Curriculum Vitae
Yuri Magarshak, Ph.D.
President, MathTech.Inc.,
President of the International Committee for Intellectual Collaboration,
President MathTech, Inc.
2925 W 5ths Str. Suite 3E Brooklyn NY 11224
(718)946-5015, ym4@nyu.edu
EXPERTISE:
-Analytical and computer modeling and statistics in molecular biology,
pharmacology, physiology and medicine.
-RNA folding and dynamics.
- Neural nets Color vision and stereo vision, new principles of computing.
-Diagrammatic analysis of structured systems with large number of components.
-Enzyme regulation and kinetics.
-Creation and managing multi-disciplinary teams. Frontiers high-tech projects in
application to internet and control systems.
EDUCATION:
1968: M.S. In Theoretical and Mathematical Physics,
Leningrad State University, School of Physics, Department of
Mathematical and Theoretical Physics. Graduated with honors.
1972: Ph.D. In Theoretical and Mathematical Physics,
Leningrad State University, School of Physics, Department of
Mathematical and Theoretical Physics
PROFESSIONAL EXPERIENCE:
1997-Present: President, MathTech, Inc. (New York, USA)
2009-Present: President, International Committee for Intellectual Collaboration
2001-2009
Executive Vice President, International Committee for Intellectual
Collaboration
2007-Present Distinguished Professor, University of Dubna (Russian Federation)
1994-Present: Visiting Professor, Courant Institute of Mathematical Sciences, NYU
1997-1998: CEO, InfoPlanet Technologies, Inc.
1994-1996: Vice President, Research and Development, PhyTech, Inc.
1991-1993: Visiting Associate Professor, Department of Biomathematical Sciences.
Mount Sinai School of Medicine of City University of New York
1989-1990: Senior Research Associate, Department of Chemistry,
New York University.
1978-1988: LTU (Leningrad, USSR), Member of Research Stuff.
1972-1978
Chair of the Lab of Biomathematical Simulations, Associate professor,
assistant professor. North-West Polytechnic Institute, Leningrad (USSR).
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OTHER PROFESSIONAL ACTIVITIES:
 Organizing committee, Advisory Committee and Program Committee
Member for several major conferences.
 Foreign Member of Russian Academy of Natural Sciences
 Chair of the organizing committee of NATO workshop Silicon vs. Carbon
(2008)
 Co-chair of the workshop Commercialiation of Nanotechnologies, Sanct
Petersburg 2008 КОММЕРЦИАЛИЗАЦИЯ НАНОТЕХНОЛОГИЙ
 Co-chair of the symposium Gray holes of history
 Co-chair of the international workshop Physics of atoms: new ideas and
prospects (2008 Co chair of the symposium Civilization of 21st century:
technological and humanitarian aspects Moscow 2006)
 Co-chair of the workshop Fragmentation and Globalization in Human
Civilization
 Chair of the organizing committee of International Advanced Research
Workshop NATO Environmental and Biological Risks of Nanobiotechnology,
Nanobionics and Hybrid Organic-Silicon Nanodevices (Silicon vs. Carbon)
 Reviewer of a number of journals.
Intellectual Forum (USA-Russia), board member
President of the Intellectual Renaissance Society (New York)
Editorial Board Member of the International Journal of Alternative Energy and
Ecology
Editorial Board Member of the Ecology and Life Journal
Editor, New and Old Ideas in Physics European Journal
Vice-Chair of Biophysical Council, Sanct Petersburg (USSR)
Board Member, Physics Council Member: Educational Alliance, Sanct Petersburg
Branch.
PUBLICATIONS: Over 100 scientific papers in referenced journal.
Over 200 publications in non-references Journals and Magazines.
CITIZENSHIP: US Citizen
References furnished upon request
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Summary
of Selected Scientific and Technical Contributions.
Invention and creation of new engine for database representation and Internet
navigation (InfoPlanet). This is ongoing project. The new principle of representing
database by surfaces has been developed. The personal US patent has been received. In
exchange for investment and cash, the work on the prototype is been performing by
InfoPlanet Technologies, Inc., and supervised by Yuri Magarshak as C.E.O.
Analysis of RNA Folding and Dynamics. Loop and gap migration models of RNA
dynamics have been suggested and analysed. . With newly developed formalism of
projective matrix analysis, equations of RNA loop migration have been derived.
