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Preprint ARTICLE | doi:10.20944/preprints201610.0131.v1

Tensor Properties of Joint Probability Densities on Riemannian Parametric Manifold

Manouchehr Amiri

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: joint probability density; tensor properties; probability on Riemannian manifold; covariant derivative; contravariant derivative

Online: 31 October 2016 (02:39:45 CET)

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Preprint ARTICLE | doi:10.20944/preprints201610.0086.v1

Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

Frank Nielsen, Ke Sun

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: information geometry; mixture models; log-sum-exp bounds

Online: 20 October 2016 (10:35:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201609.0067.v1

Zoology of Atlas-Groups: Dessins D’enfants, Finite Geometries and Quantum Commutation

Michel Planat, Hishamuddin Zainuddin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: finite groups; dessins d’enfants; finite geometries; quantum commutation; quantum contextuality

Online: 20 September 2016 (11:14:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201608.0186.v1

The Conformal Camera in Modeling Binocular Vision

Jacek Turski

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: active vision; the conformal camera; the Riemann sphere; Möbius geometry; complex projective geometry; projective Fourier transform; retinotopy; binocular vision; horopter

Online: 20 August 2016 (11:24:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202104.0654.v1

Four Spacetime Dimensions from Multifractal Geometry

Ervin Goldfain

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Multifractals, measure theory, Rényi entropy, generalized dimension, geodesic trajectories, relativistic spacetime.

Online: 26 April 2021 (10:56:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201901.0151.v1

The Line Element Approach for the Geometry of Poincare Disk

Jong Ryul Kim

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Poincare disk; inner product; cross ratio; holomorphic function; angle; line element

Online: 15 January 2019 (10:00:40 CET)

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Preprint ARTICLE | doi:10.20944/preprints201902.0097.v1

On Sliced Spaces: Global Hyperbolicity Revisited

Kyriakos Papadopoulos, Nazli Kurt, Basil K. Papadopoulos

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: sliced spaces; global hyperbolicity; product topology; Alexandrov topology

Online: 12 February 2019 (09:48:42 CET)

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Preprint ARTICLE | doi:10.20944/preprints201911.0055.v1

Renormalization and Fractals among Sets beyond (Empty) Boundaries

Shun Adachi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: topology; fractal; renormalization; species

Online: 6 November 2019 (06:47:34 CET)

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Preprint ARTICLE | doi:10.20944/preprints201910.0301.v1

On the Characteristic Properties of Geodesic Sub-$ (\alpha,b,s )$-Preinvex

Wedad Saleh, Adem Kilicman

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: E-convex sets; preinvex; E-convex functions; geodesic; sub-preinvex; Riemannian manifolds; Hadamard manifolds.

Online: 27 October 2019 (10:41:01 CET)

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Preprint ARTICLE | doi:10.20944/preprints201806.0070.v1

Theory of g-T_g-Sets

Mohammad Irshad Khodabocus, Noor-Ul-Hacq Sookia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: generalized topological space; generalized operations; generalized sets

Online: 5 June 2018 (13:34:42 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201807.0095.v1

Theory of g-Tg-Separation Axioms

Mohammad Irshad KHODABOCUS (Dr. Phil. MEng.), Noor-Ul-Hacq Sookia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Generalized topological space, generalized sepa- ration axioms, generalized sets, generalized operations

Online: 5 July 2018 (11:45:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201801.0289.v1

Construction of Fullerenes and Pogorelov Polytopes with 5-, 6- and One 7-Gonal Face

Nikolai Erokhovets

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: fullerenes; right-angled polytopes; truncation of edges; connected sum; k-belts; p-vector

Online: 31 January 2018 (02:06:27 CET)

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Preprint ARTICLE | doi:10.20944/preprints202002.0140.v1

Some Applications of Clifford Algebra in Geometry

Ying-Qiu Gu

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Clifford algebra; geometric algebra; gamma matrix; multi-inner product; connection operator; Keller connection; Spin group; cross ratio

Online: 11 February 2020 (09:31:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints201903.0199.v1

Theory of g-Tg-Compactness

Mohammad Irshad Khodabocus, Noor-Ul-Hacq Sookia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Generalized topological space, generalized compact- ness, generalized countable compactness, generalized sequential compactness, generalized local connectedness

Online: 20 March 2019 (15:38:12 CET)

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Preprint REVIEW | doi:10.20944/preprints201810.0087.v1

Review of the Progress and Process of Satellite Imagery and Road Databases Conflation

Mohamed Z.Jber, Dieter Fritsch

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Conflation, feature matching, deconfliction, road network, complexity of spatial conflation.

