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Preprint ARTICLE | doi:10.20944/preprints202409.1664.v1

Stabilization of Percolation Probability in Supercritical Regimes: A Measure Theoretic Approach

Richard Murdoch Montgomery

Subject: Computer Science And Mathematics, Mathematics Keywords: Keywords: Percolation probability, supercritical regime, measure theory, Monotone Convergence Theorem, Fatou's Lemma, lattice models, infinite systems, statistical physics, compact balls, vanishing corrections.

Online: 20 September 2024 (16:06:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202409.1562.v1

Ulam Stability of Second Order Periodic Linear Differential Equations with Periodic Damping

Jin Li, Xiaofang Xia, Chuanfang Zhang, Renlian Chen

Subject: Computer Science And Mathematics, Mathematics Keywords: Ulam stability; periodic coefficient; linear differential equation; minimal Ulam constant

Online: 20 September 2024 (09:44:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202409.1522.v1

A Three-Phase Novel Angular Perturbation Technique for Metaheuristic-Based School Bus Routing Optimization

Moses Karema, Fullgence Mwakondo, Kevin Tole

Subject: Computer Science And Mathematics, Mathematics Keywords: School bus Problem; Vehicle Routing Problem; Combinatorial optimization; NP-Hard; 13

Online: 19 September 2024 (15:55:36 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202409.1300.v1

The Straight Proof To Riemann Hypothesis

Sameer Subedi

Subject: Computer Science And Mathematics, Mathematics Keywords: Riemann Xi function; Upper Incomplete Gamma Function; Riemann Hypothesis

Online: 17 September 2024 (11:31:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202409.0991.v1

Existence and Stability for Fractional Differential Equations with a Regularized ψ–Hilfer Fractional Derivative

Wenchang He, Yuhang Jin, Luyao Wang, Jia Mu

Subject: Computer Science And Mathematics, Mathematics Keywords: regularized ψ -Hilfer fractional derivative; existence; fixed point; Ulam-Hyers-Rassias stability; semi-Ulam-Hyers-Rassias stability

Online: 12 September 2024 (11:35:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.2050.v5

General Dynamics and Generation Mapping for Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz; 3x+1; 5x+1; collatz conjecture

Online: 10 September 2024 (12:58:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202401.1070.v2

Exact Closed-Form M/D/c Queueing Delay Formula

David Tung Chong Wong

Subject: Computer Science And Mathematics, Mathematics Keywords: M/D/c Queue; Poisson Arrivals; Deterministic (Constant) Service Time; c Multiple Servers; root(s) of an equation; mean number of customers; mean queueing delay

Online: 9 September 2024 (23:41:28 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202409.0436.v1

Finding a Published Which Meaningfully Averages The Most Pathalogical Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Values; Hausdorff measure; Hausdorff dimension; Discretization; Partitions; Sample; Euclidean Distance; Choice Function; Pathalogical Functions; Functions

Online: 5 September 2024 (12:34:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.2050.v4

General Dynamics and Generation Mapping for Collatz-Type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz; 3x+1; 5x+1; collatz conjecture

Online: 4 September 2024 (14:59:10 CEST)

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Let an odd integer $\mathcal{X}$ be expressed as $\mathcal{X} = \left\{\sum\limits_{M > m} 2^M\right\} + 2^m - 1,$ where $2^m - 1$ is referred to as the Governor. In Collatz-type functions, a high index Governor is eventually reduced to $2^1 - 1$. For the $3\mathcal{Z} + 1$ sequence, the Governor occurring in the trivial cycle is $2^1 - 1$, while for the $5\mathcal{Z} + 1$ sequence, the Trivial Governors are $2^2 - 1$ and $2^1 - 1$. Therefore, in these specific sequences, the Collatz function reduces $\mathcal{X}$ to $\mathcal{X} = \left\{\sum\limits_{N > \mathcal{T}} 2^N\right\} + 2^{\mathcal{T}} - 1,$ where $2^{\mathcal{T}} - 1$ is the Trivial Governor. Once this Trivial Governor is reached, it can evolve to a higher index Governor through interactions with other terms. This feature allows $\mathcal{X}$ to reappear in a Collatz-type sequence, since $2^m - 1 = 2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1).$ Thus, if $\mathcal{X}$ reappears, at least one odd ancestor of $2^{m - 1} + \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + (2^{\mathcal{T}} - 1)$ must have a Governor $2^m - 1$. Ancestor mapping shows that all odd ancestors of $\mathcal{X}$ have the Trivial Governor for the respective Collatz sequence. This implies that odd integers that repeat in the $3\mathcal{Z} + 1$ sequence have the Governor $2^1 - 1$, while those forming a repeating cycle in the $5\mathcal{Z} + 1$ sequence have either $2^2 - 1$ or $2^1 - 1$ as the Governor. Successor mapping for the $3\mathcal{Z} + 1$ sequence further indicates that there are no auxiliary cycles, as the Trivial Governor is always transformed into a different index Governor. Similarly, successor mapping for the $5\mathcal{Z} + 1$ sequence reveals that the smallest odd integers forming an auxiliary cycle are smaller than $2^5$. Finally, attempts to identify integers that diverge for the $3\mathcal{Z} + 1$ sequence suggest that no such integers exist.

