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Preprint ARTICLE | doi:10.20944/preprints202208.0231.v1

Morphological Simulation of Phyllotactic Spiral-Ring Patterns by the Galactic Spiral Equations from the ROTASE Model

Hongjun Pan

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Phyllotactic spiral-ring pattern; Galactic spiral equations; Simulation; Fibonacci sibling sequence

Online: 12 August 2022 (08:49:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0170.v1

Impact of Astrocytic Coverage of Synapses on the Short-term Memory of a Computational Neuron-Astrocyte Network

Zonglun Li, Yuliya Tsybina, Susanna Gordleeva, Alexey Zaikin

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: neuron; astrocyte; network; short-term memory; spatial frequency; computational biology

Online: 9 August 2022 (04:04:31 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0129.v1

A Study of the Jacobi Stability of the Rosenzweig–MacArthur Predator–prey System by the KCC Geometric Theory

Florian Munteanu

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: predator–prey systems; Kolmogorov systems; KCC-theory; the deviation curvature tensor; Jacobi stability

Online: 8 August 2022 (03:58:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0016.v1

High Performance Parallel Pseudorandom Number Generator on Cellular Automata

Alla Levina, Daniyar Mukhamedjanov, Danil Bogaevskiy, Pavel Lyakhov, Maria Valueva, Dmitrii Kaplun

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Security; Pseudorandom Number Generation; Parallel Computing; Cellular Automata

Online: 1 August 2022 (09:21:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0426.v1

Predicting the Cross-Coordinated Immune Response Dynamics in Sars-Cov-2 Infection: Implications for Disease Pathogenesis

Dmitry Grebennikov, Antonina Karsonova, Marina Loginova, Valentina Casella, Andreas Meyerhans, Gennady Bocharov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: SARS-CoV-2 infection; innate immune response; antigen-specific immune response; kinetic coordination; mathematical model; pathogenesis, long COVID-19

Online: 27 July 2022 (15:11:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0291.v1

A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus

Florian Munteanu

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mathematical models; systems of ordinary differential equations; dynamical systems; stability

Online: 19 July 2022 (15:41:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0282.v1

A 4-Dimensional Mathematical Model for Interaction between the Human Immune System and a Virus

Florian Munteanu

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: population dynamics; predator-prey; covid-19; dynamical systems; stability; ODE

Online: 19 July 2022 (07:55:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0117.v2

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

Xinggui Li, Ruofeng Rao, Shouming Zhong, Xinsong Yang, Hu Li, Yulin Zhang, Jialin Huang

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Mittag-Leffler stability; Caputo fractional-order derivative; non-Lipschitz continuity; hyper-chaotic financial system; Mittag-Leffler function

Online: 8 July 2022 (10:31:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0122.v1

Approximate Analytical Solution of Unstable Ordinary Differential Equation Using Differential Evolution Algorithm

Ashiribo Wusu, Olusola Olabanjo

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Unstable; Ordinary Differential Equation; Initial Value Problems; Optimization; Differential Evolution

Online: 7 July 2022 (09:29:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0117.v1

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

Xinggui Li, Ruofeng Rao, Shouming Zhong, Xinsong Yang, Hu Li, Yulin Zhang

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Mittag-Leffler stability; Caputo fractional-order derivative; non-Lipschitz continuity; hyper-chaotic financial system; Mittag-Leffler function

Online: 7 July 2022 (09:04:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0110.v1

An Account of Models of Molecular Circuits for Associative Learning with Reinforcement Effect and Forced Dissociation

Zonglun Li, Alya Fattah, Peter Timashev, Alexey Zaikin

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: associative learning; molecular circuits; synthetic biology; mathematical modeling; Hill equation; Pavlov’s dog; reinforcement; dissociation; non-dimensionalization

Online: 7 July 2022 (04:38:20 CEST)

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Preprint REVIEW | doi:10.20944/preprints202207.0082.v1

Two Common Mistakes in Applying ANOVA Test: Guide for Biological Researchers

Fateme Azizi, Rasoul Ghasemi, Maryam Ardalan

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: ANOVA; homogeneity of variance; Levene’s test; multiple comparison analysis; post hoc test

