Ellina V. Grigorieva, Ph.D.

Professor of Mathematics

My book “Methods of Solving Complex Geometry Problems” at famous Sorbonne University bookstore, in Paris

 

 

On August 19, 2013, I published my new book, Methods of Solving Complex Geometry Problems”, which is available at http://www.springer.com/978-3-319-00704-5.  

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The book is a unique collection of challenging geometry problems and detailed solutions that will build students confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometries’ connection with different fields of mathematics, this book serves as a bridge to more advanced problem solving. 

Methods of Solving Complex Geometry Problems will interest high school and college students to prepare for exams as well as anyone who enjoys an intellectual challenge and has a special love for geometry. It will appeal to instructors of geometry, history of mathematics and math education courses.

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CV

At 2015 Students Research Symposium with graduate students

 

At Dallas Opera March 2015

I at the International SIAM CP15 conference on optimal control with colleagues

 

 

 

 

 

 

 

 

With Governor Rick Perry

 

Research Interest

Most of my papers emphasize the utility of analytical methods and have been published in the area of the application of optimal control and game theory to life science, business and economics. Within this field of application, analytical methods of nonlinear optimal control have the benefit of tractability and interpretability over the conventional numerical methods through the type structures associated with switching functions which yield in a natural way to game-theoretic analysis.

                         I am presently actively engaged in the following specific research topics:

1.  Optimization of the waste water bio-treatment. Biological treatment of the waste water involves using bacteria to remove waste products and pathogens from the treated water. Thus, this problem is closely linked with the problems of population dynamics and chemical kinetics. Furthermore, this problem includes optimization which is needed to reduce cost and bust the efficiency of the process.

 

2.  Mathematical modeling in Ecology.  During the last decades various concepts of the environmental pollution control have been developed.  Establishing optimal working conditions and control strategies is accomplished with the aid of mathematical models.

 

3.  Optimal Control of HIV Treatment.  We created a nonlinear control model, which describes the possible effects of medication intake on HIV infected patients. Lytic and nonlytic mechanisms of reducing infected cells are considered.  Methods of analytical and numerical investigation of such models are developed. 

 

4.  Differential  games.  Our study is focused on the theory and application of non-cooperative hierarchical differential games. We examine the case where the maximum of the objective function exists only on the boundary of the admissible set. Our particular interest is on differential games with restriction on controls

 

5.      Research in math education: USAMO Student Preparation. The goal of this project is to prepare highly knowledgeable mathematics teachers nationwide and particularly in Texas.

 

Selected Publications

Grigorieva E.V., E.N. Khailov and A. Korobeinikov 2012.  “Three-Dimensional Nonlinear Control Model of Wastewater Bio-treatment” Journal of Neural, Parallel, and Scientific Computation, Vol. 20: PP. 23-36

 

Grigorieva E. V. and E.N. Khailov, 2011. “Optimal Control of Pollution Stock”, Discrete and Continuous Dynamical Systems. Supplement Volume. PP 578-589

Grigorieva, E.V. and E.N. Khailov, 2011. “A Hierarchical Differential Game between a Manufacturer and the State in Ecological Setting  http://www.huichawaii.org/proceedings-publication/187-proceedings-publication-index, pp.1-10.

Grigorieva, E.V., 2011. “Using Technology to Teach and Solve Challenging Math Problems”, http://www.huichawaii.org/proceedings-publication/187-proceedings-publication-index, pp.11-21.

Grigorieva E. V. , Bondarenko N.V., E.N. Khailov,  A. Korobeinikov 2011. “Three-Dimensional Nonlinear Control Model of Wastewater Biotreatment”, Proceedings of the International Conference on Dynamic Systems and Applications 6 (forthcoming)

Grigorieva E. V. , Bondarenko N.V., E.N. Khailov,  A. Korobeinikov 2011. “Finite Dimensional Methods for optimal Control of Autothermal Thermophilic Aerobic Digestion”, book chapter in "Industrial Waste” (forthcoming)

Bondarenko N.V., Grigorieva E. V. and E.N. Khailov, 2010. “Attainable Set for a 3-Dimensional Nonlinear System Describing the Process of the Waste Water Cleaning”, Vestnik of Moscow State University (forthcoming)

