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Lessons offered by Simon
  • Individual
  • In group
The lessons will be held
  • at his home
  • at your home
Taught subjects
  • Arithmetic
  • Statistics
  • Thermodynamics
  • Precalculus & Calculus
  • College / University Preparation
  • Calculus
Levels
  • All Levels

Mathematics tutor with other 12 years of experience can give tutorials in San Diego.

Methodology

My teaching consists of talking to the student about all of the main topics in the mathematics
courses and distinguishing those which require a special effort to understand the basic concepts
and techniques thoroughly. The progress is checked through the working of homework questions.

Background

The degrees in Physics and Mathematics represent preparation for teaching of these subjects to both secondary school and university students. Having both conducted scientific research investigations
and tutored students extensively both at the secondary school and university level, experience has been gained both in helping the student with the methods of calculations and a better insight into physics
and mathematics.

Rates

Rate for 5 hours of lessons : $13
Rate for 10 hours of lessons : $12

Details

Students from grades 7 to 9 may receive tutorials at a rate of $10/hour.

Lessons offered by Simon
Individual
In group
The lessons will be held
at his home
at your home
Taught subjects
  • Arithmetic
  • Statistics
  • Thermodynamics
  • Precalculus & Calculus
  • College / University Preparation
  • Calculus
Levels
  • All Levels

Simon's resume

Curriculum Vitae

Dr Simon Davis
Research Foundation
of Southern California
8861 Villa La Jolla Drive #13595
La Jolla, CA 92037
U.S.A.

Birthplace: Cambridge, England
Permanent Resident of U.S. since 1970

Education

University Degree Dates

Worcester Junior A.A. Liberal Arts September, 1973
College (summa cum laude) - June, 1978
Worcester, MA 01618

State University of B.S. in Physics and August, 1978
New York Mathematics - May, 1981
Stony Brook, NY 11794 double major
(highest honours)

Trinity College Certificate of October, 1981
Cambridge CB2 1TQ Advanced Study - June, 1982
in Mathematics

University of Ph.D. in Theoretical October, 1982
Cambridge Physics - November, 1985


Appointments


Institution Position Dates

Lyman Laboratory of Postdoctoral and October, 1986
Physics SERC/NATO Fellow -September, 1988
Harvard University
Cambridge, Massachusetts

ICTP Visiting Scientist June, 1986
Trieste, Italy (Dual Appointment) - September, 1986;

Visiting July, 1988
Scientist - Sept. 1989

Blackett Laboratory Academic Visitor October, 1989
Imperial College and Tutor - August, 1990
London

Department of Physics Visiting Senior September, 1990
Brandeis University Scientist - August, 1991
Waltham, Massachusetts

ICTP Visiting January, 1992
Trieste, Italy Mathematician - December, 1992



Research Foundation of Research Scientist Sept.-Dec. 1991;
Southern California Jan. - Sept. 1993

Department of Applied Senior Visiting October, 1993
Mathematics & Scientist - September, 1998
Theoretical Physics & Tutor
University of Cambridge

School of Mathematics Honorary Research January, 1997
& Statistics Associate - December, 2001;
University of Sydney Technical Officer Jan. 1999-Dec. 2000
Level 7

Institut fur Mathematik Alexander von October, 2001
Universitat Potsdam Humboldt Fellow - December, 2002
Institut fur Mathematik Visiting Scientist January, 2003
Universitat Potsdam & - September, 2003
Institut fur Theoretische (SFB 288)
Physik, Freie Universitat
Berlin

Research Foundation of Research Scientist October, 2003-
Southern California and Tutor







Additional Duties

Referee for
(i) Nuclear Physics B
(ii) Proceedings of the Royal Society
(iii) Mathematical Reviews

Awards

1978 Outstanding Humanities Student
Worcester Junior College
1981 Foundation Award, SUNY-Stony Brook
Phi Beta Kappa
External Research Studentship
Trinity College, Cambridge
1982 Senior Scholarship, Trinity College
1984 J. T. Knight Prize
1985 Senior Rouse Ball Studentship
1986 SERC/NATO Fellowship
1996 Royal Society Study Visit Award
1999 Collaborator on ARC Small Grant
- Mathematical Techniques in
Quantum Gravity and Quantum
Cosmology
2000 Collaborator on ARC Small Grant
- Higher-Derivative Correction
to Standard Inflationary Cosmology
2001 Alexander von Humboldt Research
Fellowship

Seminars given

Jan. 1983 `Vacuum Energy in Gauged Extended
Supergravity', Relativity Group,
University of Cambridge
Mar. 1983 `Vacuum Energy in Gauged Extended
Supergravity', Cambridge/Imperial
College Meeting at Cambridge
Mar. 1984 `Quantum Fields in Anti-de Sitter
Space', Relativity Group,
University of Cambridge
Nov. 1985 `Asymptotically Anti-de Sitter
Space-times', Relativity Group,
University of Cambridge
Sept. 1986 `Geometry of Yang-Mills Theories',
ICTP, Trieste
Nov. 1987 `Four-Point Function on a Surface
of Infinite Genus', Harvard
University
Apr. 1988 `Poincare Series for a Class of
Infinitely Generated Kleinian
Kleinian Groups', Harvard University
Oct. 1988 `A Review of Witten's Paper on
2+1-Dimensional Gravity', ICTP,
Jan. 1989 `Large-Order String Perturbation
Theory', Relativity Group,
University of Cambridge
May 1989 `String Amplitudes on Effectively
Closed Infinite-Genus Surfaces',
ICTP, Trieste
Mar. 1990 `Genus-dependent Divergences in
Bosonic String Perturbation Theory',
Imperial College, London
Mar. 1990 `Divergences in Bosonic String
Perturbation Theory', Queen Mary
College, London
May 1990 `On the Origin of Divergences in
Bosonic String Perturbation Theory',
ITP-Stony Brook
Feb. 1991 `Resolution of the Integration
Region Problem for the Moduli
Space Integral', Brandeis University
Dec. 1992 `Divergences in the Moduli Space Integral and
Accumulating Handles in the
Infinite-Genus Limit', ICTP, Trieste
Sept. 1993 `Configurations of Handles and
Divergences in the String Partition
Function', Imperial College, London
Oct. 1993 `Large-Order Divergences in Bosonic String
Perturbation Theory',
ITP-Stony Brook
Nov. 1993 `Multi-loop Amplitudes in Bosonic
String Theory', Relativity Group,
University of Cambridge
Jan. 1995 `Modular Invariance and the
Finiteness of Superstring Theory',
Relativity Group, University of
Cambridge
Apr. 1995 `Force Unification and the Geometry
of Internal Symmetry Spaces',
Relativity Group, University of
Cambridge
May 1995 `Large-Genus Superstring Amplitudes
and Selection of Superstring Vacua',
Ecole Normale Superiore, Lyon,
France
June 1995 `Higher-Genus Superstring Amplitudes
and the Finiteness of Superstring
Theory', Universite de Lille I,
Lille, France
Oct. 1996 `Boundary Effects in String Theory'
Journal Club Talk, Nonlinear
Analysis Group, University of Sydney
Oct. 1996 `Division Algebras and Force Unification',
Univ. of Sydney/UNSW Joint Colloquium,
University of Sydney
Nov. 1996 `Force Unification and String Effective Actions in Ten
Dimensions', Department of Mathematical Physics
and Physics, University of Adelaide
Dec. 1996 `Particle Phenomenology,
Supersymmetry Breaking and
Summability of Superstring
Perturbation Series', Australian
National University, Canberra
Jan. 1997 `Higher-Derivative Superstring
Quantum Cosmology', Journal Club
Talk, Nonlinear Analysis Group,
University of Sydney
Aug. 1997 `Mathematics of String Theory',
Mathematics Half-Hour Seminars,
University of Sydney
Oct.-Dec. String Theory Seminars
1997 1. Ultraviolet Divergences in Quantum Gravity
2. Strings and Dual Resonance Models
3. Light-Cone Gauge Quantization
of the Bosonic String
4. Covariant Quantization of the
Bosonic String
5. String Effective Actions and
Higher-Order Corrections to
General Relativity
6. Light-Cone Gauge Quantization
of the Superstring
7. Superstring Actions with Manifest
Space-time Supersymmetry
8. Bosonic String and Superstring Amplitudes
9. Teichm{\"u}ller Space and Modular
Groups
University of Sydney
Dec. 1997 `The Hamilton-Jacobi Equation in
Higher-Derivative Quantum
Cosmology', UNSW
Jul. 1998 `Higher-Derivative Quantum
Cosmology' ACGRG2, University of
Sydney
Mar. 1999 `Mathematical Applications of
String Theory: Spin Structures
on Riemann Surfaces and the
Perfect Numbers', School of
Mathematical Sciences Seminar
Series, University of Technology,
Sydney
Mar. 1999 `Differential Equations in Higher-
Derivative Quantum Cosmology',
Univ. of Sydney/UNSW Joint
Colloquium, University of New South Wales
May 1999 `Boundary Conditions and the
Wavefunction in Supersymmetric
Quantum Cosmology', Applied
Mathematics Seminar, University
of Sydney
July 1999 `Mathematical Applications of
String Theory: Spin Structures on
Riemann Surfaces and the Perfect
Numbers' XXI Journees Arithmetiques,
Pontifica Universitas Laternensis,
Rome
Nov. 2001 `The Differential Equation for the
Quantum Cosmological Wave Function
of a Quadratic Gravity Theory at Early
Times in the Expansion of the Universe',
Workshop on Partial Differential
Equations: Operator Algebras and
Microlocal Analysis,
Universit{\"a}t Potsdam
Jan. 2002 `Boundary Conditions and the Physical
Interpretation of the Quantum
Cosmological Wave Function', Partielle
Differentialgleichungen Gruppe,
Universit{\"a}t Potsdam
Aug. 2002 `Conformal Transformations and the
Vanishing of the Cosmological Constant
at Classical Scales', Max Planck
Institut f{\"u}r Gravitationsphysik,
Golm
May 2003 Lectures on Moduli Space
1. The Domain of String Perturbation Theory
2. Universal Teichm{\"u}ller Space
3. The Volume of Infinite-Genus Moduli Space
Freie Universit{\"a}t Berlin
Nov. 2003 `Properties of the Fundamental
Quantum Theory at Early Times in
the Expansion of the Universe',
Department of Physics, University
of California at San Diego









