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Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

Communications on Applied mathematics and Computation 2024年第1期6卷 533-549页

作者： Luciano K.Araki Rafael B.de R.Borges Nicholas Dicati P.da Silva Chi-Wang Shu Department of Mechanical Engineering Federal University of ParanáCuritiba81531-980ParanáBrazil Mathematics and Statistics Institute Rio de Janeiro State UniversityRio de Janeiro20550-900Rio de JaneiroBrazil Department of Mechanical Engineering State University of MaringáMaringá87020-900ParanáBrazil Division of Applied Mathematics Brown UniversityProvidenceRI02912USA

Capturing elaborated flow structures and phenomena is required for well-solved numerical *** finite difference methods allow simple discretization of mesh and model ***,they need simpler meshes,e.g.,*** inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular ***-resolution and high-order methods can capture elaborated flow structures and *** also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation *** perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)***,we propose to solve a challenging engineering application without turbulence *** aim to verify and validate recent high-resolution and high-order *** check the solver accuracy,we solved vortex and Couette ***,we solved inviscid and viscous nozzle flows for a conical *** employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving *** showed the solver is high-order and captured elaborated flow structures and *** can see oblique shocks in both nozzle *** the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

关键词： High-resolution Compressible Navier-Stokes Free-shock separation Nozzle flow

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Comparative Analysis of Radial Basis Functions and Cubic Splines for Data Imputation 10

Comparative Analysis of Radial Basis Functions and Cubic Spl...

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10th International Conference on Fuzzy Systems and Data Mining, FSDM 2024

作者： Kitchainukoon, Wisut Sangsuwan, Amornrat Pongchalee, Pornthip Chanthawara, Krittidej Department of Mathematics Faculty of Science and Technology Loei Rajabhat University Loei42000 Thailand Department of Mathematics Faculty of Education Loei Rajabhat University Loei42000 Thailand Department of Applied Mathematics and Statistics Faculty of Science and Liberal Arts Rajamangala University of Technology Isan Nakhon Ratchasima30000 Thailand Program of Mathematics Faculty of Science Ubon Ratchathani Rajabhat University Ubon Ratchathani34000 Thailand

ISBN: (纸本)9781643685694

This study evaluates the effectiveness of Radial Basis Function (RBF) approaches, specifically Gaussian and Multiquadric RBFs, compared to Cubic and Adaptive Splines for data imputation in time-series datasets. Three datasets-multiseasonal, non-stationary, and spikes and drops-were used, with varying data corruption levels to simulate real-world scenarios. Imputation performance was assessed using Root Mean Square Error (RMSE). The results indicate that spline-based methods, particularly Cubic and Adaptive Splines, consistently deliver lower RMSE values, showcasing superior robustness to data variability and high corruption levels compared to RBF methods. This comparative analysis offers insights into selecting appropriate techniques for effective data imputation in time-series analysis. © 2024 The Authors.

关键词： Splines

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A New Family of Continuous Probability Distribution: Gamma-Exponential Distribution (GED)Theory and its Properties

A New Family of Continuous Probability Distribution: Gamma-E...

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2024 International Conference on Science, engineering and Business for Driving Sustainable Development Goals, SEB4SDG 2024

作者： Ogunwale, Olukunle Daniel Peter Ajewole, Kehinde Olayinka, Korede Peter Olaoluwa Omole, Ezekiel Amoyedo, Femi Emmanuel Akinremi, Oluwadamilare J. Ekiti State University Department of Statistics Ekiti State Ado-Ekiti Nigeria Mathematics Program Landmark University Department of Physical Sciences Kwara State Omu-Aran Nigeria

ISBN: (纸本)9798350358155

While probability distribution functions are crucial for simulating random processes, research on these functions and their features is required. However, studies have demonstrated that in certain cases, it is discovered that certain combinations of two or more random variables with known probability distributions follow the distributions of certain real-world data that cannot be sufficiently represented by the standard distributions now in *** order to generate a new distribution combining the gamma and exponential distributions, this research work focused on creating the two-parameter Gamma-Exponential Distribution (GED), which was obtained by using the Transformed-Transformer method. Its properties included the following: expressions for its survival function and hazard function, as well as the probability density function, cumulative distribution function, rth non-central moments, first four moments, variances, skewness and kurtosis, and maximum likelihood estimator. © 2024 IEEE.