Online: 6 July 2022 (03:41:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0029.v1

Systems Dynamics and the Analytical Network Process as A methodology for the Evaluation and Prioritization of Green Projects: A New Proposal that Involves Participative Integration

Julian Andres Castrillon-Gomez, Gerard Olivar-Tost, Johnny Valencia-Calvo

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: community participation; Systems Dynamics Model; sustainable development; multi-criteria deci-sion-making (MCDM); analytic network process (ANP)

Online: 4 July 2022 (04:22:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0357.v1

A Closed-Form Expression for the Unit Step Function

John Venetis

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Unit Step Function; closed - form expression; inverse tangent function

Online: 27 June 2022 (09:34:58 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0344.v1

Traveling Wave Solutions of the Loaded Non-linear Klein-Gordon Equation via Functional Variable Method

Bazar Babajanov, Fakhriddin Abdikarimov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: loaded Klein-Gordon equation; periodic solutions; functional variable method; trigonometric function; soliton solutions; hyperbolic function

Online: 27 June 2022 (03:23:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0222.v1

Dynamic Reduction-based Virtual Models for Digital Twins-A Comparative Study

Soumya Maulik, Daniel Riordan, Joseph Walsh

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: digital twin; Industry 4.0; MATLAB; ANSYS; simulation; crane; modal analysis; dynamic substructuring; dynamic reduction; component modal synthesis

Online: 15 June 2022 (10:19:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0081.v1

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

Igor Yadykin

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: spectral decomposition; linear and bilinear systems; Gramians; generalized Lyapunov equation; Xiao matrices; controllability; observability

Online: 6 June 2022 (09:57:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0074.v1

A Cooperative Parallel Tabu Search Meta-heuristic for the Vehicle Routing Problem with Time Windows

Hassan El Fahim

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: vehicle routing problem; time window; parallel meta-heuristic; cooperative search; tabu search

Online: 6 June 2022 (09:08:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0414.v1

Fractional Taylor Expansions and Derivative Regularization

Dimiter Prodanov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: holder classes; local fractional derivative; fractional velocity

Online: 31 May 2022 (08:15:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0352.v1

Artificial Neuron-based Model for a Hybrid Real-Time System: Induction Motor Case Study

Manuel Isidoro Capel

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Quality real-time systems; Automated Machine Learning; Real-time embedded control systems; Cyber-physical systems; Neural Networks

Online: 25 May 2022 (11:17:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0335.v1

A Model for the Proliferation-Quiescence Transition in Human Cells

Kudzanayi Z. Mapfumo, Jane C. Pagan’a, Victor Ogasa Juma, Nikos I. Kavallaris, Anotida Madzvamuse

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Cell cycle; proliferation; quiescence; system of ODEs; bifurcation analysis; numerical bifurcation analysis; sensitivity analysis

Online: 24 May 2022 (11:52:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0301.v1

An Iterated Local Search with Multiple Perturbation Operators and a Varying Perturbation Strength for the Capacitated Team Orienteering Problem with Time Windows

Hassan El Fahim

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: combinatorial optimization; orienteering problem; meta-heuristic; iterated local search

Online: 23 May 2022 (10:51:36 CEST)

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The capacitated team orienteering problem with time windows (CTOPTW) is a NP-hard combinatorial optimization problem. In the CTOPTW, a set of customers is given each with a profit, a demand, a service time and a time window. A homogeneous fleet of vehicles is available for serving customers and collecting their associated profits. Each vehicle is constrained by a maximum tour duration and a limited capacity. The CTOPTW is concerned with the determination of a preset number of vehicle tours that begin and end at a depot, visit each customer no more than once while satisfying the time duration, time window and vehicle capacity constraints on each tour. The objective is to maximize the total profit collected. In this study we propose an iterated local search (ILS) algorithm to deal with the CTOPTW. ILS is a single solution based meta-heuristic that successively invokes a local search procedure to explore the solution space. A perturbation operator is used to modify the current local optimum solution in order to provide a starting solution for the local search procedure. As different problems and instances have different characteristics, the success of the ILS is highly dependent on the local search procedure, the perturbation operator(s) and the perturbation strength. The basic ILS uses a single perturbation operator and the perturbation strength remains the same during the optimization process. To address these issues, we use three different perturbation operators and a varying perturbation strength which changes as the algorithm progresses. The idea is to assign a larger perturbation strength in the early stages of the search in order to focus on exploring the search space. The perturbation strength is gradually decreased so that we focus more on exploitation. The computational results show that the proposed ILS algorithm is able to generate high quality solutions on the CTOPTW benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both the solution quality and computational time. Moreover, the proposed ILS produces 21 best known results and 5 new best solutions.

