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Preprint ARTICLE | doi:10.20944/preprints202306.0116.v1

Functional Ghobber-Jaming Uncertainty Principle

K. MAHESH KRISHNA

Subject: Computer Science And Mathematics, Analysis Keywords: Uncertainty Principle; Orthonormal Basis; Hilbert space; Banach space

Online: 2 June 2023 (03:24:54 CEST)

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Preprint REVIEW | doi:10.20944/preprints202305.2164.v1

A Review of Machine Vision Pose Measurement

Wang Xiaoxiao, Ng Seng Beng, Rahmita Wirza bt O. K. Rahmat, Puteri Suhaiza binti Sulaiman

Subject: Computer Science And Mathematics, Analysis Keywords: machine vision; pose measurement algorithms; accuracy; applications

Online: 31 May 2023 (03:33:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.2115.v1

Initial Coefficients Bounds for Bi-univalent Functions Related to Gregory Coefficients

Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, Teodor Bulboaca

Subject: Computer Science And Mathematics, Analysis Keywords: univalent functions; bi-univalent functions; starlike and convex functions of some order; subordination; Fekete-Szeg\H{o} problem

Online: 30 May 2023 (10:38:03 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1988.v1

Representation and Stability concerning General Nonic Functional Equation

Ick-Soon Chang, Yang-Hi Lee, Jaiok Roh

Subject: Computer Science And Mathematics, Analysis Keywords: stability; Hyperstability; nonic functional equation

Online: 29 May 2023 (07:09:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1741.v1

Gaming Tree Based Evaluation Model for Badminton Tactic Benefit Analysis and Prediction

Wenming Liu, Yifan Zhu, Wenxia Guo, Xinyuan Wang, Songkun Yu

Subject: Computer Science And Mathematics, Analysis Keywords: tactic analysis; gaming tree; nash equilibrium; badminton analysis and prediction; computer-based analysis

Online: 25 May 2023 (05:35:09 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1665.v1

Higher Monotonicity Properties for Zeros of Certain Sturm-Liouville Functions

Tzong-Mo Tsai

Subject: Computer Science And Mathematics, Analysis Keywords: Sturm-Liouville equations; differences; zeros; higher monotonicity; Bessel functions; orthogonal polynomials

Online: 24 May 2023 (01:54:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1528.v1

Legendre Series Analysis and Computation via Composed Abel-Fourier Transform

Enrico De Micheli

Subject: Computer Science And Mathematics, Analysis Keywords: Legendre coefficients; Fourier coefficients; Legendre expansion; Abel transform

Online: 22 May 2023 (12:50:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0955.v3

Decaying Turbulence as a Fractal Curve

Alexander Migdal

Subject: Computer Science And Mathematics, Analysis Keywords: Turbulence; Fractal; Anomalous dissipation; Fixed point; Velocity circulation; Loop Equations

Online: 16 May 2023 (11:57:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0955.v2

Decaying Turbulence as a Fractal Curve

Alexander Migdal

Subject: Computer Science And Mathematics, Analysis Keywords: Turbulence; Fractal; Anomalous dissipation; Fixed point; Velocity circulation; Loop Equations

Online: 15 May 2023 (13:47:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.1029.v1

A Unified Representation of Q- and H-Integrals and Consequences in Inequalities

Da Shi, Ghulam Farid, B. Younis, Hanaa Abu- Zinadah, Matloob Anwar

Subject: Computer Science And Mathematics, Analysis Keywords: q-derivative; q-integral; h-derivative; h-integral; q-h-derivative; q-h-integral; inequalities

Online: 15 May 2023 (10:44:36 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0955.v1

Decaying Turbulence as a Fractal Curve

Alexander Migdal

Subject: Computer Science And Mathematics, Analysis Keywords: Turbulence; Fractal; Anomalous dissipation; Fixed point; Velocity circulation; Loop Equations

Online: 12 May 2023 (13:43:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202305.0821.v1

On a System of Hadamard Fractional Differential Equations With Nonlocal Boundary Conditions on an Unbounded Domain

Rodica Luca, Alexandru Tudorache

Subject: Computer Science And Mathematics, Analysis Keywords: Hadamard fractional differential equations; nonlocal boundary conditions; positive solutions

Online: 11 May 2023 (08:29:25 CEST)

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Preprint REVIEW | doi:10.20944/preprints202305.0060.v1

Fractional Differential Boundary Value Equation utilizing the Convex Interpolation for Symmetry of Variables

Aftab Hussain

Subject: Computer Science And Mathematics, Analysis Keywords: Interpolative convex contraction; Suzuki convex contraction; fixed point; fractional differential equation.

Online: 2 May 2023 (05:26:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1255.v1

Further Accurate Numerical Radius Inequalities

Tariq Qawasmeh, Ahmad Qazza, Raed Hatamleh, Mohammad W. Alomari, Rania Saadeh

Subject: Computer Science And Mathematics, Analysis Keywords: Numerical radius; Norm; Inequalities; Hermite-Hadamard inequality

Online: 30 April 2023 (04:19:24 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1037.v1

Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains

Mohammed Ali, Hussain Al-Qassem

Subject: Computer Science And Mathematics, Analysis Keywords: Triebel-Lizorkin space; rough kernel; parabolic Marcinkiewicz integral; product domains; extrapolation

Online: 27 April 2023 (04:35:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.1008.v1

Sharp Stability for LSI

Emanuel Indrei

Subject: Computer Science And Mathematics, Analysis Keywords: Stability; Logarithmic Sobolev Inequality; Entropic Uncertainty; LSI; H^1

