Homotopy Perturbation Laplace Method For Boundary Value Problems, 2024 Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan

#### Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain

*International Journal of Emerging Multidisciplinaries: Mathematics*

Most of the real situations are typically modeled as differential equations (DEs). Accurate solutions of such equations is one of the objective of researchers for the analysis and predictions in the physical systems. Typically, pure numerical approaches are utilized for the solution of such problems. These methods are usually consistent, but due to discretization and round-off errors, accuracy can be compromised. Also, pure numerical schemes may be computationally expensive and have large memory requirement. Due to this reason, current manuscript proposed a hybrid methodology by combining homotopy perturbation method (HPM) with Laplace transformation. This scheme provides excellent accuracy in less …

A Cohomological Perspective To Nonlocal Operators, 2024 University of Nebraska - Lincoln

#### A Cohomological Perspective To Nonlocal Operators, Nicholas White

*Honors Theses*

Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their …

Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, 2024 Pepperdine University

#### Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison

*Seaver College Research And Scholarly Achievement Symposium*

The red swamp crayfish, Procambarus clarkii, is an invasive species introduced into several streams within the Santa Monica Mountains (SMM) in Southern California. Crayfish predation decimates native aquatic species. Thus, the Mountains Restoration Trust (MRT) and Environmental Restoration Group have worked to remove crayfish through regular trapping in Malibu Creek.

To aid conservation efforts, former SURB students William Milligan and Dev Patel developed mathematical models of crayfish removal efficacy. Milligan created a differential equation model of how crayfish removal affects local newt populations. Patel expanded Milligan’s crayfish model by creating a discrete model of the crayfish life cycle that newly …

Strengthen Establishment Of Application-Supported Major Science And Technology Infrastructure To Enhance Basic Capacity Of Science And Technology For High-Quality Development, 2024 School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China

#### Strengthen Establishment Of Application-Supported Major Science And Technology Infrastructure To Enhance Basic Capacity Of Science And Technology For High-Quality Development, Congli Huang, Feite Zhou, Xiang Xu, Lingling Zhang

*Bulletin of Chinese Academy of Sciences (Chinese Version)*

From “Two Bombs and One Satellite” to Five-hundred-meter Aperture Spherical Radio Telescope (FAST), from ground zero to the center stage of the world, China has unswervingly followed the path of independent innovation with distinctive characteristics. After the development of nearly half a century, breakthroughs have been made in several key areas. The position, implication, and classification of major scientific and technological infrastructures are constantly changing under the new situation. Based on an in-depth investigation of major scientific and technological infrastructure such as high-efficiency and low-carbon gas turbine research facility, it is believed that the construction of application-supported major scientific and …

Characterization Of Biological Particles Using An Integrated Hyperspectral Imaging And Machine Learning, 2024 Purdue University

#### Characterization Of Biological Particles Using An Integrated Hyperspectral Imaging And Machine Learning, Kaeul Lim, Arezoo Ardekani

*Graduate Industrial Research Symposium*

Hyperspectral imaging (HSI) is a promising modality in medicine with many potential applications. This study focuses on developing a label-free lipid nanoparticle characterization method using a convolutional neural network (CNN) analysis of HSI images. The HSI data, hypercube, consists of a series of images acquired at different wavelengths for the same field of view, providing continuous spectra information for each pixel. Three distinct liposome samples were collected for analysis. Advanced image preprocessing and classification methods for HSI data were developed to differentiate liposomes based on their material compositions. Our machine learning-based classification method was able to distinguish different liposome types …

Resource Optimization For Air Mobility Under Emergency Situations, 2024 Embry-Riddle Aeronautical University

#### Resource Optimization For Air Mobility Under Emergency Situations, Yongxin (Jack) Liu

*Math Department Colloquium Series*

This project aims to improve air traffic management in emergencies. We first developed a GRU neural network to forecast weather-related airport capacity constraints using historical data, underscoring the value of real-time data analysis. We then optimized emergency evacuation air travel using Particle Swarm Optimization, demonstrating the ability to quickly aggregate evacuation flight resources cost-effectively. Finally, we provided a hybrid model combining a genetic algorithm with a neural network for evacuation planning, we show that neural network can be integrated accelerate genetic algorithms for efficient and performance assured system optimization.

