I. COMPLETED AND UNPUBLISHED RESEARCH WORKS

FIRST GROUP: CONTINUATION OF PREVIOUSLY PUBLISHED WORKS

1. On classical non-Euclidean geometries and kinematics in N dimensions, three and two dimensions, with physical applications. Introduces imaginary figures, a trigonometry of imaginary triangles, ruled non-Euclidean geometry, and extensive use of inversion and non-Euclidean descriptive geometry. Enables computer use, and employs spaces of infinite curvature.

2. Extension of vector calculus to spaces of constant curvature in two, three, and N dimensions, arising from intrinsic formulation of the relativistic addition of velocities.

3. On differential equations with random coefficients and Brownian motion.

4. On Relativistic Statistical Mechanics.

5. On zero-coordinate points in Hilbert space, strong and weak uncertainty relations, and quantum chaos.

6. On fractal objects, functions, and integrals, and probabilities over the Cantor set and its generalizations.

SECOND GROUP: ON NEW TOPICS

7. Extension of the complete quadrilateral and other complete—even imaginary—figures to N dimensions.

8. Stochastic processes governed by the telegraphist’s equation. Applications to Relativistic Quantum Mechanics.

9. Essay on a wave mechanics for massless, spin-one particles through the fusion method.

10. Application of a Euclidean model of a non-Euclidean geometry on the one-sheeted revolution hyperboloid in four dimensions, and on the space external to the throat sphere of the hyperboloid, to the relativistic kinematics of tachyons—particles travelling faster than light.

II. PUBLICATIONS

A. BOOKS

1. Engineering of Oscillations. Dossat Publishing, 1959.

The German Zentralblatt, vol. 92 issue 1 (Feb 1962), devoted a lengthy review stating:

“…Contains a rich collection of problems related to the theory and technique of oscillations, including several by the author himself.”

“…The term teleological oscillations was introduced by the author in the memoir…”

The review highlights chapters X, XI & XII, which were extracted from the author’s memoirs and address hereditary, teleological, fractional, and stochastic oscillations.

2. Philosophy of Mathematics. Dossat, 1961.

3. Problems of Mechanics, Vol. I. Dossat, 1962.

4. Problems of Mechanics, Vol. II. Dossat, 1963.

5. Theory and Applications of Oscillations (translated to Portuguese by Dr. Eng. Ruy Pinto da Silva). Globo, Brazil, 1964.

6. Analytic and Projective Geometry of the Plane. Dossat, 2nd ed., 1965.

7. Analytic and Projective Geometry of Space. Dossat, 2nd ed., 1961.

8. Differential Equations and Matrices (2nd ed.). Dossat, 1965.

9. Mechanics and Tensor Calculus (2nd ed.). Dossat, 1965.

10. Mathematical Methods for Engineering (with Antonio de Castro Brzezicki). Dossat, 1969.

11. Mathematical Physics. Dossat, 1966.

12. Theory of Mathematical Research. Dossat, 1969.

13. Didactics and Dialectics of Mathematics. Dossat, 1969.

14. Financial Mathematics. Dossat, 1970.

15. Great Problems of Scientific Philosophy. Editora Nacional, 1973.

16. Probability and Stochastic Processes. Paraninfo, 1974.

17. Lines of Research in Stochastic Processes and Brownian Motion. Institute of Spain, 1975.

18. Theoretical and Applied Statistics (with Juan Miguel Soler). UNED, 1st ed. 1976, 2nd ed. 1986.

19. Course of Mechanics in Problem Form. ETS Agronomical Engineers, 1978.

20. Foundations of Quantum Mechanics. ETS Agronomical Engineers, 1979.

21. Introduction to Research in Physics and Mathematics. Empeño 14 Publishing, 1981.

22. Dictionary of Modern Mathematics (2nd ed.). Editora Nacional, 1982.

23. Fundamental Physics (2nd ed.). Dossat, 1983.

24. Dictionary of Modern Mathematics (3rd ed.). Ran‑ma, 1994. A third edition was prompted by extensive use of earlier editions by Russian publisher Mir.

25 & 26. Two books in preparation with Darío Maravall Gómez‑Allende, Professor of AI, Polytechnic University of Madrid.

All these books include both instructional content and original research, and are held in many university and national/foreign research institute libraries.

27. Fiftieth Anniversary of Quantum Mechanics. Royal Academy of Exact, Physical and Natural Sciences of Madrid, 1975. Includes original research.

28. Centenary of Einstein. Same academy, 1975. Includes original research.

29. Operations Research. Same academy, 1980. Includes original research.

30. Studies of a Young Person Today. Foundation University‑Enterprise, 1982; dedicated to the Prince of Asturias. A second edition titled Cultural Proposals for Youth.

31. Men, Words, Images, commemorative volume for the X Anniversary of the University‑Enterprise Foundation, honoring authors of the previous book.

32. Course on History of Mathematics (17th–18th Centuries). Royal Academy, 1988. Includes original research.

33. Course on History of Statistics. Royal Academy, 1989. Includes original research.

34. Course on History of Mathematics in the 19th Century, Part I. Royal Academy, 1992. Chapter: “The development of Mechanics and Mathematical Physics in the 19th century” (pp 175–210). Includes original research.