Online: 27 April 2023 (02:58:02 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0722.v1

Characterization of Herz-type Besov-Morrey and Triebel-Lizorkin-Morrey Spaces

Ruslan Abdulkadirov, Pavel Lyakhov

Subject: Computer Science And Mathematics, Analysis Keywords: Herz-type Besov-Morrey spaces; Herz-type Triebel-Lizorkin-Morrey spaces; ball mean of differences; atomic and molecular decomposition; wavelet decomposition

Online: 21 April 2023 (10:43:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0085.v1

Group-Frames for Banach Spaces

K. Mahesh Krishna

Subject: Computer Science And Mathematics, Analysis Keywords: Frame; group; representation

Online: 6 April 2023 (09:59:29 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202304.0060.v1

Functional Donoho-Stark-Elad-Bruckstein-Ricaud-Torresani Uncertainty Principle

K. Mahesh Krishna

Subject: Computer Science And Mathematics, Analysis Keywords: Uncertainty Principle; Orthonormal Basis; Parseval Frame; Hilbert space; Banach space

Online: 5 April 2023 (11:50:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202302.0468.v1

Fractional Modified Bessel Function of the First Kind of Integer Order

Andres Martin, Ernesto Estrada

Subject: Computer Science And Mathematics, Analysis Keywords: Modified Bessel functions; Communicability in graphs; Estrada index; Power-series; Fractional calculus; Caputo derivative; Riemann-Liouville integral; Paths; Cycles

Online: 27 February 2023 (09:39:57 CET)

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Preprint SHORT NOTE | doi:10.20944/preprints202302.0181.v1

Modular Dvoretzky, Type-Cotype, Khinchin-Kahane and Grothendieck Inequality Problems

K. MAHESH KRISHNA

Subject: Computer Science And Mathematics, Analysis Keywords: Dvoretzky Theorem; Type-Cotype; Khinchin-Kahane Inequality; Grothendieck Inequality; C*-algebra; Hilbert C*-module

Online: 10 February 2023 (06:19:10 CET)

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Preprint ARTICLE | doi:10.20944/preprints202302.0146.v1

Absolutely Summing Morphisms between Hilbert C*-Modules and Modular Pietsch Factorization Problem

K. MAHESH KRISHNA

Subject: Computer Science And Mathematics, Analysis Keywords: Absolutely summing operator; Commutative C*-algebra; Hilbert C*-module; Hilbert-Schmidt operator

Online: 8 February 2023 (10:58:34 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0199.v2

The Suboptimal WMT Test Sets and Its Impact on Human Parity

Ahrii Kim, Yunju Bak, Jimin Sun, Sungwon Lyu, Changmin Lee

Subject: Computer Science And Mathematics, Analysis Keywords: human parity; NMT evaluation; WMT

Online: 7 February 2023 (12:12:55 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0582.v1

Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities

Stephane Malek

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

Online: 31 January 2023 (10:17:51 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0393.v1

The Spectrum of the Zariski Topology for Multiplication Krasner Hypermodules

Ergül Türkmen, Burcu Nisancı Türkmen, Öznur KULAK

Subject: Computer Science And Mathematics, Analysis Keywords: Pseudo-prime spectrum; Zariski topology; spectral hyperspace

Online: 23 January 2023 (02:25:32 CET)

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Preprint ARTICLE | doi:10.20944/preprints202301.0290.v1

On the 1st Level General Fractional Derivatives of Arbitrary Order

Yuri Luchko

Subject: Computer Science And Mathematics, Analysis Keywords: generalized Sonin condition; general fractional integral; general fractional derivative of arbitrary order; regularized general fractional derivative of arbitrary order; 1st level general fractional derivative; 1st fundamental theorem of fractional calculus; 2nd fundamental theorem of fractional calculus

Online: 17 January 2023 (01:34:12 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0226.v1

A Study of Deep Learning Model Performance for Remote Sensing Image Segmentation

Teodora Selea, Gabriel Iuhasz, Marian Neagul

Subject: Computer Science And Mathematics, Analysis Keywords: deep learning; convolutional neural networks; remote sensing

Online: 14 November 2022 (01:20:07 CET)

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Preprint ARTICLE | doi:10.20944/preprints202211.0208.v1

Analyzing Brand Awareness Strategies on Social Media in the Luxury Market: the Case of Italian Fashion

Marco Brambilla, Hoda Badrizadeh, Narges Malek Mohammadi, Alireza Javadian Sabet

Subject: Computer Science And Mathematics, Analysis Keywords: social media; marketing; user engagement; brand analysis; long-running live event; fashion

Online: 11 November 2022 (02:08:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0477.v1

FlowerPhenoNet: Automated Flower Detection from Multi-view Image Sequences using Deep Neural Networks for Temporal Plant Phenotyping Analysis

Sruti Das Choudhury, Samarpan Guha, Aankit Das, Amit Kumar Das, Ashok Samal, Tala Awada

Subject: Computer Science And Mathematics, Analysis Keywords: High Throughput Plant Phenotyping; Deep Neural Network; Flower Detection; Temporal Phenotypes; Benchmark Dataset; Flower Status Report

Online: 31 October 2022 (10:00:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0464.v1

Some Estimators and their Properties Following Kabirian-based Optinalysis

Kabir Bindawa Abdullahi

Subject: Computer Science And Mathematics, Analysis Keywords: Kabirian-based optinalysis; estimators; properties; computing codes

Online: 31 October 2022 (04:53:43 CET)

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Preprint ARTICLE | doi:10.20944/preprints202210.0192.v1

IndShaker: A Knowledge-based Approach to Enhance Multi-perspective System Dynamics Analysis

Salvatore Flavio Pileggi

Subject: Computer Science And Mathematics, Analysis Keywords: Knowledge-based Systems; Ontology; Knowledge Engineering; MCDA.

