Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulti...

Handling the procedure interface in an HPF compiler is complex due to the many possible combinations of Fortran 90/HPF properties of an actual array argument and its associated dummy argument. This paper describes an algorithm that reduces this complexity by mapping all the combinations of properties to a small set of canonical Internal Representations. These internal representations as well as...

We introduce linear-state dataflows, a canonical model for a large set of visualization algorithms that we call data-linear visualizations. Our model defines a fixed dataflow architecture: partitioning and subpartitioning of input data, ordering, graphic primitives, and graphic attributes generation. Local variables and accumulators are specific concepts that extend the expressiveness of the da...

The aim of this research work is to define and characterize a new class of n-ary multialgebra that may be called canonical (m, n)&minus hypermodules. These are a generalization of canonical n-ary hypergroups, that is a generalization of hypermodules in the sense of canonical and a subclasses of (m, n)&minusary hypermodules. In addition, three isomorphism theorems of module theory and canonical ...

Canonical Feynman integrals are of great interest in the study scattering amplitudes at multi-loop level. We propose to construct dlog-form hypergeometric type, treat them as a representation integrals, and project into master using intersection theory. This provides constructive way build canonical whose differential equations can be solved easily. use our method investigate both maximally cut...

An interesting problem in proof theory is to find representations of proof that do not distinguish between proofs that are ‘morally’ the same. For many logics, the presentation of proofs in a traditional formalism, such as Gentzen’s sequent calculus, introduces artificial syntactic structure called ‘bureaucracy’; e.g., an arbitrary ordering of freely permutable inferences. A proof system that i...

We fix an algebraically closed field k of characteristic zero. Let G be a reductive affine algebraic group over k and let V be an affine G-variety over k. We denote by A(G) and A(V ) the k-algebras of regular functions on G and V respectively. The action of G on V gives rise to a rational representation of G on A(V ). A natural question is to investigate whether the algebra A(V ) is a free modu...

Squaring and exponentiation of a number are fundamental arithmetic and widely used in the real-time applications such as image processing, digital filtering and cryptography. In this paper, we propose a squaring algorithm of an integer with canonical signed-digit (CSD) number representation. For an n-digit CSD number, our method generates n/4 CSD numbers of 2n-digit length as partial products. ...