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Preprint CONCEPT PAPER | doi:10.20944/preprints202405.1294.v2

Panel Surface Area Maximization for Increasing PV Performance

Moses Oyaro Okello

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: geometry; shape optimisation; photovoltaic; solar energy; renewable energy; system advisor model

Online: 5 September 2024 (10:13:32 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1990.v1

Projective Vector Fields on Semi-Riemannian Manifolds

Norah Alshehri, Mohammed Guediri

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Semi-Riemannian manifolds; Projective vector fields; Conformal and Killing vector fields; Ricci curvature; Hessian

Online: 28 August 2024 (10:37:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1656.v1

Compensatory Partial Derivatives and Topological Equivalence of Manifolds in ℝ ⁿ under Continuity and Non-Intersection Constraints

Richard murdoch Montgomery

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: novel approach; topological equivalence; manifolds embedded in ℝ

Online: 22 August 2024 (14:59:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1490.v1

Some Aspects of Differential Topology of Subcartesian Spaces

Liuyi Chen, Qianqian Xia

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Singular space; Subcartesian space; Partition of unity; Tubular neighborhood; Morse function; Differential topology

Online: 22 August 2024 (03:12:09 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.0840.v1

"Topological Dynamics in Ecological Biomes and Toroidal Structures: Mathematical Models of Stability, Bifurcation, and Structural Failure

Richard Murdoch Montgomery

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Keywords: Algebraic Topology, Differential Geometry, Dynamical Systems, Biomes, Ecology

Online: 12 August 2024 (15:07:15 CEST)

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This study presents two interconnected mathematical models: one describing the stability and bifurcation dynamics of ecological biomes, and another simulating the progressive deformation and structural failure of a toroidal object. Both models explore topological changes in complex systems, bridging concepts from ecology, materials science, and mathematical physics. The first part introduces a dynamic model of ecological biomes, incorporating seasonal oscillations and external pressures. We define equations for topology updates, seasonal effects, and pressure impacts, culminating in a bifurcation condition that represents a critical shift in the biome's equilibrium state. This model provides insights into the resilience and tipping points of ecological systems under varying environmental stresses.The second part extends these concepts to a three-dimensional toroidal structure. We present parametric equations describing the torus geometry and develop a time-dependent deformation model that includes both stochastic and deterministic elements. A novel twisting deformation component enhances the realism of the structural changes. We define a critical threshold for maximum displacement, beyond which the torus undergoes structural failure, analogous to the bifurcation point in the biome model. Both models are implemented computationally, providing visual representations of the systems' evolution over time. The biome model illustrates the path to and consequences of bifurcation, while the torus simulation depicts the stages of deformation leading to structural break. This work contributes to the understanding of topological changes and critical transitions in both ecological and physical systems. By presenting these models in parallel, we highlight the universal nature of stability, bifurcation, and failure across different domains. The methodologies presented here have potential applications in ecology, materials science, structural engineering, and theoretical physics, offering a framework for studying the limits of system integrity under stress.

Preprint ARTICLE | doi:10.20944/preprints202403.0390.v2

On Induced Topologies by Ideal, Primal, Filter and Grill

Milan Matejdes

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: ideal; prima; grill; filter; local function; finer topology; compatibility; codense system

Online: 9 August 2024 (07:06:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2589.v2

The Angle Trisection Impossibility-A Euclidean Proof and the Inconsistent Property

Kimuya Alex

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Angle Trisection; Euclidean Geometry; Impossibility Proof; Geometric Inconsistency; Inconsistent Property; Proof Validity; Geometric Reasoning; Incommensurability

Online: 8 August 2024 (16:55:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.0116.v1

The Symmetry Group of the Grand Antiprism

Barry Monson

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: uniform polytopes; 600-cell; grand antiprism

Online: 2 August 2024 (10:31:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2589.v1

The Angle Trisection Impossibility-A Euclidean Proof and the Inconsistent Property

Kimuya Alex

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Angle Trisection; Euclidean Geometry; Impossibility Proof; Geometric Inconsistency; Inconsistent Property; Proof Validity; Geometric Reasoning; Incommensurability

Online: 1 August 2024 (05:37:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2551.v1

Euclidean Locality in Treonic Topological Spaces: The Genesis of Treonic Manifolds