Preprint CONCEPT PAPER | doi:10.20944/preprints202409.0361.v1

Finding a Research Paper Which Meaningfully Averages Unbounded Sets

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Values; Sets; Hausdorff measure; Hausdorff dimension; Discretization; Segmentation; Partitions; Samples; Euclidean Distance; Choice Function

Online: 4 September 2024 (11:26:09 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.2050.v3

General Dynamics and Generation Mapping for Collatz-type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz; 3x+1; 5x+1; collatz conjecture

Online: 30 August 2024 (19:22:09 CEST)

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Let an odd integer $\mathcal{X}$ be expressed as $\sum \limits_{M > m} 2^M + 2^m - 1$, where $2^m - 1$ is called the Governor. The general dynamics of the Collatz-type functions is such that a high index Governor is converted to $2^1 - 1$. For the $3\mathcal{Z} + 1$ sequence, the Governor occurring in the trivial cycle is $2^1 - 1$, while for the $5\mathcal{Z} + 1$ sequence, the Trivial Governors are $2^2 - 1$ and $2^1 - 1$. Therefore, for the specific cases of $3\mathcal{Z} + 1$ and $5\mathcal{Z} + 1$ sequences, it can be said that the Collatz function reduces $\mathcal{X}$ to $\sum \limits_{N > \mathcal{T}} 2^N + 2^{\mathcal{T}} - 1$, where $2^{\mathcal{T}} - 1$ is referred to as the Trivial Governor. Further, once the Trivial Governor is reached, it can again evolve to a higher index Governor by interacting with other terms. This feature allows the $\mathcal{X}$ to reappear in a Collatz-type sequence if its original Governor is expressible as a sum of series including the Trivial Governor, that is, $2^m - 1 = \cdots + 2^{\mathcal{T} + 1} + 2^{\mathcal{T}} + 2^{\mathcal{T}} - 1$. Therefore, if $\mathcal{X}$ reappears in the sequence, at least one odd ancestor of $\mathcal{X}$ in the sum of series format must have the Governor $2^m - 1$. Ancestor mapping shows that all the odd ancestors of $\mathcal{X}$ have the Trivial Governor of the respective Collatz sequence implying that $\mathcal{X}$ can repeat only if its original Governor is the Trivial Governor. Specifically for the $3\mathcal{Z} + 1$ sequence, the odd ancestors are separated by two even integers. Successor mapping for the $3\mathcal{Z} + 1$ further indicates that there are no auxiliary cycles, as the Trivial Governor is transformed to a different index Governor. Similarly, successor mapping for the $5\mathcal{Z} + 1$ sequence reveals that the smallest odd integers that form an auxiliary cycle are smaller than $2^5$. Finally, attempts to construct integers that diverge for the $3\mathcal{Z} + 1$ sequence suggest that no such integers exist.

Preprint ARTICLE | doi:10.20944/preprints202408.2050.v2

Generalized Dynamics and Generation Mapping for Collatz-type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz; 3x+1; 5x+1; collatz conjecture

Online: 29 August 2024 (10:16:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.2120.v1

Cartan-Schouten Metrics for Information Geometry and Machine Learning

Andre Diatta, Bakary Manga, Fatimata Sy

Subject: Computer Science And Mathematics, Mathematics Keywords: Cartan-Schouten metric; dual connections; $\alpha$-connections; Fisher information matrix; biinvariant metric; Lorentz metric; exponential barycenter; center of mass; Amari-Chentov 3-tenor; Machine Learning; information geometry

Online: 29 August 2024 (08:30:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.2050.v1

Generalized Dynamics and Generation Mapping for Collatz-type Sequences

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz, 3x+1, 5x+1, collatz conjecture

Online: 28 August 2024 (11:44:44 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1612.v3

Six Dimensions for Proof of Riemann Hypothesis

seyed kazem mousavi

Subject: Computer Science And Mathematics, Mathematics Keywords: Riemann hypothesis; prime numbers; six-dimensional space time

Online: 28 August 2024 (10:51:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1857.v1

A Zassenhaus Lemma for Digroups

Guy Biyogmam

Subject: Computer Science And Mathematics, Mathematics Keywords: Digroup; Normal subdigroup; Zassenhaus Lemma

Online: 26 August 2024 (20:10:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1768.v1

Phase Transition Analysis of the Potts-SOS Model with Spin Set {-1,0, 1} on the Cayley Tree

Hasan Akin

Subject: Computer Science And Mathematics, Mathematics Keywords: Potts-SOS model; Gibbs measure; phase transition; stability analysis

Online: 26 August 2024 (03:02:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1612.v2

Six Dimension for Proof of Riemann Hypothesis

seyed kazem mousavi

Subject: Computer Science And Mathematics, Mathematics Keywords: Riemann hypothesis; prime numbers; six-dimensional space time

Online: 26 August 2024 (03:01:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.0985.v2

The Collatz Conjecture “The Nonexistence of Divergent Orbits, through a Dynamic Diophantine Linear Analysis of Codification”

Giovanny Fuentes

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz Conjecture; Dynamical System