Online: 4 October 2018 (15:51:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201805.0080.v1

Generalized Topological Notions by Operators

Ismail Ibedou

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: fuzzy operators; fuzzy separation axioms; fuzzy compactness; fuzzy connectedness

Online: 3 May 2018 (13:13:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201902.0200.v1

Univalent Functions Defined by a Generalized Multipler Differential Operator

Adnan Ghazy Alamoush

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Analytic functions; univalent function; differential operator; differential subordination; convex functions; structural formula

Online: 21 February 2019 (10:00:58 CET)

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Preprint ARTICLE | doi:10.20944/preprints201812.0223.v1

On a Duality between Time and Space Cones

Waleed Al-Qallaf, Kyriakos Papadopoulos

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: causality; chronology; chorology; Minkowski space; time cone; space cone; weak interval topology; duality

Online: 18 December 2018 (12:08:33 CET)

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Preprint ARTICLE | doi:10.20944/preprints201906.0294.v1

is*-Open Sets, is*- Mappings and is*-separation Axioms in Topological Spaces

Omar Khattabomar

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: is*-open set, is*-continuous, is*-open, is*-irresolute, is*-totally continuous, is-contra-continuous mappings, is*-separation

Online: 28 June 2019 (11:45:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201806.0338.v1

Helicoidal Hypersurfaces of Dini-Type with Spacelike Axis in Minkowski 4-Space

Erhan Güler, Ömer Kişi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Minkowski space; Dini-type helicoidal hypersurface; Gauss map; spacelike axis

Online: 21 June 2018 (12:10:54 CEST)

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In this paper, we define Ulisse Dini-type helicoidal hypersurface with spacelike axis in Minkowski 4-space

E_{1}^{4}

. We compute the Gaussian and the mean curvature of the hypersurface. Moreover, we obtain some special symmetry to the curvatures when they are flat and maximal.

Preprint ARTICLE | doi:10.20944/preprints201806.0169.v1

Theory of g-T_g-Maps

Mohammad Irshad Khodabocus, Noor-Ul-Hacq Sookia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: generalized topological space; generalized sets; generalized maps; generalized continuous maps; generalized irresolute maps; generalized homeomorphism maps

Online: 12 June 2018 (07:32:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201806.0159.v1

The Third Laplace-Beltrami Operator of the Rotational Hypersurface in 4-Space

Erhan Güler

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: 4-space; the third Laplace-Beltrami operator; rotational hypersurface; Gaussian curvature; mean curvature

Online: 11 June 2018 (12:35:51 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201906.0109.v1

Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres

Iva Dokuzova, Dimitar Razpopov

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Riemannian manifold; Einstein manifold; sectional curvatures; Ricci curvature; Lie group

Online: 13 June 2019 (05:36:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201803.0254.v1

Varieties of Coarse Spaces

Igor Protasov

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: coarse structure; coarse space; ballean; varieties of coarse spaces

Online: 30 March 2018 (04:49:57 CEST)

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A class

M

of coarse spaces is called a variety if

M

is closed under formation of subspaces, coarse images and products. We classify the varieties of coarse spaces and, in particular, show that if a variety

M

contains an unbounded metric space then

M

is the variety of all coarse spaces.

