Regularity Criteria For The
Kuramoto-Sivashinsky Equation In Dimensions
Two And Three,
2021
University of Nebraska - Lincoln
Regularity Criteria For The Kuramoto-Sivashinsky Equation In Dimensions Two And Three, Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki
Department of Mathematics: Faculty Publications
We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability criteria for the regularity of solutions in terms of the scalar solution ∅, the vector solution u ≜ ∇∅, as well as the divergence div(u) = Δ∅, and each component of u and ∇u. We also investigate these criteria computationally in the 2D case, and we include snapshots of solutions for several quantities of interest that arise in energy estimates.
Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields,
2021
Embry-Riddle Aeronautical University
Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov
Publications
A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow …
Entropy Analysis Of Boolean Network Reduction According To The Determinative Power Of Nodes,
2021
University of Nebraska at Omaha
Entropy Analysis Of Boolean Network Reduction According To The Determinative Power Of Nodes, Matthew J. Pelz, Mihaela T. Velcsov
Mathematics Faculty Publications
Boolean networks are utilized to model systems in a variety of disciplines. The complexity of the systems under exploration often necessitates the construction of model networks with large numbers of nodes and unwieldy state spaces. A recently developed, entropy-based method for measuring the determinative power of each node offers a new method for identifying the most relevant nodes to include in subnetworks that may facilitate analysis of the parent network. We develop a determinative-power-based reduction algorithm and deploy it on 36 network types constructed through various combinations of settings with regards to the connectivity, topology, and functionality of networks. We …
A Multilayer Network Model Of The Coevolution Of The Spread Of A Disease And Competing Opinions,
2021
The University of Texas Rio Grande Valley
A Multilayer Network Model Of The Coevolution Of The Spread Of A Disease And Competing Opinions, Kaiyan Peng, Zheng Lu, Vanessa Lin, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi, Mason A. Porter
School of Mathematical & Statistical Sciences Faculty Publications
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions — pro-physical-distancing and anti-physical-distancing — that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing …
Explicit Synchronized Solitary Waves For Some Models For The Interaction Of Long And Short Waves In Dispersive Media.,
2021
Utah State University
Explicit Synchronized Solitary Waves For Some Models For The Interaction Of Long And Short Waves In Dispersive Media., Bruce Brewer
Fall Student Research Symposium 2021
Four systems have recently been proposed for the study of the interaction of long and short waves in dispersive media. This poster establishes the synchronized solitary wave solutions for one of these systems.
Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?,
2021
Utah State University
Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither
Fall Student Research Symposium 2021
In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …
Computer Program Simulation Of A Quantum Turing Machine With Circuit Model,
2021
Rose-Hulman Institute of Technology
Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu
Mathematical Sciences Technical Reports (MSTR)
Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.
Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms,
2021
Missouri University of Science and Technology
Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace
Mathematics and Statistics Faculty Research & Creative Works
In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.
Fourth Derivative Singularly P-Stable Method For The Numerical Solution Of The Schrödinger Equation,
2021
Missouri University of Science and Technology
Fourth Derivative Singularly P-Stable Method For The Numerical Solution Of The Schrödinger Equation, Ali Shokri, Higinio Ramos, Mohammad Mehdizadeh Khalsaraei, Fikret A. Aliev, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.
(R1519) On Some Geometric Properties Of Non-Null Curves Via Its Position Vectors In \Mathbb{R}_1^3,
2021
Beni-Suef University
(R1519) On Some Geometric Properties Of Non-Null Curves Via Its Position Vectors In \Mathbb{R}_1^3, Emad Solouma, Ibrahim Al-Dayel
Applications and Applied Mathematics: An International Journal (AAM)
In this work, the geometric properties of non-null curves lying completely on spacelike surface via its position vectors in the dimensional Minkowski 3-space \mathbb{R}_1^3 are studied. Also, we give a few portrayals for the spacelike curves which lie on certain subspaces of \mathbb{R}_1^3. Finally, we present an application to demonstrate our insights.