Online: 23 August 2024 (17:05:28 CEST)

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We define the function $Col: \mathbb{N} \to \mathbb{N}$ as the Collatz function, given by $3n + 1$ if $n$ is odd and $\displaystyle\frac{n}{2}$ if $n$ is even \cite{Lagarias1990}. The conjecture postulates that for any positive integer, at some point, its iteration will reach 1, or equivalently, every orbit will fall into the periodic cycle $\{4, 2, 1\}$. Two conditions would invalidate the conjecture: the existence of a divergent orbit or the presence of another cycle. In 2019 Terence Tao \cite{tao} proved that almost all orbits converge to the trivial cycle of $\{1,4,2\}$, in this work we will prove the non-existence of divergent orbits. The central idea is to decompose the dynamic system $Col$ into a binary dynamic system, generated by different compositions of two functions. This differs from a typical dynamic system, which is generated by the iteration of a single function. We consider the system generated by the functions $\theta, \psi: \mathbb{R} \to \mathbb{R}$, defined as $\displaystyle\theta(x) = \frac{x}{2}$ and $\displaystyle\psi(x) = \frac{3x + 1}{2}$, denoted as $\langle \theta, \psi \rangle$. We examine sequences of functions in $\langle \theta, \psi \rangle$ of the form $S_k(x) = s_k \circ S_{k-1}(x)$ with $s_k \in \{\theta, \psi\}$. We define a function that assigns to each element of these sequences an integer, called the minimum value positive integer or simply the minimum value. This corresponds to the smallest positive integer $n$ such that $S_k(n)$ is an integer. As we will prove later, the minimum value is monotonically increasing, meaning that increasing the terms of the sequence will never result in a value lower than the previous one. Based on this behavior, we distinguish two types of sequences: stable ones, where the minimum value is constant from a certain point, and unstable ones, where the minimum value is divergent. The main result for unstable sequences is that when the slope of the sequence is divergent, the sequence is unstable. From this result, we can prove that there are no divergent orbits for the function $Col$.

Preprint ARTICLE | doi:10.20944/preprints202408.1612.v1

Six Dimension for Proof of Riemann Hypothesis

seyed kazem mousavi

Subject: Computer Science And Mathematics, Mathematics Keywords: Riemann hypothesis; prime numbers; six-dimensional space time

Online: 22 August 2024 (08:25:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0256.v7

The Collatz Conjecture: A Resolution through Inverse Function Generative Completeness

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz conjecture; 3x+1 problem; number theory; sequence analysis; cycle properties; inverse Collatz function; boundedness; divergence; mathematical induction; proof techniques

Online: 19 August 2024 (10:52:12 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.1173.v1

An Exploration of Ideals and Filters In Triangle Algebras

Euclide Noumen, Fabrice Tchoua Yinga, Blaise Bleriot NJIONOU KOGUEP, Chris Cornelis

Subject: Computer Science And Mathematics, Mathematics Keywords: filters; ideals; congruences; residuated lattices; triangle algebras; interval-valued fuzzy 10 logic

Online: 15 August 2024 (14:09:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.0985.v1

The Collatz Conjecture "The Nonexistence of Divergent Orbits, through a Dynamic Diophantine Linear Analysis of Codification

Giovanny Fuentes

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz Conjecture; Dynamical System

Online: 14 August 2024 (09:27:01 CEST)

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We define the function $Col: \mathbb{N} \to \mathbb{N}$ as the Collatz function, given by $3n + 1$ if $n$ is odd and $\displaystyle\frac{n}{2}$ if $n$ is even \cite{Lagarias1990}. The conjecture postulates that for any positive integer, at some point, its iteration will reach 1, or equivalently, every orbit will fall into the periodic cycle $\{4, 2, 1\}$. Two conditions would invalidate the conjecture: the existence of a divergent orbit or the presence of another cycle. In 2019 Terence Tao \cite{tao} proved that almost all orbits converge to the trivial cycle of $\{1,4,2\}$, in this work we will prove the non-existence of divergent orbits. The central idea is to decompose the dynamic system $Col$ into a binary dynamic system, generated by different compositions of two functions. This differs from a typical dynamic system, which is generated by the iteration of a single function. We consider the system generated by the functions $\theta, \psi: \mathbb{R} \to \mathbb{R}$, defined as $\displaystyle\theta(x) = \frac{x}{2}$ and $\displaystyle\psi(x) = \frac{3x + 1}{2}$, denoted as $\langle \theta, \psi \rangle$. We examine sequences of functions in $\langle \theta, \psi \rangle$ of the form $S_k(x) = s_k \circ S_{k-1}(x)$ with $s_k \in \{\theta, \psi\}$. We define a function that assigns to each element of these sequences an integer, called the minimum value positive integer or simply the minimum value. This corresponds to the smallest positive integer $n$ such that $S_k(n)$ is an integer. As we will prove later, the minimum value is monotonically increasing, meaning that increasing the terms of the sequence will never result in a value lower than the previous one. Based on this behavior, we distinguish two types of sequences: stable ones, where the minimum value is constant from a certain point, and unstable ones, where the minimum value is divergent. The main result for unstable sequences is that when the slope of the sequence is divergent, the sequence is unstable. From this result, we can prove that there are no divergent orbits for the function $Col$.