Other Contributions to Conferences

Aug. 1995 `Symmetric Variations of the Metric
and Extrema of the Action for Pure
Gravity', Poster Session, 14th
International Conference on General
Relativity and Gravitation, Firenze,
6-12 August 1995
May 1997 `Dependence of the String Tension
on the Compactification Radius',
Poster Session, QULEN '97, The
International Conference on Quark
and Lepton Nuclear Physics, Osaka,
20-23 May 1997








Tutorials


1983-4 General Relativity, University of Cambridge

1984 Statistical Mechanics, University of Cambridge

1986 General Relativity; Statistical Mechanics, University of

1989 Introductory Analysis; Comprehensive Physics, Imperial College,
London

1993-4 Methods; Electrodynamics, University of Cambridge

1994-5 Differential Equations; Quantum Mechanics; Foundations of Quantum
Mechanics; General Relativity; Methods; Electrodynamics; Statistical
Physics, University of Cambridge

1995-6 Differential Equations; Foundations of Quantum Mechanics; Methods of
Mathematical Physics; Quantum Mechanics; General Relativity; Linear
Algebra; Statistical Physics; Special Relativity, University of
Cambridge

1997 Differential Calculus and Linear Algebra; Life Sciences Mathematics;
Analysis; Vector Calculus; Fourier Series and Differential Equations;
Optimization; Numerical Methods, St. John's College, University of
Sydney

1998 Differential Calculus; Vector Calculus and Complex Variables,
University of Sydney

1999 First-Year Engineering Mathematics, University of Western Sydney

2006 Calculus; Linear Algebra; Graph Theory; Electromagnetism, University
of California at San Diego

2007 Particle and Nuclear Physics; Metric and Topological Spaces,
University of Cambridge















List of Publications

B. Allen and S. Davis, Vacuum Energy in Gauged
Extended Supergravity, Phys. Lett. B124
(1983) 353-356.

S. Davis, Definition of Conserved Quantities in
Asymptotically Anti-de Sitter Space-times,
Phys. Lett. B166 (1986) 127-129.

C. J. C. Burges, D. Z. Freedman, S. Davis and G. W. Gibbons,
Supersymmetry in Anti-de Sitter Space, Ann. Phys. 167
(1986) 285-316.

S. Davis, A Constraint on the Geometry of
Yang-Mills Theories, J. Geom. Phys. 4 (1987)
405-415.

S. Davis, On the Domain of String Perturbation
Theory, Class. Quantum Grav. 6 (1989) 1791-1803.

S. Davis, Genus-Dependent Divergences in
Bosonic String Perturbation Theory, Class.
Quantum Grav. 7 (1990) 1887-1894.

S. Davis, Configurations of Handles and the
Classification of Divergences in the
String Partition Function, Class. Quantum
Grav. 11 (1994) 1185-1200.

S. Davis, The Four-Point Function on a Surface
of Infinite Genus, Mod. Phys. Lett. A9
(1994) 1299-1307.

S. Davis, Divergences in the Moduli Space
Integral and the Accumulating Handles
in the Infinite-Genus Limit, J. Math. Phys.
36 (1995) 648-663.

S. Davis, The Bosonic String Measure at Two
and Three Loops and Symplectic
Transformations of the Volume Form, Lett.
Math. Phys. 34 (1995) 407-413.

S. Davis, Infinite-Genus Surfaces and the
Universal Grassmannian, Phys. Lett. B359
(1995) 93-100.

S. Davis, Symmeteric Variations of the Metric
and Extrema of the Action for Pure Gravity,
Gen. Rel. Grav. 30 (1998) 345-377.

S. Davis, Summability of Superstring Theory,
Phys. Lett. B432 (1998) 317-325.

S. Davis, Higher-Derivative Quantum Cosmology,
Gen. Rel. Grav. 32 (2000) 541-551.

S. Davis and H. Luckock, The Effect of Higher-Order
Curvature Terms on String Quantum Cosmology, Phys.
Lett. B485 (2000) 408-421.

S. Davis, Scalar Field Theory and the
Definition of Momentum in Curved Space,
Class. Quantum Grav. 18 (2001) 3395-3425.

S. Davis and H. Luckock, The Quantum Theory of
the Quadratic Gravity Action for Heterotic
Strings, Gen. Rel. Grav. 34 (2002) 1751-1765.

S. Davis, On the Absence of Large-Order Divergences
in Superstring Theory, Fortschr. der Physik
51 (2003) 22-61.

S. Davis, A Rationality Condition for the Existence
of Odd Perfect Numbers, Int. J. Math. Mathemat.
Sci. 2003(20): 1263-1291.