Grigorieva E.V., Khailov E.N. and Kharitonova E.I. 2010, “Optimal Control of Pollution Stock through Ecological Interaction of the Manufacturer and the State” Revista de Matem´atica: Teor´ıa y Aplicaciones 2011 18(1) : 69–101

 

Grigorieva E. V. and E.N. Khailov, 2010. “Minimization of Pollution Concentration on a Given Time Interval for the Waste Water Cleaning Plant”, Journal of Control Sciences and Engineering. Hindawi Publishing Corporation, Article ID 712794

                                                                                                                

Grigorieva, E.V. and E.N. Khailov, 2010. “Optimal Control of a Waste Water Cleaning Plant”, Proceedings of UAB Conference on Differential Equations and Computational Simulations. : Electron. J. Diff. Eqns. 2010, pp.161-175.

Grigorieva, E.V. and E.N. Khailov, 2010. “Differential Game between manufacturer and state incorporating ecological interaction”, in the book: “Problems of Dynamic Control” Vol. 4., Editor Academician Yu. Osipov.. Moscow, Moscow State University, pp 2.

Grigorieva E. V. and E.N. Khailov, 2009. “Hierarchical Differential Games between Manufacturer and Retailer”, Discrete and Continuous Dynamical Systems. pp. 300--314

Grigorieva E. V. and E.N. Khailov. 2009. “Hierarchical Differential Game between Manufacturer, Bank and Retailer”. Journal of Nonlinear Dynamics and Control, Vol 15(2009), No. 3 (July), pp. 359--391

 

Grigorieva E. V. and E.N. Khailov. 2008. “Nash Equilibrium in the Differential Game between Manufacturer and Retailer”. Problems of Dynamic Control. Vol.3, ISBN 978-5-89407-351-4. Moscow State University, pp. 21-31.

 

Grigorieva E. V. and E.N. Khailov. 2008. “Hierarchical Differential Games between Manufacturer and Retailer with Storage Costs”. International Review of Automatic Control,   Vol.1, No.3, pp. 396-406.

 

Grigorieva E. V. and E.N. Khailov, 2007. “Optimal Control of a Nonlinear Model of Economic Growth”, Discrete and Continuous Dynamical Systems. (Supplement Volume), pp. 456-466.

 

Grigorieva E. V. and E.N. Khailov, 2007. “Game Approach to the Description of Interaction Between Manufacturer and Retailer”, Problems of Dynamical Control. No.2, pp. 49-70.

Grigorieva E. V. and E.N. Khailov, 2005. “An Attainable Set of a Nonlinear Controlled Microeconomic Model”. Journal of Nonlinear Dynamics and Control, Vol. 11, No. 2, 157-176.

Grigorieva E. V and E.N. Khailov, 2005. “Optimal Control of a Commercial Loan Repayment Schedule”, Discrete and Continuous Dynamical Systems. (Supplement Volume), pp. 345-355.

Grigorieva, E.V. and E.N. Khailov, 2005. “An Attainable Set of a Nonlinear Control System describing the Process of Production and Sales of a Consumer Good”, in the book: “Problems of Dynamic Control” Vol. 2., Editor Academician Yu. Osipov. ISBN 5-89407-241-7. Moscow, Moscow State University, pp 312- 332.

Grigorieva, E.V. and E.N. Khailov, 2005On Solution with Increasing Switchings for a Two- Point Boundary Problem Of the Maximum Principle for a Microeconomic Problem of Optimal Control”, in the book: ”Problems of Dynamic Control” Editor Academician Yu. Osipov. ISBN 5-89407-241-7. Moscow, Moscow State University, pp. 145-158.

Grigorieva, E. V. and E. N. Khailov. 2005. “Description of an Attainable Set for a Nonlinear Controlled System in the Plane.” Vestnik of Moscow University, Vol. 15, N 3, pp. 23-28.

Grigorieva E.V. and E.N. Khailov. 2005.“Solution with the Infinitely Many Switching  for the Two-Point Boundary Value Problem of the Maximum Principle” Modern Mathematics and Its Applications in Economics”, Academy of Science Press, Moscow.

Grigorieva E.V. and E.N. Khailov. 2005. “Microeconomic Model Controlled by the Price of the Good”. Modern  Mathematics and Its Applications in Economics”, Academy of Science Press, Moscow.