Preprint ARTICLE | doi:10.20944/preprints202205.0174.v1

Analyzing Collatz Conjecture Using the Mathematical Complete Induction Method

Mercedes Orús-Lacort, Christophe Jouis

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: number theory; Collatz conjecture

Online: 13 May 2022 (03:08:42 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0050.v1

Improved Unsupervised Learning Method for Material Properties Identification Based on Mode Separation of Ultrasonic Guided Waves

Mikhail V. Golub, Olga V. Doroshenko, Mikhail A. Arsenov, Artem A. Eremin, Yan Gu, Ilya Bareiko

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: laminate; material properties; identification; guided waves; mode separation

Online: 5 May 2022 (16:08:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0025.v1

The Multifunctional Modulation Micromechanical Gyro

Lyalya Bakhtieva, Vladimir Bogolyubov, Maxim Tumakov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: gyro; micromechanical system; newtonmeter

Online: 5 May 2022 (08:04:24 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0023.v1

Random Triangle Theory: a Computational Approach

Ivano Azzini

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Random Triangle; Quasiorthogonal Dimension; Combinatorics; Computational Problems

Online: 5 May 2022 (07:58:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0019.v1

Mathematical Modeling of Seepage Velocity Influence on Transport of Dissolved Heavy Metals from Waste-Dumps to River Channel

Zablon Ombati Rogito, Joash Kerongo, Obogi Robert

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: seepage velocity; heavy metals; reservoirs pollution

Online: 5 May 2022 (03:19:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0401.v1

Collatz Conjecture: An Order Machine

Michael Williams

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Collatz conjecture; hailstone sequences; Cantor isomorphism; order embedding; Jacobsthal numbers; congruence

Online: 31 March 2022 (08:03:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0385.v1

About Adaptive Identification of Bouc-Wen Hysteresis

Nikolay Karabutov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: hysteresis; Ben-Wien model; adaptive observer; exponential dissipativity; Lyapunov vector function; uncertainty

Online: 30 March 2022 (04:18:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0362.v1

The Adaptive Reductions in Game Theory and their Applications to bOOsting

Ivano Azzini

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: game theory; economic relation; problem reductions; binary and regression problems; machine learning; boosting, neural network

Online: 28 March 2022 (12:11:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0248.v1

Some Results in Classes Of Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Neutrosophic Quasi-Order; Neutrosophic Quasi-Size; Neutrosophic Quasi-Number; Neutrosophic Quasi-Co-Number; Neutrosophic Co-t-Neighborhood

Online: 17 March 2022 (08:48:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0334.v2

Failed Independent Number in Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Neutrosophic Failed-independent Number; Failed independent Neutrosophic-Number; Minimal Set

Online: 4 March 2022 (04:18:55 CET)

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New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously; failed independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Failed-Independent Number,” and “Setting of Failed Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, two neighbors, form maximal set but with slightly differences, in cycle-neutrosophic graphs, two neighbors forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of all vertices leads us to neutrosophic failed-independent number and failed independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices containing only center and one other vertex, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices including two vertices from different parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of t vertices from different parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic failed-independent number but the neutrosophic cardinality of a set has eligibility to call failed independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connections amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202202.0343.v1

Failed Zero-Forcing Number in Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: failed zero-forcing number; maximal set; vertex

Online: 26 February 2022 (03:37:38 CET)