关键词： Probability density function

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Massive data clustering by multi-scale psychological observations

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National Science Review 2022年第2期9卷 43-51页

作者： Shusen Yang Liwen Zhang Chen Xu Hanqiao Yu Jianqing Fan Zongben Xu National Engineering Laboratory of Big Data Analytics Xi'an Jiaotong University Industrial Artificial Intelligent Center Pazhou Laboratory Department of Mathematics and Statistics University of Ottawa Center for Statistics and Machine Learning Princeton University

Clustering is the discovery of latent group structure in data and is a fundamental problem in artificial intelligence,and a vital procedure in data-driven scientific research over all ***,existing methods have various limitations,especially we ak cognitive interpretability and poor computational scalability,when it comes to clustering massive datasets that are increasingly available in all ***,by simulating the multi-scale cognitive observation process of humans,we design a scalable algorithm to detect clusters hierarchically hidden in massive *** observation scale changes,following the Weber-Fechner law to capture the gradually emerging meaningful grouping *** validated our approach in real datasets with up to a billion records and 2000 dimensions,including taxi trajectories,single-cell gene expressions,face images,computer logs and *** approach outperformed popular methods in usability,efficiency,effectiveness and robustness across different domains.

关键词： massive data clustering psychological observation Weber–Fechner law cognitive interpretability computational scalability

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Thermal optimization of MHD nanofluid over a wedge by using response surface methodology:Sensitivity analysis

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Propulsion and Power Research 2023年第4期12卷 556-567页

作者： Ahmed Zeeshan Dilawar Hussain Zaheer Asghar Muhammad Mubashir Bhatti Faisal Z.Duraihem Department of Mathematics&Statistics FBASInternational Islamic UniversityIslamabadH-10Islamabad 44000Pakistan Department of Mathematics Faculty of Natural and Health SciencesUniversity of BaltistanSkardu 16100Pakistan Centre for Mathematical Sciences Pakistan Institute of Engineering and Applied SciencesNiloreIslamabad 45650Pakistan Department of Physics and Applied Mathematics Pakistan Institute of Engineering and Applied SciencesNiloreIslamabad 45650Pakistan Department of Mathematics and System Sciences Shandong University of Science and TechnologyShandongChina Department of Mathematics College of ScienceKing Saud UniversityP.O.Box 2455Riyadh 11451Saudi Arabia

It is well documented that heat transfer is enhanced with addition of nanosized particles in ***,in a mechanical system there are variety of factors influences the heat *** factors are significant while others are *** this paper,authors will discuss sensitivity of different input parameters such as Le,Nt and Nb on output responses𝑁Nu_(x)and Sh_(x).To achieve this goal,the problem is modeled using basic conservation *** formulated model is a set of PDEs,which are converted to set of non-linear ODEs by using similarity *** these ODEs are solved numerically by using MATLAB built in package bvp4c and compared the numerical results with existing work and found good *** analysis is performed by employing RSM to determine the relationship between the input parameters such that 0.1≤Le≤1,0.1≤Nt≤1 and 0.1≤Nb≤1 and the output responses(Nu_(x)and Sh_(x)).ANOVA tables are generated by using *** using the ANOVA tables the correlations between input parameters and output response are *** check the validity of correlated equations,the residuals are plotted graphically and show best correlations between input parameters and output *** high values of R^(2)=98.65 and AdjR^(2)=97.43 for Nu_(x)and R^(2)=97.83 and AdjR^(2)=95.88 for Sh_(x)demonstrates the high validity of ANOVA results to perform sensitivity ***,we have conducted a sensitivity analysis of the responses and came to the important results that Nt and Nb is most sensitive to Nusselt number and Sherwood number respectively.

