequence of transformations. By performing these optimisations on the conceptual schema, a large part of the database optimisation can be done before actually sliding down the software development waterfall. When optimising schemas, one would like to preserve some level of equ...

Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the ν = 1 IQHE state on the ν < 1 FQHE states. Using the hydrodynamical description of the quantum Hall fluid it is shown, that these transformations are generated by the vector fields satisfying the Gauss law in the non-commutative Chern-Simons gauge theory and the corresponding field-theory Lag...

We present a semantic foundation and a collection of program combinators for bi-directional transformations on tree-structured data. In one direction, these transformations map a “concrete” tree into a simplified “abstract” one; in the other, they map a modified abstract tree, together with the original concrete tree, to a correspondingly modified concrete tree. The challenge of understanding a...

A general mathematical framework for the quantitative description of cluster size dependence in heterogeneous catalytic reactions has been developed based on an analysis Gibbs energy elementary reactions. The methodology was illustrated a generic linear sequence with three steps, multi-step mechanism ethanol oxidation comprising linear, nonlinear and quasi-equilibria steps network parallel tran...

Mathematical text is too cumbersome to write because of the need to encode a tree structure in a left to right linear order. This paper defines two novel problems, namely structure prediction from unstructured representation and sequence prediction within a mathematical session, to help address mathematical text entry. The effectiveness of our approach relies on the fact that normal mathematica...

Analysis of the equations of mathematical physics and foundations of field theories with the help of skew-symmetric differential forms Abstract In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of mathematical p...

The affine-scaling algorithm is an analogue of Karmarkar's linear programming algorithm that uses affine transformations instead of projective transformations. Although this variant lacks some of the nice properties of Karmarkar's algorithm (for example, it is probably not a polynomial-time algorithm). it nevertheless performs well in computer implementations. It has recently come to the attent...

This paper explores the development of students! knowledge of mathematical procedures. Students! tendency to develop rote knowledge of procedures has been widely commented on. An alternative, more flexible endpoint for the development of procedural knowledge is explored here, where students choose to deviate from established solving patterns on particular problems for greater efficiency. Studen...