# Data Structures and Algorithms

## 1501 Submissions

[2] **viXra:1501.0203 [pdf]**
*submitted on 2015-01-21 18:32:38*

### A Nopreprint on Algebraic Algorithmics: Paraconsistency as an Afterthought

**Authors:** Jan A. Bergstra

**Comments:** 23 Pages.

Algebraic Algorithmics, a phase taken from G.E. Tseitlin, is given a specific interpretation for
the line of work in the tradition of the program algebra and thread algebra. An application
to algebraic algorithmics of preservationist paraconsistent reasoning in the style of
chunk and permeate is suggested and discussed.
In the first appendix nopreprint is coined as a tag for new a publication category,
and a rationale for its use is given. In a second appendix some rationale is provided for the affiliation
from which the paper is written and posted.

**Category:** Data Structures and Algorithms

[1] **viXra:1501.0022 [pdf]**
*submitted on 2015-01-02 05:15:50*

### On the Completely Integrable Calogero Type Discretizations of Nonlinear Lax Integrable Dynamical Systems and the Related Markov Type co-Adjoint Orbits

**Authors:** Anatolij K. Prykarpatski

**Comments:** 7 Pages. a new approach to constructing a priori integrable discretizations of nonlinear Lax type integrable dynamical systems

The Calogero type matrix discretization scheme is applied to constructing the Lax type integrable discretizations of one wide enough class of nonlinear integrable dynamical systems on functional manifolds. Their Lie-algebraic structure and complete integrability related with co-adjoint orbits on the Markov co-algebras is discussed. It is shown that a set of conservation laws and the associated Poisson structure ensue as a byproduct of the approach devised. Based on the Lie algebras quasi-representation property the limiting procedure of finding the nonlinear dynamical systems on the corresponding functional spaces is demonstrated.

**Category:** Data Structures and Algorithms