Preprint ARTICLE | doi:10.20944/preprints202108.0557.v2

An Integral Expression for Pi Obtained by Virtue of Ramanujan’s Approximation in Conoidal Areas: Applications of the Resultant Figure in Engineering

Joseph Cabeza Lainez

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: conoid; ellipse; Ramanujan; calculus of surface areas; number Psi; number Pi; 3D-construction of complex geometries; Engineering Design Objects; Architectural Forms

Online: 21 February 2023 (03:35:09 CET)

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Preprint ARTICLE | doi:10.20944/preprints201905.0024.v1

Incorporating Topological Representation in 3D City Models

Stelios Vitalis, Ken Arroyo Ohori, Jantien Stoter

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: 3D city model; topology; combinatorial map; linear cell complex; CityJSON; CityGML

Online: 5 May 2019 (12:56:21 CEST)

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Working Paper ARTICLE

A Soft Embedding Lemma for Soft Topological Spaces

Giorgio Nordo

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: soft set; soft sets theory; soft topology; embedding lemma; soft mapping; soft topological product; soft slab; soft continuous mapping; soft diagonal mapping

Online: 30 May 2019 (10:04:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201906.0232.v1

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

Yevhen Cherevko, Volodymyr Berezovski, Irena Hinterleitner, Dana Smetanová

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Hermitian manifold; locally conformal Kähler manifold; Lee form; diffeomorphism; conformal transformation; Lie derivative

Online: 24 June 2019 (08:45:40 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201808.0265.v1

A Symmetry Motivated Link Table

Shawn Witte, Michelle Flanner, Mariel Vazquez

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: writhe; chirality; nomenclature; link symmetries; link table; knot table; lattice polygons; DNA topology

Online: 15 August 2018 (05:18:48 CEST)

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Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each topology. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number and the symmetry groups of 2-component links, a canonical link diagram for each link type is proposed. All diagrams but six were unambiguously chosen (

8_{1}^{2} 5

,

9_{5}^{2}

,

9_{3}^{2} 4

,

9_{3}^{2} 5

,

9_{3}^{2} 9

, and

9_{4}^{2} 1

). We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.

Working Paper ARTICLE

Conformal and Geodesic Mappings onto Some Special Spaces

Volodymyr Berezovski, Yevhen Cherevko, Lenka Rýparová

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: space with affine connection; Riemannian space; Ricci-m-symmetric space; conformal mapping; geodesic mapping

Online: 24 June 2019 (08:51:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201903.0010.v1

Convexity and Toeplitz Quantization: Kostant's Theorem for the symplectomorphism group of the sphere

Mohamed Lemine Hadrami Bouleryah

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Toeplitz quantization, decreasing rearrangement, majorization, spectral measure, measure preserving transformation, Hermitian matrices

Online: 1 March 2019 (12:25:47 CET)

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Preprint REVIEW | doi:10.20944/preprints201809.0430.v1

The Role of Spin(9) in Octonionic Geometry

Maurizio Parton, Paolo Piccinni

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Spin(9); octonions; vector fields on spheres; Hopf fibration; locally conformally parallel; Clifford structure; Clifford system; symmetric spaces

Online: 21 September 2018 (06:07:27 CEST)

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Preprint SHORT NOTE | doi:10.20944/preprints202109.0082.v1

Disjoint Genus-0 Surfaces in Extremal Graph Theory and Set Theory Lead To a Novel Topological Theorem

Arturo Tozzi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Combinatorics; Ramsey’s theory; Borsuk–Ulam theorem; black hole; singularity

Online: 6 September 2021 (10:09:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0126.v1

Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing

Michel Planat, Marcelo M. Amaral, Fang Fang, David Chester, Raymond Aschheim, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: $SL_2(\mathbb{C})$ character varieties; algebraic surfaces; magic state quantum computing; topological quantum computing; aperiodicity

Online: 13 April 2022 (10:37:41 CEST)

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Working Paper ARTICLE

B-Lift Curves in Euclidean 3-space

Anıl Altınkaya, Mustafa Çalışkan

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: B-Lift; , Natural Lift; Slant helix; Darboux helix

Online: 25 March 2021 (17:22:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints201810.0161.v1

Universal Quantum Computing and Three-Manifolds

Michel Planat, Raymond Aschheim, Marcelo Amaral, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: quantum computation, IC-POVMs, knot theory, three-manifolds, branch coverings, Dehn surgeries.