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New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202202.0334.v1

Independent Set in Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: neutrosophic independent number; independent neutrosophic-number; maximal set

Online: 25 February 2022 (10:18:52 CET)

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New setting is introduced to study neutrosophic independent number and independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having no edge amid vertices in a set is a key type of approach to have these notions namely neutrosophic independent number and independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which doesn’t have some vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S aren’t endpoints for an edge, simultaneously; independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S aren’t endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Independent Number,” and “Setting of Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic independent number and independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, either odd indexes or even indexes, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, either odd indexes or even indexes, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices containing one vertex leads us to neutrosophic independent number and independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding (four) vertices from one part as possible makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding vertices from all parts but one part, makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic independent number and independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic independent number but the neutrosophic cardinality of a set has eligibility to call independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have connection amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202202.0159.v1

Generative Adversarial Unsupervised Image Restoration in Hybrid Degradation Scenes

Fan Tang, Xinyu Zhu, Jinrong Hu, Juhong Tie, Jiliu Zhou, Ying Fu

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: hybrid degradation; generative adversarial network; attention mechanism; disentangled representation

Online: 11 February 2022 (08:42:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0100.v1

Quasi-Degree in Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Quasi-Co-Degree; Quasi-Degree; Vertex

Online: 7 February 2022 (16:23:20 CET)

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New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints201908.0128.v2

Synthesis of Strategic Games With Multiple Pre-set Nash Equilibria - An Artificial Inference Approach Using Fuzzy ASA

Hime Oliveira

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Nash equilibria; Mechanism design; Artificial inference; Global learning

Online: 31 January 2022 (11:19:04 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0442.v1

Global Powerful Alliance in Strong Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Modified Neutrosophic Number; Global Powerful Alliance; R-Regular-Strong

Online: 28 January 2022 (15:09:54 CET)

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New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202201.0429.v1

Global Offensive Alliance in Strong Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Modified Neutrosophic Number; Global Offensive Alliance; Complete Neutrosophic Graph

Online: 28 January 2022 (08:47:20 CET)

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New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202201.0376.v1

Methodological Analysis of Damage Estimation in Hydraulic Infrastructures

Ramón Egea Pérez, Francisco Navarro Gonzalez, Mónica Cortés Molina, Joaquín Melgarejo Moreno

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: flood damage methodology; hydraulic infrastructure; resilience; indicators

Online: 25 January 2022 (10:27:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0249.v1

Fault-Tolerant Detection Systems on the King's Grid

Devin Jean, Suk Seo

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: domination, detection system, identifying-code, open-locating-dominating set, fault-tolerant, king's grid, density

Online: 18 January 2022 (09:43:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0239.v1

Three Types of Neutrosophic Alliances based on Connectedness and (Strong) Edges

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Alliance; Offensive Alliance; Defensive Alliance

Online: 17 January 2022 (15:29:26 CET)

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New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202201.0145.v1

Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Coloring Numbers; Resolving Numbers; Dominating Numbers

Online: 11 January 2022 (13:43:56 CET)

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New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202201.0027.v1

Co-degree and Degree of classes of Neutrosophic Hypergraphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Degree, Coloring, Co-degree

Online: 5 January 2022 (10:24:32 CET)

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New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202112.0448.v1

Dimension and Coloring alongside Domination in Neutrosophic Hypergraphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Dimension; Coloring; Domination

Online: 28 December 2021 (13:42:44 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0335.v1

Different Types of Neutrosophic Chromatic Number

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Neutrosophic Connctedness; Neutrosophic Graphs; Chromatic Number

Online: 21 December 2021 (13:33:11 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0310.v1

Selection of Optimum Nonlinear Confusion Component of Information Confidentiality Mechanism Using Grey Theory Based Decision-Making Technique

Nabilah Hani Abughazalah, Majid Khan

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Grey theory; Grey set; MCDM; Decision making problem; Cryptosystem; Encryption algorithm

Online: 20 December 2021 (12:15:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0295.v1

Nanoparticle Based Water Treatment Model in Squeezing Channel under Magnetic Field