S. Davis, The Quantum Cosmological Wavefunction at
Very Early Times for a Quadratic Gravity Theory,
Class. Quantum Grav. 20 (2003) 2871-2881.

S. Davis, On the Existence of a Non-Zero Lower Bound
for the Number of Goldbach Partitions of an Even
Integer, Int. J. Math. Mathemat. Sci. 2004 (15):
789-798.

S. Davis, Effectively Closed Infinite-Genus Surfaces
and the String Coupling, Int. J. Mod. Phys. A20
(2005) 821-850.

S. Davis, Connections and Generalized Gauge Transformations,
Int. J. Geom. Meth. Mod. Phys. 2 (2005) 505-542.

S. Davis, Quantum Theory and the Category of Complex Numbers,
Int. J. Theor. Phys. 45 (2006) 1914-1929.

S. Davis, Genus-Dependence of Superstring Amplitudes, Phys.
Rev. D74 (2006) 106003: 1-13.

S. Davis, Energy in the Very Early Universe, Phys. Lett. B649
(2007) 299-309.

S. Davis, Boundary Effects in String Theory and the Effective
String Coupling, Mod. Phys. Lett. A23 (2008) 1921-1927.

S. Davis, Mass Mixing between Generations of Quarks and Neutrinos,
Hadr. J. 31 (2008) 543-552.

S. Davis, A Finite Algorithm for the Solution to an Algebraic
Equation, Int. J. Alg. 3(10) (2009) 449-460.

S. Davis, Coset Supersymmetry from Twelve Dimensions, Il Nuovo Cim.
124B (2009) 947-958.

S. Davis, A Mechanism for Obtaining a Rapidly Decreasing Cosmological
Term at Classical Scales, Gen. Rel. Grav. 41 (2009) 2361-2380.

S. Davis, The String Theoretical Description of Hadron Jets, Hadr. J.
32(2009) 609-622.

S. Davis, A Theoretical Explanation of the Cabibbo Angle,
Hadr. J. 32 (2009) 623-628.

S. Davis, The Quasilocal Supercharge and Energy of Matter in
a Space-Time of Approximately Constant Curvature,
Hadr. J. 33 (2010) 71-98.

S. Davis, The Valence Quark Momentum in the Nucleon,
Hadr. J. 33 (2010) 99-106.

S. Davis and B. K. Davis, A Complexity Minimization Principle for
Dynamical Processes, Int. J. Math. Anal. 4 (2010) 2243-2259.

S. Davis, Gravitational Field Equations with a New Tensor Term with a
Vanishing Covariant Derivative, Il Nuovo Cim. 125B (2010) 1193-1199.

S. Davis, The Non-Existence of Observable States with Fractional Charge in
${\Bbb C}{\Bbb P}^2$ Models, Hadr. J. 33 (2010) 613-622.

S. Davis, Holomorphic Factorization of Superstring Scattering Amplitudes,
Commun. Theor. Phys. 55 (2011) 1-5.

S. Davis, The Quantum Consistency of the Ten-Dimensional Heterotic String
Effective Action, Commun. Theor. Phys. 55 (2011) 857-862.

S. Davis, The Quantum Cosmological Wavefunction at Very Early Times and the
Weyl Hypothesis, New Adv. Phys. 5 (2011) 37-47.

S. Davis, String Compactifications and the Regge Trajectories for Resonances
of the Strong Interactions, Int. J. Pure and Applied Math. 70 (2011) 25-38.

S. Davis, A Computation of the Partial Width $Z^0 \to \ell^+ \ell^-$,
Hadr. J. 34 (2011) 301-318.

S. Davis, The Uncertainty Principle and Large-Genus Surfaces,
J. Uncertain Systems 6(1) (2012) 61-70.

S. Davis, Quantization of Charge in the Standard Model, Global J. Pure
Applied Math, 8(3) (2012) 287-293.

S. Davis, Univalent Functions and $Diff(S^1)/S^1$, Acta Mathematica Sinica,
English Series, 28(6) (2012) 1233-1236.

S. Davis, The Most Probable Configuration for a Quadratic Gravity Model,
Bull. Roy. Soc. Sci. Liege 81 (2012) 101-120.

S. Davis, Supersymmetry and the Hopf Fibration, Appl. Gen. Top.
13 (2012) 103-113.

S. Davis, The Truncation and Renormalizability of the Superstring and
Heterotic String Effective Actions, Rept. Math. Phys.
69 (2012) 383-418.

S. Davis, Curvature and the Planck Constant, Pac. J. Appl. Math. 5 (2013).

S. Davis, The Equipartition Theorem and the Temperature of the Cosmic
Background Radiation, J. Phys. and Astronomy. 2 (2013).

S. Davis, The Gravitational Action and Consistency of the Classical
and Quantum Theories, J. Phys. and Astronomy.

S. Davis, Supersymmetric Fixed Points for Elementary Particle Masses,
Balk. Phys. Lett. 21 (2013) 1-15.

S. Davis, An Auxiliary Polynomial aligned with the Fermat Equation,
Adv. Studies Contemp. Math. 23 (2013) 587-605.

S. Davis. The Group $E_6$ and the Formulation of String Theory, Bull. Pure
Appl. Sci., Section E: Math. & Stat. 32 (2013) 141-159.

S. Davis, Cantor Manifolds and Compact Spaces, Balk. J. Geom. Appl. 19
(2014) 60-72.

S. Davis, The Effect of Vacuum Polarization on the Propagation of Charged
Particles and Light, Rev. Bras. Aplic. Vac. 32 (2014) 33-42.

S. Davis, A Resolution of the Integration Region Problem for the Supermoduli
Space Integral, Int. J.Mod. Phys. A29 (2014) 1450190: 1-60.

S. Davis, Motion in a Medium Composed of Particles and Antiparticles,
Global J. of Sci. Frontier Res. 14(3-A) (2014) 15-25.

S. Davis, Arithmetical Sequences for the Exponents of Composite Mersenne
Numbers, Notes on Number Theory and Discrete Mathematics 20 (2014)
19-26.

S. Davis, The Algebraic Framework of the Fundamental Interactions,
Hadr. J. 37 (2014) 669-696.

S. Davis, The Intrinsic Length of a Closed Geodesic on a Riemann Surface and
the Fundamental Domain of the Modular Group, J. Adv. Math. Appl. 3(2)
(2014) 1-8.

S. Davis, The Mass of the Ninth Resonance in the Pseudoscalar Multiplet, Hadr. J.
38 (2015) 31-52.

S. Davis, The Reduction of the Exceptional Groups of String Theory and the Standard
Model, Quantum Phys. Lett. 4(1) (2015) 1-5.

S. Davis, Discrete and Continuous Indices, Research & Reviews: Discrete Math. Structures,
2(2) (2015) 25-37.

S. Davis, Quantum Variation about Geodesics, Applied Mathematics and Sciences: An
International Journal, Vol. 2, No. 1 (2015) 1-15.

S. Davis, The Coulomb Term in the Atomic Mass Formula, Hadr. J. 38 (2015) 173-196.

S. Davis, Soft Photons and the Range of the Electromagnetic Interactions in
a Medium composed of Particles and Antiparticles, Math. Sci. Lett. 4(3) (2015)
219-222.

S. Davis, The Embedding of Maximally Symmetric Hypersurfaces in Supersymmetric Theories,
Int. J. Geom. 4 (2015) 69-72.

S. Davis, Prime Values of Meromorphic Functions and Irreducible Polynomials,
Notes on Number Theory and Discrete Mathematics 21 (2015) 36-39.