Online: 8 October 2018 (16:45:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202110.0225.v1

Function Representation for Basic Processes Modeling in 3D Bioprinting

Katherine Alex Pakhomova, Alexander Alexandrovich Pasko, Iskander Shaukatovich Akhatov

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Function Representation; implicit functions; geometry and topology; 3D bioprinting; tissue spheroids; modeling and simulation; diffusion-concentration calculations; cellular necrosis; additive technologies

Online: 15 October 2021 (12:26:09 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201912.0064.v1

Theory of g-Tg-Interior and g-Tg-Closure Operators: Definitions, Essential Properties, and Commutativity

Mohammad Irshad KHODABOCUS, Noor-Ul-Hacq SOOKIA

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Generalized topological space, generalized sets, generalized interior operator, generalized closure operator, commutativity

Online: 5 December 2019 (08:52:51 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202002.0107.v1

A Topological Approach to Infinity in Physics

Arturo Tozzi, James F. Peters

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: donut-like; infinity; paths; physical geometry; networks, Alexander horned sphere

Online: 9 February 2020 (15:55:03 CET)

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Preprint ARTICLE | doi:10.20944/preprints201810.0742.v1

Theory of g-Tg-Connectedness

Mohammad Irshad Khodabocus, Noor-Ul-Hacq Sookia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: eneralized topological space, generalized local connectedness, generalized pathwise connectedness, generalized local pathwise connectedness, generalized simple connectedness, generalized components

Online: 31 October 2018 (09:00:17 CET)

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Preprint ARTICLE | doi:10.20944/preprints202108.0034.v1

Tangent Based-Path Path Planning with Distinctive Topologies in a Dynamic Environment

Zhuo Yao

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: path planning; distinctive topolgy; tangent

Online: 2 August 2021 (12:50:25 CEST)

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Working Paper ARTICLE

On a Duality between Time and Space Cones

Waleed Al-qallaf, Kyriakos Papadopoulos

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: causality; chronology; chorology; Minkowski space; time cone; space cone; weak interval topology; duality

Online: 24 May 2019 (08:22:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202003.0342.v1

Theory of g-Tg-Exterior and g-Tg-Frontier Operators: Definitions, Essential Properties and, Consistent, Independent Axioms

Mohammad Irshad Khodabocus, Noor-Ul-Hacq Sookia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: generalized topological space; generalized sets; generalized exterior operator; generalized frontier operator; consistent; independent axioms

Online: 23 March 2020 (07:14:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.1240.v1

On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

Ibtesam Alshammari, Mesfer H. Alqahtani, Islam M. Taha

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: fuzzy soft set; fuzzy soft topological space; r-fuzzy soft d-open set; fuzzy soft d-continuity; fuzzy soft almost (weakly) continuity and fuzzy soft (L,M,N,O)-continuity

Online: 18 December 2023 (06:01:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints201809.0352.v1

Generalization of Nambu-Hamilton Equation and Extension of Nambu-Poisson Bracket to Superspace

Viktor Abramov

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Nambu-Hamilton equation; Nambu-Poisson bracket; superspace; Filippov-Jacobi identity; Nambu-Hamilton mechanics

Online: 18 September 2018 (13:39:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201809.0407.v1

Extension of eigenvalue problems on Gauss map of ruled surfaces

Miekyung Choi, Young Ho Kim

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: ruled surface,; pointwise $1$-type Gauss map; generalized $1$-type Gauss map; conical surface of $G$-type

Online: 20 September 2018 (11:01:16 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202111.0179.v1

GeoSPARQL 1.1: An Almost Decadal Update to the Most Important Geospatial LOD Standard

Nicholas John Car, Timo Homburg

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: GeoSPARQL; GeoSPARQL 1.1; spatial; geospatial; Semantic Web; RDF; OWL; OGC; Open Geospatial Consortium; standard; ontology.