Existence And Uniqueness Of Solutions Of Sobolev Type Second Order Integrodifferential Equation, 2024 SRMS College of Engineering & Technology

#### Existence And Uniqueness Of Solutions Of Sobolev Type Second Order Integrodifferential Equation, Kamalendra Kumar, Manish Nath Tripathi

*Applications and Applied Mathematics: An International Journal (AAM)*

The primary concern of this article is to establish the existence, uniqueness and continuous dependence on initial data of mild solutions of second order mixed integrodifferential equations of Sobolev type in Banach spaces. For this objective, we employ the idea of strongly continuous cosine family of operators, the modified version of Banach theorem and Grownwall’s inequality. The model is demonstrated to elucidate the abstract conclusion.

A Novel Fuzzy Time Series Forecasting Method Based On Probabilistic Fuzzy Set And Cpbd Approach, 2024 Shri Ram Murti Smarak College of Engineering and Technology

#### A Novel Fuzzy Time Series Forecasting Method Based On Probabilistic Fuzzy Set And Cpbd Approach, Krishna Kumar Gupta, Suneet Saxena

*Applications and Applied Mathematics: An International Journal (AAM)*

Probabilistic fuzzy set is used to model the non-probabilistic and probabilistic uncertainties simultaneously in the system. This study proposes a cumulative probability-based discretization and probabilistic fuzzy set based novel fuzzy time series forecasting method. It also proposes a novel discretization approach based on cumulative probability to tackle the probabilistic uncertainty in partitioning of datasets. Gaussian probability distribution function has been used to construct probabilistic fuzzy set. The advantage of the proposed work is that it addresses the uncertainties due to randomness and fuzziness simultaneously and also improves accuracy rate in time series forecasting. A proposed forecasting method is applied on …

Utilization Of Caputo Fractional Derivative In Mhd Nanofluid Flow With Soret And Thermal Radiation Effects, 2024 Ganpat University

#### Utilization Of Caputo Fractional Derivative In Mhd Nanofluid Flow With Soret And Thermal Radiation Effects, Harshad Patel, Gopal Nanda

*Applications and Applied Mathematics: An International Journal (AAM)*

In existence of heat diffusion and thermal radiation, an analytical equation is found for unsteady MHD flow past an exponentially accelerating vertical plate in optically thick water based nanofluid. The governing equations are made dimensionless by similarity transformation. A definition of Caputo fractional derivative is applied to generalize governing system of partial differential equations. Laplace transform techniques are applied and obtained the analytical solutions of proposed problems. For a physical point of view, numerical results are obtained using MATLAB software and presented via graphs. From the results, it is concluded that magnetic fields tend to reduce velocity. It is also …

Effects Of Magnetic Field And Chemical Reaction On A Time Dependent Casson Fluid Flow, 2024 Government Science College

#### Effects Of Magnetic Field And Chemical Reaction On A Time Dependent Casson Fluid Flow, Akhil Mittal, Harshad Patel, Ramesh Patoliya, Vimalkumar Gohil

*Applications and Applied Mathematics: An International Journal (AAM)*

This research paper deals with the effect of chemical reactions and magnetic fields on the hydrodynamics fluid flow of Casson fluid. The novelty of this work is the inclusion of time-dependent flow across a vertical plate with a stepped concentration at the surface in a porous media. The stated phenomenon is modeled in the PDE system and is adapted in the ODE system through similarity transformation. The LT (Laplace Transform) and ILT (Inverse LT) are used to obtain the analytical results for regulating dimension-free movement, thermals, and concentration expression. The exact expression of shear rate, heat exchange rate, and mass …

Stability Of Predator-Prey Model For Worm Attack In Wireless Sensor Networks, 2024 Galgotias College of Engineering and Technology

#### Stability Of Predator-Prey Model For Worm Attack In Wireless Sensor Networks, Rajeev Kishore, Padam Singh

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, we propose a predator-prey mathematical model for analyzing the dynamical behaviors of the system. This system is an epidemic model, and it is capable of ascertaining the worm's spreading at the initial stage and improving the security of wireless sensor networks. We investigate different fixed points and examine the stability of the projected model.

Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, 2024 Embry-Riddle Aeronautical University

#### Transfer Learning In The Era Of Foundational Models: Application To Diagnosis In Rheumatology, Prashant Shekhar

*Math Department Colloquium Series*

Problems with current synovitis grading procedures

- There has been a lack of reliability in grading these images in the medical community due to a lack of universally accepted diagnostic criteria [Momtazmanesh et al., 2022]
- The human/machine variability creates an additional challenge in an efficient automated scoring system [Ranganath et al., 2022]
- There is a lack of consistency between doctors in grading these images [Momtazmanesh et al., 2022]

On A Generator Of Copulas Method Based On A Duplication-Parameter Technique, 2024 Department of Mathematics, LMNO, University of Caen-Normandie, 14032 Caen, France