关键词： Sensitivity analysis Nusselt number Sherwood number Response surface methodology(RSM) Analysis of variance(ANOVA) Nano fluid

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New Trends in Fuzzy Modeling Through Numerical Techniques

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Computers, Materials & Continua 2023年第3期74卷 6371-6388页

作者： M.M.Alqarni Muhammad Rafiq Fazal Dayan Jan Awrejcewicz Nauman Ahmed Ali Raza Muhammad Ozair Ahmad Witold Pawłowski Emad E.Mahmoud Department of Mathematics College of SciencesKing Khalid UniversityAbha61413Saudi Arabia Department of Mathematics Faculty of Sciences and TechnologyUniversity of Central PunjabLahorePakistan Department of Mathematics School of ScienceUniversity of Management and TechnologyLahorePakistan Department of Automation Biomechanics and MechatronicsLodz University of Technology1/15 Stefanowskiego St.90-924LodzPoland Department of Mathematics and Statistics University of LahoreLahorePakistan Department of Mathematics Govt.Maulana Zafar Ali Khan Graduate College WazirabadPunjab Higher Education Department(PHED)Lahore54000Pakistan Institute of Machine Tools and Production Engineering Lodz University of TechnologyPoland Department of Mathematics College of ScienceTaif UniversityP.O.Box11099Taif21944Saudi Arabia

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba *** is spread through person-toperson contact or by eating or drinking food or water contaminated with *** transmission rate depends on the number of cysts present in the *** traditional models assumed a homogeneous and contradictory transmission with *** heterogeneity of its transmission rate is a significant factor when modeling disease *** heterogeneity of disease transmission can be described mathematically by introducing fuzzy *** this context,a fuzzy SEIR Amoebiasis disease model is considered in this *** equilibrium analysis and reproductive number are studied with *** numerical schemes forward Euler method and a nonstandard finite difference(NSFD)approach,are developed for the learned model,and the results of numerical simulations are *** numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease despite the uncertainty and ***,the obtained method generates plausible predictions that regulators can use to support decision-making to design and develop control strategies.

关键词： Epidemic model fuzzy parameters amoebiasis NSFD scheme convergence

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Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

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Applied mathematics(A Journal of Chinese Universities) 2023年第3期38卷 373-391页

作者： Ubaidullah Yashkun Khairy Zaimi Suliadi Firdaus Sufahani Mohamed REid Mohammad Ferdows Centre of Excellence for Social Innovation and Sustainability Institute of EngineeringUniversiti Malaysia PerlisPauh Putra Campus02600ArauPerlisMalaysia Department of Mathematics Sukkur IBA UniversityAirport RoadSukkur65200SindhPakistan Department of Mathematics and Statistics Faculty of Applied Sciences and TechnologyUniversiti Tun Hussein Onn MalaysiaJohorMalaysia Department of Mathematics Faculty of ScienceNew Valley UniversityAl-Wadi Al-GadidAl-Kharga 72511Egypt Mathematics Department Faculty of ScienceNorthern Border UniversityArar 1321Saudi Arabia Research Group of Fluid Flow Modeling and Simulation Department of Applied MathematicsUniversity of DhakaDhaka-1000Bangladesh

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal *** governing partial differential equations(PDEs)are converted into ordinary differential equations(ODEs)using the similarity *** resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB *** was found that dual solutions exist for the shrinking parameter values up to a certain *** numerical results obtained are compared,and the comparison showed a good agreement with the existing results in the *** governing parameters’effect on the velocity,temperature and nanoparticle fraction fields as well as the skin friction coefficient,the local Nusselt number and the Sherwood number are represented graphically and *** variation of the velocity,temperature and concentration increase with the increase in the suction and magnetic field *** seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it.

关键词： stagnation point flow nanofluid porous medium suction magnetohydrodynamic thermal radiation

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Stability and Generalization of Stochastic Compositional Gradient Descent Algorithms 41

Stability and Generalization of Stochastic Compositional Gra...