Sergei Zuev, Zakir Hussain, Petr Kabalyants

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: nano-fluid; nanoparticles removing; magnetohydrodynamics; stability of the flow; water treatment; exact solution; instability of the flow

Online: 20 December 2021 (09:37:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0293.v1

Bounds for the Minimum Distance and Covering Radius of Orthogonal Arrays via Their Distance Distributions

Silvia Boumova, Peter Boyvalenkov, Maya Stoyanova

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Orthogonal Arrays; Distance distributions; Minimum distance; Covering radius

Online: 17 December 2021 (15:49:57 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0279.v1

Preconditioning the Quad Dominant Mesh Generator for Ship Structural Analysis

Luka Grubisic, Domagoj Lacmanović, Josip Tambača

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mesh generation; quad dominated surface meshes; finite element analysis; shell elements

Online: 16 December 2021 (15:44:20 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0226.v1

Neutrosophic Chromatic Number Based on Connectedness

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Neutrosophic Connctedness; Neutrosophic Graphs; Chromatic Number

Online: 14 December 2021 (11:14:50 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0177.v1

Chromatic Number and Neutrosophic Chromatic Number

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Neutrosophic Strong; Neutrosophic Graphs; Chromatic Number

Online: 10 December 2021 (13:08:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0176.v1

Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

Nathan Ritchey, Rajeev Rajaram

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Policy Value; Kolmogorov forward equations; Multi-state model; Thiele's differential equation; Hattendorff differential equation

Online: 10 December 2021 (12:29:58 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0094.v1

Complex Numbers for Relativistic Operations

Dmitry S Kulyabov, Anna V Korolkova, Leonid A Sevastianov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Cayley-Klein model; hypercomplex numbers; hyperbolic complex numbers; special relativity; superluminal motion

Online: 6 December 2021 (17:38:41 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0528.v2

Taming Hyperchaos with ESDDFD Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

Gregory Gibson, Dominic Clemence-Mkhope

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Conformable calculus; Fractional-order financial system; ESDDFD and NSFD methods; Hyperchaotic attractor; Market confidence; Ethics risk

Online: 6 December 2021 (12:48:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0576.v1

Modeling and Numerical Simulation of a Vegetation Cover

Arturo Hidalgo, Lourdes Tello

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: vegetation cover; latent heat of fusion; climate model; climate change; energy balance models; finite volume method; WENO reconstruction; Runge-Kutta TVD

Online: 30 November 2021 (17:35:17 CET)

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Preprint ARTICLE | doi:10.20944/preprints201908.0150.v3

Notes on the Lie Symmetry Exact Explicit Solutions for Nonlinear Burgers' Equation

Bohua Sun

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Lie group; Burgers equation; exact solution; general solution; elementary function

Online: 29 November 2021 (12:00:06 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0528.v1

Taming Hyperchaos with ESDDFD Discretization of a Conformable Fractional Derivative Financial System with Market Confidence and Ethics Risk

Gregory Gibson, Dominic Clemence-Mkhope

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Conformable calculus; Fractional-order financial system; ESDDFD and NSFD methods; Hyperchaotic attractor; Market confidence; Ethics risk

Online: 29 November 2021 (11:59:42 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v7

Metric Dimension in fuzzy(neutrosophic) Graphs-VII

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs; Neutrosophic Graphs; Dimension

Online: 26 November 2021 (10:03:20 CET)

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New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

Preprint ARTICLE | doi:10.20944/preprints202111.0466.v1

Efficient and Stable Voxel-Based Algorithm for Computing 3D Zernike Moments and Shape Reconstruction

An-Wen Deng, Chih-Ying Gwo

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: 3D Zernike moments; 3D Zernike radial polynomials; 3D Zernike polynomials; Spherical harmonics; Recurrence formula; Matrix Lie Group; Group action

Online: 25 November 2021 (09:54:08 CET)

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Preprint ARTICLE | doi:10.20944/preprints202109.0399.v2

Exact Solutions and Dynamic Properties of Perturbed Nonlinear Schrodinger Equation Arised From Nano Optical Fibers

