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Preprint ARTICLE | doi:10.20944/preprints202305.1602.v1

The Convergence of Discrete Models for Nonlinear Schrödinger Equation in Dark Solitons Motion

Yazhuo Li, Qian Luo, Quandong Feng

Subject: Computer Science And Mathematics, Mathematics Keywords: Nonlinear schrödinger equation; Space discretization models; Time-space discretization models; Crank-Nicolson method; New-Difference method.

Online: 23 May 2023 (07:45:25 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1569.v1

On Geometry of p-adic Coherent States and Mutually Unbiased Bases

Evgeny I. Zelenov

Subject: Computer Science And Mathematics, Mathematics Keywords: p-adic quantum theory; mutually; mutually unbiased bases; Hadamard matrix

Online: 23 May 2023 (04:42:51 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1498.v1

Hypergraph Regularized Lp Smooth Nonnegative Matrix Factorization for Data Representation

Yunxia Xu, Linzhang Lu, Qilong Liu, Zhen Chen

Subject: Computer Science And Mathematics, Mathematics Keywords: hypergraph regularization; Lp smooth; nonnegative matrix factorization; data clustering

Online: 22 May 2023 (10:20:53 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1356.v1

On Nearly Sasakian and Nearly Kähler Statistical Manifolds

Siraj Uddin, Esmaeil Peyghan, Leila Nourmohammadifar, Rawan Bossly

Subject: Computer Science And Mathematics, Mathematics Keywords: Information geometry; nearly Kähler statistical manifold; nearly Sasakian statistical manifold

Online: 18 May 2023 (15:13:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0947.v1

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Their Applications in QSPR Studies of Octane and Its Isomers

Suha Wazzan, Hanan Ahmed

Subject: Computer Science And Mathematics, Mathematics Keywords: Domination indices; QSPR; Sigma index; Octane isomers; Book graph; Join graph; Windmill graph

Online: 12 May 2023 (12:49:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0775.v1

Coexistence of Thread and Sheet Chaotic Attractors for Three Dimensional Lozi Map

René LOZI

Subject: Computer Science And Mathematics, Mathematics Keywords: chaotic attractor; hyperchaotic attractor; Lozi map; sheet-attractor; thread-attractor

Online: 11 May 2023 (03:48:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0599.v1

Hybrid Functions Approach to Solving Nonlinear Integral Equations in Two Dimensions

Sahar M. Abusalim, Mohamed A. Abdou, Mohamed A. Abdel-Aty, Mohamed E. Nasr

Subject: Computer Science And Mathematics, Mathematics Keywords: Two- dimensional nonlinear integral equation; Banach fixed point theorem; Block-pulse function; Hybrid functions; Legendre polynomials

Online: 9 May 2023 (08:21:21 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0096.v1

Exploring the Symmetry of Curvilinear Regression Models for Enhancing the Analysis of Fibrates Drug Activity through Molecular Descriptors

Suha Wazzan, Nurten Urlu Ozalan

Subject: Computer Science And Mathematics, Mathematics Keywords: Topological indices; Fibrates; Curvilinear regression; QSPR analysis

Online: 3 May 2023 (04:48:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1139.v1

On the Jacobi Stability of Two SIR Epidemic Patterns With Demography

Florian Munteanu

Subject: Computer Science And Mathematics, Mathematics Keywords: SIR pattern; KCC theory; the deviation curvature tensor; Jacobi stability

Online: 28 April 2023 (07:57:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0844.v1

Extended Exton’s Triple and Horn’s Double Hypergeometric Functions and Associated Bounding Inequalities

Rakesh K. Parmar, Junesang Choi, Saravanan S.

Subject: Computer Science And Mathematics, Mathematics Keywords: Extended Beta function; Extended hypergeometric function; Extended confluent hypergeometric function; Extended Appell function; Mellin transforms; Inverse Mellin transforms; H-functions; Laguerre polynomials; Transformation formulas; Recurrence relation; Generating function; Bounding inequalities

Online: 24 April 2023 (09:45:32 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0842.v1

Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form

Qilong Liu, Qingshui Liao

Subject: Computer Science And Mathematics, Mathematics Keywords: $k$-mode symmetric tensor; tensor complementary problem; $m$-person game; symmetric Nash equilibrium

Online: 24 April 2023 (09:40:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0613.v1

Criteria on Contraction and Incremental Stability of Dynamical Systems with Time Delay

Yingying Lang, Wenlian Lu

Subject: Computer Science And Mathematics, Mathematics Keywords: Time-delay System; v(t)-Incremental Stability; Discontinuous Right-hands; Filippov solutions

Online: 20 April 2023 (07:10:26 CEST)

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Preprint ESSAY | doi:10.20944/preprints202304.0518.v1

Machine Learning-Based Classification of Digital Media Traffic

Yan-shuang Zhou, Xiang-yu Han, Ling-hui Liu, Zhi-han Dong

Subject: Computer Science And Mathematics, Mathematics Keywords: Digital media; Traffic classification; Machine learning; Decision trees; Support vector machines; Neural networks.