Alejandro Jesús Bermejo Valdés

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: treonic spaces; Euclidean locality; topological manifolds; homeomorphisms; Bermejo algebras

Online: 31 July 2024 (14:13:20 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2462.v1

A Multi-Scale Mask Convolution based Blind Spot Network for Hyperspectral Anomaly Detection

Zhiwei Yang, Rui Zhao, Xiangchao Meng, Gang Yang, Weiwei Sun, Shenfu Zhang, Jinghui Li

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: hyperspectral anomaly detection; multi-scale anomaly targets; blind spot network; multi-scale mask convolution

Online: 30 July 2024 (11:39:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.1612.v1

On \v{C}ech-Completeness of the Space of $\tau$-Smooth Idempotent Probability Measures

Ljubisa D. R. Kocinac, Adilbek A. Zaitov, Muzaffar R. Eshimbetov

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: \v{C}ech-complete space; compact space; probability measure; $\tau$-smooth idempotent probability measure; neighbourhood system

Online: 19 July 2024 (16:57:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.1483.v1

Construction of a Second-Countable Treon Space From a New Metric Structure

Alejandro Jesús Bermejo Valdés

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Bermejo Algebras; Treon Algebra; second-countable space; metric topology; manifolds

Online: 18 July 2024 (10:31:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.0940.v1

Hausdorff Spaces in Bermejo Algebras: The Birth of Treonic Manifold Construction

Alejandro Jesús Bermejo Valdés

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Bermejo Algebra; Treons; Algebra B; Topology; Hausdorff Space

Online: 11 July 2024 (16:33:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1569.v1

Ricci–Bourguignon Almost Solitons with Special Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds

MANCHO MANEV

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Ricci– Bourguignon; almost contact B-metric manifold; almost contact complex Riemannian manifold; Sasaki-like manifold; vertical potential; conformal potential

Online: 23 May 2024 (14:16:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1453.v1

A New Approach for the Circular Inversion in l1- Normed Spaces

Temel Ermiş, Ali Osman Şen, Johan Gielis

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Finite-Dimensional Banach Spaces; Minkowski Geometry; Metric Geometry; l1-Norm; Manhattan Metric, Taxicab Metric

Online: 22 May 2024 (15:12:02 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202405.1294.v1

Panel Surface Area Maximization for Increasing PV Performance

Moses Oyaro Okello

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: solar energy; surface manifold; topology optimization

Online: 21 May 2024 (03:42:02 CEST)

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Solar energy is one of the most important renewable energy sources for many settings, such as households, solar-powered vehicles, power grid support, etc. However, the amount of solar energy produced is directly proportional to the surface area of the solar panel exposed to the sun rays, and so the challenges arise for the space required to install solar panels in order to get maximum area coverage of sun radiation energy absorption in constricted spaces such as vehicles powered by solar, small residential apartments, etc. The challenge with solar energy is that once a plate is installed, the space under it or above it cannot be used for another solar panel installation. This is due to the fact that the shadow cast by the above solar panel or structure prevents sun rays from reaching the below solar panel. The introduction of flexible solar panels that can take on any shape has given us the opportunity to explore the possibility of maximising solar plate surface area using surface manifold techniques. In this optimisation study, the constraint is that we have a space with fixed dimensions of length, width, and height, and the objective is to maximise the surface area of the panel within the given space dimensions to maximise solar energy absorption. Thus, this paper then proposes curving the panel surface and/or protruding the surfaces of the panel using the concept of a topology surface manifold to maximise the surface area: Protruding panel surface with shapes such as pyramidal, cone, hemisphere, sinusoidal wavy curve, etc. are analysed to check if the panel surface increases at all. The geometrical design result shows that the panel surface can increase by more than 20%. Although this paper only presents concept work and details of experimental design are yet to be performed, it should also be noted that curving surfaces have drawbacks, such as some protruding parts of solar panels when the plate is tilted, not facing the sun directly, which may cast shadows on parts of the solar panel, causing hindrance.

