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Department of Mathematical Sciences

Andrushkiw, Roman I.

Contact Info
Title: Professor
Email: andrushkiw@njit.edu
Office: CULM 207B
Phone: 973-596-3487
Dept: Mathematical Sciences
Webpage:

About Me

The research of Roman Andrushkiw has focused on the spectral theory of operator-valued functions and the analysis of free boundary problems, with application to numerical modeling in the area of cryosurgery and medical diagnostics. His study of operator-valued functions deals with spectral theory and approximation methods for eigenvalue problems that depend nonlinearly on the spectral parameter. His study of Stefan-type free boundary problems is concerned with modeling of heat transfer phenomena in the freezing of living tissue, involved in cryosurgery. His current projects include the development of a variational method for approximating the eigenvalues of polynomial differential operator pencils, and the study of a pattern recognition algorithm in medical diagnostics related to breast cancer.

Education

  • PhD, Mathematics, Stevens Institute of Technology
  • MS, Mathematics, The University of Chicago
  • MS, Electrical Engineering, Newark College of Engineering
  • BE, Engineering, Stevens Institute of Technology

Professional Activities

ACADEMIC

  • Professor, Mathematical Sciences Dept., NJIT, 1984 - present
  • Associate Professor, Mathematical Sciences Dept., NJIT, 1978 - 1984
  • Assistant Professor, Mathematics Dept., Newark College of Engineering, 1970 - 1978
  • Instructor, Mathematics Dept., Newark College of Engineering, 1968 - 1970
  • Research Assistant, Mathematics Dept., The University of Chicago, 1966 - 1968
  • Instructor, Mathematics Dept., Newark College of Engineering, 1964 - 1966

INDUSTRIAL

  • Sen. Elec. Engineer, Weston Instruments & Electronics Co., 1962-64
  • Elec. Engineer, Weston INstruments & Electronics Co., 1959-62
  • Numer. Data Analyst, Union Carbide Corp., Linde Air Products Co., 1957

CONSULTING

  • Bendix Corporation, Teterborough, NJ, 1981-1982.
  • E.T. Killam Associates, Millburn, NJ, 1980-1981.

 PROFESSIONAL ACTIVITIES

  • Associate Editor, Proceedings METMBS´03
  • Organizer and Chair, Technical Session #7, International Conference on Mathematics and Enginering Techniques in Medicine and Biological Sciences (METMBS´02), Las Vegas, 2002.
  • Associate Editor, Proceedings METMBS´02
  • Chair, Dean´s Search Committee, College of Science and Liberal Arts, New Jersey Institute of Technology, 1990 - 1992.
  • Chair, Special Session on Computational Mathemtics and Applications, 834th Meeting of the American Mathematical Society, Newark, 1987.
  • Chair, Special Session on Mathematical Modeling in Geophysics, 11th IMACS Congress on System Simulation and Scientific Computing, Oslo, Norway, 1985.
  • Chair, Mathematical Sciences Sect., Shevchenko Sci. Soc., (1987 - ), V.P. (1993 - ).
  • Reviewer for Mathematical Reviews, Bulletin of the AMS, and contributor to Zentralblatt fur Matematik and other journals.

Conferences

  • GrantInternational Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS ´03), Las Vegas, 2003.
  • Fourth International Conference on Dynamical Systems and Applications, IFNA, Atlanta, 2003.
  • International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS ´02), Las Vegas, 2002.
  • International Conference on Nonlinear Partial Differential Equations, Institute of Mathematics Nat. Ac. Sci. Ukraine, Kyiv, 2001.
  • International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS´01), Las Vegas, 2001.
  • The Third World Congress of Nonlinear Analysts, Catania, 2000.
  • XIII Summer School on Biometrics, Cikhaj, Czech Republic, 1999.
  • Second International Conference on Symmetry in Nonlinear Mathematical Physics, Kyiv, 1997.
  • International Conference on Applied Statistics in Medical Sciences, Ankara, 1997.
  • Second World Congress of Nonlinear Analysts, IFNA, Athens, 1996.
  • International Conference on Symmetry in Nonlinear Mathematical Physics, Kyiv, 1995.
  • 14th IMACS World Congress on Computational and Applied Mathematics, Atlanta, 1994.