Preprint ARTICLE | doi:10.20944/preprints202406.0256.v6

Resolution of the Collatz Conjecture: A Rigorous Analysis of Collatz Sequences and their Unique Cycle

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz conjecture; 3x+1 problem; number theory; sequence analysis; cycle properties; inverse Collatz function; boundedness; divergence; mathematical induction; proof techniques

Online: 13 August 2024 (03:11:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0256.v5

Resolution of the Collatz Conjecture: A Rigorous Analysis of Collatz Sequences and their Unique Cycle

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz conjecture; 3x+1 problem; number theory; sequence analysis; cycle properties; inverse Collatz function; boundedness; divergence; mathematical induction; proof techniques

Online: 8 August 2024 (03:57:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0256.v4

Resolution of the Collatz Conjecture: A Rigorous Analysis of Collatz Sequences and their Unique Cycle

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz conjecture; 3x+1 problem; number theory; sequence analysis; cycle properties; inverse Collatz function; boundedness; divergence; mathematical induction; proof techniques

Online: 6 August 2024 (02:32:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.0319.v1

A generalisation of Pythagoras’ theorem

Christiaan Mantz

Subject: Computer Science And Mathematics, Mathematics Keywords: Pythagoras; inner product; hypersurface

Online: 5 August 2024 (12:48:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202408.0021.v1

Simplified Proof of the Collatz Conjecture Using Regularity General solution‐Calculation Method by Multiples of 6 and Remainder

Haruhiro Shiraishi, Hajime Shiraishi

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz conjecture; 6n; regularity

Online: 1 August 2024 (12:33:24 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2585.v1

Greedoids and Violator Spaces

Yulia Kempner, Vadim Levit

Subject: Computer Science And Mathematics, Mathematics Keywords: violator space; linear programming; closure operator; greedoid; antimatroid

Online: 1 August 2024 (05:30:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2614.v1

Integral Forms and Connections of Multi-Parameter Mittag-Leffler Functions with Fox-Wright and Hypergeometric Functions

Pooja Singh

Subject: Computer Science And Mathematics, Mathematics Keywords: Mittag-Leffler functions; Wright hypergeometric functions; Fox-Wright function; generalized hypergeometric function

Online: 31 July 2024 (15:34:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2192.v2

Crafting Integers That ‘May’ Diverge for Collatz Sequence

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: collatz; 3x+1

Online: 30 July 2024 (11:50:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2299.v1

Non-local Problems for the Fractional Order Diffusion Equation and the Degenerate Hyperbolic Equation

Menglibay Ruziev, Roman Parovik, Rakhimjon Zunnunov, Nargiza Yuldasheva

Subject: Computer Science And Mathematics, Mathematics Keywords: boundary value problem; fractional order differential equation; Gauss hyper-geometric function; uniqueness of a solution; existence of a solution; singular coefficient; Wright type function

Online: 29 July 2024 (11:50:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2242.v1

The Second Critical Exponent for a Time Fractional Reaction-Diffusion Equation

Takefumi Igarashi

Subject: Computer Science And Mathematics, Mathematics Keywords: time fractional diffusion equation; blow-up; global existence; critical exponent

Online: 29 July 2024 (11:13:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2280.v1

The p-Frobenius Number for the Triple of the Generalized Star Numbers

Ruze Yin, Jiaxin Mu, Takao Komatsu

Subject: Computer Science And Mathematics, Mathematics Keywords: frobenius problem; Frobenius numbers; centered 2a-gonal numbers; the number of representations

Online: 29 July 2024 (09:50:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2180.v1

A Fibration of Fermat Surface in Characteristic

Xiaokun Zhong

Subject: Computer Science And Mathematics, Mathematics Keywords: positive characteristic; fibrations; automorphisms of surfaces

Online: 27 July 2024 (07:02:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2192.v1

Crafting Integers That ‘May’ Diverge for Collatz Sequence

Gaurav Goyal

Subject: Computer Science And Mathematics, Mathematics Keywords: collatz; 3x+1

Online: 26 July 2024 (13:38:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.2155.v1

A Novel Approach Using Fuzzy TOPSIS and COPRAS for Analyzing the Causes of Divorce in India

T. Nagalakshmi, A. Selvaraj, Maria Singaraj Rosary, Nasir Ali

Subject: Computer Science And Mathematics, Mathematics Keywords: linguistic variable; triangular fuzzy number; fuzzy TOPSIS and COPRAS

Online: 26 July 2024 (13:20:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.1982.v1

p-Numerical Semigroups of Triples from the Three-Term Recurrence Relations

Takao Komatsu, Jiaxin Mu

Subject: Computer Science And Mathematics, Mathematics Keywords: Frobenius problem; Frobenius numbers; Horadam numbers; Apé; ry set

Online: 24 July 2024 (14:19:20 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0256.v3

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Inverse Algebraic Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 15 July 2024 (09:50:14 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.1015.v1

Periodic and Quasi periodic Orbits in the Collinear Four-Body Problem: A Variational Analysis