Online: 13 October 2022 (09:54:49 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0181.v1

Regularity for Quasi-Linear p-Laplacian Type Non-homogeneous Equations in the Heisenberg Group

Chengwei Yu

Subject: Computer Science And Mathematics, Analysis Keywords: p-Laplacian type; non-homogeneous equations; Heisenberg group; regularities; Riesz potentials.

Online: 12 October 2022 (13:49:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202210.0079.v1

Algebraic Ando Dilation

K. MAHESH KRISHNA

Subject: Computer Science And Mathematics, Analysis Keywords: Dilation; And\^{o} dilation; vector space; linear map

Online: 7 October 2022 (11:54:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0433.v1

p-adic Magic Contractions, p-adic von Neumann Inequality and p-adic Sz.-Nagy Dilation

K. Mahesh Krishna

Subject: Computer Science And Mathematics, Analysis Keywords: Dilation, von Neumann inequality, Non-Archimedean valued field, p-adic Hilbert space, Contraction, Unitary operator

Online: 28 September 2022 (07:13:18 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0271.v1

Does the Restriction of Human Mobility Significantly Control COVID-19 Transmission in Jakarta, Indonesia? Global Versus Local Regression Models

I Gede Nyoman Mindra Jaya, Anna Chadidjah, Gumgum Darmawan, Jane Christine Princidy, And Farah Kristiani

Subject: Computer Science And Mathematics, Analysis Keywords: COVID-19; human mobility; spatial autocorrelation; temporal autocorrelation; Facebook mobility data

Online: 19 September 2022 (09:33:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0224.v2

Small Divisors Effects in Some Singularly Perturbed Initial Value Problem with Irregular Singularity

Stephane Malek

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

Online: 15 September 2022 (02:00:35 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0142.v1

Continuous Non-Archimedean and p-adic Welch Bounds

K. Mahesh Krishna

Subject: Computer Science And Mathematics, Analysis Keywords: Non-Archimedean valued field; Non-Archimedean Banach space; p-adic number field; p-adic Banach space; Welch bound; Zauner conjecture

Online: 12 September 2022 (09:51:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0068.v1

Global Impact of COVID-19 Pandemic on Physical Activity Habits of Competitive Runners: an Analysis of Wearable Device Data

Julia Lee Romero, Qin Lv

Subject: Computer Science And Mathematics, Analysis Keywords: wearable device; physical activity; behavior; COVID-19; pandemic; exercise habits; analysis; objectively-measured physical activity

Online: 5 September 2022 (13:49:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202209.0005.v1

Non-Archimedean and p-adic Functional Welch Bounds

K. MAHESH KRISHNA

Subject: Computer Science And Mathematics, Analysis Keywords: Non-Archimedean valued ﬁeld; Non-Archimedean Banach space; p-adic number ﬁeld; p-adic Banach space; Welch bound; Zauner conjecture

Online: 1 September 2022 (04:13:43 CEST)

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We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results. \begin{enumerate}[\upshape(i)] \item Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying $\left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2$ for all $ \lambda_j \in \mathbb{K}, 1\leq j \leq n$, for all $n \in \mathbb{N}.$ Let $\mathcal{X}$ be a $d$-dimensional non-Archimedean Banach space over $\mathbb{K}$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and the operator $S_{f, \tau} : \text{Sym}^m(\mathcal{X})\ni x \mapsto \sum_{j=1}^nf_j^{\otimes m}(x)\tau_j^{\otimes m} \in \text{Sym}^m(\mathcal{X})$, is diagonalizable, then \begin{align}\label{NONFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds. \item For a prime $p$, let $\mathbb{Q}_p$ be the p-adic number field. Let $\mathcal{X}$ be a $d$-dimensional p-adic Banach space over $\mathbb{Q}_p$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and there exists $b \in \mathbb{Q}_p$ such that $ \sum_{j=1}^{n}f_j^{\otimes m}(x) \tau_j^{\otimes m} =bx$ for all $ x \in \text{Sym}^m(\mathcal{X}),$ then \begin{align}\label{PADICFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds. \end{enumerate} We formulate non-Archimedean functional and p-adic functional Zauner conjectures.

Preprint ARTICLE | doi:10.20944/preprints202208.0492.v1

Non-Archimedean Welch Bounds and Non-Archimedean Zauner Conjecture

K. Mahesh Krishna

Subject: Computer Science And Mathematics, Analysis Keywords: Non-Archimedean valued field; non-Archimedean Hilbert space; Welch bound; Zauner conjecture

Online: 29 August 2022 (12:35:07 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0322.v1

Weighted Hermite-Hadamard inequalities for r−Times Differentiable Preinvex Functions for k−Fractional Integrals

Fiza Zafar, Sikander Mehmood, Asim Asiri

Subject: Computer Science And Mathematics, Analysis Keywords: Hermite-Hadamard-Fejér inequality; k−fractional integral; Preinvex function; r-times; differentiable function

Online: 17 August 2022 (11:01:57 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202208.0140.v1

