The paper contains a rigorous proof of existence symbolic dynamics chaos in the generalized H\'enon map's 4th iterate $H^4$, which was conjectured \textit{A 3D Smale Horseshoe Hyperchaotic Discrete-Time System} Li and Yang, 2007. We prove also uniform hyperbolicity invariant set with dynamics. proofs are computer-assisted use C++ library \textit{CAPD} for interval arithmetic, differentiation in...

The concepts of arithmetic building blocks (ABB) and combinational arithmetic (CA) nets as well as their applications have been previously reported in References 3, 4, and 5. The unique ABB, resulting from the efforts of minimizing the set of building blocks in Reference 3, is designed at the arithmetic level, employing the redundant signed-digit number system,2 and is to be implemented as one ...

Developing a generalized useful DNA computer has been one of the main interests since the inception of molecular computation. Toward that goal it is important to equip DNA with the ability to perform mathematical calculations. Here, a simple procedure that allows DNA-based bit arithmetic calculations is presented. Oligonucleotides encoding input bit numbers serve as primers for PCR to carry out...

We propose in this paper a new algorithm and architecture for performing divisions in residue number systems. Our algorithm is suitable for residue number systems with large moduli, with the aim of manipulating very large integers on a parallel computer or a specialpurpose architecture. The two basic features of our algorithm are one one hand the use of a high-radix division method, and on the ...

Redundant operators such as adders and multipliers increase performance (timing and area) of high computational digital circuits. Mixing redundant operators with classical ones is nevertheless complex for circuit designers who might not have necessarily the required arithmetic knowledge. In this context, Computer Aided Design tools considering redundant arithmetic are of interest. In this paper...

We classify all cocompact torsion-free derived arithmetic Fuchsian groups of genus two by commensurability class. In particular, we show that there exist no such groups arising from quaternion algebras over number fields of degree greater than 5. We also prove some results on the existence and form of maximal orders for a class of quaternion algebras related to these groups. Using these results...

Data movement across computer memory hierarchy and across hosts of distributed systems is known to be a limiting factor for applications processing large data sets. We use the Data Cube Operator on an Arithmetic Data Set, called ADC, to benchmark computer capability to handle large datasets. To compute the operator we implement a parallel algorithm that computes a view from the smallest parent....

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

A solid is a connected orientable compact subset of R 3 which is a 3-manifold with boundary. Moreover, its boundary consists of finitely many components, each of which being a subset of the union of finitely many almost smooth surfaces. Motivated by numerical robustness issues, we consider a finite collection of boxes, with faces parallel to the coordinate planes, which covers the boundary of t...

This paper represents the combination of Reduced Instruction Set Computer (RISC) system using VHDL and implement. This paper presents a RISC processor designing to achieve various arithmetic operations. The RISC is a 20 bit processor. KeywordsArithmetic Logic(AL), Central Processing Unit(CPU), Control Unit(CU), Field Programmable Logic Array(FPGA), General Purpose Register(GPR), Program Counter...