Roman Kvasov, PhD

Associate Professor

Office: Math Department (3d floor)

(787) 890-2681 x2236

math.uprag.edu/roman

Education

Ph.D. Scientific Computing, 2013
University of Puerto Rico at Mayaguez

M.S. Applied Mathematics, 2008
University of Puerto Rico at Mayaguez

M.S. Computer Science, 2006
National Technical University of Ukraine

B.S. Mathematics, 2004
National Technical University of Ukraine

Areas of Interest

Scientific Computing, Computational Mechanics, Mathematics Education, Math Olympiads

Books

Steinberg L., Kvasov R., Cosserat Plate Theory, Taylor &Francis, CRC Press: ISBN 9781032040233 (2022).
This book presents the foundation and validation of the Cosserat Plate Theory, numerical experiments of deformation and vibration, and the unique properties of the Cosserat plates. The validation of the theory is based on the comparison with the three-dimensional Cosserat Elastostatics and Elastodynamics. The numerical results are obtained using the Finite Element Method (FEM). The analysis of deformation of a variety of Cosserat plates shows the stress concentration reduction, higher stiffness of Cosserat plates, and the size-effect related to the microstructure. The analysis of vibration of Cosserat plates predicts size-related properties of the plate vibration, the existence of the additional so-called Cosserat plate resonances, and the dynamic anisotropy, related to the dependency of the resonances on the microelement's shapes and orientations.

Kvasov R., MATH OLYMPIAD ALGEBRA, 42 Points: ISBN-13: 979-8354539123 (2022).
This book provides an introduction to the most popular topics, ideas and techniques that are used in math olympiad algebra. It also contains 120 practice problems with full solutions.

Kvasov R., MATHCOUNTS Preparation, 42 Points: ISBN-13: 979-8354539123 (2022).
This book presents the most popular methods and techniques that are used to solve the problems from MATHCOUNTS competitions. It also contains 240 practice problems in MATHCOUNTS format with full solutions.

Kvasov R., AMC 10 Preparation, 42 Points: ISBN-13: 979-8452006701 (2021).
This book presents the most popular methods and techniques that are used to solve the problems from AMC 8 (American Mathematics Contest). It also contains 120 practice problems in AMC 8 format with full solutions.

Kvasov R., AMC 8 Preparation, 42 Points: ISBN-13: 979-8507158034 (2020).
This book provides the complete preparation for the AMC 10 (American Mathematics Contest). It presents the most popular methods and techniques that are used to solve the problems from AMC 10, and contains 180 practice problems in AMC 10 format with full solutions.

Kvasov R., 42 Ideas for AMC 8 and MATHCOUNTS, 42 Points: ISBN-13: 979-8668235971 (2020).
This book presents the most popular ideas that are used in AMC 8 and MATHCOUNTS. It also contains more than 130 examples with full solutions.

Kvasov R., JUNIOR MATH OLYMPIADS of 2018-2019, 42 Points (2019).
This book presents selected problems from the Junior Math Olympiads of the 2018-2019 competition cycle from eight different countries. The problems were translated from Polish, Ukrainian, Italian, German and Spanish, and cover the topics in number theory, combinatorics, geometry and algebra. All problems come with the author's own detailed solutions and are organized as 8 separate exams that can be solved in any order or used as a collection of mock exams.

Kvasov R., JUNIOR MATH OLYMPIADS of 2017-2018, 42 Points ISBN-13: 979-8357350619 (2018).
This book presents selected problems from the Junior Math Olympiads of the 2017-2018 competition cycle from eight different countries. The problems were translated from Polish, Ukrainian, Italian, German and Spanish, and cover the topics in number theory, combinatorics, geometry and algebra. All problems come with the author's own detailed solutions and are organized as 8 separate exams that can be solved in any order or used as a collection of mock exams.

Articles

Steinberg L., Kvasov R., Dislocations in Cosserat Plates, Journal of Applied Mathematics and Physics, Vol.10 No.11 (2022).
This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed in (Steinberg, Kvasov, 2013).

Steinberg L., Kvasov R., Distinctive Characteristics of Cosserat Plate Free Vibrations, Dynamical Systems Theory, Intechopen (2019).
In this book chapter we present the research of the plate free vibrations based on the extended version of the dynamic plate theory published earlier (Steinberg, Kvasov, 2015).

Kvasov R., Steinberg L., Modeling of Size Effects in Bending of Perforated Cosserat Plates, Modelling and Simulation in Engineering, Volume 2017, Hindawi (2017).
This journal paper presents the Finite Element method for the modeling of the size effect in Cosserat Plates with holes based on the Enhanced Cosserat Plate Theory (Steinberg, Kvasov, 2013).

Steinberg L., Kvasov R., Analytical Modeling of Vibration of Micropolar Plates , Applied Mathematics (6): 817-836 (2015).
In this journal paper we present the dynamics extension of the static Enhanced Cosserat Plate Model (Steinberg, Kvasov, 2013).

Kvasov R., Steinberg L., Numerical Modeling of Micropolar Elastic Plates , Thin-Walled Structures (69): 67-78 (2013).
This journal paper presents the complete numerical modeling of Cosserat plates based on the recently published Enhanced Cosserat Plate Theory (Steinberg, Kvasov, 2013)

Kvasov R., Cruz-Pol S., Colom-Ustariz J., Rees P., Weather Radar Data Visualization Using First-Order Interpolation, Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (2013).