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41st International Conference on Machine Learning, ICML 2024

作者： Yang, Ming Wei, Xiyuan Yang, Tianbao Ying, Yiming Department of Mathematics and Statistics State University of New York at Albany AlbanyNY12222 United States Department of Computer Science and Engineering Texas A&M University College StationTX77843 United States The University of Sydney School of Mathematics and Statistics SydneyNSW2006 Australia

Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization and meta-learning, where the objective function involves a nested composition associated with an expectation. Although many studies have been devoted to studying the convergence behavior of SCO algorithms, there is little work on understanding their generalization, that is, how these learning algorithms built from training data would behave on future test examples. In this paper, we provide the stability and generalization analysis of stochastic compositional gradient descent algorithms in the framework of statistical learning theory. Firstly, we introduce a stability concept called compositional uniform stability and establish its quantitative relation with generalization for SCO problems. Then, we establish the compositional uniform stability results for two notable stochastic compositional gradient descent algorithms, namely SCGD and SCSC. Finally, we derive dimension-independent excess risk bounds for SCGD and SCSC by balancing stability results and optimization errors. To the best of our knowledge, these are the first-ever known results on stability and generalization analysis of stochastic compositional gradient descent algorithms. Copyright 2024 by the author(s)

关键词： Expectation maximization algorithm

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A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect

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South African Journal of Chemical engineering 2023年 43卷 135-145页

作者： Ahmad, Bilal Ozair Ahmad, Muhammad Farman, Muhammad Akgül, Ali Riaz, Muhammad Bilal Department of Mathematics and Statistics The University of Lahore Lahore Pakistan Department of Mathematics Khawaja Fareed University of Engineering and Information Technology Rahim Yar Khan Pakistan Art and Science Faculty Department of Mathematics Siirt University Siirt 56100 Turkey Near East University Mathematics Research Center Department of Mathematics Near East Boulevard PC: 99138 Nicosia /Mersin 10 Turkey Faculty of Applied Physics and Mathematics Gdansk University of Technology Gdansk 80-233 Poland Department of Mathematics University of Management and Technology Lahore 54770 Pakistan

The aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations are nonlinear, the partial differential equations are transformed into ordinary differential equations using a workable similarity transformation. By using the Bvp4c module of the MATLAB program, the simplified mathematical framework can be numerically solved. The computation of Coefficients of skin friction, Nusselt numbers, different patterns of velocity profiles, fluid temperature, and concentration profiles reveals the physical nature of this study. As compared to earlier investigations, it was found that the obtained results demonstrated high degrees of symmetry and precision. A decline observes in velocity for boosted values of MHD, inclination, and rotatory parameter. However thermal transportation increases by increasing brownien motion, thermophoresis, radiation and Sorrot effect. The study has significant application in heat control systems, food factories, thermal exchangers, biomechanics, biomedical engineering, and aero dynamical systems © 2022

关键词： Doufoure and sorret effect Inclined MHD Micro motile organisms Multi slip conditions Nanofluid Nonlinear radiations Numerical modeling

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Hybrid Smart Contracts for Securing IoMT Data

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Computer Systems Science & engineering 2023年第1期44卷 457-469页

作者： D.Palanikkumar Adel Fahad Alrasheedi P.Parthasarathi S.S.Askar Mohamed Abouhawwash Department of Computer Science and Engineering Dr NGP Institute of TechnologyCoimbatore641048India Department of Statistics and Operations Research College of ScienceKing Saud UniversityRiyadh11451Saudi Arabia Department of Computer Science and Engineering Bannari Amman Institute of TechnologySathy638401India Department of Mathematics Faculty of ScienceMansoura UniversityMansoura35516Egypt Department of Computational Mathematics Scienceand Engineering(CMSE)Michigan State UniversityEast LansingMI48824USA

Data management becomes essential component of patient *** of Medical Things(IoMT)performs a wireless communication between E-medical applications and human *** of consulting a doctor in the hospital,patients get health related information remotely from the *** main issues in the E-Medical application are lack of safety,security and priv-acy preservation of patient’s health care *** overcome these issues,this work proposes block chain based IoMT Processed with Hybrid consensus protocol for secured *** health data is collected from physician,smart devices *** main goal is to store this highly valuable health related data in a secure,safety,easy access and less cost-effective *** this research we combine two smart contracts such as Practical Byzantine Fault Tolerance with proof of work(PBFT-PoW).The implementation is done using cloud technology setup with smart contracts(PBFT-PoW).The accuracy rate of PBFT is 90.15%,for PoW is 92.75%and our proposed work PBFT-PoW is 99.88%.

关键词： PoW byzantine fault tolerance IoMT cloud computing health care data

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