Preprint ARTICLE | doi:10.20944/preprints202405.1133.v1

Modular Quasi-pseudo Metrics and the Aggregation Problem

Maria del Mar Bibiloni-Femenias, Oscar Valero

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: modular quasi-pseudo metric; quasi-pseudo metric; aggregation; monotony; subadditivity; triangle triplet

Online: 17 May 2024 (17:22:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.0781.v1

A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies

Fahad Alsharari, Wafa Alqurashi, Islam M. Taha

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: intuitionistic fuzzy set; double fuzzy topology; (r, s) − g f sc set; (r, s) − g⊛ f sc set; continuity; (r, s)-GF S-regular space; (r, s)-GF S-normal space; compactness

Online: 13 May 2024 (12:30:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1371.v1

Non Computer Proof of the Four Color Theorem: N-Color Theory

Sheng Qin

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: The Four Color Theorem；N-Color Theory; N-order graph structure

Online: 22 April 2024 (16:28:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1125.v1

On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness

Islam M. Taha

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: intuitionistic fuzzy set; double fuzzy topology; continuity; compactness

Online: 17 April 2024 (09:00:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1007.v1

DSTree: A Spatio-Temporal Indexing Data Structure for Distributed Networks

Majid Hojati, Steven Roberts, Colin Robertson

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: spatio-temporal indexing; temporal topology; query processing; IPFS; distributed systems; smart contracts; blockchain

Online: 18 March 2024 (10:29:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0910.v1

When Four Cyclic Antipodal Points Are Ordered Counterclockwise in Euclidean and Hyperbolic Geometry

Abraham A. Ungar

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: cyclic antipodal points; relativistic model of hyperbolic geometry; gyrovector space; gyrotrigonometry

Online: 15 March 2024 (11:09:32 CET)

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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/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/preprints202401.2038.v1

Fractal Dimension of the Generalized Z-Entropy of The Rényian Formalism of Stable Queue with Some Potential Applications of Fractal Dimension to Big Data Analytics

Dr Ismail A Mageed

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Fractal Dimension(D), Generalized Z-Entropy, Google Earth satellite (GEs),GNU Image Manipulation, Big Data Analytics(BDAs).

Online: 29 January 2024 (14:39:18 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.2001.v1

Fractal Dimension(D_f )Theory of Ismail's entropy(IE) with Potential D_f applications to Smart Cities

Dr Ismail A Mageed

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Fractal dimension((D_f ); Ismail entropy (IE); Information theory; smart cities

Online: 29 January 2024 (08:32:25 CET)

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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/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/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/preprints202312.1533.v1

Presymmetric w-Distances on Metric Spaces

Salvador Romaguera, Pedro Tirado

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: metric space; presymmetric w-distance; basic p-contraction of Suzuki-type; p-contractive self map; fixed point

Online: 20 December 2023 (15:50:04 CET)

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Preprint ARTICLE | doi:10.20944/preprints202312.1477.v1

The Strong Ekeland Variational Principle in Quasi-Pseudometric Spaces

Stefan Cobzas

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: quasi-metric space; completeness in quasi-metric spaces; variational principles; Ekeland variational principle; strong Ekeland principle

Online: 20 December 2023 (12:18:48 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/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/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/preprints202311.0799.v1

Hypersurfaces in a Euclidean Space with a Killing Vector Field

Mohammed Guediri, Sharief Deshmukh

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Euclidean space; Hypersurface; Killing vector field

Online: 13 November 2023 (10:21:04 CET)

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Preprint ARTICLE | doi:10.20944/preprints202311.0474.v1

Determination of the Integral Curves of the Completely Integrable Gradient System on the Three-Parameter Beta Bivariate Statistical Manifold of the First Kind

Prosper Rosaire MAMA ASSANDJE, Joseph Dongho, Thomas Bouetou Bouetou

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Hamiltonian function; gradient system; Lax pair representation

Online: 7 November 2023 (14:19:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202311.0354.v1

SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle

Viktor Abramov, Olga Liivapuu

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: tensors; rotation group; tensor irreducible representations; complex manifolds; special geometries; connection; Pauli’s exclusion principle

Online: 7 November 2023 (02:50:08 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.1798.v1

Ricci Vector Fields

Hanan Alohali, Sharief Deshmukh

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: r-Ricci vector fields; Fischer-Marsden equation; m-sphere; Ricci curvature

Online: 27 October 2023 (11:18:20 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/preprints202310.0802.v1