C*-algebraic Bieberbach, Robertson, Lebedev-Milin, Zalcman, Krzyz and Corona Conjectures

K. MAHESH KRISHNA

Subject: Computer Science And Mathematics, Analysis Keywords: C*-algebra; Bieberbach conjecture; de Branges theorem; Robertson conjecture; Lebedev-Milin conjecture; Zalcman conjecture; Krzyz conjecture; Corona conjecture; Riemann mapping theorem

Online: 8 August 2022 (09:53:02 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0175.v1

Orthogonal Frames in Krein Spaces

Osmin Oberto Ferrer Villar, Arley Yessit Sierra Acosta, Osvaldo De Jesus Polo Flórez

Subject: Computer Science And Mathematics, Analysis Keywords: Krein space; fundamental symmetry; Hilbert associated; frames

Online: 12 July 2022 (08:10:52 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0166.v1

Vorticity and Micro-Rotation in Micropolar Flows

Paulo Zingano, César Niche, Cilon Perusato, Wilberclay Melo, Robert Guterres

Subject: Computer Science And Mathematics, Analysis Keywords: incompressible micropolar ﬂows; vorticity and micro-rotation; dissipative systems; monotonicity method; upper and lower estimates

Online: 12 July 2022 (04:03:22 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0137.v1

Upper and Lower H^m Estimates for Solutions to Dissipative Systems

Robert Guterres, César Niche, Cilon Perusato, Paulo Zingano

Subject: Computer Science And Mathematics, Analysis Keywords: dissipative systems; upper and lower estimates; decay estimates; monotonicity method

Online: 8 July 2022 (10:13:41 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202207.0068.v1

Requirements, Challenges, and Use of Digital Devices and Apps for Blind and Visually Impaired

Sahar Busaeed, Rashid Mehmood, Iyad Katib

Subject: Computer Science And Mathematics, Analysis Keywords: blind; visually impaired; assistive devices; object recognition; navigation; virtual assistants; Smart Cities; Saudi Arabia

Online: 5 July 2022 (08:24:38 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0365.v1

GN-Operators

Reza Ahmadi, Gholamreza Rahimlou

Subject: Computer Science And Mathematics, Analysis Keywords: Hilbert space; Lebesgue integral; trace class operator; frame; measure space

Online: 27 June 2022 (11:07:31 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0311.v1

On Fuzzy Locally Convex Spaces

Murphy Emeke Egwe

Subject: Computer Science And Mathematics, Analysis Keywords: t-norms; fuzzy seminorm; Minkowski functional; fuzzy topology

Online: 22 June 2022 (08:47:09 CEST)

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Preprint REVIEW | doi:10.20944/preprints202206.0285.v1

Analysis of Blockchain in the Healthcare Sector: Application and Issues

Ammar Odeh, Ismail Keshta, Qasem Abu Al-Haija

Subject: Computer Science And Mathematics, Analysis Keywords: Blockchain; Healthcare; Privacy; Cybersecurity; Healthcare-records

Online: 21 June 2022 (05:05:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202206.0224.v1

Small Divisors Effects in Some Singularly Perturbed Initial Value Problem With Irregular Singularity

Stephane Malek

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

Online: 15 June 2022 (10:36:54 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0203.v1

The Nonlinear Analysis Related to Schauder Fixed Points, Best Approximation, Birkhoff-Kellogg Problems and Principle of Leray-Schauder Alternatives in p-Vector Spaces

George X. Yuan

Subject: Computer Science And Mathematics, Analysis Keywords: nonlinear analysis; best approximation; Birkhoff-Kellogg theorem; schauder conjecture; fixed point theorem; nonlinear alternative; Leray-Schauder alternative; p-convex; p-inward and p-outward set; p-vector space

Online: 21 April 2022 (10:22:55 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202204.0020.v1

Containing COVID: “To Trace or Not to Trace?” - That Is Not the Question!

Inavamsi Enaganti, Shirshendu Chatterjee, Kuldeep Meel, Bud Mishra

Subject: Computer Science And Mathematics, Analysis Keywords: Epidemics; Optimal Policy; Trace and Quarantine strategy; Agent networks

Online: 4 April 2022 (15:12:26 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202203.0329.v1

Plagiarism Detection in the Bengali Language: A Text Similarity-Based Approach

Satyajit Ghosh, Aniruddha Ghosh, Bittaswer Ghosh, Abhishek Roy

Subject: Computer Science And Mathematics, Analysis Keywords: Plagiarism Detection; Plagiarism checker for Bengali text; Bengali Literature Corpus; OCR in Bengali text

Online: 24 March 2022 (09:36:56 CET)

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Preprint ARTICLE | doi:10.20944/preprints202107.0645.v2

Asymptotics and Confluence for a Singular Nonlinear Q-Difference-Differential Cauchy Problem

Stephane Malek

Subject: Computer Science And Mathematics, Analysis Keywords: asymptotic expansion; confluence; formal power series; partial differential equation; q-difference equation

Online: 22 March 2022 (11:41:03 CET)

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Preprint REVIEW | doi:10.20944/preprints202202.0212.v1

Knowledge Graph Embedding for Link Prediction Models

Ehtisham Ur Rehman, Aamir Saeed, Nasru Minallah, Abdul Hafeez

Subject: Computer Science And Mathematics, Analysis Keywords: Knowledge Graphs; Link Prediction; Semantic-Based Models; Translation Based Embedded Models

Online: 17 February 2022 (11:49:24 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0151.v1