Online: 18 April 2023 (10:41:32 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0072.v1

On the Question of Fermat’s Last Theorem

Elkhan B Beylarov, Ilyas R Hasanov

Subject: Computer Science And Mathematics, Mathematics Keywords: Fermat's last theorem; triangle inequalities; Elba curves; ellipse; geometric proof; circle

Online: 6 April 2023 (04:59:00 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202303.0424.v1

Splitting Algorithm for Numerical Solving of Parabolic Nonlinear Multi - Component Convection – Diffusion Mass Transfer Equations

Gheorghe Juncu, Constantin Popa, Gheorghe Sarbu

Subject: Computer Science And Mathematics, Mathematics Keywords: multi-component diffusion; splitting; splitting error; non-linear convection – diffusion equations; finite differences

Online: 24 March 2023 (03:28:04 CET)

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Preprint DATA DESCRIPTOR | doi:10.20944/preprints202303.0379.v1

NJN: A Dataset for the Normal and Jaundiced Newborns

Ahmad Yaseen Abdulrazzak, Ali Al-Naji, Saleem Latteef Mohammed

Subject: Computer Science And Mathematics, Mathematics Keywords: Jaundice; Hyperbilirubinemia; skin color analysis; NICU; artificial intelligence (AI) techniques

Online: 21 March 2023 (14:01:10 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v7

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 17 March 2023 (04:04:07 CET)

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Preprint REVIEW | doi:10.20944/preprints202303.0292.v1

Tutorial on Bayesian Optimization

Loc Nguyen

Subject: Computer Science And Mathematics, Mathematics Keywords: Bayesian optimization; Gaussian process regression; acquisition function; machine learning; reinforcement learning

Online: 16 March 2023 (01:36:11 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v6

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 14 March 2023 (01:38:37 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v5

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 9 March 2023 (06:42:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202303.0139.v1

Mathematical Modeling and Exact Optimizing of University Course Scheduling COnsidering Preferences of Professors

Mo Chen, Frank Werner, Mohammad Shokouhifar

Subject: Computer Science And Mathematics, Mathematics Keywords: university course scheduling; mathematical modeling; integer programming; GAMS optimization; exacrt search; sensitivity analysis

Online: 8 March 2023 (02:49:43 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v4

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 1 March 2023 (07:17:23 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v3

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 28 February 2023 (04:56:00 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0450.v1

A Theorem on Separated Transformations of Basis Vectors of Polynomial Space and Its Applications in Special Polynomials and Related Lie Algebra

Manouchehr Amiri

Subject: Computer Science And Mathematics, Mathematics Keywords: special polynomials; Hermite; Laguerre; Legendre; differential operators; Lie algebra; Baker-Campbell-Hausdorff formula; separated basis transformation; Forbenius covariant; Rodrigues formula; differential equations

Online: 27 February 2023 (06:44:12 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v2

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 23 February 2023 (03:45:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202106.0221.v2

Peter Chew Triangle Diagram and Application

Peter Chew

Subject: Computer Science And Mathematics, Mathematics Keywords: Peter Chew Triangle Diagram; Peter Chew

Online: 22 February 2023 (10:41:15 CET)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202302.0367.v1

Defining the Most Generalized, Natural Extension of the Expected Value on Measurable Functions

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Expected Value; Uniform Measure; Measure theory; Prevalence; Entropy; Sample; Linear; Superlinear; Choice Function; Bernard's Paradox; Pseudo-random

Online: 22 February 2023 (02:06:52 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0310.v1

Optimal UAV Hangar Locations for Emergency Services Considering Restricted Areas

Hannes Braßel, Thomas Zeh, Hartmut Fricke, Anette Eltner

Subject: Computer Science And Mathematics, Mathematics Keywords: Unmanned Aerial Vehicle; Facility Location Problem; Mission Planning; Restricted Airspace; UAS Geographical Zone; Water Search & Rescue; Open Source Georeferenced Data

Online: 17 February 2023 (11:46:40 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0235.v1

Homotopic Quantum Fuzzy Adaptive Simulated Annealing [ HQF ASA ]

Hime A. e Oliveira Jr.

Subject: Computer Science And Mathematics, Mathematics Keywords: Quantum Annealing; Tunneling; Artificial Inference; Simulated Annealing; Global Learning

Online: 14 February 2023 (04:47:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0208.v1

The M-basis Functions and Their Application

Mehran Emadi Andani

Subject: Computer Science And Mathematics, Mathematics Keywords: M-basis function; Fourier basis function; optimization; minimum jerk

Online: 13 February 2023 (08:59:47 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0201.v1

Ramsey Theory and Geometry of Closed Loops

Edward Bormashenko, Nir Shvalb, Shraga Shoval, Mark Frenkel

Subject: Computer Science And Mathematics, Mathematics Keywords: Ramsey theory; closed contour; Jordan theorem; complete graph.