An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces

Xuefei Wang

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: bivariate continuous functions; fractal dimension; the Box dimension; superposition of 9 fractal surfaces

Online: 12 October 2023 (09:57:26 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/preprints202309.2080.v1

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: 3 October 2023 (03:16:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1223.v1

Properties of Topologies for the Continuous Representability of All Weakly Continuous Preorders

Gianni Bosi, Laura Franzoi, Gabriele Sbaiz

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: strongly useful topology; weakly continuous preorder; hereditarily separable topology; Lindelöf property

Online: 19 September 2023 (03:49:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.1094.v1

Weak Nearly Sasakian and Weak Nearly Cosymplectic Manifolds

Vladimir Rovenski

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: n/a; weak nearly Sasakian manifold; weak nearly cosymplectic manifold; Killing vector field; hypersurface

Online: 18 September 2023 (14:19:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202309.0918.v1

Categorical Join and Generating Families in Diffeological Spaces

Enrique Macías -Virgós, Reihaneh Mehrabi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Diffeological space; Generating family; Categorical join

Online: 14 September 2023 (08:36:11 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0773.v1

A New Definition of Dual Spline Curves for Curve Modeling and Geometry Defeaturing

Baotao Chi, Shengmin Bai, Qianjian Guo, Yaoming Zhang, Wei Yuan, Can Li

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Dual spline curves; Adaptive curve refinement; Curve modeling; Geometry defeaturing

Online: 12 July 2023 (05:50:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202307.0670.v1

Fuzzy Approximating Metrics, Approximating Parametrized Metrics and Their Relations With Fuzzy Partial Metrics

Raivis Bēts, Alexander Šostak

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Fuzzy metrics; fuzzy approximating metrics; approximating parametrized metrics; fuzzy partial metrics

Online: 11 July 2023 (10:11:29 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/preprints202306.1809.v1

On the Rigidity of the Sasakian Structure and Characterization of Cosymplectic Manifolds

Dhriti Sundar Patra, Vladimir Rovenski

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: weak contact structure; Sasakian structure; cosymplectic structure; contact vector field.

Online: 27 June 2023 (02:53:13 CEST)

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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/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/preprints202306.0214.v1

Pairs of Associated Yamabe Almost Solitons with Vertical Potential on Almost Contact Complex Riemannian Manifolds

Mancho Manev

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Yamabe soliton; almost contact B-metric manifold; almost contact complex Riemannian manifold; Sasaki-like manifold; torse-forming vector field

Online: 2 June 2023 (14:33:49 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/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/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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Preprint ARTICLE | doi:10.20944/preprints202304.1148.v1

A Note on Nearly Sasakian Manifolds

Fortuné Massamba, Arthur Nzunogera

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Nearly Sasakian space forms; k-nullity distribution; locally symmetric manifold; semi-symmetric manifold; Ricci-symmetric manifold

Online: 28 April 2023 (08:40:49 CEST)

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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 BRIEF REPORT | doi:10.20944/preprints202303.0490.v1

An Proposed Algorithm for Generating Criteria Necessary to Establish Congruence between Two Convex N-Sided Polygons in Euclidean Geometry

Shakil Rafi

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Triangles; Geometry; Euclidean Geometry

Online: 28 March 2023 (13:50:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0223.v1

On an Indefinite Metric on a 4-Dimensional Riemannian Manifold

Dimitar Razpopov, Georgi Dzhelepov, Iva Rumenova Dokuzova

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Riemannian manifold; indefinite metric tensor; length; area; Green’s formula

Online: 13 March 2023 (08:38:55 CET)

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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/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/preprints202301.0529.v2

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: 14 February 2023 (01:43:07 CET)

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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/preprints202301.0385.v1

WEA: A Node Importance Algorithm in Weighted Networks

Na Zhao, Linjie Chen, Jie Li, Zhen Long, Ming Jing, Jian Wang

Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Complex Network; Weighted Network; Node Importance; Dynamic Programming

Online: 23 January 2023 (01:45:54 CET)

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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/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 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.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/preprints202209.0089.v3

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: 19 September 2022 (10:21:05 CEST)

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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/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/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/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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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/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/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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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.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/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.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.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.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/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/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/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.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/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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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/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/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/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 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/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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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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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/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.

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/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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Computer Science and Mathematics