Online: 9 November 2021 (14:05:34 CET)

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Preprint ARTICLE | doi:10.20944/preprints201811.0500.v1

Classification Theorems in Minkowski 3-space

Miekyung Choi, Young Ho Kim

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: ruled surface; null scroll; Minkowski space; pointwise 1-type Gauss map; generalized $1$-type Gauss map; conical surface of $G$-type

Online: 20 November 2018 (11:37:03 CET)

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Preprint ARTICLE | doi:10.20944/preprints201809.0366.v1

Cut-and-Project Schemes for Pisot Family Substitution Tilings

Jeong-Yup Lee, Shigeki Akiyama, Yasushi Nagai

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Pisot substitution tilings; pure point spectrum; regular model set; algebraic coincidence

Online: 19 September 2018 (07:44:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202001.0267.v1

Almost Hypercomplex Manifolds with Hermitian-Norden Metrics and 4-dimensional Indecomposable Real Lie Algebras Depending on One Parameter

Hristo Manev

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Almost hypercomplex structure; Hermitian metric; Norden metric; Lie group; Lie algebra

Online: 23 January 2020 (14:50:08 CET)

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Preprint ARTICLE | doi:10.20944/preprints202011.0747.v1

Theory of g-T_g-Derived and g-T_g-Coderived Operators: Definitions, Essential Properties, Iterations, and Ranks

Mohammad Irshad KHODABOCUS, Noor-Ul-Hacq SOOKIA

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Generalized topological space, generalized sets, generalized derived operator, generalized coderived operator, iterations, ranks

Online: 30 November 2020 (20:21:55 CET)

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In a generalized topological space T_g = (Ω, T_g) (T_g-space), the g-topology T_g : P (Ω) −→ P (Ω) can be characterized in the generalized sense by specifying the generalized open, generalized closed sets (g-T_g-open, g-T_g-closed sets), generalized interior, generalized closure operators g-Intg, g-Cl_g : P (Ω) −→ P (Ω) (g-T_g-interior, g-T_g-closure operators), or generalized derived, generalized coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω) (g-T_g-derived, g-T_g-coderived operators), respectively. For very many T_g-spaces, the δ^th-iterates g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω) of g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, defined by transfinite recursion on the class of successor ordinals are also themselves g-T_g-derived, g-T_g-coderived operators for new g-topologies in the generalized sense on Ω. Thus, the use of novel definitions of g-T_g-derived, g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, based on a very clever construction, together with their δ^th-iterates g-T_g-operators g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω), defined by transfinite recursion on the class of successor ordinals, will give rise to novel generalized g-topologies on Ω. The present authors have been actively engaged in the study of g-T_g-operators in T_g-spaces. The study of the essential properties and the commutativity of novel definitions of g-T_g-interior and g-T_g-closure operators g-Int_g, g-Cl_g : P (Ω) −→ P (Ω), respectively, in T_g has formed the first part, and the study of the essential properties and sets of consistent, independent axioms of novel definitions of g-T_g-exterior and g-T_g-frontier operators g-Ext_g, g-Fr_g : P (Ω) −→ P (Ω), respectively, has formed the second part. In this work, which forms the last part on the theory of g-T_g-operators in T_g-spaces, the present authors propose to present novel definitions and the study of the essential properties of g-T_g-derived and g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, and their δ^th-iterates, and the notions of g-T_g-open and g-T_g-closed sets of ranks δ in T_g-spaces.

Preprint ARTICLE | doi:10.20944/preprints201912.0360.v1

Separation Axioms Interval-Valued Fuzzy Soft Topology via Quasi-Neighbourhood Structure

Mabruka Ali, Adem Kılıçman, Azadeh Zahedi Khameneh

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: interval-valued fuzzy soft set; interval-valued fuzzy soft topology; interval-valued fuzzy soft point; interval-valued fuzzy soft neighborhood; interval-valued fuzzy soft quasi-neighbourhood; interva

Online: 27 December 2019 (08:44:19 CET)

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Preprint ARTICLE | doi:10.20944/preprints201906.0109.v2

Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres

Iva Dokuzova, Dimitar Razpopov

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Riemannian manifold; Einstein manifold; sectional curvatures; Ricci curvature; Lie group

