An Integrable Semidiscretization Of The Modified Camassa-Holm Equation With Linear Dispersion Term,
2022
The University of Texas Rio Grande Valley
An Integrable Semidiscretization Of The Modified Camassa-Holm Equation With Linear Dispersion Term, Han-Han Sheng, Guo-Fu Yu, Bao-Feng Feng
School of Mathematical & Statistical Sciences Faculty Publications
In the present paper, we are with integrable discretization of a modified Camassa-Holm (mCH) equation with linear dispersion term. The key of the construction is the semidiscrete analog for a set of bilinear equations of the mCH equation. First, we show that these bilinear equations and their determinant solutions either in Gram-type or Casorati-type can be reduced from the discrete Kadomtsev-Petviashvili (KP) equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semidiscrete bilinear equations and their general soliton solution in Gram-type or Casorati-type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, …
Covering Systems And The Minimum Modulus Problem,
2022
University of South Carolina
Covering Systems And The Minimum Modulus Problem, Maria Claire Cummings
Theses and Dissertations
A covering system or a covering is a set of linear congruences such that every integer satisfies at least one of these congruences. In 1950, Erdős posed a problem regarding the existence of a finite covering with distinct moduli and an arbitrarily large minimum modulus. This remained unanswered until 2015 when Robert Hough proved an explicit bound of 1016 for the minimum modulus of any such covering. In this thesis, we examine the use of covering systems in number theory results, expand upon the proof of the existence of an upper bound on the minimum modulus in the case of …
Numerical And Theoretical Investigations Of Fractional Differential Equations,
2022
United Arab Emirates University
Numerical And Theoretical Investigations Of Fractional Differential Equations, Sara Rafiq Al Fahel
Theses
Fractional calculus has been recently received huge attention from Mathematicians and engineers due to its importance in many real-life applications such as: fluid mechanics, electromagnetic, acoustics, chemistry, biology, physics and material sciences. In this thesis, we present numerical algorithms for solving fractional IVPs and system of fractional IVPs where two types of fractional derivatives are used: Caputo-Fabrizio, and Atangana-Baleanu-Caputo derivatives. These algorithms are developed based on modified Adams-Bashforth method. In addition, we discuss the theoretical solution of special class of fractional IVPs. Several examples are discussed to illustrate the efficiency and accuracy of the present schemes.
Mathematical Modelling Of Syphilis Transmission Dynamics: Impacts Of Mass Media Report, Risky Sexual Behavior And Treatment,
2022
Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, University of Dar es Salaam, Tanzania
Mathematical Modelling Of Syphilis Transmission Dynamics: Impacts Of Mass Media Report, Risky Sexual Behavior And Treatment, Gasper G. Mwanga
Tanzania Journal of Science
Syphilis is one of the deadly sexually-transmitted diseases. This paper studied the impacts of sexual behavior, mass media report and treatment of infected individuals on the dynamics of syphilis transmission. The analytical and numerical analyses of the model are presented. The disease free equilibrium of the model is both locally and globally asymptotic stable when the associated reproduction number is less than unity. Analysis of the Reproduction number shows that it is not possible to control syphilis disease transmission if the rate of individuals practicing risky sexual behavior is high. Furthermore, the treatment of late (latent and tertiary) syphilis infection …
Investigation Of The Effects Of Some Statistical Data Components On The Selection Of Optimum Smoothing Constant,
2022
Mechanical Engineering Department, Osun State University, Osogbo, Nigeria
Investigation Of The Effects Of Some Statistical Data Components On The Selection Of Optimum Smoothing Constant, Musibaudeen O. Idris, Busayo S. Adeboye, Buliaminu Kareem, Godwin C. Enwerem, Selimot A. Adekanye
Tanzania Journal of Science
Simple exponential smoothing is one of the best forecast methods, especially for time series data. Its efficacy depends on a parameter called smoothing constant (α) which, if optimally determined, minimises the mean square error (MSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE). The widely used method for selecting the optimum smoothing constant is to conduct a grid search within a wide range of possible values of α using the trial-and-error method. Not only that this method involves the knowledge of advanced statistical processes, but it is also time-consuming, and its results are limited to the …
Resource Efficient Advanced Metering Infrastructure Model,
2022
College of Information and Communication Technologies, University of Dar es Salaam P. O. Box 33335, Dar es Salaam, Tanzania
Resource Efficient Advanced Metering Infrastructure Model, Josephina Kimambo, Kwame S Ibwe, Ellen Kalinga, Abdi T. Abdalla
Tanzania Journal of Science
Advanced Metering Infrastructure (AMI) enables two-way communication between smart devices and utility control centers. This involves remote monitoring and control of energy consumption as well as other parameters in the electrical power network in real time. However, increasing technologies in AMI due to huge deployment of smart meters, integration of devices and application of sensors, demand a strong architectural model with the best network topology to guarantee efficient usage of network resources with minimal latency. In this work, a resource efficient multi-hop network architecture is proposed using hybrid media access protocols. The architecture combines queuing and random-access protocol to achieve …
Trends In The Development Of Industrial Sector Of Uzbekistan,
2022
Karakalpak State University, Uzbekistan
Trends In The Development Of Industrial Sector Of Uzbekistan, Bakhtiyar Kalmuratov, Aydos Bekbosinov
Karakalpak Scientific Journal
The article presents the main directions of industrial transformation at the new stage of economic reforms in 2016-2020. The key achievements during this period in the development of manufacturing industry production and exports, the development of industrial and territorial structures, and the improvement of market mechanisms for the development of commodity markets are highlighted.