Computer analysis of structure of a number of genome sequences has been
performed. It was demonstrated that the distribution of sequence symmetries in HIV
genome is region-dependent. Experiments with an RNA spliced leader, which reveal the
switch between two alternative structure forms, have been analyzed. The model of knot
dynamics, which follows from this approach, has been suggested and tested. Knot
Invariants of RNA secondary structures have been found and analyzed (in collaboration
with L.Kauffman). The statistical-mechanical approach to secondary structure formation
during RNA chain elongation has been tested on Ala-tRNA sequence. Computations
demonstrate bifurcation of secondary structure pathways as intermediate state, and
convergence to the unique final secondary structure, known from experiment.
Electron Transfer in Macromolecules. This work was started in 1989 at NYU and
continued at Mount Sinai School of Medicine of City University of New York. First,
diagrammatic solution of Dyson system for electron tunneling has been suggested. The
method reminds Anderson technique for solid state physics, but is applicable to large
structured systems without translation symmetry. Second, the diagrammatic solutions for
Green functions has been derived for alpha-helical peptides, for graphs with one
backbone and side groups touching it at a single site, for tree-like pathways scheme (like
hydrocarbons) and other biologically important models. The computation of electron
transfer rate, based on this theory along with 3D-energy minimization, has been
performed for a number of organic molecules. Further, the formula of Green function for
the systems which can be subdivided into weakly coupled clusters, has been derived.
The method of topological renormalization has been generalized on the schemes with
arbitrary number of cycles, if cyclic sub-schemes (for instance, side-groups) form a tree.
Vertices of transformed diagram correspond to Hamiltonians of sub-schemes. The
possible resonance phenomena caused by bifurcation of in electron paths, has been
predicted. As a result of resonance, at bifurcation point of electronic paths, electron can
tunnel through one barrier rather than through another. To brake the symmetry in such a
way, a small perturbation of hopping integral is sufficient. Such a resonance can explain
the effect of electron transfer along only one of two paths, in particular, in photo reaction
center.
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Pattern Recognition and signal analysis. In 70-ies in the lab of Biomathematical
Simulations the investigation of pattern recognition in application to radio location has
been performed under my supervision. This work was supported by grants of Navy of the
USSR, so results and reports in this field were classified. In general, I have directed the
work on Spectral Analysis of Pseudo-Random Signals in Aqua Media. Evaluation Error
of Statistic Characteristics of Pseudo-Random Signals With Discrete Sampling were
thoroughly investigated. The computations were performed with signals from submarines
in Baltic Sea. A number of criteria have been tested. As a result, new algorithm for early
detection of submarines has been developed.
Diagrammatic Solutions of Equation Systems. In many applications, one has a set of
hundreds, thousands or millions of equations, in which most of the elements are equal to
zero, and the disposition of non-zero elements is regular. This situation is pretty typical
for molecular biology, economy, computer sciences, electronics and other fields. In
such system, main properties of solution depend on the structure of the system rather then
on values of coefficients. For instance, the Green-function of tree-like Dyson system is
also tree-like branched continued fraction, and the structure of this continued fraction has
one-to-one correspondence with the structure of Dyson system itself (Magarshak,
Malinsky, 1991). One also can derive continued fraction solution for electric resistance of
regular hexagonal net (we derived it first in application to analysis of lipid bilayers). The
project was started in collaboration with M.Volkenstein 20 years ago. Since than we
have solved diagrammatically a number of equation systems of diverse structured forms.
This approach has been applied on electron tunneling, enzyme kinetics, RNA dynamics,
lipid bilayer and neural nets. The general theory of solution of structured systems is not
developed yet, so the project is on-going.
Electrical Properties and Topological Transformations in Membranes. This
work was performed in University of Texas (Galveston), in order to explain experiments
of H.Fishman with Earthworm Medial Giant Nerve Fiber and Squid Giant Axon. The
model of the resistance of regular hexagonal nets with different dislocations and diverse
shapes of holes in it has been developed. The continued-fraction solutions for finite
number of elements, which was derived, tend to the experimentally measured values.