Online: 28 May 2020 (02:58:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0318.v2

A Spatially Bounded Airspace Axiom

Peter Szabó, Miroslava Ferencová, Monika Blišťanová

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Airspace Axiom; Simple Airspace Polygon; Free Route Airspace; Earth-centered Earth-fixed

Online: 5 May 2022 (03:25:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v9

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 8 June 2022 (12:29:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0386.v1

Some Tightness-Type Properties of the Space of Permutation Degree

Ljubisa Kocinac, Farkhod G. Mukhamadiev, Anvar K. Sadullaev

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: functor of permutation degree; tightness; set tightness; $T$-tightness; functional tightness; minitightness

Online: 22 August 2022 (15:43:42 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201811.0465.v1

Type I Almost-Homogeneous Manifolds of Cohomogeneity One—IV

Zhuang-dan Guan, Pilar Orellana, Anthony Van

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Kahler manifolds, Einstein metrics, Ricci curvature, ﬁbration, almost-homogeneous, cohomogeneity one, semisimple Lie group, Sasakian Einstein, Calabi-Yau metrics

Online: 19 November 2018 (12:04:09 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0389.v1

A Formalization of the Concept of a Numeral System

Boris Averbukh

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: topological monoid; numeral system

Online: 26 October 2021 (14:15:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202003.0068.v1

Complexes of Tournaments, Directionality Filtrations and Persistent Homology

Ran Levi, Dejan Govc, Jason Smith

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Tournaments; Semi-Simplicial Sets; Neural networks; Persistent homology

Online: 4 March 2020 (11:40:12 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0073.v1

Esakia Duality for Heyting Small Spaces

Artur Piękosz

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Esakia duality; small space; spectral space; Heyting algebra

Online: 3 November 2022 (08:39:44 CET)

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Preprint SHORT NOTE | doi:10.20944/preprints202003.0261.v1

On Bounds of the Sine and Cosine along a Circle on the Complex Plane

Feng Qi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: bound; double inequality; norm; sine function; cosine function; circle; complex plane

Online: 16 March 2020 (09:51:10 CET)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v8

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 1 June 2022 (09:43:58 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v1

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Integer Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular; convex polytopes; negative dimensional spectra

Online: 27 April 2022 (14:19:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202401.1551.v1

On Fuzzy Soft Beta-Continuity and Beta-Irresoluteness: Properties and Applications

Ibtesam Alshammari, Islam M. Taha

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: fuzzy soft set; fuzzy soft topological space; r-fuzzy soft β -closed (β -open) set; fuzzy soft
β -closure (β -interior) operator; fuzzy soft β -continuity; fuzzy soft almost (weakly) β -continuity; fuzzy
soft β -irresolute (strongly β -irresolute) function; connectedness

Online: 22 January 2024 (09:55:40 CET)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v10

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 10 June 2022 (16:13:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v11

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 16 June 2022 (10:39:40 CEST)

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Working Paper ARTICLE

Quantum Computation and Measurements from an Exotic Space-time $R^4$

Michel Planat, Raymond Aschheim, Marcelo Amaral, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Topological quantum computing; $4$-manifolds; Akbulut cork; exotic $R^4$; fundamental group; finite geometry; Cayley-Dickson algebras

Online: 18 March 2020 (16:45:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202203.0318.v1

A Spatially Bounded Airspace Axiom

Peter Szabó, Miroslava Ferencová, Monika Blišťanová

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Earth-centered Earth-fixed; Free Route Airspace; Significant Points; Simple Airspace Polygon; Airspace Axiom

Online: 24 March 2022 (02:17:23 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.0114.v1

Dynamics of Fricke-Painlevé VI surfaces

Michel Planat, David Chester, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: isomonodromic deformation; Painlev\'e VI; $SL(2,\mathbb{C})$ character variety, algebraic surfaces; DNA/RNA

Online: 4 December 2023 (03:27:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202206.0423.v1

Calculating the Segmented Helix Formed by Repetitions of Identical Subunits thereby Generating a Zoo of Platonic Helices

