相关论文: Note on Integer Factoring Methods I
In this talk, I reviewed the role of factorization in diffraction hard scattering.
We study some problems in metric Diophantine approximation over local fields of positive characteristic.
An elementary method for computing various prime sequences using the sequence of Farey sequences is described.
The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…
A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from…
In this paper we discourse basises of representable algebras. This question lead to arithmetic problems. We prove algorithmical solvability of exponential-Diophantine equations in rings represented by matrices over fields of positive…
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
We deal with various Diophantine equations involving the Euler totient function and various sequences of numbers, including factorials, powers, and Fibonacci sequences.
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer…
In this extended abstract we deal with the relations between the numerical/diophantine approximation and the symbolic/algebraic geometry approachs to solving of multivariate diophentine polynomial systems, obtaining several consecuences…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
Factorization of an $n\times n$ unitary matrix as a product of $n$ diagonal matrices containing only phases interlaced with $n-1$ orthogonal matrices each one generated by a real vector as well as an explicit form for the Weyl factorization…
For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a…
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…
In this Note we introduce a new methodology for Bayesian inference through the use of $\phi$-divergences and the duality technique. The asymptotic laws of the estimates are established.
Recently we proposed an information entropy based method for electronic structure calculations within the density-matrix functional theory(DMFT) (Phys. Rev. Lett. 128, 013001), dubbed as $i$-DMFT. Comments have been raised regarding the…
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic…
In this paper, we discuss a systematic and self consistent procedure to factorize a rather general class of coupled nonlinear ordinary differential equations (ODEs), namely coupled quadratic and mixed Li\'enard type equations, which include…
A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…