S. Davis, String Field Solutions and Perturbation Series, Pac. J. Applied
Math. 7 (2016) 143-147.

S. Davis, The Quantum Consistency of the Twelve-Dimensional Theory, Int. J.
Mod. Phys. A31 (2016) 1650010: 1-20.

S. Davis, Physical Consistency of Theories with Fermions in the Division
Algebras, Quantum Phys. Lett. 5 (201ons and Irreducible Polynomials, 6) 1-5.

S. Davis, The Relation between Finiteness and Unitarity in Superstring Theory:
Froissart-Gribov Bounds and Spin, SPIN 6 (2016) 1-8.

S. Davis, The Phase Space of Higher-Derivative Gravity Theories, J. Nonl. Syst. Appl.
5 (2016) 95-99.

S. Davis, Reduction over Coset Spaces and Residual Gauge Symmetry, J. Gen.
Lie Theory Appl. 10 (2016): 249-256.

S. Davis, Boundary Value Problems at Infinite Genus, J. Math. Research.
9 (2017) 146-154.

S. Davis, Particles and General Coordinate Transformations, Hadr. J. 40 (2017) 57-70.

S. Davis, A Conjecture on Degrees of Algebraic Equations, Notes Number Theory
and Discrete Mathematics 23 (2017) 84-90.

S. Davis, The Intersection Form on Four-Manifolds and Exceptional Group Symmetries,
Quantum Phys. Lett. 6 (2017) 91-93.

S. Davis, The Distribution of Prime Pairs Differing by 2, J. Discr. Math.
Sci. Crypt. 20 (2017) 1053-1068.

S. Davis, Legendre's Conjecture, Int. J. Math. & Stat. 19 (2018) 100-112.

S. Davis, Galois Theory and the Uniformization of Riemann Surfaces,
Adv. Math. Sci. Appl. 27 (2018) 45-63.

S. Davis, A Physical Theory of Dynamics with the Invariance of a Sixteen-Dimensional Algebra,
Algebras, Groups and Geometries 35 (2018) 93.

S. Davis, Zeta Functions from Graphs, AKCE Int. J. Graphs & Combinatorics 15 (2018)
224-228.

S. Davis, A Condition on the Masses of Composite Particles, Bull. Pure Appl. Sci.
Sect. E: Mathematics & Statistics, 37 (2018) 208-222.

S. Davis, The Coset Space of the Unified Field Theory, Appl. Sci. 20 (2018) 54-101.

S. Davis, Nonperturbative Contributions to the Massive Propagator in a
Class of Strong Interactions, Bull. Pure Appl. Sci. Sect. D: Physics 37 (2018)
137-145.

S. Davis, Supersymmetry and the Magnetic Moment, Quantum Phys. Lett. 7 (2018) 47-50.

S. Davis, Quantum Riemann Surfaces and the Measure of Noncommutativity, Quantum Phys.
Lett. 7 (2018) 51-56.

S. Davis, Realizations of Three-Dimensional Group Actions, Int. Res. J. Pure Algebra
9 (2019) 1-7.

S. Davis, The Classification of Riemann Surfaces and Conditions on the Quantum Theory,
Ann. Acad. Rom. Sci. Ser. Math. Appl. 11 (2019) 24-48.

S. Davis, Hyperelliptic Curves and Arithmetic Functions, Int. J. Geom. 8 (2019) 46-54.

S. Davis, Analytic Continuation of Functions and Uniformization of Riemann Surfaces,
Functional Anal. Approx. Comp. 11 (2019) 39-51.

S. Davis, Sums of Reciprocals of Integers, Notes on Number Theory and Discrete Mathematics
25 (2019) 1-7.

S. Davis, Estimate of Integrals within the Fundamental Region of the Modular Group,
Pac. J. Appl. Math. 9 (2019) 271-287.

S. Davis, Parallelizability of the Basic Four-Geometries, Balkan J. Geom. Appl. 24 (2019) 6-17.


S. Davis, Goldbach Partitions and Norms of Cusp Forms, J. Num. Anal. Approx. Theory
48 (2019) 16-31.

S. Davis, Renormalization and Dimension, to be published in Int, J. Math. Mod. Meth. Appl.
Sci.

S. Davis, Superstring-Derived Theories and Improved Renormalizability
Properties, to be published in Anal. Theory Appl.

S. Davis, Prime Divisors and the Perfect Numbers,
to be published in Adv. Theor. Appl. Math.

S. Davis, Partitions in Function Fields, to be published in J. Inf. Comput. Sci.

S. Davis, The Existence of Instantons in String Theory, to be published in
Balkan Phys. Lett.

S. Davis, Homology Calculations and Homotopy Groups, to be published in Alg. Lett.

S. Davis, The Generalized Geometric Structure of String Theory, to be published in
Adv. Theor. Appl. Math.

S. Davis, Number Fields and Quantum Theory, to be published in Int. J. Math. Computer
Science

S. Davis, Sequences of Prime Exponents and Compositeness, to be published in Int. J. Math.
Comp.

S. Davis, Nontrivial Zeros of L-Functions, to be published in J. Interdisciplinary Math.

S. Davis, Twistors and Superstrings, to be published in Int. J. High Energy Phys.

S. Davis, The Geometry of Mass Distributions, to be published in Nonlinear Dyn. Syst.
Theory.

Written Work

S. Davis, Quantum Fields in Anti-de Sitter Space, Knight Prize
Essay (1984)

S. Davis, Supersymmetry in Anti-de Sitter Space, University of
Cambridge Ph. D. Thesis (1985).

S. Davis, A Proof of the Odd Perfect Number Conjecture, RFSC-04-01 (2004).

S. Davis, A Method for Generating Mersenne Primes and the Extent of
the Sequence of the Even Perfect Numbers, RFSC-04-02 (2004).

S. Davis, A Recursion Relation for the Number of Goldbach Partitions
of an Even Integer, RFSC-04-06 (2004).

S. Davis, Functional Relations for Roots of Polynomials, RFSC-05-02 (2005).

S. Davis, N=2 Supersymmetry in Curved Space, RFSC-05-05 (2005).

S. Davis, The Riemann Hypothesis, RFSC-05-06 (2005).

S. Davis, On the Physical Interpretation of the Breit-Wigner Formula,
RFSC-07-10 (2007).

S. Davis, A New Prime Algorithm, RFSC-07-12 (2007).

S. Davis, The Common Factor of an Integer Solution to the Generalized Fermat
Equation with Degrees Larger than 2, RFSC-08-01 (2008).

S. Davis, Matter-Anti-Matter Antisymmetry and the Weak Interactions, RFSC-08-06 (2008).

S. Davis, The Momentum Space Propagator for Decaying Particles, RFSC-09-04 (2009).

S. Davis, Nonlinear Quantization of Field Theories, RFSC-09-13 (2009).

S. Davis, The Moduli Space of Two-metrics in Four-Dimensional
Gravity, RFSC-09-14 (2009).

S. Davis, On the Finiteness of Superstring Theory after Supersymmetry
Breaking, RFSC-09-15 (2009).

S. Davis, Transcendental Numbers and Finite Algebraic Relations, RFSC-09-16 (2009).

S. Davis, Interacting Higher-N Supersymmetric Theories in Curved Spaces of
Constant Curvature, RFSC-09-17 (2009).

S. Davis, The Boundary of Conformally Compactified Space-Times and Physical
Configurations in the Interior Region, RFSC-09ons aons and Irreducible Polynomials, nd Irreducible Polynomials, -18 (2009).

