Under the background of digitization, basic algorithm minimal surface provides novel and rich creative themes for architectural design. However, due to high complexity extreme thinness, how convert mathematical model mechanical has become biggest challenge in application large-size surface. On basis analysing relation between force form, this paper explores verifies concept method transforming ...

AbstractGeometric transformations are fundamental aspects of all computer graphics rendering and are found throughout the computer graphics pipeline. In earlier work we presented mathematical treatment of this topic. The different concepts were combined into a general mathematical procedure based on the concept of vector spaces in linear algebra. While we established the mathematical aspects of...

bainitic transformation at low transformation temperatures leads to a microstructure involving fine plates of bainitic ferrite and thin films of retained austenite. this microstructure has shown ultimate tensile strength of about 2.2 gpa, noticeable uniform elongation in the range of 5 to 30%, hardness values of about 600 to 670 hv and impact toughness in the range of 30 to 40 mpa m1/2. with ca...

Given a program P , an unfold/fold program transformation system derives a sequence of programs P = P0, P1, : : : , Pn, such that Pi+1 is derived from Pi by application of either an unfolding or a folding step. Existing unfold/fold transformation systems for de nite logic programs di er from one another mainly in the kind of folding transformations they permit at each step. Some allow folding u...

This paper considers various aspects of the canonical coordinate transformations in a complex phase space. The main result is given by two theorems which describe two special families of mappings between integrable Hamiltonian systems. The generating function of these transformations is determined by the entropy and a second arbitrary function which we take to be the energy function. For simple...

Transformation-based optimizers that explore a search space exhaustively usually apply all possible transformation rules on each alternative, and stop when no new information is produced. In general, diierent sequences of transformations may end up deriving the same element. The optimizer must detect and discard these duplicate elements. In this paper we consider two questions: How many duplica...

During the last decade, ecologists and particularly mathematical ecologists have focused on different approaches to the problem of spatial distribution of species. When the spatial distribution is not considered explicitly, the mathematical models are called spatially implicit. They consider the proportion of territory occupied by given species, but there is no information on which particular s...

In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and gauge transformations. Two different approaches to noncommutative geometry are covered: the one based on derivations and the one based on spectral triples. Ex...

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit several descriptions as superfields on different superspaces. In particular, this is the case for on-shell massless superfields. This allows a description of sh...

Automatic differentiation is a semantic transformation that applies the rules of differential calculus to source code. It thus transforms a computer program that computes a mathematical function into a program that computes the function and its derivatives. Derivatives play an important role in a wide variety of scientific computing applications, including numerical optimization, solution of no...