Experiments with cut giant axon reveal a lot of spherical vesicles of various diameters
which a. move to the hole, b. Change the shape so that the contact surface between them
is maximized, c. close the gap forming the plug, d. fuse, so that in some cases one huge
bubble is formed, and e. at least in some cases, seal the axon. The problem of vesicle
fusions has been analyzed as 3D-percolation problem. The problem of vesicles shape in
the plug region has been treated as the set of minimal energy surfaces. The possible
structures of dislocation regions in the hexagonal net (bilayer) is under study. In these
and other experiments it has been demonstrated that interaction of membrane hole
with a vesicle requires the formation of bifurcation of bilayer. The work is continued.
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Entropy Production by Enzymes in Non Equilibrium Range, and Analysis of
Stationary and Non Stationary Multi Enzyme Systems. In 1985-1988, in collaboration
with Prof. Stephanov (Leningrad State University), the theory of enzymeуs entropy
production has been developed. As a result of computer simulations, the entropy
production for main mechanisms of enzyme reaction was computed. In particular,
calculations show that kinetics of at least some allosteric enzymes can be unstable in the
sense of Lyapunov. In 1989 at Courant (NYU) the non-linear behavior of a number of
multi enzyme systems in the far-from-equilibrium zone have been simulated and plotted.
The plots demonstrate diverse time-dependent
behavior and limit-cycles. The approach was also applied to creatine kinase reaction
complex.
Projective Geometry in Application to Color Vision and Neural Nets. The
principles of neural net functioning on cognition level are still unknown. It is commonly
accepted that in the brain some kind of algebraic structures are formed. On the other
hand, all chemical signals are non-negative, and actually the set of such signals forms the
cone rather than ring or algebra. One can get algebra of complex numbers by projectivegeometrical transformations on cones with dimensions 3 and 4 and non-negative
components, and algebra of quaternions, as well as that of dual numbers, by projectivegeometrical transformation on cones with dimension 8 (the last formalism one can
consider as generalized spinors). In this approach, oscillation of the image on retina
generates kind of Feynman integral along trajectories. The projective geometrical
model of neural nets functioning is suggested (in collaboration with professor
F.Bogomolov). The application of this approach to color vision sounds natural and
straightforward. These results might be equally useful in application to computer science,
imaging and pattern recognition.
Analysis of spectral properties or biological micromolecules. In order to diminish
drastically the probe dose and improve treatment of mentally ill and other patients,
spectral properties of proteins of spinal fluid of mentally have been analyzed. Now
standard, at that time this method was new. The work was performed under my
supervision and supported by the grant of Ministry of Health of Russian Federation.
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Diagrammatic Methods in Application to Enzymatic Activity. The work was
started as graduate research (advisor Michael V.Volkenstein). At first, it has been proven
that cycled and uncycled graphs give identical solutions for balance equations (sum of
matrix element of each column is zero), if the product of rate constant in clockwise and
counter clockwise directions are equal for each cycle. This, now well know, result
allowed drastically improve method of King and Altman by uncycling kinetic schemes
and getting partition function rather then series of rate constants. A number of kinetic
mechanisms of enzyme reaction (ping pong, allosteric enzymes etc.) have been analyzed.
Diagrammatic method of kinetic predictions based just on the reaction scheme has been
suggested. For a number of biologically important enzyme systems, one-to-one
correspondence between the kinetic diagram, which elements are considered
symbolically as mathematical operations, and rate dependence on metabolites
concentrations, has been demonstrated. It has also proven, that in the presence of
symmetry group, equations can be simplified and solutions degenerate. the
symmetry brake removes degeneration and splits solutions. For systems in which
clusters are connected by rate-limited steps, the diagrammatic solution has been given.
On the bases of this theory, computer simulation of kinetic behavior of a number of
allosteric enzymes has been performed.
Short term projects.
 Three dimensional periodic table of elements (Publication in ‘Nature’, 1992).
 Group-theoretical approach to the structural analysis of poetry (1989). Application of
the graph-theoretical approach on the analysis of the plot of ‘Hamlet’ Shakespeare
(1991).
 Creation of the interactive computer programs ‘Intel 100’ and ‘Intel 200’ for
improving reading, memorizing and comprehension abilities (1987-1989).
 Creation of the computer programs for ultraviolet and infrared color vision with
global and local adjustment of colors and applications of this approach on medicine.
 The design of computer programs in order to investigate experimentally non-linear
effects of human vision (in collaboration with professor O.Franzen, University of
Uppsala, Sweden) has been performed. At present, some of newly discovered effects
are under study.