S. Davis, The Four-Dimensional Diffeomorphic Poincare Conjecture, RFSC-09-19 (2009).

S. Davis, Local Gauge-Invariant Fields and Nonlocal Operators in Unified Field
Theories, RFSC-09-20 (2009).

S. Davis, Primes in Arithmetic Sequences and the Goldbach Partitions, RFSC-09-22 (2009).

S. Davis, The Path Integrals for String Theory and Quantum Gravity, RFSC-09-24 (2009).

S. Davis, Approximate Roots to a Thue Equation, RFSC-09-31 (2009).

S. Davis, Interactions in Infinite Dimensions, RFSC-09-33 (2009).

S. Davis, The Matching of the Quantum Cosmological Wavefunctions of the
Quadratic Gravity Model, RFSC-09-34 (2009)

S. Davis, Solutions to Differential Equations in Nested Form, RFSC-12-01 (2012).

S. Davis, Parallelizability of Four-Manifolds in Quantum Gravity, RFSC-12-03 (2012).

S. Davis, String-Theoretical Basis for the Dimensional of Canonical
Phase Space, RFSC-12-05 (2012).

S. Davis, The Homology and Homotopy Groups of Hermitian Symmetric
Spaces, RFSC-12-08 (2012).

S. Davis, The Automorphisms of the Mapping Class Groups of Punctured
Surfaces, RFSC-12-09 (2012).

S. Davis, Fermat's Theorem and Irreducibility, RFSC-13-01 (2013).

S. Davis. Summation over the Gravitational Instantons and the
Temperature of the Cosmic Background Radiation, RFSC-13-02 (2013).

S. Davis, The Scalar Potentials of the Supersymmetric Phase and the Grand
Unified Theory, RFSC-13-03 (2013).

S. Davis, Instantons and Point-Like Structure in Nonperturbative String Theory,
RFSC-13-04 (2013).

S. Davis, Wilson Loop Variables and Global Lagrangians, RFSC-13-06 (2013).

S. Davis, Curves of Infinite Genus and the Zeta Function, RFSC-13-07 (2013).

S. Davis, The Exceptional Group Symmetry of the Four-Dimensional
Heterotic String Effective Action, RFSC-13-08 (2013).

S. Davis, The Mass Spectrum of String States in Anti-de Sitter Space, RFSC-13-09 (2013).

S. Davis, Goldbach Partitions and Norms of Cusp Forms, RFSC-13-10 (2013).

S. Davis, The Neutrality of Massless Fields, RFSC-13-14 (2013).

S. Davis, States on the Ideal Boundary, RFSC-13-15 (2013).

S. Davis, Supermanifolds in the Superstring Path Integral, RFSC-14-01 (2014).

S. Davis, Gauge Theory on $S_3$, RFSC-14-02 (2014).

S. Davis, The Continuum Hypothesis, RFSC-14-05 (2014).

S. Davis, Primes of the Form $2p+1$, RFSC-14-06 (2014).

S. Davis, New Factors in the Quantum Numbers of Nuclei, RFSC-14-07 (2014).

S. Davis, Uniqueness of the Potential, RFSC-14-08 (2014).

S. Davis, Enumeration of Primitive Elements of the Schottky Group
and the Lengths of Closed Geodesics, RFSC-14-09 (2014).

S. Davis, The Prime Counting Function Inequality, RFSC-14-11 (2014).

S. Davis, Desingularization of Black Hole Space-times, RFSC-14-12 (2014).

S. Davis, The Dirac Quantization and Poincare Duality, RFSC-14-15 (2014).

S. Davis, Instantons and the Point Particle Field Theory derived from
Strings, RFSC-14-16 (2014).

S. Davis, String Worldsheets with Boundaries, RFSC-14-20 (2014).

S. Davis, Higher-Genus Contributions to the Supergravity Action,
RFSC-14-21 (2014).

S. Davis, The Effect of Infinite-Genus Surfaces in Generalized Yang-Mills
Theories, RFSC-14-22 (2014).

S. Davis, The Spherical Model in Particle Phenomenology, RFSC-14-24 (2014).

S. Davis, The Contributions of Fermions to the Energy at Very
Early Times, RFSC-14-25 (2014).

S. Davis, Linear Independence of Complex Zeros of the Zeta Function,
RFSC-14-31 (2014).

S. Davis, Exponential Sums and Prime Partitions, RFSC-14-32 (2014).

S. Davis, Conformally Flat Hypersurfaces and Prime Manifolds,
RFSC-14-33 (2014).

S. Davis, The Finiteness Problem for Polynomial Differential Equations,
RFSC-14-34 (2014).

S. Davis, Conserved Charges in Stochastic Dynamics, RFSC-14-36 (2014).

S. Davis, The Unification of Symmetries in the Bosonic and Fermionic
Sectors of the Strong Interactions, RFSC-14-37 (2014).

S. Davis, Anomaly Cancellation in String Theory, RFSC-14-38 (2014).

S. Davis, Cardinality and Geometry, RFSC-14-39 (2014).

S. Davis, The Scale for the Existence of Conserved Quantities for the
Gravitational Field, RFSC-15-01 (2015).

S. Davis, The Exponentiation of Transcendence, RFSC-15-03 (2015).

S. Davis, The Finite Range of Interactions and Bound States, RFSC-15-04 (2015).

S. Davis, Quadratic Forms and Diophantine Equations, RFSC-15-05 (2015).

S. Davis, The Formulation of Field Equations by Frenet Vectors, RFSC-15-06 (2015).

S.Davis, Quantum Theory, Manifolds and Matter, RFSC-15-07 (2015).

S. Davis, Coverings of Surfaces and Nonperturbative Effects in String Theory,
RFSC-15-08 (2015).

S. Davis, Propagation on Spaces with Noninteger Dimension and the
Gravitational Force, RFSC-15-10 (2015).

S. Davis, Nonoverlapping Partitions of a Surface, RFSC-15-11 (2015).

S. Davis, The Nonperturbative State of Negative energy, RFSC-15-12 (2015).

S. Davis, The Bound for Coefficients of Univalent Functions on the
Superdisk, RFSC-15-14 (2015).

S. Davis, Compositeness of Vector Bosons in Ten Dimensions and the Reduction
to Four Dimensions, RFSC-15-16 (2015).

S. Davis, Vanishing of the Cosmological Term under a Finite Conformal
Transformation of the Hypersurface, RFSC-15-17 (2015).

S. Davis, The Existence of Interaction Models with Higher Supersymmetry
in Curved Space, RFSC-15-18 (2015).

S. Davis, The Physical States of a Boundary Conformal Field Theory, RFSC-15-22 (2015).

S. Davis, Galois Symmetries and Special Values of L-Functions, RFSC-15-24.

S. Davis, Supersymmetry Constraints with $\Lambda\ne 0$, RFSC-15-25 (2015).

S. Davis, Superstring Amplitudes and Elementary Particles, RFSC-15-26 (2015).

S. Davis, Bounded Rigidity and Quantum Fluctuations of the Metric, RFSC-15-30 (2015).

S. Davis, Renormalization Group Flow on Surfaces with Boundaries, RFSC-15-31 (2015).

S. Davis, Magnetic Variables in the Very Early Universe, RFSC-15-32 (2015)

S. Davis, The Bounds for the Coefficients in the Limit for Manifolds with Smooth Structures,
RFSC-16-01 (2016).

S. Davis, Stability of Envelopes of Classical Trajectories under the Formation of
New Types of Singularities, RFSC-16-02 (2016).