Online: 13 February 2023 (06:56:36 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0402.v1

Separated Model for Stopping Point Prediction of Autoregressive Sequence

Tingzhen Liu, Shengxi Zhang, Qianqian Xiong

Subject: Computer Science And Mathematics, Mathematics Keywords: Sequence Encoder; Autoregressive Sequence; Separated Model; Statistical Test; Neural Network

Online: 23 January 2023 (08:30:48 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0307.v1

Voronoi Diagrams Generated by the Archimedes Spiral

Mark Frenkel, Irina Legchenkova, Nir Shvalb, Shraga Shoval, Edward Bormashenko

Subject: Computer Science And Mathematics, Mathematics Keywords: Archimedes Spiral; Voronoi tessellation; Voronoi entropy; surface patterns; aesthetic attraction; phyllotaxis; golden ratio.

Online: 17 January 2023 (10:07:18 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0193.v1

A Different Geometric Approach to the Proof of Fermat’s Last Theorem

Elkhan Beylar Beylarov, Ilyas Ravan Hasanov

Subject: Computer Science And Mathematics, Mathematics Keywords: Fermat's last theorem; triangle inequalities; Elba curves; ellipse; geometric proof; circle

Online: 11 January 2023 (03:38:42 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0472.v1

Evaluation and Optimization of In-Vehicle HUD Design by Applying an Entropy Weight-VIKOR Hybrid Method

Yunuo Cheng, Xia Zhong, Liwei Tian

Subject: Computer Science And Mathematics, Mathematics Keywords: Entropy weight; VIKOR method; Head-up display; Interface design; Design evaluation; Scheme optimization

Online: 26 December 2022 (04:47:50 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0277.v1

A Numerical Quadrature Solution for Time Period of Simple Pendulum Under Magnetic Action

Bawar Mohammed Faraj, Viyan Jamal Jalal, Bnar Hama Zaman Hama Ali, Dana Taha Mohammed Salih, Shewa Abid Hama, Sarkhel Akbar Mahmood, Sarkew Salah Abdulkareem, Bahadin Muhammad Hussien

Subject: Computer Science And Mathematics, Mathematics Keywords: Simple Pendulum; Time Period; Magnetic Action; Numerical Integration; Error Analysis

Online: 15 December 2022 (08:57:20 CET)

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Preprint ARTICLE | doi:10.20944/preprints202212.0075.v1

On One-Point Time on an Oriented Set

Yaroslav Grushka

Subject: Computer Science And Mathematics, Mathematics Keywords: Oriented sets; changeable sets; time; ordered sets; axiom of choice

Online: 5 December 2022 (11:27:04 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0343.v1

Vehicle Directional Cosine Calculation Method

Derek Hall, Timothy Sands

Subject: Computer Science And Mathematics, Mathematics Keywords: kinematics; direction cosine matrixes; education

Online: 18 November 2022 (02:16:41 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0023.v1

Two-Parameter Exponentially-Fitted Taylor Method for Oscillatory/Periodic Problems

Ashiribo Senapon Wusu, Olusola Aanu Olabanjo, Manuel Mazzara

Subject: Computer Science And Mathematics, Mathematics Keywords: Taylor; exponentially-fitted; two-parameter; periodic; oscillatory; frequency

Online: 1 November 2022 (07:29:50 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0011.v1

Reinforcement Learning-based Wi-Fi Contention Window Optimization

Sheila C. da S. Cruz, Messaoud Ahmed Ouameur, Felipe A. P. de Figueiredo

Subject: Computer Science And Mathematics, Mathematics Keywords: Wi-Fi; contention-based access scheme; channel utilization optimization; machine learning; reinforcement learning; NS-3, NS3-gym

Online: 1 November 2022 (02:39:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0473.v1

Parameter Estimation for Some Probability Distributions Used in Hydrology

Cornel Ilinca, Cristian Gabriel Anghel

Subject: Computer Science And Mathematics, Mathematics Keywords: probability distributions; estimation parameters; approximate form; method of ordinary moments; method of L-moments

Online: 31 October 2022 (08:37:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0462.v1

Newton’s Like Normal S-iteration under Weak Conditions

Manoj Kumar Singh, Ioannis K. Argyros, Arvind K. Singh

Subject: Computer Science And Mathematics, Mathematics Keywords: Newton’s method; normal S-iteration; weak condition; simple root

Online: 31 October 2022 (02:23:04 CET)

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Preprint ESSAY | doi:10.20944/preprints202210.0364.v1

An Expository Medley on the Probabilistic Aspects and Insights of the Schrödinger Systems

Chaoyi Sheng

Subject: Computer Science And Mathematics, Mathematics Keywords: Schrödinger systems; Differential equations; Evolutions

Online: 24 October 2022 (12:45:15 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0277.v1

A Relative Difference System Involving Newton's Equations of Celestial Mechanics

Jocelyn Quaintance, Harry Gingold

Subject: Computer Science And Mathematics, Mathematics Keywords: Newton's celestial mechanics equations; $N$-body problem; Kepler problem; relative difference; origin invariance; integrals of motion; conservation of energy; conservation of angular momentum; inertia; Lagrange-Jacobi formula; total collapse.