Multiple-Trait Model through Bayesian Inference Applied to Flood-Irrigated Rice (Oryza sativa L)

Antonio Carlos da Silva Junior, Isabela de Castro Sant’Anna, Marco Antônio Peixoto, Lívia Gomes Torres, Michele Jorge Silva, Weverton Gomes da Costa, Camila Ferreira Azevedo, Plinio César Soares, Cosme Damião Cruz

Subject: Computer Science And Mathematics, Analysis Keywords: high-performance; heritable; multi-environments; credibility interval

Online: 10 February 2022 (11:14:21 CET)

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Preprint ARTICLE | doi:10.20944/preprints202202.0145.v1

Predictive Optimization Based Energy Cost Minimization and Energy Sharing Mechanism for Peer-to-Peer Nanogrid Network

Faiza Qayyum, Harun Jamil, Faisal Jamil, Do-Hyeun Kim

Subject: Computer Science And Mathematics, Analysis Keywords: Smart grids; Optimization; Prediction methods; Energy exchange

Online: 10 February 2022 (07:55:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0270.v1

Trends in Road Accidents on Brazil’s Highways: Evidence of Persistence

Luis Alberiko Gil-Alana, Peter Wanke, Yong Tan

Subject: Computer Science And Mathematics, Analysis Keywords: Road accidents; Brazil; fractional integration; long memory

Online: 19 January 2022 (11:45:26 CET)

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Preprint ARTICLE | doi:10.20944/preprints202201.0199.v1

A Generalized Construction Model for CT Reconstruction Filters on the SDBP Technique

Yi-ming Jiang, Jin-tao Zhao, Xiao-dong Hu, Jing Zou

Subject: Computer Science And Mathematics, Analysis Keywords: inverse Radon transform; CT; SDBP; filter design; kernel function; Hilbert transform; basic filters

Online: 14 January 2022 (10:34:32 CET)

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Preprint ARTICLE | doi:10.20944/preprints202112.0304.v1

Strongly Recurrent Transformation Groups

Massoud Amini, Jumah Swid

Subject: Computer Science And Mathematics, Analysis Keywords: ordered groups; $\sigma$-finite spaces; strongly recurrent actions; strictly recurrent actions; weakly wandering sets

Online: 20 December 2021 (10:28:50 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0408.v1

Global Well-Posedness for the Fractional Navier-Stokes-Coriolis Equations in Function Spaces Characterized by Semigroups

Xiaochun Sun, Jia Liu, Jihong Zhang

Subject: Computer Science And Mathematics, Analysis Keywords: Cauchy problem; The generalized Navier-Stokes-Coriolis equation; Global well-posedness

Online: 22 November 2021 (15:03:54 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0139.v1

Solutions and Drift Homogenization for a Class of Viscous Lake Equations in

Maoting Tong

Subject: Computer Science And Mathematics, Analysis Keywords: viscous lake equations，Navier-Stokes equation, Existence and uniqueness, Semigroup of operators, Fractional powers.

Online: 8 November 2021 (13:10:30 CET)

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Preprint ARTICLE | doi:10.20944/preprints202111.0024.v1

Efficiencies of Feature Engineering in the Machine Learning approach for Fake News Classification

Katrin Donetski

Subject: Computer Science And Mathematics, Analysis Keywords: Fake news detection; Deep learning; Feature Engineering

Online: 1 November 2021 (15:34:46 CET)

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Preprint ARTICLE | doi:10.20944/preprints202110.0380.v1

Mapping Maternal Health in the New Media Environment: A Scientometric Analysis

Yinghua Xie, Dong Lang, Chengxu Long, Shangfeng Tang

Subject: Computer Science And Mathematics, Analysis Keywords: maternal health; new media; bibliometric analysis; cited reference analysis; structural variation analysis; hot spots

Online: 26 October 2021 (12:17:49 CEST)

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Background: The new media provides a convenient digital platform to access, use and exchange health information. As a special group of health care, maternal is still of international concern due to their high mortality rate. Improving maternal health as a Millennium Development Goal of the United Nations is an important quest for the health care system. Scientific research provides advice on how to improve maternal health through stringent reasoning and accurate data. However, the dramatic increase of publications, the diversity of themes, and the dispersion of researchers may reduce efficiency. Objective: This study aims to analyze the research progress on maternal health under the global new media environment, exploring the current research hotspots and research frontiers. Methods: A scientometric analysis was carried out by CiteSpace5.7.R1, searching in the core database of Web of Science for articles published in English from 1998 to 2021, and combined topic words such as new media, maternal, and health. In total, 3312 articles have been retrieved, of which 2270 studies have been included for further analysis. Top countries and institutions, potentially high-impact literature, research frontiers, and hotspots were analyzed in this study. Results: The number of publications grew rapidly after 2008, from 29 publications sharply increasing to 472 publications by 2020. Research centers concentrated in Latin America, such as the University of Toronto, the University of California. The work of Larsson M, Lagan BM, Tiedje L, and Helle C had a high potential impact. Most of the research subjects were maternal and newborn babies, and the research frontiers focused on health education and maternal psychological problems. Maternal mental health, maternal and infant nutrition, weight, production technology, and equipment were hotspots. Conclusion: The development of new media has brought a new era for maternal health, characterized by psychological qualities, healthy and reasonable physical conditions, and advanced technology.