Socio-Economic Factors Of Environmental Problems,
2022
National University of Uzbekistan named after Mirzo Ulugbek
Socio-Economic Factors Of Environmental Problems, Manzura Kamalova, D. Shakenov
Karakalpak Scientific Journal
People consciously and intensively rebuild their nature according to their own needs, creating rural and urban areas in which they live. People care about the quality of life in the context of the unity of nature and culture. Social is a relatively new discipline that deals with urban space and environmental issues. One way to imagine what is beneficial to people is to find out what is economically best for the person. The article examines the economic factors that form the attitude towards social ecology in Kazakhstan. The article concludes that society should cooperate to achieve common things, both for …
Identification Of Loop Current Ring Separation Events In The Gulf Of Mexico,
2022
Rowan University
Identification Of Loop Current Ring Separation Events In The Gulf Of Mexico, Helga Huntley
College of Science & Mathematics Departmental Research
No abstract provided.
Program Review: Mathematics And Statistics Department,
2022
University of Nebraska at Kearney
Program Review: Mathematics And Statistics Department, Katherine Kime, University Of Nebraska At Kearney Department Of Mathematics And Statistics Faculty & Staff
Academic Program Reviews
No abstract provided.
Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?,
2022
New Jersey Institute of Technology
Proceedings State Of Stem 2022: How Does Virtual Hands-On Stem Work?, Cristo Leon, James Lipuma, Michele Rittenhouse, Louis Wells, Edgar Meritano, Ricardo Morales-Carbajal, Miguel Angel Bastarrachea Magnani, Ten80 Education, Llc, New Jersey School Boards Association, International Stem League, Inc (Insl), Red De Investigadores De Juegos De Rol
STEM for Success Resources
Proceedings of the "State of STEM 2022: How does virtual hands-on STEM work?"
Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation,
2022
University of South Florida
Application Of The Riemann-Hilbert Method To Soliton Solutions Of A Nonlocal Reverse-Spacetime Sasa-Satsuma Equation And A Higher-Order Reverse-Time Nls-Type Equation, Ahmed Ahmed
USF Tampa Graduate Theses and Dissertations
For many years, the study of integrable systems has been one of the most fascinating branches of mathematics and has been thought to be an interesting area for both mathematicians and physicists alike.Many natural phenomena can be predicted by using integrable systems, particularly by studying their different solutions, as well as analyzing and exploring their properties and structures. They are commonly found in nonlinear optics, plasmas, ocean and water waves, gravitational fields, and fluid dynamics. Typical examples of integrable systems include the Korteweg-de Vries (KdV) equation, the nonlinear Schrödinger (NLS) equation, and the Kadomtsev-Petviashvili (KP) equation. Solitons are intrinsic solutions …
Euler Archive Spotlight,
2022
Pittsburg State University
Euler Archive Spotlight, Cynthia Huffman Ph.D.
Euleriana
A spotlight on the Euler Archive focusing on Euler and the Basel Problem.
Leonhard Euler’S Correspondence Schedule,
2022
Central Washington University
Leonhard Euler’S Correspondence Schedule, Dominic Klyve
Euleriana
In addition to his large number of published articles and books, Leonhard Euler engaged in a prolific correspondence with scientists, mathematicians, and administrators throughout his career. By compiling the dates of all of his known letters, as described in the Opera Omnia, we can get some understanding of Euler’s weekly schedule. We report here for the first time Euler’s preference, particularly during his Berlin Period, of writing letters on Tuesdays and Saturdays.
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I,
2022
Colorado State University - Pueblo
Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker
Euleriana
This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …
The Solution Of A Problem Of Searching For Three Numbers, Of Which The Sum, Product, And The Sum Of Their Products Taken Two At A Time, Are Square Numbers,
2022
Carthage College
The Solution Of A Problem Of Searching For Three Numbers, Of Which The Sum, Product, And The Sum Of Their Products Taken Two At A Time, Are Square Numbers, Mark R. Snavely, Philip Woodruff
Euleriana
This paper first appeared in Novi Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 64-73 and is reprinted in Opera Omnia: Series 1, Volume 2, pp.519-530. Its Eneström number is E270. Euler improves his results significantly in "On Three Square Numbers, of Which the Sum and the Sum of Products Two Apiece will be a Square" (E523).
On A New Class Of Oscillations,
2022
University of Sao Paolo
On A New Class Of Oscillations, Sylvio R. Bistafa
Euleriana
In this publication, Euler derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely, the motion of an object subjected to two acting forces, one proportional to the distance travelled, the other one varying sinusoidally with time.
On A New Class Of Oscillations,
2022
Independent Researcher
On A New Class Of Oscillations, Sylvio R. Bistafa
Euleriana
This publication was motivated by Krafft’s accidental observation of a suspended clock setting itself in constant motion as a pendulum. His analysis of the phenomenon led him to conclude that the vibration of the clock was solely due to imbalances in the clock's balance wheel. Next, he conceives a 'little machine' as he called it, in which a straight bar loaded by small weights at its extremities is free to oscillate about the center of gravity of a regular suspended clock. He then investigates different oscillating conditions, by calculating moments with different weights and lengths of the bar arms, to …
Review Of Change And Variations,
2022
Adelphi University
Review Of Change And Variations, Robert E. Bradley
Euleriana
Review of Change and Variations: A History of Differential Equations to 1900, by Jeremy Gray, Springer Undergraduate Mathematics Series, 2021, 419 + xxii pages.
Conversations On Change,
2022
University of the Pacific
Conversations On Change, Christopher Goff, Erik Tou
Euleriana
Welcome to Volume 2 of Euleriana! One of the pleasures of studying the his- tory of mathematics is reading how historical figures conversed with each other on topics of their era. In this volume, those conversations focus on differential equations—a subject which occupied Euler’s attention for much of his 56-year career. Throughout, we will see how he corresponded with many scholars of the day as he developed and refined his mathematical ideas.