Online: 19 October 2022 (10:06:06 CEST)

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Preprint ESSAY | doi:10.20944/preprints202210.0209.v1

Arzela-Ascoli's Theorem and Applications

Chaoyi Sheng

Subject: Computer Science And Mathematics, Mathematics Keywords: Arzela-Ascoli's theorem; functional analysis; topology

Online: 14 October 2022 (10:13:19 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0073.v1

Approximate Solution of Elliptic Poission Equation with IBVP using Finite Difference Scheme

Vladimir Jaćimović

Subject: Computer Science And Mathematics, Mathematics Keywords: Poissons equation; IBVP; Numerical Solution; Finite difference method

Online: 7 October 2022 (07:35:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0402.v1

UAV-assisted WRSN Online Charging Strategy Based on Dynamic Queue and Improved K-means

Tianle Shan, Yang Wang, Chuanxin Zhao, Rongyu Zou, Yanzhe Sun

Subject: Computer Science And Mathematics, Mathematics Keywords: Rechargeable Sensor Network; Unmanned Aerial Vehicle; One-to-one Charging; Space-time Collaboration; Optimal Charging Trajectory

Online: 27 September 2022 (02:07:41 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0378.v1

Factors Affecting Success and Failure in Higher Education Mathematics: Students and Teachers’ Perspectives

Mili Saha, Shobha Islam, Asma Akter Akhi, Goutam Saha

Subject: Computer Science And Mathematics, Mathematics Keywords: Mathematics; Factors; Success; Failure; Students; Teachers;

Online: 26 September 2022 (05:35:23 CEST)

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Background: Bangladeshi students from science, technology, engineering, and mathematics (STEM) often struggle with solving many mathematical problems in different pedagogic contexts. They mostly lack the considerable prior learning or strong basics required to cope with the teaching and learning materials used at the undergraduate levels, which leads many students to take readmissions every year. Objective: This research aims at investigating the factors affecting the success and deficit of university undergraduate mathematics students in Bangladesh. The mixed-method research incorporates quantitative and qualitative data analysis on the students' and teachers’ perspectives regarding the issues. The authors focus more on categorizing the reasons influencing effective mathematics pedagogies than on identifying new or unknown causes. Methodology: This study is outlined in three phases. The phases include i. Exploratory qualitative survey ii. Quantitative triangulation survey, iii. Explanatory semi-structured interviews. Findings: First, the qualitative survey exposes the important factors that highlight the student’s success and failure in mathematics. Next, the quantitative data confirm that there are some similarities and dissimilarities between students’ and teachers’ perceptions. Also, the coefficient correlation analysis shows male students lack consistency and passion for study resulting in poor performances. Conversely, female students emphasize the inability to connect mathematical theories to real-life usages, curriculum loads, and unavailable resources as the reasons for underperformance. Finally, the interview data demonstrate the students attribute their failure to inadequate practices, memorizing habits, poor teaching, low motivation, and external distractions. Also, students acknowledge the necessity of steady practice, clear understanding, regular study, and working strategies for successful mathematics education. Teachers emphasize students’ clear concepts, aptitude, motivation, and curiosity for successful learning. Conclusion: This conclusion proposes a fresh start with the local mathematics pedagogic practices by analyzing teacher-student feedback on the success and failure factors impacted by varied individual and contextual elements. The study offers inclusive feedback on the part of both stakeholders. However, an open discussion or interaction between students and teachers might be needed to enhance mutual trust and understanding between them.

Preprint ARTICLE | doi:10.20944/preprints202209.0157.v1

Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-metric Spaces with Applications

Tahair Rasham, Muhammad Nazam, Hassen Aydi, Ravi P. Agarwal

Subject: Computer Science And Mathematics, Mathematics Keywords: ordered complete multiplicative GM−metric space; closed ball; integral equations; locally generalized ∆-implicit contraction

Online: 13 September 2022 (04:44:36 CEST)

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Preprint BRIEF REPORT | doi:10.20944/preprints202208.0399.v1

Almost Global Pullback Attraction In Non-Autonomous Systems

Özkan Karabacak

Subject: Computer Science And Mathematics, Mathematics Keywords: pullback attractors; nonautonomous systems; almost global stability

Online: 23 August 2022 (11:21:11 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0288.v1

A Direct Prediction of the Shape Parameter in the Collocation Method of Solving Poisson Equation

Lin-Tian David Luh

Subject: Computer Science And Mathematics, Mathematics Keywords: radial basis function; multiquadric; shape parameter; collocation; Poisson equation

Online: 16 August 2022 (11:04:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0324.v1

Complex Network Formation as Antagonistic Game: Numerical Modeling

Pavel Bocharov, Alexander Goryashko

Subject: Computer Science And Mathematics, Mathematics Keywords: Graph complexity; antagonistic game theory; partition networks; neural networks; numeric modellng; Nash equilibrium; Neumann equilibrium

Online: 21 July 2022 (10:51:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0361.v1

A Short Study on Minima Distribution

Loc Nguyen

Subject: Computer Science And Mathematics, Mathematics Keywords: global optimization; minima distribution; particle swarm optimization; PSO

Online: 27 June 2022 (10:34:51 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0356.v1