Abdalla Mansur, Muhammad Shoaib, Iharka Szücs-Csillik, Daniel Offin, Jack Brimberg, Hedia Fgaier

Subject: Computer Science And Mathematics, Mathematics Keywords: four-body problem; action minimizing orbits; celestial mechanics

Online: 12 July 2024 (10:12:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202407.0282.v1

Enhancing Cyber Defense Strategies with Discrete Multidimensional Z-Numbers: A Multi-Attribute Decision-Making Approach

Aiting Yao, Chengzu Dong, Weiqi Zhang, Xiaoming Jiang, Junjun Mao, Xiao Liu, Xuejun Li

Subject: Computer Science And Mathematics, Mathematics Keywords: Network Defence; Cyber Security; Discrete Multidimensional Z-numbers; Hidden Probability; Multidimensional Z+-number; Utility Function; Multi-attribute Group Decision Making

Online: 3 July 2024 (10:40:17 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202311.0053.v3

Theory of Relationships Between Spaces to Obtain Numerical Knowledge

Carlos Eduardo Ramos Cardoso

Subject: Computer Science And Mathematics, Mathematics Keywords: relationships between spaces; numerical knowledge; sense of mathematics; even and odd numbers

Online: 2 July 2024 (11:18:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.2081.v1

The Generalized Mehler-Fock Transform over Lebesgue Spaces

Jeetendrasingh Maan, Benito J. González, Emilio R. Negrín

Subject: Computer Science And Mathematics, Mathematics Keywords: Generalized Mehler-Fock transform; Lebesgue spaces; inversion formula; boundedness properties; Parseval-Goldstein type relations

Online: 29 June 2024 (00:21:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1880.v2

Theory of Major and Minor Numerical Progressions

Carlos Eduardo Ramos Cardoso

Subject: Computer Science And Mathematics, Mathematics Keywords: bigger numbers; smaller numbers; varied numbers; simple numbers

Online: 26 June 2024 (14:43:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202311.0053.v2

Theory of Relationships between Spaces to Obtain Numerical Knowledge

Carlos Eduardo Ramos Cardoso

Subject: Computer Science And Mathematics, Mathematics Keywords: relationships between spaces; numerical knowledge; sense of mathematics; even and odd numbers

Online: 24 June 2024 (04:22:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.1363.v1

Application of the Transmutation Operator Method to the Solution of an Initial Boundary Value Problem for the Equation of Multidimensional Free Transverse Vibration of a Thin Elastic Plate Containing the Bessel Operator

Shakhobiddin Karimov, Yorkinoy Tulasheva

Subject: Computer Science And Mathematics, Mathematics Keywords: fourth-order equation; plate vibration equation; Bessel operator; transmutation operator; Erdélyi–Kober operator

Online: 19 June 2024 (15:02:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1895.v3

Bounded Number Theory :A Study on the Negation of Infinite Numbers in Parts or Completely

Carlos Eduardo Ramos Cardoso

Subject: Computer Science And Mathematics, Mathematics Keywords: limited number; different physical spaces; mathematical sense; number belongs to space

Online: 18 June 2024 (12:18:58 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0985.v1

Arithmetic Sequences without Arithmetic Operations

Md. Shouvik Iqbal

Subject: Computer Science And Mathematics, Mathematics Keywords: Number patterns; Arithmetic sequence; Concatenation; Multiplication table; Arithmetic operations; Times table

Online: 14 June 2024 (08:39:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0619.v1

On Mittag-Leffler Function and Consequent Fractional Integral Operator Inequalities

Yonghong Liu, Ghulam Farid, Abaker A. Hassaballa, Jongsuk Ro, Mnahil M. Bashier, B. A. Younis

Subject: Computer Science And Mathematics, Mathematics Keywords: Mittag-Leffler function; fractional integral operators; convex function

Online: 11 June 2024 (08:56:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.1895.v2

Bounded Number Theory: A Study on the Negation of Infinite Numbers in Parts or Completely

Carlos Eduardo Ramos Cardoso

Subject: Computer Science And Mathematics, Mathematics Keywords: limited number; different physical spaces; mathematics sense; number belongs to space

Online: 6 June 2024 (11:05:08 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0238.v1

Brezis-Nirenberg type critical problems on H-type groups

Jialin Wang, Shuijin Zhang, Dongni Liao

Subject: Computer Science And Mathematics, Mathematics Keywords: CR Yamabe problem; Brezis-Nirenberg problem; Folland-Stein inequality; H-type group

Online: 5 June 2024 (10:46:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202406.0012.v1

Existence and multiplicity of nontrivial solutions for semilinear elliptic equations involving Hardy-Sobolev critical exponents

Yonghong Fan, Wenheng Sun, Linlin Wang

Subject: Computer Science And Mathematics, Mathematics Keywords: semilinear elliptic equation; Hardy-Sobolev critical exponent; mountain pass lemma; (PS)c condition

Online: 3 June 2024 (11:16:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1885.v1

The Existence and Construction of Palindrome Numbers Divisible by 37

Fan Jiang

Subject: Computer Science And Mathematics, Mathematics Keywords: palindrome numbers; 37; properties of 37