Baoshu Xin, Shuangqing Chen

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: perturbed nonlinear schrodinger equation; conformal fractional derivative; prior estimate; bifurcation method; complete discrimination system for polynomial method

Online: 24 November 2021 (13:04:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v6

Metric Dimension in fuzzy(neutrosophic) Graphs-VI

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs; Neutrosophic Graphs; Dimension

Online: 22 November 2021 (14:01:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v5

Metric Dimension in fuzzy(neutrosophic) Graphs-V

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs; Neutrosophic Graphs; Dimension

Online: 19 November 2021 (14:51:27 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v4

Metric Dimension in fuzzy(neutrosophic) Graphs-IV

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs; Neutrosophic Graphs; Dimension

Online: 18 November 2021 (13:44:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0276.v1

Mathematical Incorrectnes of So Called Higuchi‘S Fractal Dimension

Dalibor Martišek

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Higuchi’s method; Higuchi’s fractal dimension; distance; metric space

Online: 16 November 2021 (08:46:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v3

Metric Dimension in fuzzy(neutrosophic) Graphs-III

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs; Neutrosophic Graphs; Dimension

Online: 12 November 2021 (14:46:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v2

Metric Dimension in fuzzy (neutrsophic) Graphs-II

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs; Neutrosophic Graphs; Dimension

Online: 9 November 2021 (11:22:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0146.v1

The Bipolar Logic of Feedforward and Feedback Circuits

Arturo Tozzi

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: bipolar fuzzy set; decision making problem; non-classical logic; scholasticism; transcranial magnetic stimulation.

Online: 8 November 2021 (13:38:04 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0142.v1

Metric Dimension in Fuzzy Graphs and Neutrosophic Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fuzzy Graphs, Neutrosophic Graphs, Dimension

Online: 8 November 2021 (13:21:27 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0063.v1

Solution of Fractional Autonomous Ordinary Differential Equations

Rami AlAhmad, Qusai AlAhmad, Ahmad Abdelhadi

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fractional derivatives; Caputo fractional derivative; the Caputo-Fabrizio fractional derivative; Laplace transform

Online: 3 November 2021 (08:29:12 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0005.v1

Prevention of hazards induced by a Radiation Fireball through Computational Geometry and Parametric Design

Francisco Salguero-Andújar, Joseph M. Cabeza-Lainez, Federico Blasco-Macias

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: prevention of explosion risks; fireball; thermal radiation; computational geometry; geometric algorithms.

Online: 1 November 2021 (11:18:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0127.v1

Governance and Socioeconomic Factors Contributing to Antimicrobial Resistance in European Countries: A Data Panel and Machine-Learning Analysis

Julian Riaño-Moreno, Jhoana P. Romero-Leiton, Kernel Prieto

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Descriptive analysis; principal components analysis; k-means clustering; data panel regression method; machine learning; XGBoost algorithms; random forest algorithms

Online: 8 October 2021 (08:30:13 CEST)

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Working Paper ARTICLE

Generation of Fractals using Polynomial Iterations in Polar Coordinates

Serguei Charonov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Fractals, Julia set, Mandelbrot set.

Online: 24 September 2021 (12:39:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0423.v1

Higher Dimensional Bianchi Type-III String Cosmological Models in Lyra Geometry

Kangujam Priyokumar Singh, Jiten Baro, Asem Jotin Meitei, S. Romaleima Devi

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Five dimension; Cloud String; Bianchi Type-III Space-Time; Lyra Geometry; Expansion Scalar and Big-bang

Online: 24 September 2021 (09:17:54 CEST)

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Working Paper ARTICLE

Randomized Projection Learning Method for Dynamic Mode Decomposition

Sudam Surasinghe, Erik M. Bollt

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Koopman Operator; Dynamic Mode Decomposition(DMD); Johnson-Lindenstrauss Lemma; Random Projection; Data-driven method

Online: 24 September 2021 (09:14:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0399.v1

Exact Solutions and Dynamic Properties of Perturbed Nonlinear Schrodinger Equation Arised From Nano Optical Fibers