Optimization of Hue, Brightness, Luminance, and Saturation Parameters for Video Segmentation Based on Evolutionary Algorithms

Fuangfar Pensiri, Porawat Visutsak

Subject: Computer Science And Mathematics, Mathematics Keywords: optimization; video segmentation; decision tree; random forest; gradient boost tree

Online: 27 June 2022 (08:56:21 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0331.v1

Two-State Alien Tiles: A Coding-Theoretical Perspective

Hoover H. F. Yin, Ka Hei Ng, Shi Kin Ma, Harry W. H. Wong, Hugo Wai Leung Mak

Subject: Computer Science And Mathematics, Mathematics Keywords: Alien Tiles; Coding Theory; Lights Out; Recreational Mathematics; Abstract Algebra

Online: 24 June 2022 (05:13:05 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0290.v1

Different Modes of Combustion Wave on a Lattice Burner

Vasily Novozhilov, Boris Lidskii, Vladimir Posvyanskii

Subject: Computer Science And Mathematics, Mathematics Keywords: premixed lattice burner; flame stabilization; analytical model

Online: 21 June 2022 (06:20:52 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202206.0068.v4

Generalizing The Mean From Hausdorff Measure and Fractal-Measures

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Hausdorff Measure; Fractals; Gauge Function; Dimension Function; Set Theory

Online: 17 June 2022 (08:54:36 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0187.v1

Generalization and Expansion of the Hermia Model for a Better Understanding of Membrane Fouling

Gustavo Dias Pereira, Lucio Cardozo Filho, Veeriah Jegatheesan, Reginaldo Guirardello

Subject: Computer Science And Mathematics, Mathematics Keywords: Membrane fouling; Hermia model; Fouling model; Pore blocking; Blocking mechanism

Online: 13 June 2022 (12:54:53 CEST)

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Preprint CASE REPORT | doi:10.20944/preprints202206.0158.v1

Statistical Error Calculation of Pandemic Predictive Models

Muhammad Harris Nazir, Faheem Awan Gohar, Umar Rashid, Muhammad Hassan Yousuf

Subject: Computer Science And Mathematics, Mathematics Keywords: Epidemic Model; SEIQRDP; fractional-order SEIQRDP; COVID-19

Online: 10 June 2022 (09:49:18 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202206.0068.v3

Generalizing The Mean

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Hausdorff Measure; Fractals; Gauge Function; Dimension Function; Set Theory

Online: 9 June 2022 (09:02:53 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202206.0068.v2

Generalizing The Mean

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Hausdorff Measure; Fractals; Gauge Function; Dimension Function; Set Theory

Online: 7 June 2022 (08:17:39 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202206.0068.v1

Generalizing The Mean

Bharath Krishnan

Subject: Computer Science And Mathematics, Mathematics Keywords: Hausdorff Measure; Fractals; Gauge Function; Dimension Function; Set Theory

Online: 6 June 2022 (08:37:20 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202205.0138.v1

Shifted Chebyshev Spectral Method for Two-Dimensional Space-Time Fractional Partial Differential Equations

Shina Oloniiju, Nolwazi Nkomo, Sicelo Goqo, Precious Sibanda

Subject: Computer Science And Mathematics, Mathematics Keywords: Shifted Chebyshev polynomials; Chebyshev-Gauss-Lobatto quadrature; space-time FPDE

Online: 10 May 2022 (10:19:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0161.v1

Identification of Material Properties of Elastic Plate Using Guided Waves Based on the Matrix Pencil Method and Laser Doppler Vibrometry

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

Subject: Computer Science And Mathematics, Mathematics Keywords: laminate; material properties; identification; guided waves

Online: 18 April 2022 (08:49:59 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0102.v1

Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements

Sergey Grigor'evich Pyatkov, Denis Shilenkov

Subject: Computer Science And Mathematics, Mathematics Keywords: inverse problem; surface flux; convection-diffusion equation; heat and mass transfer; pointwise measurements

Online: 11 April 2022 (14:24:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0098.v1

A Method for Real-time Adaptive Propagation Loss Modeling and Estimation Over LOS and NLOS Microcellular Radio Communication Links

Emmanuel Nwelih Nwelih

Subject: Computer Science And Mathematics, Mathematics Keywords: Adaptive; Tuning; Modelling; Estimation parameters; Propagation loss; NLOS; LOS

Online: 11 April 2022 (13:53:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0312.v1

A Monolithic Eulerian Formulation for non-Classical Fluid-Structure Interaction (nCFSI): Modeling and Simulation

Nazim Hussain, Muhammad Sabeel Khan, Lisheng Liu

Subject: Computer Science And Mathematics, Mathematics Keywords: monolithic variational scheme; cosserat fluids; fluid structure interaction; finite elements; Eulerian formulation; FreeFEM++

Online: 23 March 2022 (08:48:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0147.v2

Two-stage Algorithm for Solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations

Ahmed AbdelAziz Elsayed, Bassem Saassouh, Nazihah Ahmad, Ghassan Malkawi

Subject: Computer Science And Mathematics, Mathematics Keywords: Fully fuzzy Sylvester matrix equations; Fuzzy matrix equation; Numerical fuzzy solution; Trapezoidal fuzzy multiplication