Robert Lee Read

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: solid geometry; helix; Chasles’ theorem; platonic helix; tetrahelix; linear algebrea; computer graphics

Online: 30 June 2022 (08:56:22 CEST)

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Working Paper ARTICLE

Completeness in Quasi-Pseudometric Spaces

Ştefan Cobzas

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: quasi-pseudometric space; Cauchy sequence; Cauchy net; Cauchy filter; completeness

Online: 15 July 2020 (08:49:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v6

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 26 May 2022 (08:54:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v3

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensional spectra; fractal dimensions

Online: 9 May 2022 (09:39:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202312.1240.v2

On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

Ibtesam Alshammari, Mesfer H. Alqahtani, Islam M. Taha

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Fuzzy soft set; fuzzy soft topological space; fuzzy soft δ -closure operator; r-fuzzy soft δ -connected set; weaker forms of fuzzy soft continuity; fuzzy soft (L,M,N,O)-continuity.

Online: 24 January 2024 (02:52:14 CET)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v5

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 25 May 2022 (09:54:32 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v4

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensional spectra; fractal dimensions

Online: 20 May 2022 (09:09:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0089.v6

Omnidimensional Convex Polytopes

Szymon Łukaszyk, Andrzej Tomski

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular basic convex polytopes; circumscribed and inscribed polytopes; negative dimensions; fractal dimensions; complex dimensions; emergent dimensionality; mathematical physics

Online: 24 February 2023 (15:41:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v7

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 30 May 2022 (11:28:08 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v12

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 20 June 2022 (09:40:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0125.v1

Fricke Topological Qubits

Michel Planat, David Chester, Marcelo Maciej Amaral, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: n/a; Topological quantum computing; $SL(2,\mathbb{C})$ character variety; knot theory

Online: 10 October 2022 (11:14:48 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0089.v5

Volumes and surfaces of $n$-simplices, $n$-orthoplices, $n$-cubes, and $n$-balls are holomorphic functions of $n$, which makes those objects omnidimensional

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular basic convex polytopes; circumscribed and inscribed polytopes; negative dimensions; fractal dimensions; complex dimensions; emergent dimensionality

Online: 26 December 2022 (11:08:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v2

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Integer Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensional spectra

Online: 5 May 2022 (10:21:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202402.0734.v1

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

Islam Taha, Wafa Alqurashi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Fuzzy soft set; fuzzy soft topological space; r-fuzzy soft α -closed (α -open) set; fuzzy soft α -closure (α -interior) operator; fuzzy soft α -continuity; fuzzy soft almost (weakly) α -continuity; connectedness; compactness.

Online: 13 February 2024 (12:46:23 CET)

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Preprint ARTICLE | doi:10.20944/preprints202209.0089.v2

On the Basic Convex Polytopes and n-Balls in Complex Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular basic convex polytopes; negative dimensions; fractal dimensions; complex dimensions; circumscribed and inscribed polytopes

Online: 14 September 2022 (08:37:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1184.v1

Topological Approach with Decision Making Based on Nano Beta Closure, Nano Beta Interior and its Application with Fractals in Medical Fields

M. A. El Safty, Mohamed El Sayed, Hadba F Al-Qahtani, Elhadi E. Elamir, A Al Qarni

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Medical diagnosis; rough sets; Nano Beta-topological space; Decision-making; Accuracy

Online: 19 October 2023 (03:52:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0263.v13

Novel Recurrence Relations for Volumes and Surfaces of N-Balls, Regular N-Simplices, and N-Orthoplices in Real Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular convex polytopes; negative dimensions; fractal dimensions

Online: 27 June 2022 (11:17:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0089.v1

On the Basic Convex Polytopes and n-Balls in Complex Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular basic convex polytopes; negative dimensions; fractal dimensions; complex dimensions; circumscribed and inscribed polytopes

Online: 6 September 2022 (10:13:02 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.2023.v1

