Let Z = X1×· · ·×Xn be a product of Drinfeld modular curves. We characterize those algebraic subvarieties X ⊂ Z containing a Zariski-dense set of CM points, i.e. points corresponding to n-tuples of Drinfeld modules with complex multiplication (and suitable level structure). This is a characteristic p analogue of a special case of the André-Oort conjecture.

Abstract— In this paper high-speed hardware architectures of point multiplication based on Montgomery ladder algorithm for binary Edwards and generalized Hessian curves in Gaussian normal basis are presented. Computations of the point addition and point doubling in the proposed architecture are concurrently performed by pipelined digitserial finite field multipliers. The multipliers in parallel...

We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for ŝl(n). This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials.

Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinate-free description of these structures. It turns out that the tangent sheaf multiplication has a cohomological origin, while the Levi–Civita connection is related to 1-dimensional isomonodromic deformations.

Non-Boolean computations implementing operations on multi-valued variables beyond base 2 allow enhanced computational complexity. We introduce DNA as a functional material for ternary computing, and in particular demonstrate the use of three-valued oligonucleotide inputs to construct a 3 × 3 multiplication table. The system consists of two three-valued inputs of -1; 0; +1 and a fluorophore/quen...

This work is devoted for the design and FPGA implementation of a 16bit Arithmetic module, which uses Vedic Mathematics algorithms. For arithmetic multiplication various Vedic multiplication techniques like Urdhva Tiryakbhyam Nikhilam and Anurupye has been thoroughly analyzed. Also Karatsuba algorithm for multiplication has been discussed. It has been found that Urdhva Tiryakbhyam Sutra is most ...

We use presentations and identities among relations to give a generalisation of the Schreier theory of nonabelian extensions of groups. This replaces the usual multiplication table for the extension group by more efficient, and often geometric, data. The methods utilise crossed modules and crossed resolutions.

In this paper, we propose an efficient design of a reversible single precision floating point multiplier based on compressor. The single precision floating point multiplier requires the design of an efficient 24x24 bit integer multiplier. In the proposed architecture, the 24x24 bit multiplication operation is fragmented to nine parallel reversible 8x8 bit multiplication modules. In this paper, ...

This paper explains the design and implementation of 8-bit ALU (arithmetic and logic unit) using VHDL by using mixed style of modeling in Xilinx ISE 8.1i. The ALU takes two8-bits numbers and performs different principal arithmetic and logic operations like addition, multiplication, logical AND, OR, XOR, XNOR, NOR. The major focus of concern in this ALU is the multiplication operation using radi...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...