(R1466) Ideals And Filters On A Lattice In Neutrosophic Setting,
2021
University of M’sila
(R1466) Ideals And Filters On A Lattice In Neutrosophic Setting, Lemnaouar Zedam, Soheyb Milles, Abdelhamid Bennoui
Applications and Applied Mathematics: An International Journal (AAM)
The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, …
(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model,
2021
University of Kashmir
(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat
Applications and Applied Mathematics: An International Journal (AAM)
The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …
Negations Of Probability Distributions: A Survey,
2021
Instituto Politecnico Nacional
Negations Of Probability Distributions: A Survey, Ildar Z. Baryrshin, Nailya I. Kubysheva, Venera R. Bayrasheva, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-by-element PD into a negation of PD. Negators are non-increasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. …
(R1514) Nano Continuous Mappings Via Nano M Open Sets,
2021
Government Arts College (Autonomous); Annamalai University
(R1514) Nano Continuous Mappings Via Nano M Open Sets, A. Vadivel, A. Padma, M. Saraswathi, G. Saravanakumar
Applications and Applied Mathematics: An International Journal (AAM)
Nano M open sets are a union of nano θ semi open sets and nano δ pre open sets. The properties of nano M open sets with their interior and closure operators are discussed in a previous paper. In this paper, we discuss about nano M-continuous and nano M-irresolute functions are introduced in a nano topological spaces along with their continuous and irresolute mappings. Also, nano M-open and nano M-closed functions are introduced and compare with their near open and closed mappings in a nano topological spaces. Further, nano M homeomorphism is also discussed in nano …
Predicting Lifespan Of Drosophila Melanogaster: A Novel Application Of Convolutional Neural Networks And Zero-Inflated Autoregressive Conditional Poisson Model,
2021
Missouri University of Science and Technology
Predicting Lifespan Of Drosophila Melanogaster: A Novel Application Of Convolutional Neural Networks And Zero-Inflated Autoregressive Conditional Poisson Model, Yi Zhang, V. A. Samaranayake, Gayla R. Olbricht, Matthew S. Thimgan
Mathematics and Statistics Faculty Research & Creative Works
A model to classify the lifespan of Drosophila, the fruit fly, into short- and long-lived categories based on a sleep characteristic, extracted from activity data, is developed using a two-stage process. Stage 1 models the per-minute activity counts of each fly using a zero-inflated autoregressive conditional Poisson model. These probabilities are allowed to vary hourly, reflecting the circadian and other cycles present in a fly's sleep architecture. A 5-day moving window is used to model data allowing the model parameters to vary over the course of the fly's life. The resulting probabilities capture information about changes in sleep patterns with …
Generalization Of Mitrinović–Pečarić Inequalities On Time Scales,
2021
Missouri University of Science and Technology
Generalization Of Mitrinović–Pečarić Inequalities On Time Scales, Ahmed A. El-Deeb, Elvan Akin, Billur Kaymakçalan
Mathematics and Statistics Faculty Research & Creative Works
We prove some new inequalities of Mitrinović–Pečarić inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. The main results will be proved by using Hölder and Jensen inequalities and a simple consequence of Keller's and Poetzsche's chain rules on time scales.
Discrete Fractional Boundary Value Problems And Inequalities,
2021
Missouri University of Science and Technology
Discrete Fractional Boundary Value Problems And Inequalities, Martin Bohner, Nick Fewster-Young
Mathematics and Statistics Faculty Research & Creative Works
In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer's fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral …
Oscillation And Nonoscillation Criteria For Four-Dimensional Advanced And Delay Time-Scale Systems,
2021
Missouri University of Science and Technology
Oscillation And Nonoscillation Criteria For Four-Dimensional Advanced And Delay Time-Scale Systems, Elvan Akin, Gülşah Yenpi
Mathematics and Statistics Faculty Research & Creative Works
We obtain oscillation and Non oscillation criteria for solutions to four-dimensional advanced and delay systems of first-order dynamic equations on time scales. To establish oscillation criteria, we eliminate Non oscillatory solutions of the systems based on the sign of components of the solutions. Furthermore, some of our results are new in the discrete case.
How To Select Typical Objects,
2021
The University of Texas at El Paso
How To Select Typical Objects, Mariana Benitez, Jeffrey Weidner, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we have a large number of objects, too many to be able to thoroughly analyze each of them. To get a general understanding, we need to select a representative sample. For us, this problem was motivated to analyze the possible effect of an earthquake on buildings in El Paso, Texas. In this paper, we provide a reasonable formalization of this problem, and provide a feasible algorithm for solving thus formalized problem.
How To Simulate If We Only Have Partial Information But We Want Reliable Results?,
2021
The University of Texas at El Paso
How To Simulate If We Only Have Partial Information But We Want Reliable Results?, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
The main objective of a smart energy system is to make control decisions that would make energy systems more efficient and more reliable. To select such decisions, the system must know the consequences of different possible decisions. Energy systems are very complex, they cannot be described by a simple formula, the only way to reasonably accurately find such consequences is to test each decision on a simulated system. The problem is that the parameters describing the system and its environment are usually known with uncertainty, and we need to produce reliable results -- i.e., results that will be true for …