Warped Product Pointwise Hemi-Slant Submanifolds of Nearly Kaehler Manifolds

Lamia Saeed Alqahtani, Siraj Uddin, Rawan Bossly

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: slant; pointwise slant; pointwise hemi-slant; warped products; nearly Kaehler manifolds

Online: 29 June 2023 (02:24:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.1240.v1

A New Tool to Study the Binding Behavior of Intrinsically Disordered Proteins

Aakriti Upadhyay, Chinwe Ekenna

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Intrinsically Disordered Proteins; protein-protein interaction; Geometric features; Binding affinity; Rigid-body docking

Online: 16 June 2023 (12:31:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202301.0529.v1

SL(2, C) Scheme Processing of Singularities in Quantum Computing and Genetics

Michel Planat, Marcelo Amaral, David Chester, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Finitely generated group; SL(2,C) character variety; algebraic surfaces; schemes; exotic R4; topological quantum computing; microRNAs.

Online: 30 January 2023 (01:21:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202209.0089.v4

On the Omnidimensional Convex Polytopes and n-Balls in Negative, Fractional and Complex Dimensions

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: regular basic convex polytopes; circumscribed and inscribed polytopes; negative dimensions; fractal dimensions; complex dimensions

Online: 7 October 2022 (08:30:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.0082.v1

The (α, p)-Golden Metric Manifolds and Their Submanifolds

Cristina E. Hretcanu, Mircea Crasmareanu

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Golden Riemannian manifold; Metallic Riemannian manifold; submanifold

Online: 1 June 2023 (11:47:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202306.0171.v1

Heyting Locally Small Spaces and Esakia Duality

Artur Piękosz

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: tame topology; Esakia duality; locally small space; up-spectral space

Online: 2 June 2023 (09:40:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202401.1551.v2

On Fuzzy Soft Beta-Continuity and Beta-Irresoluteness: Properties and Applications

Ibtesam Alshammari, Islam M. Taha

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: fuzzy soft set; fuzzy soft topological space; r-fuzzy soft β -closed (β -open) set; fuzzy soft
β -closure (β -interior) operator; fuzzy soft β -continuity; fuzzy soft almost (weakly) β -continuity; fuzzy soft β -irresolute (strongly β -irresolute) function; connectedness

Online: 13 March 2024 (12:39:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.0707.v1

Constructability and Rigor of Angles Multiples of 3 in Euclidean Geometry

Alex Kimuya

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: geometric rigor; non-Euclidean methods; straightedge and compass; trisection of angles; Euclidean axioms; geometric foundations

Online: 11 December 2023 (14:49:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202304.0413.v1

Non-Integer Dimension of Seasonal Land Surface Temperature (LST)

Sepideh Azizi, Tahmineh Azizi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Land Surface Temperature; Climate Change; Fractal Geometry; Discrete Wavelet Transform

Online: 17 April 2023 (07:01:24 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202312.0114.v2

Dynamics of Fricke-Painlevé VI surfaces

Michel Planat, David Chester, Klee Irwin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: isomonodromic deformation; Painlev\'e VI; $SL(2,\mathbb{C})$ character variety; algebraic surfaces; DNA/RNA

Online: 25 December 2023 (05:36:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202306.1681.v1

The Hyperbolic Ptolemy’s Theorem in the Poincare Ball Model of Analytic Hyperbolic Geometry

Abraham A. Ungar

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Ptolemy’s Theorem; Poincar´e ball model; Hyperbolic geometry; M¨obius addition; Gyrogroups; Gyrovector spaces; Gyrotrigonometry

Online: 23 June 2023 (12:31:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.2080.v2

Angle Trisection With Growth Rate Of The Golden Ratio

seyed kazem mousavi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Angle trisection; Six-dimensional time-space; Golden ratio.

Online: 4 October 2023 (08:02:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1002.v1

Geometry of CR-Slant Warped Products in Nearly Kaehler Manifolds

Siraj Uddin, Bang-Yen Chen, Rawan Bossly

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: CR-product; CR-warped product; CR-slant warped product; Chen’s inequality; nearly Kaehler manifolds

Online: 15 May 2023 (08:05:56 CEST)

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Computer Science and Mathematics