Preprint COMMUNICATION | doi:10.20944/preprints202110.0299.v1

Air Quality Estimation in Ukraine Using SDG 11.6.2 Indicator Assessment

Andrii Shelestov, Hanna Yailymova, Bohdan Yailymov, Nataliia Kussul

Subject: Computer Science And Mathematics, Analysis Keywords: air quality monitoring; PM2.5; sustainable development goals; SDG indicator 11.6.2

Online: 20 October 2021 (22:52:38 CEST)

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Ukraine is an associate member of the European Union and in the coming years it is expected that all the data and services already used by European Union countries will become available for Ukraine. An important program, which is the basis for building European monitoring services for Smart Cities, is the Copernicus program. The two most important services of this program are Copernicus Land Monitoring Service (CLMS) and Copernicus Atmosphere Monitoring Service (CAMS). CLMS provides important information on Land Use in Europe. In the context of Smart Cities, the most valuable one is the Urban Atlas service, which is related to local CLMS services and provides a detailed digital city plan in vector form, which is segmented into small functional areas classified by the CORIN nomenclature. The Urban Atlas is a geospatial layer with high-resolution, which is built for all European cities with a population of more than 100,000 that combines high-resolution sat-ellite data, city segmentation by blocks and functional areas, important city infrastructure, etc. This product is used as a basis for city planning and obtaining analytics on the most important indicators of city development including air quality monitoring. For Ukraine, such geospatial products are not provided under the Copernicus program. It is important to start work on its development and implementation as early as possible, so that when the first city atlas appears, Ukraine will be ready to work with it together with the European community. This requires preparing the basis for na-tional research and training national stakeholders and users to use this product. To make this happen it’s necessary to have national geospatial product, which can be used as an analogue of the city atlas. In this article authors analyzed the existing methods of air quality assessment and assessment of the SDG indicator 11.6.2 achieving for European cities, based on which the indicator 11.6.2 for Ukraine for 5 years was evaluated for the first time. The obtained results are analyzed and the values of indicator 11.6.2 for Ukraine are compared with European countries.

Preprint ARTICLE | doi:10.20944/preprints202110.0199.v1

The Suboptimal WMT Test Sets and Its Impact on Human Parity

Ahrii Kim, Yunju Bak, Jimin Sun, Sungwon Lyu, Changmin Lee

Subject: Computer Science And Mathematics, Analysis Keywords: human parity; NMT evaluation; WMT

Online: 13 October 2021 (11:37:27 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202109.0371.v1

Qualitative Data Collection under the ‘New Normal’ in Zimbabwe

Emmanuel Ndhlovu

Subject: Computer Science And Mathematics, Analysis Keywords: COVID-19; digital data collection; qualitative; Zimbabwe

Online: 22 September 2021 (10:20:11 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202108.0577.v1

Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

Hayel N. Saleh, Mohammad Imdad, Salvatore Sessa, Ferdinando Di Martino

Subject: Computer Science And Mathematics, Analysis Keywords: fuzzy $(\sigma,\mathcal{Z})$-contractive mappings; fuzzy metric spaces; fuzzy-$\mathcal{Z}$-contractive mappings}

Online: 1 September 2021 (09:21:14 CEST)

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Preprint HYPOTHESIS | doi:10.20944/preprints202106.0118.v1

Customer Churn - Prevention Model – Unsupervised Classification

JULIAN GRIJALBA FACUNDO

Subject: Computer Science And Mathematics, Analysis Keywords: Churn 1; customer churn; customer segmentation; churn prevention; predictive churn 21 model; recommendation system engine.

Online: 3 June 2021 (13:34:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202103.0738.v1

Impact of the Coronavirus Pandemic on Science and Society: Insights from Temporal Bibliometric Networks

Ramya Gupta, Abhishek Prasad, Suresh Babu, Gitanjali Yadav

Subject: Computer Science And Mathematics, Analysis Keywords: bibliometry; coronavirus; text and data mining; SARS; MERS; COVID-19

Online: 31 March 2021 (17:30:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202012.0021.v1

Predicting Trends of Coronavirus Disease (COVID19) Using SIRD and Gaussian-SIRD Models

Ahmad Sedaghat, Amir Mosavi

Subject: Computer Science And Mathematics, Analysis Keywords: Coronavirus disease; COVID-19; outbreak model; Gaussian-SIRD model; SIRD model; epidemiological model

Online: 1 December 2020 (13:11:02 CET)

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Preprint ARTICLE | doi:10.20944/preprints202011.0464.v1

Analytic Automorphisms and Transitivity of Analytic Mappings

Zoriana Novosad, Andriy Zagorodnyuk

Subject: Computer Science And Mathematics, Analysis Keywords: topologically transitive operator; hypercyclic operators; function space; analytic functions on Banach spaces; symmetric polynomials on Banach spaces

Online: 18 November 2020 (10:39:35 CET)

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Working Paper ARTICLE

Some Notes on the Parametric Gevrey Asymptotics in two Complex Time Variables through Truncated Laplace Transforms

Guoting Chen, Alberto Lastra, Stephane Malek

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

Online: 11 September 2020 (08:11:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202008.0578.v1

The Mapping of the Main Functions and Different Variations of YH-DIE

Gilbert Mason, Yuanjue Chou, Springer Pind

Subject: Computer Science And Mathematics, Analysis Keywords: complete Riemannian manifolds; entire solutions; minimal graphs; differential equat; algebraic variety

Online: 26 August 2020 (10:19:32 CEST)

