DESCRIPTION OF RESEARCH

I. Brief Summary of research activity

1. Publications
   
   Professor M.A.Shubov is the author of more than 60 substantial research papers published in leading archival journals. Since 1996, she published 38 papers and 3 long papers are currently submitted.
    

2. Grants
   
   During her career at Texas Tech, she has received 12 research grants, totaling over
   $600, 000. Six of these grants came from NSF (total amount nearly $500,000). She also received five grants from the Advanced Research Program of Texas (ARP).
    

3. Invited talks
   
   Since 1996, she has presented 51 invited talks. Most of these have been the talks at International Conferences, both in the United States and abroad. She also presented several colloquium addresses and seminar talks at other universities and research centers. Among these talks are colloquium and seminar presentations at UCLA, seminar talks at NASA Dryden Flight Research Center, and, most recently, colloquium talk at the Aeronautics Department of UT at Austin. Her invited talks prior to 1996 include a seminar talk at Caltech, a colloquium address at the Applied Mathematics Department of Rice University, and a presentation at a prestigious International Conference in Oberwolfach, Germany. In summer of 2002, Dr. Shubov had an invited scientific tour to five universities and Aerospace Engineering Research Centers in Germany and present there, her recent results on mathematical analysis of flutter in aircraft wings.
    

4. Main directions of research
   
   

   1. During the past seven years, one of two main directions of Dr. Shubov’s research has been related to an Interdisciplinary Project joint with the Flight Systems Research Center (FSRC) at the University of California at Los Angeles (UCLA). The main objective of the project is mathematical (both computational and theoretical) analysis of the flutter phenomenon and flutter suppression in aircraft wings. In 1999–2000 academic year, her work on this project was supported by an NSF grant, which provided funding for a one – year visit to FSRC (DMS #9972748, Interdisciplinary Grants in Mathematical Sciences Program; amount $100,000. Only nine such grants were awarded in the U.S.). In July of 2000, she was awarded a three–year NSF grant to support her work in this direction (DMS #0072247; Applied Mathematics Pro-gram; amount $92,000). Again in September, 2000, an additional NSF Proposal on the flutter suppression was funded (Program Name: Control, Networks, and Computational Intelligence of the Division of Electrical and Communications Systems; Proposal # 0080441; amount $120,000 for three years). Most recently, on October 25, 2001 her proposal “ Mathematical analysis of flutter control problem in aircraft wings” was funded by the Advanced Research Program of Texas (amount $59; 354).The major part of her current research plans consists in the continuation of the work on this project.
      
      Professor Shubov’s work on the flutter suppression project started as a result of an invitation from the Director of FSRC, Professor A.V. Balakrishnan, who is one of the world leading experts in Applied Mathematics and Aircraft Engineering. His attention had been attracted by a series of Dr. Shubov's works on asymptotic and spectral analysis and control of elastic structures. He suggested that the methods of her works could be very useful for mathematical analysis of aircraft wing models developed at FSRC in collaboration with NASA Dryden. Since that time, she has published/accepted 15 very substantial papers (see Ref [1-7, 10-15] in "Publications") on the wing project in leading journals and has submitted 2 long papers (Ref [1*, 2*]). Her results have attracted a significant interest both in Aerospace Engineering and the Applied Mathematics communities. So far she has presented these results in 29 invited talks.
       

   2. In recent years, another direction of her research has focused on two closely related topics: (a) spectral and asymptotic analysis of nonselfadjoint operators in a Hilbert space, operators which are the dynamics generators of damped hyperbolic equations and systems describing nonconservative vibrating elastic structures; (b) application of the results of this analysis to the control of the corresponding distributed parameter systems. This research has been supported by three grants: three-year NSF grant (1997, DMS #9706882, Analysis Program; amount $102,000), Advanced Research Program of Texas (1997, #003644 – 045; duration – two years; amount: $53,162), and Advanced Research Program of Texas (1995, #003644 –121, duration – two years, amount: $28,400).
      
      Since 1996 she has produced 25 papers on the aforementioned topics that have been published or accepted in leading journals (Ref, [8, 9, 16-38]). She has presented 30 invited talks on the results of these works.
       

   3. Before 1995, Professor Shubov’s research was related to the mathematical problems of quantum scattering theory and propagation of acoustical waves. More precisely, her work was devoted to the following topics.
      
      

      1. Mathematical analysis of resonance phenomena in the scattering of quantum particles.

      
      

      2. Resonance phenomena in the scattering of acoustical waves.

      
      

      3. Topics from abstract functional analysis such as Riesz bases in a Hilbert space and Sz. Nagy–Foias functional model for nonselfadjoint operators.

      This research was supported by four grants: Advanced Research Program 1993, #003644 – 116, duration – two years; amount: $42,000, NSF grant (DMS #9219037, Modern Analysis Program; amount $13,000), Organized Research Fund of Texas Tech grant, duration one year (1990 – 1991) ; amount $3,500, and NSF/AWM Travel Grant (amount $1,000) to present an invited talk at a conference in Oberwol-fach, Germany, May 1990.
       

   4. Direction of graduate students. Currently Dr. Shubov is directing two Ph.D. student, Tina Gaumond and Theresa Busse, and two M.S. students, Akash Deep Singh and Robert Plant III. Two of Dr.Shubov's Ph.D. students, Cheryl Peterson and Cynthia Martin, have recently graduated. Cheryl Peterson defended her dissertation in May 2002. She was awarded with two Texas Space Grant Consortium Fellowships (2000-2001 and 2001-2002) and has accepted a post-doctoral position at UCLA. Cynthia Martin graduated in May 2003, and accepted a tenure-track position at McMurrey Christian University, TX.