S. Davis, A Condition for Periodicity for Aliquot Sequences of Large Integers,
RFSC-16-03 (2016).

S. Davis, Instantons and Nonperturbative Series, RFSC-16-04 (2016).

S. Davis, The Correlation between Two-Qubit States, RFSC-16-06 (2016).

S. Davis, Rationality in Hodge Theory, RFSC-17-01 (2017).

S. Davis, Quantization about Rotating String Solutions, RFSC-17-02 (2017).

S. Davis, The Number of Diffeomorphism Structures on Four-Manifolds in the
Path Integral for Quantum Gravity, RFSC-17-03 (2017).

S. Davis, Accessible States in Space and the Geometric Complexity, RFSC-17-04 (2017).

S. Davis, Lorentzian Path Integrals and Moduli Space, RFSC-17-05 (2017).

S. Davis, Energy on the Ideal Boundary, RFSC-17-06 (2017).

S. Davis, The Classical Limit of Quantum Commutation Relations, RFSC-17-07 (2017).

S. Davis, The Mode Expansion of the String Fields, RFSC-17-08 (2017).

S. Davis, Soliton Sectors of Sigma Models and the Fractional Quantum Hall Effect,
RFSC-17-09 (2017).

S. Davis, The Equation for the Wavefunction in Nonrelativistic
Quantum Mechanics, RFSC-17-10 (2017).

S. Davis, Relativistic Quantum Scalar Fields, RFSC-17-11 (2017).

S. Davis, A Physical Model constructed of Purely Electromagnetic
and Gravitational Forces, RFSC-17-12 (2017).

S. Davis, Intersection Products and Division Algebras, RFSC-17-13 (2017).

S. Davis, A Theory of Interactions with Quadratic Integrals, RFSC-17-14 (2017, rev. 2019)).

S. Davis, Almost Fuchsian Groups and Green Functions, RFSC-17-15 (2017).

S. Davis, The Generation of the Division Algebra $K_\nu$ and Diffeomorphism
Structures, RFSC-17-16 (2017).

S. Davis, The Quantum Cosmological Constant, RFSC-17-17 (2017).

S. Davis, The Rotation of Galaxies and the Cosmological Metric, RFSC-17-18 (2017).

S. Davis, The Rationality of Coefficients in Series Expansions of Amplitudes
in Quantum Electrodynamics, RFSC-17-19 (2017).

S. Davis, The Generators of the Extensions of the Rational Numbers to Quadratic
Fields, RFSC-17-20 (2017).

S. Davis, Spherical Symmetry of Spinless Particles, RFSC-17-21 (2017).

S. Davis, The Action of the Absolute Galois Group on Twistor Diagrams, RFSC-17-22 (2017).

S. Davis, Extremal Disks and Superstring Amplitudes, RFSC-17-23 (2017).

S. Davis, The Average Complexity of Compound Sequences, RFSC-17-24 (2017).

S. Davis, The Number of Products of $N$ Elements in a Nonassociative
Algebra, RFSC-17-25 (2017, rev. 2019).

S. Davis, Quantum Theory of the Fermion Field near Classical Scales,
RFSC-17-26 (2017).

S. Davis, The Nonrelativistic Matrix Differential Equation for Spinors,
RFSC-17-27 (2017).

S. Davis, The Nonrelativistic Wave Equation with the Harmonic Oscillator
Potential, RFSC-17-28 (2017).

S. Davis, The Quantization of Energy Levels of the Hydrogen Atom, RFSC-17-29 (2017).

S. Davis, The Wavefunction in Classical Models of Nuclear Potentials, RFSC-17-30 (2017).

S. Davis, Tunneling through a Potential Barrier in the Nonrelativistic Theory,
RFSC-17-31 (2017).

S. Davis, Solution to a Matrix Wave Equation with a Linear Potential, RFSC-17-32 (2017).

S. Davis, The Energy Levels in a Quartic Potential, RFSC-17-33 (2017).

S. Davis, Methods for Solving the Nonrelativistic Wave Equation, RFSC-17-34 (2017).

S. Davis, Quantum Effects on the Molecular Forces, RFSC-17-35 (2017).

S. Davis, The Electron in a Periodic Potential, RFSC-17-36 (2017).

S. Davis, The Evaluation of $\phi^4$ Diagrams in a Quantum Scalar Field
Theory, RFSC-17-37 (2017).

S. Davis, The Renormalizability of the $\phi^3$ Theory, RFSC-17-38 (2017).

S. Davis, The Quantization of a Theory of Charged Scalar Fields, RFSC-17-39 (2017).

S. Davis, Divergences in Interactions of Four Fermions, RFSC-17-40 (2017).

S. Davis, The Renormalizability of the Scalar Yukawa Theory near Classical
Scales, RFSC-17-41 (2017).

S. Davis, The Quantum Theory of the Pseudoscalar Meson, RFSC-17-42 (2017).

S. Davis, The Thirring Model near Classical Scales, RFSC-17-43 (2017).

S. Davis, Quantization of a Fermion Model in Two Dimensions, RFSC-17-44 (2017).

S. Davis, The Diagrammatic Expansion for a Theory of Strongly Coupled Quarks,
RFSC-17-45 (2017).

S. Davis, The Probability of Cosmic Coincidence, RFSC-18-01 (2018).

S. Davis, A Theoretical Prediction for a Special Class of Gluonic Spectra,
RFSC-18-02 (2018).

S. Davis, Quaternions and the Minimum Mass Rule, RFSC-18-03 (2018).

S. Davis, The Theoretical Foundations of the Integer Multiple Rule, RFSC-18-04 (2018/19).

S. Davis, Geometrical Transformations of Differential Equations, RFSC-18-05 (2018/19)).

S. Davis, The Wavefunction for Quasiperiodic Lattices, RFSC-18-06 (2018/19).

S. Davis, On the Existence of Zero Divisors in the Spinor Space of the Fundamental
Interactions, RFSC-18-07 (2018/19).

S. Davis, The Consistencey of Superstrings in Friedmann-Robertson-Walker Space-times,
RFSC-18-08 (2018/19).

S. Davis, Quasiconformal Transformations of the Isoperimetric Ratio, RFSC-18-09 (2018/19).

S. Davis, The String Network of Space-time, RFSC-18-10 (2018/19).

S. Davis, The Fermat Equation of Degree 3 over the Complex Plane, RFSC-19-01 (2019).

S. Davis, Cusp Forms and Uniformizing Connections on Punctured Surfaces, RFSC-19-02 (2019).

S. Davis, Primes of the Form $n^2+1$, RFSC-19-03 (2019).

S. Davis The Extrinsic Complexity of Surfaces, RFSC-19-04 (2019),

S. Davis, Integral Equations for Correlation Functions in Quantum Field Theory,
RFSC-18-05 (2019).

S. Davis, The Complexity of Singular Solutions to the Gravitational Field Equations,
RFSC-19-06 (2019).

S. Davis, Physical Interpretation of the Spinor Conditions for the Wave Equation, RFSC-19-07 (2019).

S. Davis, An Equation related to the Motion of Quarks in the Nucleons, RFSC-19-08 (2019).

S. Davis, Differentiable Structures on ${\Bbb R}^n$, RFSC-19-09 (2019).

S. Davis, Central Integers between Consecutive Primes, RFSC-19-10 (2019).

S. Davis,The Equations $x^m-y^n=\kappa x^{\lambda m}$ with a Finite Number of Solutions,
RFSC-19-11 (2019).

S. Davis, A Sequence with Differences equal to a Multiple of Consecutive Primes,
RFSC-19-12 (2019).

S. Davis, The Finiteness of a Numerical Algorithm, RFSC-19-13 (2019).




















































CHRONOLOGY

A brief description of research is given in the following chronolog

1983 Vacuum energy regularization in gauged supergravity
Calculation of regularized free energy for higher N supermultiplets
Yang-Mills and fermion Lagrangians derived from the seven-sphere
as the internal symmetry space
Evaluation of Feynman digrams in anti-de Sitter space
Axiomatic field theory in anti-de Sitter space