Online: 23 February 2022 (12:17:04 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0289.v1

Tandem Recurrence Relations for Coefficients of Logarithmic Frobenius Series Solutions about Regular Singular Points

Ramses Van Der Toorn

Subject: Computer Science And Mathematics, Mathematics Keywords: ordinary differential equations; Frobenius method; tandem recurrence relations; Bessel's equation

Online: 23 February 2022 (10:24:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0157.v1

Identify the Mathematical Models Generated by the Table Curve 3 D Program

Emilian Mosnegutu, Mirela Panainte-Lehadus, Valentin Nedeff, Claudia Tomozei, Narcis Barsan, Dana Chitimus, Marcin Jasinski

Subject: Computer Science And Mathematics, Mathematics Keywords: mathematical models; Table Curve 3D; correlation coefficient

Online: 11 February 2022 (08:35:16 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0116.v1

Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution

Alison K. Cheeseman, Edward R. Vrscay

Subject: Computer Science And Mathematics, Mathematics Keywords: Fractal dimension; self-similarity; box-counting method; sandbox method; fractal trees; canopies; vascular networks; branching structures

Online: 8 February 2022 (13:59:05 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0383.v1

On shape parameter $\alpha$ based approximation properties and $q$-statistical convergence of Baskakov-Gamma operators

Ming-Yu Chen, Md. Nasiruzzaman, Mohammad Ayman Mursaleen, Nadeem Rao

Subject: Computer Science And Mathematics, Mathematics Keywords: Baskakov operators; gamma operators; rate of convergence; Lipschitz maximal space; q-density; q-statistical convergence.

Online: 25 January 2022 (13:34:35 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0047.v1

Lost in Optimization of Water Distribution Systems: Better Call Bayes

Antonio Candelieri, Andrea Ponti, Ilaria Giordani, Francesco Archetti

Subject: Computer Science And Mathematics, Mathematics Keywords: Pump scheduling optimization; Bayesian optimization; Optimal sensor placement; Wasserstein distance; Robustness

Online: 6 January 2022 (09:26:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0002.v1

PFDA-FMEA-VSM Application for Outsourcing Risk Analysis

Pedro Angel García Aguirre, Luis Perez-Dominugez, David Luviano-Cruz, Roberto Romero-López, Ernesto Leon-Castro

Subject: Computer Science And Mathematics, Mathematics Keywords: Failure Mode and Effect Analysis (FMEA); Pythagorean Fuzzy Dimensional Analysis (PFDA); Value Stream Mapping (VSM); Outsourcing Process (OP); Risk Analysis (RA).

Online: 4 January 2022 (12:23:06 CET)

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Preprint REVIEW | doi:10.20944/preprints202112.0329.v1

On the Minimum Polynomial and Applications

Nikos Halidias

Subject: Computer Science And Mathematics, Mathematics Keywords: Minimum polynomial; characteristic polynomial; exponential matrix; Drazin inverse; Leverrier - Faddeev algorithm

Online: 21 December 2021 (12:38:45 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0209.v1

The Multi-Attributive Border Approximation Area Comparison (Mabac) Method for Decision Making under Interval-Valued Fermatean Fuzzy Environment for Green Supplier Selection

Manoj Mathew, Ripon K. Chakrabortty, Michael J. Ryan, Muhammad Fazal Ljaz, Syed Abdul Rehman Khan

Subject: Computer Science And Mathematics, Mathematics Keywords: Interval-valued Fermatean fuzzy; MABAC; Green supplier selection; MCDM; Hamming distance

Online: 13 December 2021 (13:51:29 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0171.v1

The Value of Sector Coupling for the Development of Offshore Power Grids

Juan Gea-Bermúdez, Lena Kitzing, Matti Koivisto, Kaushik Das, Juan Pablo Murcia Leon, Poul Sørensen

Subject: Computer Science And Mathematics, Mathematics Keywords: Sector coupling; Offshore grid; Optimization; Sustainability Transition; Energy System Modelling

Online: 10 December 2021 (11:45:59 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0147.v1

Two-stage Algorithm for solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations

Ahmed AbdelAziz Elsayed, Bassem Saassouh, Nazihah Ahmad, Ghassan Malkawi

Subject: Computer Science And Mathematics, Mathematics Keywords: Fully fuzzy Sylvester matrix equations; Fuzzy matrix equation; Numerical fuzzy solution; Trapezoidal fuzzy multiplication.