Online: 29 May 2024 (07:03:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1626.v1

Phase portraits of a class of Liénard equations

Rachid Cheurfa, Jaume Llibre, Ahmed Bendjeddou

Subject: Computer Science And Mathematics, Mathematics Keywords: Liénard equation; Poincaré disc; phase portraits

Online: 24 May 2024 (09:42:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1207.v1

Exponential Convergence-(t, s)-Weak Tractability of Approximation in Weighted Hilbert Spaces

Jia Chen, Huichao Yan

Subject: Computer Science And Mathematics, Mathematics Keywords: L_2-approximation; information complexity; tractability; weighted Hilbert spaces

Online: 20 May 2024 (06:52:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1019.v1

Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time

A.N. Beloiarov, V.A. Beloiarov, Raúl C. Cruz-Gómez, C. O. Monzón, J.L. Romero

Subject: Computer Science And Mathematics, Mathematics Keywords: Kepler’ s equation; quasi-analytical solution; celestial bodies; Kepler’ s laws

Online: 15 May 2024 (10:54:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.1010.v1

Differentiation of Solutions of Caputo Boundary Value Problems with respect to Boundary Data

Jeffrey W. Lyons

Subject: Computer Science And Mathematics, Mathematics Keywords: continuous dependence; Caputo fractional derivative; fractional differential equation; variational equation

Online: 15 May 2024 (07:45:48 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202405.0635.v1

Optimal Harvesting Strategies for Timber and Non-timber Forest Products with Nonlinear Harvesting Term

Yaning Zhang, Lina Hao, Shan Zhang

Subject: Computer Science And Mathematics, Mathematics Keywords: biomathematics model; nonlinear harvest; optimal control; non-timber forest products; sustainable timber harvest

Online: 10 May 2024 (11:31:01 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1570.v2

Numerical Approach on Collatz Conjecture

Youngik Lee

Subject: Computer Science And Mathematics, Mathematics Keywords: collatz conjecture; 3x+1 problem; Terras Theorem

Online: 3 May 2024 (11:22:09 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1884.v1

Investigating Effective Factors in Solving Partial Differential Equations using Deep Learning Techniques

Parastoo Kabi-Nejad

Subject: Computer Science And Mathematics, Mathematics Keywords: Partial Differential Equations; Machine learning; Neural Networks; Computational Modeling; Feature Identification

Online: 29 April 2024 (10:25:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0773.v18

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 29 April 2024 (09:46:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1570.v1

Numerical Approach on Collatz Conjecture

Youngik Lee

Subject: Computer Science And Mathematics, Mathematics Keywords: collatz conjecture; 3x+1 problem; Terras Theorem

Online: 25 April 2024 (15:14:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1413.v1

Fractional Neutral Integro-Differential Equations with Neumann-Type Boundary Conditions

Zhiyuan Yuan, Luyao Wang, Wenchang He, Ning Cai, Jia Mu

Subject: Computer Science And Mathematics, Mathematics Keywords: Fractional neutral integro-differential equations; Resolvent family; Probability density function; Mild solutions

Online: 23 April 2024 (03:16:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1460.v1

Three Cubes Packing for All Dimensions

Peter Adamko

Subject: Computer Science And Mathematics, Mathematics Keywords: packing of cubes; extreme

Online: 22 April 2024 (18:18:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.1149.v1

Center and Hopf Bifurcation of High-order Singularity in a Class of Three-dimensional Systems

Jingping Lu, Wentao Huang, Qinlong Wang

Subject: Computer Science And Mathematics, Mathematics Keywords: high-order degenerate singularity; singular point value; limit cycle; center condition

Online: 17 April 2024 (12:03:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0872.v1

Enhancing Portfolio Allocation: A Random Matrix Theory Perspective

Fabio Vanni, Asmerilda Hitaj, Elisa Mastrogiacomo

Subject: Computer Science And Mathematics, Mathematics Keywords: portfolio selection; networks; dependence structure; Random Matrix Theory; Hilbert Transformation

Online: 15 April 2024 (11:25:46 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0725.v1

Green Measures for a Class of Non-markov Processes

Herry P. Suryawan, José L. da Silva

Subject: Computer Science And Mathematics, Mathematics Keywords: Fractional Brownian motion; generalized grey Brownian motion; Green measure; subordination

Online: 10 April 2024 (09:55:43 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202402.1120.v2

Introducing Novel Geometric Insights and Three-Dimensional Depictions of the Pythagorean Theorem for Any Triangles

Marco Aurélio Dos Santos Bernardes

Subject: Computer Science And Mathematics, Mathematics Keywords: Pythagorean theorem; three-dimensional space; triangles; three-dimensional geometric shape; Triangle Midsegment Theorem

Online: 9 April 2024 (12:17:11 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0484.v1

On Approximate Variational Inequalities and Bilevel Programming Problems

Balendu Bhooshan Upadhyay, I. M. Stancu-Minasian, Subham Poddar, Priyanka Mishra

Subject: Computer Science And Mathematics, Mathematics Keywords: limiting subdifferentials; ϵ-quasi solutions; approximate convex functions; variational inequalities

