Lorentzian matrix multiplication and the motions on Lorentzian plane

Halit Gundogan

doi:10.3336/gm.41.2.15

Lorentzian matrix multiplication and the motions on Lorentzian plane

Glasnik Matematicki ◽

10.3336/gm.41.2.15 ◽

2006 ◽

Vol 41 (2) ◽

pp. 329-334 ◽

Cited By ~ 10

Author(s):

Halit Gundogan

Keyword(s):

Matrix Multiplication ◽

Lorentzian Matrix Multiplication ◽

Lorentzian Plane

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The derivative and tangent operators of a motion in Lorentzian space

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781750058x ◽

2017 ◽

Vol 14 (04) ◽

pp. 1750058 ◽

Cited By ~ 2

Author(s):

Olgun Durmaz ◽

Buşra Aktaş ◽

Hali̇t Gündoğan

Keyword(s):

Matrix Multiplication ◽

Spatial Motion ◽

Lorentzian Space ◽

Matrix Groups ◽

Multiplication Formula ◽

Tangent Operator ◽

Special Matrix ◽

Lorentzian Matrix Multiplication

In this paper, by using Lorentzian matrix multiplication, [Formula: see text]-Tangent operator is obtained in Lorentzian space. The [Formula: see text]-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. [Formula: see text]-Tangent operators are related to vectors. Some illustrative examples for applications of [Formula: see text]-Tangent operators are also presented.

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Stable and Supported Semantics in Continuous Vector Spaces

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning ◽

10.24963/kr.2020/7 ◽

2020 ◽

Author(s):

Yaniv Aspis ◽

Krysia Broda ◽

Alessandra Russo ◽

Jorge Lobo

Keyword(s):

Logic Program ◽

Matrix Multiplication ◽

Vector Spaces ◽

Continuous Space ◽

Continuous Vector ◽

Novel Approach ◽

Gradient Based ◽

Normal Logic ◽

Parameter Values ◽

Normal Logic Program

We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.

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