Advances in Mathematics Research. Volume 32


Albert R. Baswell (Editor)

Series: Advances in Mathematics Research
BISAC: MAT000000

Chapter 1 is an introduction to meta-regression analysis. The authors demonstrate that meta-regression analysis is a methodological framework that allows modeling and correcting problems of publication bias while explaining the variability of results usually found in social sciences literature. In Chapter 2, a new model order reduction technique for the simplification of the complex large-scale stable linear dynamic systems is presented. Chapter 3 discusses the importance of identifying variables, scales, and methods for the sensory analysis of novel food products. Chapter 4 focuses on structural stability and dynamic quantum models. Chapter 5 is an introduction to linear difference equations. Chapter 6 includes a survey of various measures used in cohort analysis with alternative multifaceted indices used in theory and often by practitioners. The chapter is intended to offer a concise description of these measures and elaborate where and how they may be used in different cohort analysis. In Chapter 7, two mixed initial-boundary value problems describing motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are analytically investigated. In Chapter 8, new permanent solutions for Stokes’ second problem of incompressible burgers fluids and their applications is explored. Next, for the first time, the authors propose the definitions of the fractional sum and fractional difference on non-uniform lattices in two different ways. Chapter 10 focuses on the Carleman linearization method for boundary value problems. In the last chapter, Chapter 11, the authors review some of the recent work on pattern packing, superpatterns, and pattern avoidance when colored or circular patterns/permutations are considered.

Table of Contents


Chapter 1. An Introduction to Meta-Regression Analysis
N. Fonseca, PhD
Department Economics and Management, Superior School of Technology and Management, Polytechnic Institute of Viana do Castelo, Viana do Castelo, Portugal

Chapter 2. Balanced Truncation-Padé Approximation Method Extended to Large-Scale Linear Dynamic Systems
Santosh Kumar Suman, Awadhesh Kumar and Shekhar Yadav
Department of Electrical Engineering,Madan Mohan Malaviya University of Technology, Gorakhpur, Uttar Pradesh, India

Chapter 3. Statistical Methods Used for the Sensory Evaluation of Food
Yessica Enciso-Martínez¹, MSc, César O. Sepúlveda-Moreno², PhD, Cristóbal J. González-Pérez³, PhD, and Jesús F. Ayala-Zavala¹, PhD
¹Coordinación de Tecnología de Alimentos de Origen Vegetal, Centro de Investigación en Alimentación y Desarrollo, Hermosillo, Sonora, México
²Departamento de Ciencias Económico-Administrativo, Universidad de Sonora, Caborca, Sonora, México
³Departamento de Investigación en Polímeros y Materiales, Universidad de Sonora, Hermosillo, Sonora, México

Chapter 4. Structural Stability and Dynamic Quantum Models
A. Weissblut
Kherson State University, Kherson, Ukraine

Chapter 5. Introduction to Linear Difference Equations
S. K. Kydyraliev¹, ScD, A. B. Urdaletova², PhD, and A. A. Doolotova³
¹Department of Applied Mathematics, American University of Central Asia, Bishkek, Kyrgyzstan
²Department of Mathematics, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan
³Department of Business Administration, American University of Central Asia, Bishkek, Kyrgyzstan

Chapter 6. Cohort Measurement and Indices
Morteza Aalabaf-Sabaghi
ECO College of Insurance, Allameh Tabatabai University, Tehran, Iran

Chapter 7. Mixed Boundary Value Problems Which Describe Motions of Maxwell Fluids with Power-Law Dependence of Viscosity on Pressure
Constantin Fetecau¹, Dumitru Vieru², Abdul Rauf³ and Tahir Mushtaq Qureshi4
¹Section of Mathematics, Academy of Romanian Scientists, Bucharest, Romania
²Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania
³Department of Computer Science and Mathematics, Air University Islamabad, Multan, Pakistan
4Department of Mathematics, COMSATS University Islamabad, Pakistan

Chapter 8. New Permanent Solutions for Stokes’ Second Problem of Incompressible Burgers Fluids and Their Applications
Constantin Fetecau¹, Dumitru Vieru², Masood Khan³ and Shehraz Akhtar4
¹Section of Mathematics, Academy of Romanian Scientists, Bucharest, Romania
²Department of Theoretical Mechanics, Technical University of Iasi, Iasi, Romania
³Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
4Department of Mathematics, The Islamia University of Bahawalpur, Rahim Yar Khan Campus, Pakistan

Chapter 9. On the Definitions of Fractional Sum and Difference on Non-Uniform Lattices
Jinfa Cheng
School of Mathematical Sciences, Xiamen University

Chapter 10. The Carleman Linearization Method for Boundary Value Problems
Svantnerné Sebestyén Gabriella
Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

Chapter 11. Pattern Containment and Pattern Avoidance in Colored and/or Circular Permutations
Daniel Gray and Hua Wang
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USA