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Yuri Magarshak
LIST OF SELECTED PUBLICATIONS.
Yu. Magarshak Gluconics as the Universal Renewable Energetic the SITA Journal Vol.
12 . 189-194 (2010)
E. Levich, A. Libin, Y. Magarshak “Helical theory of turbulence in fluids and plasma and
possible Implications for coherent organization in Cosmos” J. Scientific Israel –
Technological Advantages (SITA), Vol.12 1-2. pp. 186-191 (2010)
O.Figovsky, Y.Magarshak “Altervital Energy – Nanotechnology in Vivo” (2010)
International Scientific Journal of Alternaеive Energy and Ecology volume 2 (82) pp.
104-108 (2010)
F. Karpeshin, Yu. Magarshak “On the Possible Influence of Resonance Conversion on
Formation of the Organic Structures” ; Springer, Proceedings of ARW NATO
Environmental and Biological Risks of Nanobiotechnology, Nanobionics and Hybrid
Organic-Silicon Nanodevices (Silicon vs. Carbon) 149-164 (2009)
L. Gribov, V. Baranov, Yu. Magarshak “Is “Silicate Life” Possible?” ; Springer,
Proceedings of ARW NATO Environmental and Biological Risks of Nanobiotechnology,
Nanobionics and Hybrid Organic-Silicon Nanodevices (Silicon vs. Carbon) pp 1-8
(2009)
I. Ruban, M. Sharipov, N. Voropaeva, Yu. Magarshak “Modern Risks of the
Antropogenic Influence on Living Spieces: Nano-level Fluctuation”;
Springer, Proceedings of ARW NATO Environmental and Biological Risks of
Nanobiotechnology, Nanobionics and Hybrid Organic-Silicon Nanodevices (Silicon vs.
Carbon) pp 353-378 (2009)
Y. Magarshak, "Alpha-Particles And Pauli Principle In Bara Atom "
Scientific Israel – Technological Advantages (SITA) v.10, No. 4, pp. 171-176 (2008).
Y. Magarshak, “Superresonant Atom Model as an element of the united theory of
matter”. Scientific Israel – Technological Advantages (SITA) vol. 10 pp.145-150 (2008)
Y. Magarshak “The Role of Empirical Relation in the Process of ab initio Modeling in
Chemistry”. Eastern European Journal of Enterprise Technologies Vol. 34 # 4/1 69-75
(2008)
Y. Magarshak Ellectron-Nucleons Resonance Atom Model of valence bonds. J Nuclear
Physics, v. 71 #5, pp 1-9 (2008)
Y. Magarshak On the issue of completeness of the modern conception of atomic and
molecular structure J. The old and new concepts of Physics v 3 (2008)
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L. A. Gribov, Y.B. Magarshak, To the Problem of Formulation of Basic Principles
in the Theory of the Molecular Structure and Dynamics Concepts of Physics vol.V Nr.2
p 191 (2008)
Y.Magarshak To the problem of EPN-resonant mechanism of the stabilization of the
structure of molecules Proceedings of Russian Academy of Sciences volume 415 №5
pp. 1-6 (2007) (Original Russian Text © Yu.B. Magarshak, 2007, published in Doklady Akademii
Nauk, 2007, Vol. 415, No. 5, pp. 600–605)
F.Bogomolov Y.Magarshak Chemical Elements as the States of I-particle. Scientific
Israel-Technological Advantages, vol. 8, issue 3-4 (2007)
Y.Magarshak epn-Resonances and Atom Structure J. of Nuclear Physics, to appear
Y. Magarshak The Resonance Approach to the Formation and Structure of Atoms and
Molecules. Biophysics, vol. 52 no. 1 pp.95-108 (2007)
F.Bogomolov Y.Magarshak Chemical Elements as the States of I-particle; Scientific
Israel-Technological Advantages (SITA) vol. 9, issue 1- 2 pp. 116-119 (2007)
Y.Magarshak, To the problem of completeness of our understanding of the atom
structure. Power and Knowledge N9, 61-62 (2007)
Y.Magarshak, Resonance Atom Model and the Formation of Valence Bonds; Scientific
Israel-Technological Advantages, vol 9 issue 1-2 2007, pp.112-114
F.Bogomolov, Yu.B.Magarshak, ‘ Complementary Algebra and Applications on Neural
Nets’. Biophysics, to appear.