Online: 8 April 2024 (16:35:51 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202404.0536.v1

Multi-Dimensional Integral Transform with Fox Function in Kernel on Lebesgue-Type Spaces

Sergey Sitnik, Oksana Skoromnik

Subject: Computer Science And Mathematics, Mathematics Keywords: Multi-dimensional integral transform; Fox H-function; Melling transform; weighted space; fractional integrals and derivatives

Online: 8 April 2024 (11:43:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1598.v2

The Elba Curves

Elkhan B Beylarov, Ilyas R Hasanov

Subject: Computer Science And Mathematics, Mathematics Keywords: Fermat's last theorem; circle; ellipse; triangle; n-degree curves; equations

Online: 5 April 2024 (16:27:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202403.1316.v2

Peter Chew Sum: Beyond Newton Sum in Quadratic Root Function Computations

Peter Chew

Subject: Computer Science And Mathematics, Mathematics Keywords: Peter Chew Sum; Newton's Sum; Quadratic; Root; Function; Computations ;

Online: 5 April 2024 (03:16:41 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0773.v17

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 2 April 2024 (11:53:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202310.0773.v16

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 29 March 2024 (11:23:27 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1680.v1

Existence and Nonexistence of Positive Solutions for Semilinear Elliptic Equations Involving Hardy-Sobolev Critical Exponents

Lin-Lin Wang, Yong-Hong Fan

Subject: Computer Science And Mathematics, Mathematics Keywords: semilinear elliptic equation; Hardy-Sobolev critical exponents; Mountain Pass Lemma; (PS)c condition

Online: 27 March 2024 (15:07:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1687.v1

Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative

Hadeel Z. Alzumi, Wafa Shammakh, Abdeljabbar Ghanmi

Subject: Computer Science And Mathematics, Mathematics Keywords: Fractional calculus; Variational methods; $\psi$-Hilfer operators, Existence of solution.

Online: 27 March 2024 (13:38:19 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1598.v1

The Elba Curves

Elkhan B Beylarov, Ilyas R Hasanov

Subject: Computer Science And Mathematics, Mathematics Keywords: Fermat's last theorem; circle; ellipse; triangle; n-degree curves; equations

Online: 26 March 2024 (12:27:57 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1535.v1

The General Solution to a Classical Matrix Equation AXB=C over the Dual Split Quaternion Algebra

Kai-Wen Si, Qing-Wen Wang

Subject: Computer Science And Mathematics, Mathematics Keywords: dual split quaternion; real representation; matrix equation; general solution

Online: 26 March 2024 (11:51:23 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.0773.v15

Resolving the Collatz Conjecture: A Rigorous Proof through Inverse Discrete Dynamical Systems and Algebraic Inverse Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: discrete dynamical systems; inverse modeling; topological equivalence; topological transport; algebraic trees; collatz conjecture; homeomorphic invariance

Online: 26 March 2024 (11:50:16 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1551.v1

Exploring the Impact of Deep Learning Activities in the Mathematics Classroom on Students’ Academic Performance: A Comprehensive Study

Enoch Suglo

Subject: Computer Science And Mathematics, Mathematics Keywords: Deep learning; academic performance; mathematics

Online: 26 March 2024 (08:23:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1316.v1

Weighing the Pros and Cons of Newton’s Sum in Quadratic Root Function Computations Analysis

Peter Chew

Subject: Computer Science And Mathematics, Mathematics Keywords: Newton's Sum; Quadratic; ; Root; Function; Computations ;

Online: 26 March 2024 (02:48:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1461.v1

On δP-approximation Spaces

Faik Mayah, Huda Mohsin

Subject: Computer Science And Mathematics, Mathematics Keywords: Rough sets; Upper and lower approximations; P-open sets; δ P-open sets

Online: 25 March 2024 (11:15:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1386.v1

A Nonlinear ODE Model for a Consumeristic Society

Marino Badiale, Isabella Cravero

Subject: Computer Science And Mathematics, Mathematics Keywords: Human and nature dynamics; ODE systems for society dynamics; Ecological- Economic Modeling

Online: 22 March 2024 (14:44:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.1214.v1

The Feit-Thompson Conjecture: An Example for Mathematical Research Based on Contradictory Sources

Carolin Hannusch

Subject: Computer Science And Mathematics, Mathematics Keywords: Feit-Thompson conjecture; prime numbers; mathematical research; research education; twin primes, generalized twin prime conjecture

Online: 21 March 2024 (01:53:40 CET)

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Preprint ARTICLE | doi:10.20944/preprints202310.0773.v14

The Collatz Conjecture: A New Proof using Algebraic Inverse Trees

Eduardo Diedrich

Subject: Computer Science And Mathematics, Mathematics Keywords: Discrete dynamical systems; Inverse modeling; Topological equivalence; Topological transport; Algebraic trees; Collatz Conjecture; Homeomorphic invariance

Online: 18 March 2024 (10:42:38 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0390.v1

On Induced Topologies by Ideal, Primal, Filter and Grill

Milan Matejdes

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

Online: 7 March 2024 (08:09:59 CET)

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Preprint ARTICLE | doi:10.20944/preprints202403.0016.v1

