scholarly journals Binary relations as single primitive notions for hyperbolic three-space and the inversive plane

2000 ◽  
Vol 11 (4) ◽  
pp. 587-592 ◽  
Author(s):  
Victor Pambuccian
Keyword(s):  
Binary Relations ◽  
Inversive Plane ◽  
Three Space

FACTOR ANALYSIS OF GEOGRAPHIC COORDINATES AT POINTS OF THE CHANNEL OF A SMALL RIVER ON SPACE IMAGES

2020 ◽  
Author(s):  
Peter Matveevich Mazurkin ◽  
Yana Oltgovna Georgieva
Keyword(s):  
Correlation Coefficient ◽  
Geographical Location ◽  
Small River ◽  
Binary Relations ◽  
Catchment Basin ◽  
Space Images ◽  
The North ◽  
Inverse Effect ◽  
Characteristic Points ◽  
Fractal Representation

The purpose of the article is the analysis of asymmetric wavelets in binary relations between three coordinates at 290 characteristic points from the source to the mouth of the small river Irovka. The hypsometric characteristic is the most important property of the relief. The Irovka River belongs to a low level, at the mouth it is 89 m high, and at the source it is 148 m above sea level. Modeling of binary relations with latitude, longitude, and height has shown that local latitude receives the greatest quantum certainty. In this case, all paired regularities received a correlation coefficient of more than 0.95. Such a high adequacy of wave patterns shows that geomorphology can go over to the wave multiple fractal representation of the relief. The Irovka River is characterized by a small anthropogenic impact, therefore, the relief over a length of 69 km has the natural character of the oscillatory adaptation of a small river to the surface of the Vyatka Uval from its eastern side. This allows us to proceed to the analysis of the four tributaries of the small river Irovka, as well as to model the relief of the entire catchment basin of 917 km2. The greatest adequacy with a correlation coefficient of 0.9976 was obtained by the influence of latitude on longitude, that is, the geographical location of the relief of the river channel with respect to the geomorphology of the Vyatka Uval. In second place with a correlation of 0.9967 was the influence of the height of the points of the channel of the small river on local longitude and it is also mainly determined by the relief of the Vyatka Uval. In third place was the effect of latitude on height with a correlation coefficient of 0.9859. And in last sixth place is the inverse effect of altitude on local latitude in the North-South direction.

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

scholarly journals Finite representability of semigroups with demonic refinement

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Robin Hirsch ◽  
Jaš Šemrl
Keyword(s):  
Partial Order ◽  
Turing Machines ◽  
Binary Relations ◽  
Finite Representation ◽  
First Order ◽  
Finite Structures ◽  
Finite Base ◽  
Finite Set ◽  
Finite Representability ◽  
Representation Class

AbstractThe motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

RELEVANCE LOGIC AND THE CALCULUS OF RELATIONS

2010 ◽  
Vol 3 (1) ◽  
pp. 41-70 ◽  
Author(s):  
ROGER D. MADDUX
Keyword(s):  
Propositional Logic ◽  
Relevance Logic ◽  
Binary Relations ◽  
Classical Propositional Logic

Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.

scholarly journals On the Number of Tetrahedra with Minimum, Unit, and Distinct Volumes in Three-Space

2008 ◽  
Vol 17 (2) ◽  
pp. 203-224 ◽  
Author(s):  
ADRIAN DUMITRESCU ◽  
CSABA D. TÓTH
Keyword(s):  
Unit Volume ◽  
Time Algorithm ◽  
Combinatorial Problems ◽  
List Type ◽  
Type Number ◽  
Point Sets ◽  
Minimum Number ◽  
Three Space

We formulate and give partial answers to several combinatorial problems on volumes of simplices determined bynpoints in 3-space, and in general inddimensions.(i)The number of tetrahedra of minimum (non-zero) volume spanned bynpoints in$\mathbb{R}$3is at most$\frac{2}{3}n^3-O(n^2)$, and there are point sets for which this number is$\frac{3}{16}n^3-O(n^2)$. We also present anO(n3) time algorithm for reporting all tetrahedra of minimum non-zero volume, and thereby extend an algorithm of Edelsbrunner, O'Rourke and Seidel. In general, for every$k,d\in \mathbb{N}, 1\leq k \leq d$, the maximum number ofk-dimensional simplices of minimum (non-zero) volume spanned bynpoints in$\mathbb{R}$dis Θ(nk).(ii)The number of unit volume tetrahedra determined bynpoints in$\mathbb{R}$3isO(n7/2), and there are point sets for which this number is Ω(n3log logn).(iii)For every$d\in \mathbb{N}$, the minimum number of distinct volumes of all full-dimensional simplices determined bynpoints in$\mathbb{R}$d, not all on a hyperplane, is Θ(n).

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