G.Magarshak & Y. Magarshak, ‘Complementary Arithmetics in Molecular
Biology, Physiology and Technology’, Biophysics, accepted.
F.Bogomolov, Y.Magarshak, On commuting operators related to asymptotic symmetries
in the atomic theory; Scientific Israel-Technological Advantages, vol 8, issues 1-2,
pp. 161-165 (2006)
Y.Magarshak, Complementarity as the universal principle. Ecology and life, 3(52) pp.1116 (2006)
Y.Magarshak, "Four-Dimensional Pyramidal Structure of the Periodic Properties of
Atoms and Chemical Elements", Scientific Israel - Technological Advantages vol. 7,
No.1,2 , pp. 134-150 (2006)
Y. Magarshak, A. Sakharov Creative Destruction, in book “Russia without the Soviet
Union”, Moscow, Nauman publishing house pp 116-119 (2006)
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Y.Magarshak, “The end of the Prometheus Era”, International Journal of the alternative
energy and ecology (ISJAEE ) 2,2006
Yuri Magarshak Tabu of the evolution and tabu of the civilization ”, International Journal
of the alternative energy and ecology (ISJAEE ) 3,2006
O.Figovsky, Y.Magarshak. Non-Waste Civiliztion: Utopia or Reality? Letters to
Alternative Energy and Ecology Journal, volume 1 Issue 1, May 2005
O. Figovsky, Yu. Magarshak: Aims of mankind in thousand years to come (in Russian).
Proceedings of XIII International Scientific-Practical Conference on Ecology and Health
of Human Being; Utilization of Waste. Schelkino, Krym, Ukraine, 6-10 Jine, 2005, pp. 719..
О.Фиговский, Ю.Магаршак. Цели человечества в грядущем тысячелетии. Сборник
научных статей 13 международной научно - практической конференции "Экология
и здоровье человека. Охрана воздушного и водного бассейнов. Утилизация
отходов. т.1. с.7-19. Харьков, 2005.
Юрий Магаршак, Евгений Левич. Энергетические инварианты хомобиоценоза.
Сборник научных статей 13 международной научно - практической конференции
"Экология и здоровье человека. Охрана воздушного и водного бассейнов.
Утилизация отходов. т.1. с.20-22. Харьков, 2005.
Ю.Магаршак. Табу эволюции и табу цивилизации. Сборник научных статей 13
международной научно - практической конференции "Экология и здоровье
человека. Охрана воздушного и водного бассейнов. Утилизация отходов. т.1. с.
167- 171. Харьков, 2005.
Олег Фиговский, Юрий Магаршак. Безотходная цивилизация: утопия или
реальность? Сборник научных статей 13 международной научно - практической
конференции "Экология и здоровье человека. Охрана воздушного и водного
бассейнов. Утилизация отходов. т.2. с. 148- 155. Харьков, 2005.
Yu.Magarshak, The third and the fourth dimensions of the chemical elements periodicity,
Biophysics, vol. 50 number 4 (2005)
Yu.Magarshak To the problem of the influence of sun batteries power station on climate;
Ecology and Life, 3, 44-45 (2005)
Yuri Magarshak, To the Problem of Four-Dimensional Symmetries in the Properties of
Chemical Elements; "Scientific Israel - Technological Advantages", volume 7, issue 1-2,
(2005).
Yuri Magarshak, Eugene Levich, Humanity Energy Consumption, Ecology and Life, №2,
42 (2005)
9
Yuri Magarshak and Eugene Levich Energy utilized by a human as a subject of industrial
civilization and as a part of nature. ."Scientific Israel - Technological Advantages",
volume 7, issue 1, (2005).
Y.Magarshak, Intellectual Renaissance, Proceedings of Russian Academy of Natural
Sciences.. - Т. 4. - № 2. - С. 65-68 (2004).
O.Figovsky, Yu.B.Magarshak, "Altera Vitae Civilization: problems and perspectives"
"Scientific Israel – Technological Advantages", vol. 6, No. 3, pp.1-9, 2004.