RBF Neural Networks-Based Near-Optimal Tracking Control of Partially Unknown Discrete-Time Nonlinear Systems

Huang Jiashun, Xu Dengguo, Li Yahui, Ma Yan

Subject: Computer Science And Mathematics, Mathematics Keywords: adaptive dynamic programming; optimal tracking control; RBF neural network; nonlinear systems

Online: 1 March 2024 (13:12:53 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1667.v1

On Gohar Fractional Calculus

Abdelrahman Gohar, Mayada Younes, Salah Doma

Subject: Computer Science And Mathematics, Mathematics Keywords: ; Gohar fractional calculus; Gohar fractional Laplace transform; Gohar fractional power series expansion; Left and right Gohar fractional derivatives; Left and right Gohar fractional integrals ;

Online: 29 February 2024 (09:13:33 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1463.v1

About Bellman Principle and Solution Properties of Navier–Stokes Equations in the 3d Cauchy Problem

Vladimir I. Semenov

Subject: Computer Science And Mathematics, Mathematics Keywords: Navier-Stokes equations 1; blow up solution 2; regular solution 3

Online: 26 February 2024 (14:14:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1328.v1

Removable Singularities of Harmonic Functions on Stratified Sets

Nurlan S. Dairbekov, Oleg M. Penkin, Denis V. Savasteev

Subject: Computer Science And Mathematics, Mathematics Keywords: stratified measure; soft Laplacian; mean value; gradient flux

Online: 23 February 2024 (08:35:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1327.v1

Strict Sense Minimizers Which Are Not Extended Minimizers and Abnormality

Giovanni Fusco, Monica Motta

Subject: Computer Science And Mathematics, Mathematics Keywords: Optimal control problems; Maximum principle; State constraints; Gap phenomena; Impulsive optimal control

Online: 23 February 2024 (08:33:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202309.0513.v5

A Modest Contribution to the Riemann Hypothesis Using the Poincaré Index

Hime Oliveira

Subject: Computer Science And Mathematics, Mathematics Keywords: Riemann hypothesis; Riemann zeta function; Poincaré; index; Dirichlet eta function.

Online: 21 February 2024 (04:40:09 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1134.v1

Division by Zero: Using Semi-structured Complex Numbers to Find the Inverse of a Singular Matrix and Show Its Applications

Peter Jean Paul, Shanaz Wahid

Subject: Computer Science And Mathematics, Mathematics Keywords: division by zero; inverse of a singular matrix; singular matrix; semi-structured complex numbers; projective geometry

Online: 21 February 2024 (03:45:11 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1120.v1

Introducing Novel Geometric Insights and Three-Dimensional Depictions of the Pythagorean Theorem for any Triangles

Marco Aurélio Dos Santos Bernardes

Subject: Computer Science And Mathematics, Mathematics Keywords: Pythagorean theorem; three-dimensional space; triangles; three-dimensional geometric shape; Triangle Midsegment Theorem

Online: 20 February 2024 (09:00:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.1042.v1

A First Approach to Quantum Logical Shape Classification Framework

Alexander Köhler, Marvin Kahra, Michael Breuß

Subject: Computer Science And Mathematics, Mathematics Keywords: quantum logic; principal component analysis; shape classification; Hilbert space

Online: 19 February 2024 (10:24:49 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0399.v1

On Adaptive Identification of Interconnected Systems

Nikolay Karabutov

Subject: Computer Science And Mathematics, Mathematics Keywords: excitation constancy, geometric structure, Lyapunov exponent, structural identification, structural identifiability, S-synchronization

Online: 7 February 2024 (11:50:18 CET)

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Preprint ARTICLE | doi:10.20944/preprints202402.0242.v1

A Unified Statistical Relativistic Theory of the Generalized Brownian Motion Manifold

Dr Ismail A Mageed

Subject: Computer Science And Mathematics, Mathematics Keywords: Einsteinian Relativities; the Generalized Brownian Motion; information geometry

Online: 5 February 2024 (07:59:57 CET)

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Preprint COMMUNICATION | doi:10.20944/preprints202401.0551.v4

Metallic Ratios and Angles of a Real Argument

Szymon Łukaszyk

Subject: Computer Science And Mathematics, Mathematics Keywords: metallic ratios; metallic angles; Pythagorean triples; emergent dimensionality; mathematical physics

Online: 2 February 2024 (04:33:46 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.2213.v1

Solvability Criterion for a System Arising from Monge-Amp`ere Equations with Two Parameters

Liangyu Wang, Hongyu Li

Subject: Computer Science And Mathematics, Mathematics Keywords: fixed point theorem; Monge-Ampere equations; boundary value problem

Online: 31 January 2024 (11:05:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202401.1488.v2

A Proof of Collatz Conjecture Using Pyramid Fractions

Mehdi Khoshakhlagh Varnosfaderani

Subject: Computer Science And Mathematics, Mathematics Keywords: Collatz conjecture; 3x+1 problem; Syracuse problem; pyramid fraction; Ulam’ s conjecture; Kakutani’ s problem

Online: 30 January 2024 (12:51:11 CET)

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Computer Science and Mathematics