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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

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.

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.

Rate for 5 hours of lessons : $13

Rate for 10 hours of lessons : $12

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

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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Sara

1st lesson free!

El Cajon

$15

Randa

1st lesson free!

Bonita

$20

Ravisha

1st lesson free!

Chula Vista

$23

Iliana

1st lesson free!

San Diego

$15

Nelson

1st lesson free!

National City

$30

Isaiah

1st lesson free!

Lakeside

$16

Taylor

1st lesson free!

at his home | at your home | By webcam | |

1 hour | $15 | $15 | Not available |

5 hours | $13 | $13 | Not available |

10 hours | $12 | $12 | Not available |