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Working Paper ARTICLE

Two Nested Limit Cycles in Two-Species Reactions

Ilona Nagy, Valery G. Romanovski, János Tóth

Subject: Computer Science And Mathematics, Analysis Keywords: Limit cycles; Two-species reactions; Third order reaction step; Hopf bifurcation

Online: 25 August 2020 (10:27:34 CEST)

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Preprint REVIEW | doi:10.20944/preprints202008.0495.v1

Coronavirus Pandemic (COVID-19): A Survey of Analysis, Modeling and Recommendations

Tehmina Amjad, Ali Daud, Malik Khizar Hayat, Muhammad Tanvir Afzal, Hussain Dawood

Subject: Computer Science And Mathematics, Analysis Keywords: coronavirus pandemic (COVID-19); analysis; modeling; recommendations; surveillance; social media analytics; meteorological effects; image processing; business and economy

Online: 24 August 2020 (02:54:47 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202008.0479.v1

Epidemic Evolution: Multiple Analytical Solutions for the SIR Model

Ian Lerche

Subject: Computer Science And Mathematics, Analysis Keywords: SIR model; epidemic; multiple analytical solutions

Online: 21 August 2020 (10:50:39 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202008.0458.v1

Coronavirus Disease (COVID-19) Dynamics: Age and Gender-based Analysis of Surveillance Variables

Malik Khizar Hayat, Ali Daud, Rabeeh Ayaz Abbasi, Tehmina Amjad, Xiuzhen Jenny Zhang

Subject: Computer Science And Mathematics, Analysis Keywords: Coronavirus disease (COVID-19); Correlation and analysis; Age and Gender; Hospitalization; Tests performed; Recovery

Online: 20 August 2020 (13:02:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202008.0159.v1

Experimental Study for Determining the Parameters Required for Detecting ECG and EEG Related Diseases During the Timed-Up and Go Test

Vasco Ponciano, Ivan Miguel Pires, Fernando Reinaldo Ribeiro, María Vanessa Villasana, Maria Canavarro Teixeira, Eftim Zdravevski

Subject: Computer Science And Mathematics, Analysis Keywords: Diseases; electrocardiography; electroencephalography; Timed-Up and Go test; sensors; mobile devices; feature detection; diseases; older adults

Online: 6 August 2020 (10:46:57 CEST)

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Working Paper ARTICLE

On Gevrey Asymptotics for Linear Singularly Perturbed Equations with Linear Fractional Transforms

Guoting Chen, Alberto Lastra, Stephane Malek

Subject: Computer Science And Mathematics, Analysis Keywords: asymptotic expansion; Lambert W function; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; singular perturbation

Online: 17 July 2020 (15:42:50 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202007.0114.v1

A Note on Type 2 Degenerate Poly-Cauchy Polynomials and Numbers of the Second Kind

Waseem Khan

Subject: Computer Science And Mathematics, Analysis Keywords: degenerate polylogarithm functions; degenerate poly-Cauchy polynomials; degenerate unipoly-Cauchy polynomials

Online: 7 July 2020 (08:20:34 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202007.0103.v1

A Note on Type 2 Degenerate Poly-Frobenius-Genocchi Polynomials

Waseem A. Khan

Subject: Computer Science And Mathematics, Analysis Keywords: polylogarithm function; Frobenius-Genocchi polynomials; degenerate poly-Frobenius-Euler polynomials

Online: 6 July 2020 (09:47:06 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202006.0353.v1

Analysis and Forecast of COVID-19 Pandemic in Pakistan

Abdul Bari Malik

Subject: Computer Science And Mathematics, Analysis Keywords: COVID-19; Epidemiology; COVID-19 Analysis and Forecast in Pakistan; Forecasting; Estimation; ARIMA; Prophet; SIRD; Diffusion; Analysis

Online: 29 June 2020 (10:50:47 CEST)

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Working Paper ARTICLE

Parametric Gevrey Asymptotics in Two Complex Time Variables through Truncated Laplace Transforms

Stephane Malek, Alberto Lastra, Guoting Chen

Subject: Computer Science And Mathematics, Analysis Keywords: asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; partial differential equation; singular perturbation

Online: 14 June 2020 (13:06:30 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202006.0039.v2

A Compartmental Epidemiological Model for the Dissemination of the COVID-19 Disease

Evangelos Matsinos

Subject: Computer Science And Mathematics, Analysis Keywords: Epidemiology; infectious disease; compartmental model; mathematical modelling and optimisation; COVID-19; SARS-CoV-2

Online: 12 June 2020 (12:14:28 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202006.0039.v1

A Compartmental Epidemiological Model for the Dissemination of the COVID-19 Disease

Evangelos Matsinos

Subject: Computer Science And Mathematics, Analysis Keywords: Epidemiology; infectious disease; compartmental model; mathematical modelling and optimisation; COVID-19; SARS-CoV-2

Online: 4 June 2020 (14:47:56 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202005.0399.v2

Optimistic Prediction Model for the COVID-19 Coronavirus Pandemic Based on the Reported Data Analysis

Khalid Aloufi

Subject: Computer Science And Mathematics, Analysis Keywords: IR; ML; Data Analysis; COVID-19; Coronavirus; Pandemic

Online: 28 May 2020 (03:09:38 CEST)

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Preprint BRIEF REPORT | doi:10.20944/preprints202005.0405.v1

COVID 19 Data Visualization through Automatic Phase Detection

Pradipta Biswas, Kamalpreet Singh Saluja, Somnath Arjun, LRD Murthy, Gowdham Prabhakar, Vinay Krishna Sharma, Jeevitha Shree DV