Grigorieva. E.V. 2005. “On the boundary of an attainability set for a nonlinear microeconomic systems controlled by the rate of production and price of the good.” Mathematical Models in Economics and Ecology, Moscow: MAX Press, pp. 39-43.

Grigorieva. E.V. 2004. “On the Attainability Set of a Nonlinear Controlled Model with the Price as a Control Parameter.” Mathematical Models in Economics and Ecology, Moscow: MAX Press, pp. 35-38.

Grigorieva, E.V. and E. Khailov, 2003. “A Nonlinear Controlled System of Differential Equations Describing the Process of Production and Sales of a Consumer Good”. Discrete and Continuous Dynamical Systems. Supplement Volume, pp 358-365.

Grigorieva, E. V. 2003. “On Attainable Set of a Bilinear Controlled Microeconomic System” Mathematical Models in Economics and Biology, MAX Press, pp. 44-47.

Grigorieva, E. V. and E. Khailov, 2002. “On the Attainability Set for a Nonlinear System in the Plane”, Vestnik of Moscow University.  Allerton Press, Vol.15, No 4, pp. 25-30.

Grigorieva, E. V. 2001. “The Attainable Set of a Bilinear Controlled System Describing the Process of Production, Storage and Sales of Merchandise”. Mathematical Models in Economics and Biology, MAX Press, Moscow, Russia, pp. 43-46.

  

Selected  Presentations

 

Grigorieva E.V. presented “Analytical methods in the Optimal control of HIV treatment” at the 9th International conference on Dynamical systems and differential equations , Orlando, FL, July 4, 2012.

 

AIMS Grigorieva E.V. presented 30 minutes talk “Optimal Control of HIV treatment” at the AMS Special Session on Optimal Control in Applied Mathematics Modeling, at the Joint AMS-MAA Mathematics Meeting, Boston, MA, January 4, 2012

 

Grigorieva E.V. presented 20 minutes talk “Reduction of the operation cost via optimal control of an industrial wastewater bio-treatment process” at the MAA Special Session on Mathematics Experience in Business, Industry, and Government, at the Joint AMS-MAA Mathematics Meeting, Boston, MA, January 5, 2012.

 

 

Grigorieva E.V. (Invited Speaker) and E.N. Khailov “A nonlinear three- dimensional model describing a waste water treatment plant”, 6th International Conference on Dynamical Systems and Application, May 24-29, 2011, Atlanta, Georgia, USA

 

Grigorieva E.V. (Invited Speaker) “Optimal control of a waste water cleaning    plant”,  8th AIMS International Conference on Dynamical Systems, Differential Equations and Application, May 23, 2010 , Dresden, Germany.

Grigorieva E.V. CAS Faculty Spotlight Series: "Preparing Math Olympiad Winners" / Wed., March 3, 2010

Grigorieva E.V. and Khailov E.N. “Hierarchical Game between Manufacturer and the State Incorporating Ecological Interactions” Invited 45 minutes talk at the XVII SIMMAC International Conference, San Jose, Costa Rica, February 17, 2010.

Grigorieva E.V. "Optimal control of the activated sludge process" the 8th International Mississippi State-UAB Conference on Differential Equations & Computational Simulations, May 8, 2009. Starkville, MI

 

Grigorieva E.V. "Differential games between manufacturer and retailer with storage costs”, the 89th Annual MAA Meeting, April 17, 2009.

 

Grigorieva E.V. (Keynote Speaker, 45 minutes talk)”Hierarchical Differential Games between Manufacturer and Retailer”, International Conference "Differential Equations and Topology” in commemoration of the 100th   anniversary of Lev Pontryagin (1908-1988). (June 17-22, 2008)

Grigorieva E.V. (Invited Speaker) “Bilinear Hierarchical Differential Games Between Manufacturer and Retailer”, 7th AIMS International Conference on Dynamical Systems, Differential Equations and Application, May 19, 2008 , Arlington, TX, USA .

 

 

Presently Teaching

·         Linear Algebra

·         History of Math for Graduate Students

·         Business Analysis I 

·         Number Theory

·         Advanced Calculus MATH 5033   

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