Grants and Awards

  • METMBS´03, Achievement Award, 2003.
  • National Research Council of the National Academy of Sciences (two grants) to conduct joint research in applied mathematics with scientists from the former Soviet Union under the Cooperation in Applied Science and Technology (CAST) program, 1993-94.
  • NRC/NAS Supplementary grant, CAST Program, 1995.
  • NAFSA grant under the REAP Program, 1/1/95 - 6/1/95.
  • Embassy of Ukraine in USA award for contributions to the strengthening of scientific ties between Ukraine and the United States, 1998.
  • IMACS award for contributions to the scientific program and organization of the 11th World Congress on System Simulation and Scientific Computing, Oslo, 1985.
  • NSF award for college teachers of mathematics, 1966.
  • Union Carbide Corporation Scholar, 1955-59.

Affiliations

  • Center for Applied Mathematics and Statistics, International Federation of Nonlinear Analysts, International Association for Mathematics and Computers in Simulation, Shevchenko Scientific Society.

Courses I Teach

Not teaching any courses this semester

Courses I Teach

Not teaching any courses this semester

Research Interests

  • Spectral theory and eigenvalue approximation of operator-valued functions
  • Pattern recognition methods in medical diagnostics
  • Integrable dynamical systems
  • Free boundary problems
  • Mathematical modeling in biophysics