1984 Generalized plane waves and the Fourier transform in Euclidean anti-de
Sitter space
Generalization of Goldstone's theorem to maximally symmetric
space-times
Green functions in anti-de Sitter space
Coordinate-dependent proof of equivalence of the Abbott-Deser formula
for the energy of an asymptotically anti-de Sitter space-time and the
expression based on conformal compactification
Evaluation of improved supercurrents and the superfield formulation of
the anti-de Sitter Wess-Zumino model

1985 Three-surface twistors and quasi-local expressions for conserved
quantities in asymptotically anti-de Sitter space-times
Ward identities and regularized expectation values of conserved
quantities in the anti-de Sitter Wess-Zumino model
Representations of the anti-de Sitter supergroups and multiplet
shortenings
Construction of free N=2 hypermultiplet models in anti-de Sitter space
and de Sitter space
Proof of the existence of negative-norm states in theories with global de Sitter
supersymmetry

1986 Kaluza-Klein theory and new ansatzes
Number and consistency of conditions on the gauge matrix
Gauge transformation constraints for an SO(4) action on an
$S^3$ bundle and an SO(8) action on an $S^7$ bundle
Quartic terms in the gauge transformation rule

1987 Proof of the principal bundle as the unique solution to physical constraints
on the connection in a smooth finite-dimensional bundle
String field theory and the generalization of the gauge principle in the
fibre description
Conformal transformations and the causal structure of space-time
Asymptotic completeness in two-dimensional free fermion theories and
string theories
Uniformization of surfaces of infinite-genus
Proof of convergence of the Poincare series for a class of infinitely
generated Kleinian groups

1988 Four-point tachyon correlation function on a class of infinite-genus
surfaces
Classification theory of Riemann surfaces and convergence of the series
expansion of the scalar field Green function
Surfaces of $P_G$ type and obstructions to the construction of state vectors
in the universal Grassmannian
Conformal field theories, Chern-Simon actions for string field theory and
stable bundles on moduli space
Non-renormalization theorems, the Hausdorff dimension of the ideal
boundary of a Riemann surface and convergence of the Poincare series

1989 Classification of surfaces uniformized by infinitely-generated groups of
Schottky typeons and Irreducible Polynomials,
Definition of the domain of string perturbation theory
Desingularization of black-hole space-times
Application of space-time topology change to string theory
The range of Donaldson invariants of four-manifolds and the Poincare conjecturr
Summation over path histories based on a calculus adapted to topology
Renormalization group flows and the Zamalodchikov c-function in the
space of renormalizable 2-dimensional field theories
Polyakov measure in the Schottky parameterization at arbitrary genus

1990 Number of primitive elements at each level in the set of Schottky group
elements
Bounds for the primitive-element products and determinant factors in the
Polyakov measure
Equivalence of different representations of the Polyakov measure
Fundamental region of the symplectic modular group at large genus

1991 Coverings of the region of an infinite-genus surface near the accumulation
point of the handles
String states and the properties of the Schottky covering
Category theory and the complex numbers
Variations of the determinant of the metric with respect to
dependent components
Field equations for a metric with a non-symmetric source term

1992 Refined lower bounds for the determinant of the imaginary part of the
period matrix at large genus
Finiteness of the number of conditions defining the fundamental region
of the genus-g modular group
Role of infinite-genus surfaces in the superstring path integral
Hexagonal configurations of isometric circles in bounded areas of the
complex plane

1993 Configurations of handles and the classification of divergences in
the string partition function
Number of ends of a surface the growth of the string partition
function
Curved space amplitudes and embeddings in target space
Analysis of the large-order behaviour of the superstring measure in
the singular limits of the Schottky variables
Phase factor in the transformation of the differential volume element
of the string measure at two and three loops
Moduli space integral in the infinite-genus limit for a class of surfaces
uniformized by an infinitely-generated group of Schottky type

1994 Interaction terms and hypermultiplets in two-dimensional anti-de Sitter
space
New actions for the gravitational field invariant under a special group of
coordinate transformations
Estimate of the inverse of the period matrix for a class of infinite-genus
surfaces
Symplectic measure in terms of Schottky group parameters and the
finiteness of supermoduli space at genus g
Modular invariance of the string measure at twelve loops
Integration of the superstring measure over super-Schottky space

1995 Computation of divergences in the bosonic string integral over a general
class of regions in Sd,chottky parameter space
Generalized gauge theories based on the enlargement of the category of bundles
beyond principal bundles
The flux condition for free fermion theories and $O_{HD}$ surfaces
Force unification and division algebras
Large-genus superstring amplitudes and the selection of superstring vacua

1996 Condition imposed on the spinor space of the standard model based on the
nonvanishing of fermion vertex factors
Improved bounds for the primitive-element products in the superstring measure
Nonperturbative effects in string theory and finiteness of the non-perturbative
contribution to the superstring amplitude
Field equations of gravitational actions with higher-order curvature terms
Generalized symmetries of the Einstein field equations and dilation of
regions with vanishing cosmological term
String effective actions in ten dimensions
Expression of massless vector bosons in ten dimensions in terms of spinor
bilinears and the Fierz rearrangements of four-fermion terms
Classical solutions of a quadratic gravity theory
Uncertainty relations in string theory

1997 Scalar field theory and the generalization of momentum-space Feynman
rules to curved space
Product rules for horospherical functions describing generalized plane
waves on the four-dimensional hyperboloid
Equivalence of different vacua in anti-de Sitter space scalar field theory
Momentum shifts in curved space and the bosonic string Hamiltonian
Interactions between phases of different $\Lambda$ and the decay of the
of the cosmological term
Upper bound for the superstring amplitude given a genus-independent limits
upon different degenerations of the Riemann surface
Counting of the number of ends of infinite-genus surfaces and the contribution
to the scattering amplitude
Application of the Ostrogradski formalism to the canonical quantization of
a quadratic gravity theory and the Wheeler-DeWitt equation

1998 Quantum cosmology of higher-derivative gravity theories
Exponential bound for superstring amplitudes and summability of
superstring theory
Mathematical applications of string theory
Spin structures on Riemann surfaces and the even perfect numbers
Rationality condition for the existence of odd perfect numbers

1999 The applications of number-theoretical theorems on primes to the problem
of the extent of the sequence of Mersenne primes
Boundary conditions for the sixth-order differential equation for the
quantum cosmological wavefunction of the quadratic gravity theory
Congruence conditions for the compositeness of Mersenne numbers
Point symmetries of higher-order partial differential equations
One-parameter family of vacua in maximally symmetric space-times
and the one-parameter family of string vacua

2000 Effect of higher-order curvature terms on string quantum cosmology
Bounce solutions to the string effective equations of motion in the
minisuperspace of Friedmann-Robertson-Walker metrics
Catalan's conjecture
Proof of non-existence of odd perfect numbers for a large class of odd integers
Gauge symmetries defined by submanifolds of fibres admitting parallelisms