Subject: Computer Science And Mathematics, Analysis Keywords: Data Visualization; Information Visualization; COVID 19 Pandemic

Online: 24 May 2020 (20:23:04 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202005.0399.v1

Optimistic Prediction Model for the COVID-19 Coronavirus Pandemic Based on the Reported Data Analysis

Khalid Aloufi

Subject: Computer Science And Mathematics, Analysis Keywords: IR; ML; Data Analysis; COVID-19; Coronavirus; Pandemic

Online: 24 May 2020 (19:03:18 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202005.0154.v1

LMM-22: An Enhanced Linear Mixed Model (LMM) Approach for Genome-Wide Association Studies (GWAS) for the Prediction of Diseases and Traits among Humans from Genomics Data

Siddharth Sharma

Subject: Computer Science And Mathematics, Analysis Keywords: GWAS Studies; Linear Mixed Models; GPU Acceleration

Online: 9 May 2020 (08:20:12 CEST)

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Preprint CONCEPT PAPER | doi:10.20944/preprints202005.0054.v1

The J-Generalized P - K Mittag-Leffler Function

Kuldeep Singh Gehlot, Anjana Bhandari

Subject: Computer Science And Mathematics, Analysis Keywords: the j-generalized p - k Mittag-Lefflerr Function; the p - k Mittag-Leffler Function; generalized k-Mittag-Leffler Function; two parameter pochhammer symbol; two parameter Gamma function

Online: 5 May 2020 (02:43:50 CEST)

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Working Paper ARTICLE

On Inner Expansions for A Singularly Perturbed Cauchy Problem with Confluent Fuchsian Singularities

Stephane Malek

Subject: Computer Science And Mathematics, Analysis Keywords: asymptotic expansion; Borel-Laplace transform; Cauchy problem; formal power series; integro-differential equation; partial differential equation; singular perturbation

Online: 23 April 2020 (04:33:13 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202004.0288.v1

Solvability of Nonlinear Equations in Case of Branching Solutions

Nikolai A. Sidorov, Denis Sidorov, Aliona Dreglea

Subject: Computer Science And Mathematics, Analysis Keywords: branch points; bifurcation points; Fredholm operator; uniformization; asymptotics; iterations; regularization

Online: 17 April 2020 (01:34:37 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202004.0140.v1

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

Amjad S. Shaikh, Iqbal N. Shaikh, Kottakkaran Sooppy Nisar

Subject: Computer Science And Mathematics, Analysis Keywords: mathematical models; coronavirus; caputo-fabrizio derivative; basic reproduction number; existence and stability; numerical simulations

Online: 9 April 2020 (08:12:53 CEST)

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Working Paper ARTICLE

Parametric Gevrey Asymptotics in Two Complex Time Variables through Truncated Laplace Transforms

Stephane Malek, Alberto Lastra, Guoting Chen

Subject: Computer Science And Mathematics, Analysis Keywords: asymptotic expansion; Borel-Laplace transform; Fourier transform; initial value problem; formal power series; partial differential equation; singular perturbation

Online: 3 April 2020 (15:35:10 CEST)

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Preprint ARTICLE | doi:10.20944/preprints202003.0218.v1

Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

M. Mursaleen, Md Nasiruzzaman, Adem Kilicman, Siti Hasana Sapar

Subject: Computer Science And Mathematics, Analysis Keywords: Szász operator; dunkl analogue; generalization of exponential function; korovkin type theorem; modulus of continuity; order of convergence

Online: 12 March 2020 (14:28:31 CET)

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Preprint ARTICLE | doi:10.20944/preprints202002.0347.v1

Resonance Enhancement by Suitably Chosen Frequency Detuning

Denys Dutykh, Elena Tobisch

Subject: Computer Science And Mathematics, Analysis Keywords: nonlinear resonance; frequency detuning; 3-wave system; resonance enhancement

Online: 24 February 2020 (05:32:49 CET)

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Preprint ARTICLE | doi:10.20944/preprints202002.0303.v1

Fixed Point Results for a New Class of Multi-Valued Mappings Under (θ; R)-Contractions With an Application

MD Hasanuzzaman Hasanuzzaman, Salvatore Sessa, Mohammad Imdad, W. M. Alfaqih

Subject: Computer Science And Mathematics, Analysis Keywords: fixed point; integral equation; binary relation

Online: 21 February 2020 (03:22:12 CET)

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Working Paper ARTICLE

Taming the Natural Boundary of Centered Polygonal Lacunary Functions: Restriction to the Symmetry Angle Space

L.K. Mork, Keith Sullivan, Darin J. Ulness

Subject: Computer Science And Mathematics, Analysis Keywords: lacunary function; gap function; centered polygonal numbers; Natural boundary; singularities; broom topology

Online: 19 February 2020 (11:43:50 CET)

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Preprint ARTICLE | doi:10.20944/preprints202002.0269.v1

Implementing a Novel Use of Multicriteria Decision Analysis to Select IIoT Platforms for Smart Manufacturing

Roberto Contreras-Masse, Alberto Ochoa-Zezzatti, Vicente García, Luis Perez-Dominguez, Mayra Elizondo

Subject: Computer Science And Mathematics, Analysis Keywords: IIoT; Platform Selection; Multi criteria analysis; MCDA; AHP; PROMETHEE-II; Cloud; Methodology

Online: 19 February 2020 (04:02:12 CET)

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Computer Science and Mathematics