[4] **viXra:1708.0473 [pdf]**
*submitted on 2017-08-30 20:26:27*

**Authors:** Yuly Shipilevsky

**Comments:** 10 Pages.

A polynomial-time algorithm for integer factorization, wherein integer factorization
reduced to a polynomial-time integer minimization problem over the
integer points in a two-dimensional rational polyhedron with conclusion that
P = NP

**Category:** Data Structures and Algorithms

[3] **viXra:1708.0373 [pdf]**
*replaced on 2018-07-25 09:30:51*

**Authors:** Wolfgang Fischl, Georg Gottlob, Reinhard Pichler

**Comments:** 17 Pages.

The authors have recently shown that recognizing low fractional hypertree-width (fhw) is NP-complete
in the general case and that the problem becomes tractable if the hypergraphs under consideration have degree and intersection width bounded by a constant, i.e., every vertex is contained in only constantly many different edges and the intersection of two edges contains only constantly many vertices. In this article, we show that bounded degree alone suffices to ensure tractability.

**Category:** Data Structures and Algorithms

[2] **viXra:1708.0117 [pdf]**
*submitted on 2017-08-10 13:08:30*

**Authors:** George Rajna

**Comments:** 33 Pages.

Concepts for information storage and logical processing based on magnetic domain walls have great potential for implementation in future information and communications technologies." [21] Research at the National Institute of Standards and Technology (NIST) suggests it also may be true in the microscopic world of computer memory, where a team of scientists may have found that subtlety solves some of the issues with a novel memory switch. [20] Los Alamos National Laboratory has produced the first known material capable of single-photon emission at room temperature and at telecommunications wavelengths. [19] In their paper published in Nature, the team demonstrates that photons can become an accessible and powerful quantum resource when generated in the form of colour-entangled quDits. [18] But in the latest issue of Physical Review Letters, MIT researchers describe a new technique for enabling photon-photon interactions at room temperature, using a silicon crystal with distinctive patterns etched into it. [17] Kater Murch's group at Washington University in St. Louis has been exploring these questions with an artificial atom called a qubit. [16] Researchers have studied how light can be used to observe the quantum nature of an electronic material. [15] An international team of researchers led by the National Physical Laboratory (NPL) and the University of Bern has revealed a new way to tune the functionality of next-generation molecular electronic devices using graphene. [14] Researchers at the Department of Physics, University of Jyväskylä, Finland, have created a theory that predicts the properties of nanomagnets manipulated with electric currents. This theory is useful for future quantum technologies. [13] Quantum magnetism, in which – unlike magnetism in macroscopic-scale materials, where electron spin orientation is random – atomic spins self-organize into one-dimensional rows that can be simulated using cold atoms trapped along a physical structure that guides optical spectrum electromagnetic waves known as a photonic crystal waveguide. [12]

**Category:** Data Structures and Algorithms

[1] **viXra:1708.0034 [pdf]**
*replaced on 2018-02-14 22:49:05*

**Authors:** Nicholas R. Wright

**Comments:** 8 Pages. Changed Moore's Law from "<" to ">".

We use the whole order approach to solve the problem of P versus NP. The relation of the whole order within a beautiful order is imperative to understanding the total order. We also show several techniques observed by the minimum element, we call a logical minimum. The perfect zero-knowledge technique will deliver exactly the same. We conclude with a demonstration of the halting problem.

**Category:** Data Structures and Algorithms