Selected Publications

  • Interface Dynamics For Quasi-Stationary Stefan Problem (V. Gafiychuk, B. Datsko), Mathematical And Computer Modeling, Vol. 45, Pp. 892-898, 2007.
  • Computer-Aided Cytogenetic Method Of Breast Cancer Diagnosis, Part I – Decision Rule (Yu.I. Petunin, N.V. Boroday, I.V. Dosenko), Proc. 2006 Int’l Conf. Bio-Informatics And Computational Biology, Csrea, Pp. 205-209, 2006.
  • Computer-Aided Cytogenetic Method Of Breast Cancer Diagnosis, Part II: Test Criteria (D.A. Klyushin, K.N. Golubova, A.V. Romanov), Proc.2006 International Conference On Bioinformatics & Computational Biology, Csrea, Pp. 210-213, 2006.
  • The Exact Confidence Limits For Unknown Probability In Bernoulli Models, (D.A. Klyushin, Yu. Petunin, M. Savkina), Proc. 27thinternational Conference On Information Technology Interfaces, Srce Univ. Comp. Ctr., Cavtat/Dubrovnik, Pp. 175-179, 2005.
  • Analysis Of Malignancy-Associated Dna Changes In Interphase Nuclei Of Buccal Epithelium In Patients With Breast Cancer (N. Boroday, D.Klyushin, Yu.Petunin), Experimental Oncology, V. 26, No. 2, Pp. 158-160, 2004.
  • Retrospective Cohort Investigation Of Risk Factors In Breast Cancer (N.V.Boraday D.A. Klyushin, Yu.I. Petunin, F. Miropolska), Proc. Int’l Conf. On Mathematics And Engineering Techniques In Medicine And Biological Sciences, V.1,Pp.385-390, 2004.
  • Equations Of Interface Dynamics For Quasi-Stationary Stefan Problem (V. Gafiychuk), Proc. Fourth International Conference On Dynamic Systems And Applications, Ifna, V.4, Pp. 571-580, 2004.
  • Stratification Of General Population And Its Application In The Analysis Of Resistant Tumor Cells (D.A. Klyushin, Yu.I. Petunin, A. German, M. Savkina) Proc. International Conference On Mathematics And Engineering Techniques In Medicine And Biological Sciences, Pp.490-494, 2003.
  • Spectral Problem For A Class Of Polynomial Operator Pencils, Nonlinear Boundary Problems, Inst. Applied Math. & Mech. N.A.S.U., V.12, Pp.13-18, 2002.
  • Analysis Of Malignancy-Associated Dna Changes In The Nuclei Of Buccal Epithelium In The Pathology Of The Thyroid And Mammary Glands (D.A. Klyushin, Yu.I. Petunin, N.V.Boroday, K.P. Ganina), Annals Of New York Academy Of Sciences, V. 980, 1-12, 2002.
  • Diagnosis Of Breast Cancer By The Modified Nearest Neighbor Recognition Method, (D.A. Klyushin, Yu.I. Petunin, N.V. Boroday), Proc. Intl. Conf. On Math And Eng. Techniquesin Medicine And Biological Sciences, V.1, 176-189, 2002.
  • A Variational Method For Eigenvalue Problems Nonlinearly Dependent On The Spectral Parameter (V. Slastikov), Nonlinear Analysis, V.47, 3561-3566, 2001.
  • Computer-Aided Diagnosis Of Breast Cancer And Fibroadenomatosis Based On Malignancy Associated Changes In Buccal Epithelium (Petunin, Klyushin, Ganina, Boroday), Automedica, V.19, No. 3-4, 135-164, 2001.
  • Retrospective Linear Regression Analysis Of Survival Data For Patients Suffering From Malignant Melanoma (Petunin, Klyushin, Naleskina), In Applied Statistical Sciences IV, M. Ahnsanullah (Ed.), Nova Science Publ., 139-158, 1999.
  • Higher Symmetries Of The Wave Equation With Scalar And Vector Potentials (Nikitin), Proc. Second International Conference On Symnmetry In Nonlinear Mathematical Physics, Inst. Math, Kyiv, V.2, 321-327, 1997.
  • Nonlinear Algorithm Of Pattern Recognition (Petunin, Klyushin), Nonlinear Analysis, V.30, 5431-5436, 1997.
  • On The Spectral Theory Of Operator Pencils In A Hilbert Space, J. Nonlinear Mathematical Physics, V.2, 356-365, 1995.
  • Geometric Quantization Of Neuman-Type Completely Integratable Hamiltonian Systems, J. Mathematical Physics (I. Mykytiuk, A.K. Prykarpatsky, V.Hr. Samoilenko), V.35, 1532-1548, 1994.
  • Algebraic Structure Of The Gradient-Holonomic Algorithm For Lax-Integrable Nonlinear Dynamica Systems (Part I), (A.K.Prykarpatsky,V.Hr. Samoilenko), J. Mathematical Physics, V.35, 1763-1777, 1994.
  • Algebraic Structure Of The Gradient-Holonomic Algorithm For Lax-Integrable Nonlinear Dynamica Systems (Part II), (A.K. Prykarpatsky, V.Hr. Samoilenko, Yu.O. Mitropolsky, M.M. Prytula), J. Mathematical Physics, V.35, 2237-2265, 1994.
  • Two Boundary Model For Freezing Processes In Living Tissue (Gafiychuk, Lubashevskii), Proc. 14th Imacs World Congress On Computational And Applied Mathematcis, V.2, 546-548, 1994.
  • Iterative Method For A Class Of Nonlinear Eigenvalue Problems, Applicable Analysis, V.51, 211-220, 1993.
  • A Trace Identity And Its Application To Integrable Systems Of 1+2 Dimensions (Tue, Huang), J. Mathematical Physics, V.32, 392-396, 1991.
  • Mathematical Modeling Of Freezing Front Propagation In Biological Tissue, Mathematical And Computer Modeling, V.13, 1-9, 1990.

Books

  • Computer-Aided Cytogenetic Method Of Cancer Diagnosis (N. Boroday, D. Klyushin, Y. Petunin), Nova Science Publishers, New York, Isbn-13: 978-1-59454-882-6, Isbn-10: 59454-882-X, 303p., 2007.
  • Development Of Mathematical Ideas Of Mykhailo Kravchuk (N.Virchenko, I. Katchanovski, V.Haidey,R. Voronka), Nat. Technical Univ./Kpi& Shev. Sci. Soc., Kyiv-New York, Isbn: 0880541415, 780 P., 2004.