#### On A Generator Of Copulas Method Based On A Duplication-Parameter Technique, Christophe Chesneau

*International Journal of Emerging Multidisciplinaries: Mathematics*

A two-dimensional copula is a function that accurately depicts the pattern of dependence between two quantitative variables. The demand for new two-dimensional copulas is as strong as ever, driven by the emergence of contemporary data from various sources. This paper makes a contribution to this area by presenting a novel modification of the well-known convex sums of copulas method. This modification is based on a thorough duplication-parameter technique: we transform one parameter into two, and we apply the classical convex sums method to only one of these parameters in the unit distribution setting. The main goals are (i) to solve …

New Algorithmic Support For The Fundamental Theorem Of Algebra, 2024 The Graduate Center, City University of New York

#### New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman

*Dissertations, Theses, and Capstone Projects*

Univariate polynomial root-finding is a venerated subjects of Mathematics and Computational Mathematics studied for four millenia. In 1924 Herman Weyl published a seminal root-finder and called it an algorithmic proof of the Fundamental Theorem of Algebra. Steve Smale in 1981 and Arnold Schonhage in 1982 proposed to classify such algorithmic proofs in terms of their computational complexity. This prompted extensive research in 1980s and 1990s, culminated in a divide-and-conquer polynomial root-finder by Victor Pan at ACM STOC 1995, which used a near optimal number of bit-operations. The algorithm approximates all roots of a polynomial p almost as fast as one …

Cognitive Load Scale In Learning Formal Definition Of Limit: A Rasch Model Approach, 2024 Universitas Serang Raya

#### Cognitive Load Scale In Learning Formal Definition Of Limit: A Rasch Model Approach, Rina Oktaviyanthi, Ria Noviana Agus, Mark Lester B. Garcia, Kornkanok Lertdechapat

*Mathematics Faculty Publications*

Constructing proofs for the limit using the formal definition induces a high cognitive load. Common assessment tools, like cognitive load scales, lack specificity for the concept of limits. This research aims to validate an instrument tailored to assess cognitive load in students focused on the formal definition of limits, addressing the need for diverse strategies in education. The research employs a quantitative survey design with a Rasch model approach, utilizing a data collection instrument in the form of a questionnaire. Subsequently, the data are analyzed by focusing on three aspects: (1) item fit to the Rasch model, (2) unidimensionality, and …

Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, 2024 Bucknell University

#### Characterizing Linearizable Qaps By The Level-1 Reformulation-Linearization Technique, Lucas Waddell, Warren Adams

*Faculty Journal Articles*

The quadratic assignment problem (QAP) is an extremely challenging NP-hard combinatorial optimization program. Due to its difficulty, a research emphasis has been to identify special cases that are polynomially solvable. Included within this emphasis are instances which are *linearizable*; that is, which can be rewritten as a linear assignment problem having the property that the objective function value is preserved at all feasible solutions. Various known sufficient conditions for identifying linearizable instances have been explained in terms of the continuous relaxation of a weakened version of the level-1 reformulation-linearization-technique (RLT) form that does not enforce nonnegativity on a subset …

Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, 2024 University of Missouri-St. Louis

#### Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich

*Undergraduate Research Symposium*

In this project, we explore radial solutions to the Total Variation Flow (TVF) equation with the help of the Sign Fast Diffusion Equation (SFDE) and prior results in the 1-dimensional case. Specifically for radial solutions, we derive equations and explicit solutions relating to the n-dimensional case. Lastly, we look at how level sets and (time) profiles change.

Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, 2024 CUNY Hostos Community College

#### Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince

*Numeracy*

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of …

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, 2024 Purdue University Fort Wayne

#### Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

*The Journal of Purdue Undergraduate Research*

No abstract provided.

Machine Learning Of Big Data: A Gaussian Regression Model To Predict The Spatiotemporal Distribution Of Ground Ozone, 2024 Purdue University

#### Machine Learning Of Big Data: A Gaussian Regression Model To Predict The Spatiotemporal Distribution Of Ground Ozone, Jerry Gu

*The Journal of Purdue Undergraduate Research*

Tracking pollution levels on the ground is important to the environment and public health. One of the pollutants of concern is ozone, which, at high concentrations, can cause respiratory and cardiovascular problems. The National Center for Atmospheric Research (NCAR) has published valuable ozone data obtained from ground-based sensors installed at selected locations. Because it is unfeasible to measure the exact ozone levels everywhere at any time, it would be valuable to predict the temporal-spatial distributions of ozone concentration based on existing data. This would help us better understand the patterns and trends in the data and make better decisions to …