2001 Integral transforms of higher-order partial differential equations
Difference-differential equations of mixed type
Calculation of higher-order corrections to the quantum cosmological
wavefunction resulting from the additional curvature terms
Reduction of odd-perfect number conjecture to three conditions on the primes
and exponents of the odd integer
Analysis and proof of the exponential bounds for the
primitive-element products in the superstring measure
Bound on the number of integer solutions to the three auxiliary equations in
in the theorem on odd perfect numbers

2002 Boundary conditions and the physical interpretation of the quantum
cosmological wavefunction
Third-order contributions to the deviation in the expectation value of the
scale factor and dilaton from the expressions for their classical time-dependence
Proof of the existence of a lower bound for the number of Goldbach partitions
of an even integer
Projections of fibre parallelism onto group submanifolds
Consistency of theories with the number of vector bosons different from the
dimension of the fibre of a principal bundle with the energy-dependence
of the strong-interaction coupling
Effect of spatial conformal isometries on the field equations for the
hypersurface three-metric
Products of Mersenne numbers
Sequence where $p$ is a Mersenne prime index
Expansion of the two-loop string-integrand in powers of the
coordinate in the neighbourhood of the compactification divisor
and the exponential bound for the superstring amplitudes at arbitrary genus
Numerical solution of the third-order differential equation for the
wavefunction when the derivatives with respect to the dilaton are
set to zero

2003 Demonstration of singular solution to the third-order differential equation
in the scale factor in the $a\to 0$ limit
Application of integral transform techniques to the sixth-order partial
differential equation for the wavefunction and the necessity of a scalar
for the consistency of the quantum cosmology of the quadratic gravity theory
Identification of the domain of superstring perturbation theory with the
with the space of effectively closed surfaces having boundary with zero capacity
Unitarity and the contribution of infinite-genus surfaces to the vacuum
amplitude
Solution to the condition on the partitioning of the interval yielding the
generalized Cantor set of ends of an $O_G$ surface
Coefficients of the normalized superstring amplitudes and the equality
of the base of the exponential with the unified gauge coupling
Estimate of the path integral with the Neveu-Schwarz-Ramond
superstring action by summation over dominant contributions and the
string coupling

2004 Odd perfect number conjecture
Generation of Mersenne primes and the sequence of even perfect numbers
Variants of Yang-Mills theory based on exotic structures on seven spheres
Generalized gauge theory defined by the Chern class
Derivation of the dependence of the string tension on the compactification
radius
Slope of the pomeron trajectory
Decrease of the cosmological term based on the interaction of domains of
different $\Lambda$
Recursion relation for the number of Goldbach partitions of an even integer
Goldbach partitions of twice an even integer

2005 Functional relations for roots of polynomials
Real formulation of the scattering matrix in quantum field theory
Complexity of curves and the geometrical characterization of dynamical
processes
Supersymmetric extension of the quadratic gravity theory derived
from the heterotic string effective action
Physical consistency of supersymmetric theories in a cosmological background
Interacting supersymmetric field theories in curved space with $N=2$
supersymmetry
The precise value for the string coupling including non-perturbative effects

2006 Truncation and renormalizability of superstring and heterotic string
effective actions
Classification of Riemann surfaces and string theory
Resolution of the integration region problem for supermoduli space integral
Genus-dependence of superstring amplitudes
Geometrical complexity of curves
Energy in the very early universe
Coset space of the unified field theory
A prime generating algorithmeS. Davis, Rationality in Hodge Theory, RFSC-17-01.
with improved efficiency
A numerical computation of the decrease of the cosmological term from
the Planck era to present times

2007 Conditions for supersymmetry of space-times with an eight-dimensional
coset space in an ansatz for the metric of the Freund-Rubin kind
Valence quark momentum distribution in nucleons
String theoretical description of hadron jets
Effect of vacuum polarization on the propagation of charged particles and light
A condition on the masses of composite particles
Mass mixing between generations of quarks and neutrinos
Finite algorithm for the solution to an algebraic equation
Coulomb energy term in the atomic mass formula and the charge distribution
based on the quark distribution of the nucleons
Physical interpretation of the Breit-Wigner formula
Computation of the partial width of $Z^0\to \ell^+ \ell^{-}$
Meson multiplets and the mass of the $\eta^\prime$ meson

2008 A computation of the percentage of $s{\bar s}$ quarks in the sea of quark-anti-quark
pairs in a nucleus with equal numbers of protons and neutrons
Connection between algebraic roots and existence of a proper normal
subgroup of the Galois group of roots
Automorphism group of the spinor space of the standard model and the
wreath product of the isometry group of the coset space of the unified
field theory and the symmetric permutation group $S_3$
Localization of the proof of the equivalent of Fermat's theorem in a
function field
Derivation of the Cabibbo angle through coupling of quarks to gluons
Theoretical basis for the fractional charges of quarks
Equivalence between isometry group of $(D-1)$-dimensional de Sitter group
$D$-dimensional Lorentz group and sequence of reductions of dimension
Superfield representations of N=2 anti-de anti-de Sitter supersymmetry
Standard topology of the coset space ${{G_2\times SU(2)\times U(1)}\over
{SU(3)\times U(1)^\prime \times U(1)^{\prime\prime}}}$ and presence of
$N=1$ supersymmetry
Relation between gauge coupling and string tension and scale of supersymmetry
breaking eS. Davis, Rationality in Hodge Theory, RFSC-17-01.

Separation of transcendental factors from the diagonalization of the coefficient
matrix of the linear system equivalent to an algebraic equation and
independence of transcendental numbers of ${\Bbb Q}$
CPT theorem in curved space, non-conservation of PT and the weak interactions
during the creation of the imbalance between matter and anti-matter
Reduced homology group of the empty set and the quantum creation of matter
Serre spectral sequences and the Hopf fibrations
Solution to the Tijdeman-Zagier-Beal conjecture
Even-power polynomials and the product of composition-irreducible polynomials
Preparation of composite states of ultrarelativistic particles
Lagrangian derivation of the geodesic equation and the existence of
complete trajectories within the distribution defined by quantum
variations surrounding a geodesic congruence

2009 Residual symmetry groups in the infrared limit of the strong interactions
Extrinsic complexity of various curves
Low-curvature limit of field equations in quadratic gravity theories
Derivation of the momentum-space propagator for particles with finite lifetimes
Superficial degree of divergence of diagrams in S-matrix expansion of the
quartic sector of the heterotic string effective action
The role of instantons in field theory and superstring theory
Virtual string states in diaeS. Davis, Rationality in Hodge Theory, RFSC-17-01.
grams with arbitrarily large genus and the uncertainty
principle
Scale invariance of the differential equation in the scale factor for the quantum
cosmological wavefunction and the Weyl hypothesis
$E_6$ invariance of the string vertex algebra and interactions
Supersymmetric generalization of the Bieberbach conjecture
New tensor term with vanishing covariant divergence in the gravitational field
equations
Nonperturbative propagator for a nonlinear field theory
Moduli space of two-metrics in four-dimensional gravity
Finiteness of superstring theory after supersymmetry breaking
Transcendental numbers and finite algebraic relations
Interacting higher-N supersymmetric theories in spaces of constant curvature
Boundary of conformally compactified space-times and physical configurations
in the interior region
Bound on the number of diffeomorphism structures on the four-sphere
Local gauge-invariant fields and nonlocal operators in unified field theories
Vestiges of supersymmetry in the masses of strongly interacting particles
Primes in arithmetic sequences and the Goldbach partitions
A medium containing particle-antiparticle pairs and the law of planetary
distances
Boundary conditions for the quantum gravitational path integral and

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