Online: 9 December 2021 (10:29:28 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0097.v2

Accelerating Symmetric Rank-1 Quasi-Newton Method with Nesterov’s Gradient for Training Neural Networks

S. Indrapriyadarsini, Shahrzad Mahboubi, Hiroshi Ninomiya, Takeshi Kamio, Hideki Asai

Subject: Computer Science And Mathematics, Mathematics Keywords: Neural networks; quasi-Newton; symmetric rank-1; Nesterov’s accelerated gradient; limited memory; trust-region

Online: 8 December 2021 (17:51:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0097.v1

Accelerating Symmetric Rank-1 Quasi-Newton Method with Nesterov’s Gradient for Training Neural Networks

S. Indrapriyadarsini, Shahrzad Mahboubi, Hiroshi Ninomiya, Takeshi Kamio, Hideki Asai

Subject: Computer Science And Mathematics, Mathematics Keywords: Neural networks; quasi-Newton; symmetric rank-1; Nesterov’s accelerated gradient; limited memory; trust-region

Online: 7 December 2021 (10:58:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0495.v1

Double-Scale Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Linear Initial Value Problems

Stephane Malek

Subject: Computer Science And Mathematics, Mathematics Keywords: Asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; singular perturbation

Online: 26 November 2021 (09:56:11 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0453.v1

On the Nonlocal Problems in Time for Time-fractional Subdiffusion Equations

Ravshan Ashurov, Yusuf Fayziev

Subject: Computer Science And Mathematics, Mathematics Keywords: Nonlocal problems; the Riemann-Liouville and the Caputo derivatives; subdiffusion equation; inverse problems

Online: 24 November 2021 (12:44:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0169.v1

An Interpolation-Based Polynomial Method of Estimating the Objective Function Value in Scheduling Problems of Minimizing the Maximum Lateness

Alexander Alekseevich Lazarev, Darya Vladimirovna Lemtyuzhnikova, Andrey Alexandrovich Tyunyatkin

Subject: Computer Science And Mathematics, Mathematics Keywords: discrete mathematics; scheduling; optimization; interpolation; approximation; objective function.

Online: 9 November 2021 (13:24:19 CET)

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Preprint ARTICLE | doi:10.20944/preprints202109.0412.v1

Ramsey’s Theory Meets The Human Brain Connectome

Arturo Tozzi

Subject: Computer Science And Mathematics, Mathematics Keywords: Computer Science; Machine Learning; extremal set theory; Turán's theorem; Ramsey’s theorem

Online: 23 September 2021 (13:33:41 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202102.0559.v3

Euler-Bernoulli Beam Theory: First-Order Analysis, Second-Order Analysis, Stability, and Vibration Analysis Using the Finite Difference Method

Valentin Fogang

Subject: Computer Science And Mathematics, Mathematics Keywords: Euler Bernoulli beam; finite difference method; additional points; element stiffness matrix; tapered beam; first-order analysis; second-order analysis; vibration analysis; direct time integration method

Online: 23 September 2021 (13:08:38 CEST)

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This paper presents an approach to the Euler-Bernoulli beam theory (EBBT) using the finite difference method (FDM). The EBBT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally, the finite difference approximations are derived based on fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection curve; the FOPH is made for the fourth and third derivative of the deflection curve while the SOPH is made for its second and first derivative. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, the FOPH was made for all of the derivatives of the deflection curve, and additional points were introduced at the beam’s ends and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. First-order analysis, second-order analysis, and vibration analysis of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis). Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid. Further research will be needed to investigate polynomial refinements (higher-order polynomials such as fifth-order, sixth-order…) of the deflection curve; the polynomial refinements aimed to increase the accuracy, whereby non-centered finite difference approximations at beam’s ends and positions of discontinuity would be used.

Preprint ARTICLE | doi:10.20944/preprints202109.0269.v1

The System of Differential Equations Associated With Involutions

Farrukh Nuriddin ugli Dekhkonov

Subject: Computer Science And Mathematics, Mathematics Keywords: Involution; linear differential equation; fixed point; boundary value problem

Online: 15 September 2021 (15:19:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0247.v1

The Expansion Theorems for Sturm-Liouville Operators with an Involution Perturbation

Abdizhahan Sarsenbi

Subject: Computer Science And Mathematics, Mathematics Keywords: differential equations; involution; boundary value problems; Green’s function; eigen6 function expansions; equiconvergence; Riesz basis; spectral properties

Online: 14 September 2021 (15:41:08 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202008.0072.v2

Optinalysis: A New Method of Data Analysis and Comparison

Kabir Bindawa Abdullahi

Subject: Computer Science And Mathematics, Mathematics Keywords: Autoreflectivity; Identity; Isoreflectivity; Kabirian coefficient; Similarity; Symmetry

Online: 13 September 2021 (13:27:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints201911.0268.v2

Statistical Mirroring: A Good Alternative Estimator of Dispersion

Kabir Bindawa Abdullahi

Subject: Computer Science And Mathematics, Mathematics Keywords: isomorphic optinalysis; dispersion; statistical mirrors; estimators; statistical properties

Online: 13 September 2021 (13:26:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0155.v1

On Tribonacci Functions and Gaussian Tribonacci Functions

Yüksel Soykan, Melih Göcen, İnci Okumuş

Subject: Computer Science And Mathematics, Mathematics Keywords: Tribonacci numbers; Tribonacci functions; Gaussian Tribonacci functions; f-even functions

Online: 8 September 2021 (14:23:33 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0067.v1

Fuzzy Ensemble Ideal Solution Based Multi-Criteria Decision-Making Support for Heat Energy Transition in Danish Households