Steinberg L., Kvasov R., Enhanced Mathematical Model for Cosserat Plate Bending, Thin-Walled Structures (63): 51-62 (2013).
This fundamental work presents the enhanced Cosserat plate theory and the comparison with the three-dimensional exact Cosserat elasticity.

Kvasov R., Mathematical Modeling and Finite Element Computation of Cosserat Elastic Plates, Doctoral Dissertation, University of Puerto Rico (2013).
The doctoral dissertation where the complete Enhanced Cosserat Plate Theory was developed. This research also includes the validation and numerical modeling for the plate theory and later resulted in several publications (Steinberg, Kvasov, 2013 and Kvasov, Steinberg, 2013).

Kvasov R., Steinberg L., Numerical Modeling of Bending of Cosserat Elastic Plates, Proceedings of the 5th Computing Alliance of Hispanic-Serving Institutions: 67-70 (2011).
This conference paper presents the first numerical results of the modeling of Cosset plates based on the Steinberg model published in 2010.

Presentations

Kvasov R., Unique Properties of Cosserat Elastic Plates, XXXVII Mathematical Sciences Research Seminar (SIDIM), Rio Piedras, Puerto Rico (2022).

Kvasov R., Cosserat Plates as Two-Dimensional Structural Elements, University of Puerto Rico, Aguadilla (2022).

Kvasov R., Math Olympiad Problems as a Teaching Tool of the Future Mathematicians, University of Puerto Rico, Aguadilla (2022).

Kvasov R., Numerical Simulation of Dislocation in Cosserat Elastic Plates, XXXIII Mathematical Sciences Research Seminar (SIDIM), Rio Piedras, Puerto Rico (2018).

Kvasov R., Mathematical Model and Analysis of Micro Vibration of Cosserat Plates, XXXII Mathematical Sciences Research Seminar (SIDIM), Ponce, Puerto Rico (2017).

Kvasov R., Educational System of Ukraine, Educación comparada: Enfocada en las Experiencias Educativas Internacionales, Inter American University of Puerto Rico, San German (2016).

Kvasov R., Efficient Finite Element Method for Micropolar Plates, Department of Mathematics, University of Puerto Rico, Aguadilla (2015).

Kvasov R., Analytical Modeling of Vibration of Micropolar Plates, XXIX Mathematical Sciences Research Seminar (SIDIM), Mayaguez, Puerto Rico (2015).

Kvasov R., Dynamics Model of Vibration of Micropolar Plates, Department of Mathematics, University of Puerto Rico, Aguadilla (2014).

Kvasov R., Bending of Micropolar Plates, Department of Mathematics, University of Puerto Rico, Aguadilla (2013).

Kvasov R., Weather Radar Data Visualization Using First-Order Interpolation, IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Melbourne, Australia (2013).

Kvasov R., Finite Element Modeling of Micropolar Elastic Plates, XXVIII Mathematical Sciences Research Seminar (SIDIM), Cupey, Puerto Rico (2013).

Kvasov R., Finite Element Modeling of Bending of Micropolar Plates, XXVII Mathematical Sciences Research Seminar (SIDIM), Mayaguez, Puerto Rico (2012).

Kvasov R., Finite Element Modeling of Plates, Sigma Xi XVI Poster Day, Mayaguez, Puerto Rico (2011).

Kvasov R., Numerical Modeling of Bending of Cosserat Elastic Plates, 5th Computing Alliance of Hispanic-Serving Institutions, San Juan, Puerto Rico (2011).

Kvasov R., Micropolar Elastic Plates and their Numerical Modeling, XXVI Mathematical Sciences Research Seminar (SIDIM), Humacao, Puerto Rico (2011).

Kvasov R., Boundary Approximation in the Finite Element Modeling of Micropolar Plates, CISE Lecture, Mayaguez, Puerto Rico (2010)

Essays

Kvasov R., Teaching Differentiation: A Rare Case for the Problem of the Slope of the Tangent Line, Repository for Scholarly Material arXiv: 1805.00343 (2018).

Kvasov R., On Real People and Imaginary Numbers, Revista ICONO de Universidad de Puerto Rico en Aguadilla, Volume 21: 48-50, Aguadilla (2015).

Math Olympiad Seminars

Kvasov R., Problems from Chinese Mathematical Olympiads (OMPR, 2014).

Kvasov R., How to Solve IMO-level Problems (OMPR, 2014).

Kvasov R., Invariants (OMPR, 2014).

Kvasov R., Processes and Operations in Olympiad Problems (OMPR, 2014).

Kvasov R., Challenging IMO Geometry Problems (OMPR, 2013).

Kvasov R., Similar Triangles (OMPR, 2013).

Kvasov R., Just Add the Numbers (OMPR, 2012).

Kvasov R., Locus (OMPR, 2012).

Kvasov R., Angles and Parallel Lines (OMPR, 2012).

Kvasov R., About the Midpoints of the Sides of a Quadrilateral (OMPR, 2011).

Kvasov R., Introduction to Functional Equations (OMPR, 2011).

Kvasov R., Ceva's Theorem (OMPR, 2011).

Kvasov R., Unexpected Solutions (OMPR, 2011).

Kvasov R., When Area Helps (OMPR, 2010).

Kvasov R., Method of Coloring (OMPR, 2010).

Kvasov R., Inscribed Angles (OMPR, 2010).

Kvasov R., 10 Ideas for Olympiad Geometry (OMPR, 2009).

Kvasov R., Introduction to Inequalities (OMPR, 2009).

Kvasov R., Rotation (OMPR, 2008).

Kvasov R., Homothetic Transformation (OMPR, 2007).