Baoshu Xin

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: perturbed nonlinear schrodinger equation; conformal fractional derivative; prior estimate; bifurcation method; complete discrimination system for polynomial method

Online: 23 September 2021 (10:31:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0300.v1

A Mathematical Modeling Approach for Targeted Radionuclide and Chimeric Antigen Receptor-T Cell Combination Therapy

Vikram Adhikarla, Dennis Awuah, Alex Brummer, Enrico Caserta, Amrita Krishnan, Flavia Pichiorri, Megan Minnix, John E. Shively, Jeffrey Y.C. Wong, Xiuli Wang, Russell C. Rockne

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: CAR T; Targeted Radionuclide Therapy; TRT; Mathematical Model; Multiple Myeloma; Immunotherapy; Daratumumab; CS1; Combination Therapy

Online: 17 September 2021 (09:32:33 CEST)

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Preprint SHORT NOTE | doi:10.20944/preprints202109.0217.v1

Harmonisation of Classical Wave Equation

Alireza Jamali

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: harmonic analysis; nonlinear partial differential equation

Online: 13 September 2021 (15:36:10 CEST)

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Preprint REVIEW | doi:10.20944/preprints202109.0141.v1

Asymptotic Methods

Mohammed Akram Fellah

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Regular & Singular Perturbations; WKB Method; Watson's Lemma, Laplace's Method

Online: 8 September 2021 (11:20:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0557.v1

A Meaning for the Second Power of the Number Pi. Determining the Surface of a Regular Conoid by Virtue of Ramanujan’s Approximation

Joseph Cabeza Lainez

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Conoid; Ellipse; Ramanujan; Calculus of surface areas; number Psi; number Pi; 3D-construction of complex Geometries; Engineering Design Objects; Architectural Forms.

Online: 31 August 2021 (11:04:18 CEST)

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Working Paper ARTICLE

Denoising of Spectra by Adaptive Multiwindow Model Fitting.

Serguei Charonov

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Denoising; Savitzky-Golay filter; polynomial fitting.

Online: 23 August 2021 (12:28:24 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0229.v1

Valued Number And Set

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Valued Number, Valued Set, Longest Path, Valued Graph

Online: 10 August 2021 (10:13:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0508.v1

Set And Its Operations

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Set, Ghost Set, Edge, Neighbor Edges.

Online: 21 June 2021 (11:36:18 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0392.v1

Metric Dimensions Of Graphs

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Metric Dimension, Metric Number, Metric Set, Metric Vertex.

Online: 15 June 2021 (09:41:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0189.v1

Big Sets Of Vertices

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Special Set, Set's Weight, Special Number, Number's Position.

Online: 7 June 2021 (14:52:32 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0080.v1

Matroid And Its Relations

Henry Garrett

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Edge, Groupoid, Named and unnamed graphs, Matroid

Online: 2 June 2021 (14:10:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202105.0323.v1

A Mathematical Description of the Bone Marrow Dynamics of CAR T-Cell Therapy in B-cell Childhood Acute Lymphoblastic Leukemia

Álvaro Martínez-Rubio, Salvador Chulián, Cristina Blázquez Goñi, Antonio Pérez Martínez, Manuel Ramírez Orellana, Alfonso Navarro-Zapata, Cristina Ferreras, Victor Manuel Pérez-García, María Rosa

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: CAR T; Bone Marrow; Mathematical Model; Acute Lymphoblastic Leukemia; B cell

Online: 14 May 2021 (11:26:20 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202105.0031.v1

Taking Stock of Some Recent and Notable Contribution to Research in Portfolio Analysis

Tony S. Wirjanto, Danqiao Guo, Chengguo Weng

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: finance; portfolio optimization; tail eigenvalue amplification; high-dimensional setting; factor models

Online: 5 May 2021 (10:40:08 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202104.0541.v1

Sinc Based Inverse Laplace Transforms, Mittag-Leffler Functions and their Approximation for Fractional Calculus

Gerd Baumann

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Sinc methods; inverse Laplace transform; indefinite integrals; fractional calculus; Mittag−Leffler function; Prabhakar function; variable fractional order differentiation; variable fractional order integration

Online: 20 April 2021 (12:45:42 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202104.0125.v1

Impact of Partial lockdown on Time-Dependent Effective Reproduction Number of COVID-19 infection in Ghana: Application of change point analysis

Joseph Armachie, Agnes Adom-Konadu, Morrison Asiamah, Duah Dwomoh

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: COVID-19; Effective reproductive number; Lockdown.