-----------------------------------------------------------------Magarshak IuB. ‘Analysis of the dynamics of transitions in Leptomonas collosoma
spliced leader RNA and a possible role of gaps upon splicing’. Biofizika. 1997 Nov-Dec;
42(6):1216-23.
Magarshak IuB
42(4):855-63.
‘Dynamic superhelicity in vivo and in vitro’. Biofizika. 1997 Jul-Aug;
Y.Magarshak, ‘Projective geometry of color vision, generating the field
of complex numbers’, Biophysics, 41, 3, 734-743 (1996).
L.H. Kauffman and Y.B. Magarshak, "Vassiliev Knot Invariants and the
Sructure of RNA Foldings ". In book "Knots and applications".,World
Sci.Pub., editor L.H.Kauffman, 343-394 (1995).
T.Krause, Yu.Magarshak, H.Fishman and G.Bittner, ‘Membrane potential and
input resistance are ambiguous measures of sealing of transsected
cable-like structures’, Biophysical Journal, 68: 795-799 (1995).
L.H. Kauffman and Y.B. Magarshak, "Graph Invariants and The Topology of
RNA Foldings’. Journal of Knot Theory and its Ramifications.,
vol.3,No 3 (Special Issue): 233-245 (1994).
G.N.Sarkisov, D.A.Tikhonov, J.Malinsky, Y.Magarshak,"Martinov-Sarkisov
Integral Equation for the Simple Fluids ", Journal of Chemical Physics,
99, 5: 3927-3932 (1993).
J. Malinsky, Y. Magarshak, A. Smolyar, and A. Lipman
“Single-electron transfer in organic molecules “
The Journal of Chemical Physics Vol 98(5) pp. 3968-3971. March 1, 1993
G.N.Sarkisov, D.A.Tikhonov, J.Malinsky, Y. J.Magarshak, "Thermodynamics
and structural properties of a fluid with the square well potential ",
Journal of Structural Chemistry, 34,2: 88-95 (1993).
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Y.Magarshak, C.Benham, J.Malinsky, L.Blumenfeld, "RNA secondary
structure dynamics and the symmetry of nucleic vectors ", Biophysics,
37, 4 (1993).
Y.Magarshak, J.Malinsky, "Single Electron Transfer in Organic Molecules", J. Chem.
Phys., 98, 5: 3968-3971 (1993).
G. Sarkisov, D. Tikhonov, J. Malinsky, and Yu. Magarshak
Martynov–Sarkisov integral equation for the simple fluids
J. Chem. Phys. 99(5) 3926 (01 Sep 1993)
Y.Magarshak, "Double transpositions and the classification of RNA secondary structures
", Biophysics, 38, 5, 886-887 (1993).
Y.Magarshak, "Quaternion Representation of RNA Sequences and Tertiary
Structures ", BioSystems, Elsevier Science Publishers, 30: 21-29 (1993).
A.Kister, Y.Magarshak, J.Malinsky, "The Theoretical Analysis of the
Process of RNA Molecule Self-Assembly ", BioSystems, Elsevier Science
Publishers, 30: 31-48 (1993).
Y.Magarshak, C.Benham, "An Algebraic Representation of RNA Secondary
Structures ", J.Biom. Str. & Dyns., Vol.10, 465-488 (1992).
Yu. Magarshak, J.Malinsky,"A Three-Dimensional Periodic Table ", Nature,
vol.360: 113-114 (1992).
J.Malinsky, Y.Magarshak, "A Green's Function Approach to Long Range
Electron Transfer in Macromolecules ", The Journal of Physical
Chemistry, Vol.96, 7: 2849-2851 (1992).
J.Malinsky, Y.Magarshak, L.Blumenfeld, "Kinetics of Eectron Transfer in
Macromolecules ", Biophysics, 37, 5: 923-926 (1992).
J.Malinsky, Y.Magarshak, "Electron Transfer in Macromolecules: Green's
Function and Diagrammatic Techniques (Continued Fraction
Representation) ", International Journal of Quantum Chemistry, 40, 25:
183-192 (1991).
J.Malinsky, Y.Magarshak, A.D.Joran, "Diagram Techniques for Solving
Schvinger-Dyson Equation: Electron Transfer Pathways in Biological
Molecules ", J.Chem.Phys., 95, 1: 418-432(1991).
V.Stefanov, Y.Magarshak, "Calculation of the production of entropy in
the chain of single-substrate enzymatic reactions ", Biophysics, 28, 3:
560 (1983).