Qianyun Wen, Qiyao Yan, Junjie Qu, Yang Liu

Subject: Computer Science And Mathematics, Mathematics Keywords: MCDM; Individual Heating; Fuzzy; Energy Transition; Ensemble

Online: 3 September 2021 (14:07:23 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0053.v1

Analytical and Numerical Evaluation of Co-Scheduling Strategies and Their Application

Ruslan Kuchumov, Vladimir Korkhov

Subject: Computer Science And Mathematics, Mathematics Keywords: Co-scheduling; HPC; scheduling theory; stochastic optimization

Online: 3 September 2021 (10:14:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0503.v1

Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary

Alaa Melhem, Malik Bataineh, Rashid Abu-Dawwas

Subject: Computer Science And Mathematics, Mathematics Keywords: Graded 1-absorbing primary ideals; graded primary ideals; graded semi-primary ideals.

Online: 26 August 2021 (09:57:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202107.0063.v1

Optimal Charging Schedule Planning for Electric Buses Using the Aggregated Day-Ahead Auction Bids

Izabela Zoltowska, Jeremy Lin

Subject: Computer Science And Mathematics, Mathematics Keywords: aggregator; coordinated charging; double auction; mixed-integer linear programming

Online: 2 July 2021 (14:22:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0634.v1

Unsupervised Classification of Hyperspectral Images using PCA and K-Means

Ayesha Malik, Mamoona Waheed

Subject: Computer Science And Mathematics, Mathematics Keywords: Hyperspectral image; HSI; PCA; K-means clustering; unsupervised; classification; bands; satellite; ROSIS; AVIRIS

Online: 28 June 2021 (10:01:41 CEST)

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Working Paper ARTICLE

Inevitable Variance of Electric Field of Plasma Membrane

Bernard Delalande, Hirohisa Tamagawa, Titus Mulembo, Vladimir Matveev

Subject: Computer Science And Mathematics, Mathematics Keywords: membrane potential, constant electric field , resting potential, action potentia, GHK eq., HH model

Online: 22 June 2021 (16:03:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0481.v1

Inevitable Variance of Electric Field of Plasma Membrane

Bernard Delalande, Hirohisa Tamagawa, Titus Mulembo, Vladimir Matveev

Subject: Computer Science And Mathematics, Mathematics Keywords: membrane potential, constant electric field , resting potential, action potentia, GHK eq., HH model

Online: 18 June 2021 (13:51:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0425.v1

Binomial Cubic Fibonacci Sums

Kunle Adegoke

Subject: Computer Science And Mathematics, Mathematics Keywords: Fibonacci number; Lucas number; summation identity; series; binomial coefficient; cubic Fibonacci identity

Online: 16 June 2021 (08:39:35 CEST)

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Preprint REVIEW | doi:10.20944/preprints202106.0266.v1

Adaptive Wavelet Methods for Earth Systems Modelling

Nicholas Kevlahan

Subject: Computer Science And Mathematics, Mathematics Keywords: daptive mesh refinement; adaptive numerical methods; atmosphere modelling; climate modelling; Earth systems models; large-eddy simulation; ocean modelling; wavelets

Online: 9 June 2021 (12:18:45 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202106.0221.v1

Peter Chew Triangle Diagram and Application

Peter Chew

Subject: Computer Science And Mathematics, Mathematics Keywords: Peter Chew Triangle Diagram; Peter Chew

Online: 8 June 2021 (12:31:24 CEST)

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Abstract: The objective of Peter Chew Triangle Diagram is to clearly illustrate the topic solution of triangle and provide a complete design for the knowledge of AI age. Peter Chew's triangle diagram will suggest a better single rule that allows us to solve any problem of topic solution of triangle problems directly, more easily and more accurately. There are two important rules for solving the topic solution of triangle today [1,2], namely the sine rule and the cosine rule. The sine rule is used to find a non-included angle when are given two sides and a non-included angle or the opposite side angle given when are given two angles and one side. The cosine rule normally is used to find the included angle when are given three sides or the third side when are given two sides and the included angle. Generally, we only think that when given two sides and an included angle, the cosine rule is used to find the third side. In fact, when two sides and one non included angle are given, the cosine rule is also more easier for finding the third side. For problem given 2 sides and an included angle, directly find the non included angle. We need to use Peter Chew rule [1] to solve this problem. Peter Chew Rule allows us to find the non included angles directly, easier and more accurately. The application of Peter Chew's triangle diagram in the PCET calculator allows the PCET calculator to directly solve any problem in the topic solution of triangle, which is easier and more accurate. The Peter Chew diagram provides a complete design of the topic solution of triangle, which can help students solve any problems in the topic solution of triangle directly, more easily, and more accurately. Apply Peter Chew diagram to the new calculator (PCET calculator) , allows the PCET calculator to solve any problems in the topic solution of triangle and solve some problem that can not solve by current online calculator such as Math Portal and Symbolab. Which can make PCET calculator effectively help the teaching of mathematics, especially when similar covid-19 problems arise in the future.

Computer Science and Mathematics