Online: 5 April 2021 (12:25:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202104.0082.v1

Dynamics of a System of Higher Order Difference Equations with Quadratic Terms

Erkan Taşdemir

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Difference equations; global asymptotic stability; boundedness; rate of convergence; oscillation

Online: 5 April 2021 (11:48:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202103.0151.v2

A Hybrid Modelling Technique of Epidemic Outbreaks With Application to COVID-19 Dynamics in West Africa

Chénangnon Frédéric Tovissodé, Jonas Têlé Doumatè, Romain Glèlè Kakaï

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Growth model; Epidemic latency period; Reproduction number; West Africa

Online: 19 March 2021 (11:22:38 CET)

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Working Paper ARTICLE

Real Time Aircraft Atypical Approach Detection for Air Traffic Control

Gabriel Jarry, Daniel Delahaye, Stephane Puechmorel, Eric Feron

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Approach Path Management; Atypical Flight Event; Non-Compliant Approach; Real Time; Anomaly Detection; Functional Principal Component Analysis; Unsupervised Learn- ing; Dubins Path

Online: 12 March 2021 (21:17:22 CET)

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Preprint ARTICLE | doi:10.20944/preprints202103.0042.v1

Determination of the modulus of elasticity using a Smartphone and mode of unsupport beam Euler-Bernoulli

Newton Huamaní Castro

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Modulus of elasticity; frequency spectrum; mic; Euler-Bernoulli equation

Online: 1 March 2021 (18:31:31 CET)

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Preprint ARTICLE | doi:10.20944/preprints202102.0135.v1

Estimating Algorithmic Information using Quantum Computing for Genomics Applications

Aritra Sarkar, Zaid Al-Ars, Koen Bertels

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: algorithmic information theory; universal distribution; Kolmogorov complexity; quantum algorithms; quantum circuit model; quantum Turing machine; genomics; viral genomics; meta-biology

Online: 4 February 2021 (12:04:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202101.0080.v1

Community Detection Problem Based on Polarization Measures. An application to Twitter: the COVID-19 case in Spain

Inmaculada Gutiérrez García-Pardo, Juan Antonio Guevara Gil, Daniel Gómez González, Javier Castro Cantalejo, Rosa Espínola Vílchez

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Networks; Community Detection; Extended Fuzzy Graphs; Polarization; Fuzzy Sets; Ordinal Variation

Online: 5 January 2021 (11:18:08 CET)

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Preprint ARTICLE | doi:10.20944/preprints202012.0626.v1

Degenerate Sumudu Transform and Its Properties

Ugur Duran

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Degenerate exponential function; degenerate gamma function; Sumudu transform; Laplace transform

Online: 24 December 2020 (13:52:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202012.0614.v1

Modified Sumudu Transform and Its Properties

Ugur Duran

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Gamma function, Sumudu transform, Laplace transform, convolution

Online: 24 December 2020 (09:45:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202009.0622.v2

Global Dynamics of a Higher Order Difference Equation with a Quadratic Term

Erkan Taşdemir

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: difference equations; global stability; rate of convergence; boundedness; periodicity; semicycle

Online: 23 November 2020 (09:27:44 CET)

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Preprint REVIEW | doi:10.20944/preprints202010.0250.v1

Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

Rodrigo Cofré, Cesar Maldonado, Bruno Cessac

Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Thermodynamic formalism; neuronal networks dynamics; maximum entropy principle; free energy and pressure; linear response; large deviations, ergodic theory

Online: 12 October 2020 (15:28:38 CEST)

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MATHEMATICS & COMPUTER SCIENCE