11
V.Stefanov, Y.Magarshak, "Computation of Entropy Production in a Chain
of Enzymes ", Papers of All-Union Institute of Scientific and Technical
Information, USSR, 804: 83-92 (1983).
Y.Magarshak, O.Sokolov, M.Turbovich,"Spectral Analysis of Several
Pseudo-Random Signals in Aqua Media ", Papers of polytechnic Institute,
Leningrad, 2, 31:126-134 (1979).
V.Stefanov.Y.Magarshak, "Description of the Relationship Between the
Concentrations of Metabolites in a Polyenzyme System ", Biophysics, 24,
6: 1025-1028 (1979).
Y.Magarshak,V.Stefanov,"Graphic Method for the Analysis of the
Steady-State Kinetics of Multienzime Systems ", Journal of the Mol.
Biol., 13, 2: 347-352 (1979).
Y.Magarshak, "Use of a Graphical Method for Analysing the Course of
Poly-Enzimatic Reactions ", Biophysics, 57:157-158 (1978).
Y.Magarshak, O.Sokolov,"Correlational Analysis of Several Nonstationary
Acoustic Signals in Aqua Media ", Papers of Polytechnic Institute,
Leningrad, 3: 38-48 (1977).
Y.Magarshak, M.Turbovich, V.Frolov, "Evaluation Error of Statistic
Characteristics of Several Pseudo-Random Signals With Desctete
Sampling", Papers of Institute of Electric Instruments,1: 123-130
(1976).
Y.Magarshak, "Use the Methods of Group Theory for Analysing the Knetics
of Enzymes with Symmetry ", Biophysics, 19, 2: 219-224 (1974).
Y.Magarshak, M.Volkenstein, "Representations of the Enzyme Symmetry
Group and Their use for Solving of Enzymological Problems ",
Biophysics,19, 4: 619-623 (1974).
Y.Magarshak, O.Sokolov, M.Turbovich,V.Frolov, "Evaluation error of
statistic characteristics of several nonstationary random processes with
discrete sampling ", Papers of the 7th All Union Symposium
Representation methods and apparatus analysis of random processes and
fields, Leningrad, 3: 160 (1974).
M.Volkenstein, Y.Magarshak, "Diagrams of Enzyme Kinetics :
Transformation rules ", Proceedings of the Academy of Sciences of the
USSR, 210, 3, 717-720 (1973).
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M.Volkenstein, Y.Magarshak, V.Stefanov, "Transformed Diagrams of Steady
Enzymatic Reactions ", Biophysics, 17, 3: 392-398 (1972).
M.Volkenstein, Y.Magarshak, V.Stefanov, "Group Theory Applied to the
Solution of Kinetics Equations of Enzyme Reactions ", Proceedings of
the Academy of Sciences of the USSR, 204, 2: 474 (1972).
V.Stefanov, Y.Magarshak, M.Volkenstein, "Diagrammatic Method for
Analyzing Ping-Pong Mechanisms of Enzyme Reactions ", Proceedings of the
Academy of Sciences of the USSR, 205, 1: 248 (1972).
M.Volkenstein, Y.Magarshak, V.Stefanov, "Analysis of Enzyme Mechanism by
Graphic Method ", Proceedings of the Academy of Sciences of the USSR,
197, 4: 949 (1971).
M.Volkenstein, Y.Magarshak, V.Stefanov, "Diagrams of Enzyme Systems
which Contain Isozymes ", Proceedings of the Academy of Sciences of the
USSR 197, 5: 1193 (1971).
Y.Magarshak, "Application of the Diagrammatic Method to Enzyme Kinetics
Problems ", Synopsis of theses, Leningrad State University (1971).
B.Goldstein,Y.Magarshak,M.Volkenstein,"Graphical Method of Analysis of
Multienzyme Reactions ", Proceedings of the Academy of Sciences of the
USSR,191, 5: 1120-1123 (1970).
Y.Magarshak, M.Volkenstein, "Rate Formula Using Potential diagrams of
Enzymes with Several Exit Paths ", Proceedings of the Academy of
Sciences of the USSR, 192, 3: 665 (1970).
M.Volkenstein, Y.Magarshak, "Application of the Diagrammatic Method of
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