35. Course on History of Mathematics in the 19th Century, Part II. Royal Academy, 1994. Chapter: “The development of Mechanics and Mathematical Physics in the 19th century. Second part” (pp 233–274). Includes original research.

36. In the 1996 course on History of 20th‑Century Mathematics, delivered a lecture on Einstein, “soon to be published.” Includes original research.

37. Published by the Creativity & Inventiveness Committee of the Spanish Institute of Engineering, featuring his work “Modes of scientific production.”

38. Three Informatics courses edited by the Royal Academy and the Polytechnic University of Madrid (1992, 1993, 1994). His contributions include:

• Hereditary and teleological phenomena, with delay and memory, in Systems Engineering and Cybernetics.

• Extension of the Laplace transform, submetric spaces, and applications.

• The N‑sphere and incomplete inversive space, Euclidean models of classical non‑Euclidean geometries. Applications.

39. Tribute to Professor and Academician Obdulio Fernández. Royal Academy.

40. Tribute to Professor and Academician Manuel Lora Tamayo. Royal Academy.

41. Tribute to Professor and Academician Sixto Ríos, published by Trabajos de Estadística e Investigación Operativa.

42. Mathematical Contributions, Complutense University, in tribute to Professor Academician Javier Etayo. His research: “Projective definition of angle and the double ratio of two circles; spheres in one dimension; N+1‑orthocentric polyhedra and orthogonal spheres in N‑dimensional Euclidean spaces” (1994)—introducing the new concept of circle‑ratio and its inversion invariance.

43. Encounters with Innovation, Institute of Engineering of Spain, 1994. Contribution: “Reflections on modes of scientific production and researcher evaluation.”

44. Book on the Fiftieth Anniversary of José de Ribera Institute of Játiva, 1984. His piece: “The humanistic education of engineers.”

45. Four volumes on Cosmology, Galileo, the Solar System and Matter (1992–1996). Contains his original research.

46. Economy and Sociology as Drivers of Mathematical Research. Inaugural address to the Royal Academy of Sciences, 1968. Contains original research.

47. Mathematical Structures Suggested by Quantum Mechanics. Opening lecture for 1975 academic year at the Royal Academy. Contains original research.

48. Mathematics of Hereditary Phenomena. Inaugural address to the Royal Academy of Doctors, 1980. Contains original research.

49. The Usefulness of Philosophy for the Scientific Researcher. Marcelino Botín Foundation and Scientific Culture Classroom, 1981. Contains original research.

B. ARTICLES AND RESEARCH MEMOIRS

1. New types of differential or integro-differential equations. New oscillation phenomena.

2. New models of distributions and stochastic processes.

3. Some new stochastic processes and their applications.

(On items 2 and 3, Professor Richter wrote in the Mathematischen Nachrichten of the Berlin Academy of Sciences (Vol. 29, Issues 5/6, p. 347, 1965): “Among the new investigations, the works of D. Maravall are particularly noteworthy.”)

4. L-algebras, multivalent logics, and bionic networks.

5. G-compactification of a topological space, distributions, and currents.

6. Generalized homology, cohomology, and exterior differential algebra.

7. Phenomenology of diffusion, circle and sphere theorems in field physics.

8. Relativistic logic.

9. Stochastic theories of interest, usufruct, and bare ownership. Non-Markovian chains.

10. Unified theory of amortization. Application of distributions to financial mathematics.

11. Theory of random annuities. Unified theory of insurance.

12. Probabilistic spaces. Generalized Hilbert and Banach spaces.

13. Aberration and gravitational acceleration.

14. Non-convergence of the Fourier integral and discontinuity waves in physics.

15. Uniqueness theorems for nonlinear integral equations.

16. Mathematical theory of singular functions in quantum mechanics.

17. Structure of axially symmetric media in generalized relativity.

18. The non-Euclidean metric of spacetime inside a spherically symmetric barotropic fluid mass.

19. Relativistic theory of the attraction of a pulsating or spinning sphere.

20. Theoretical investigations on random functions in microphysics.

21. Issues in mathematics applied to experimentation.

22. Impulsive random movements and hereditary stochastic processes.

23. Essay on a unified theory of gravitation and electromagnetism.

24. The measurement of contagion in physics and biology.

25. The addition of a random number of random variables and the stochastic process of the offspring from a single progenitor.

26. New theorems on Brownian motion and stochastic oscillations.

27. Issues in classical kinematics.

28. The mathematical foundations of physical phenomena of pollution and sedimentation.

29. G-topologies and distribution theory.

30. A new formalism for singular functions or distributions in physics and the Laplace and Fourier transforms in N variables.

31. Contractive applications in uniform spaces. Fixed point theorem.

32. T-contractive applications in topological spaces.

33. Profit maximization in credit programming. An application of Markov chains to financial mathematics.

34. The semigroup of frequency distributions and the analytical theory of probability.

35. Aberration and the speed of light.

36. Energy flow and medium dispersion.

37. On invariants common to a circle and a conic.

38. On the dynamics of variable-mass systems.

39. The quadratic complex of lines of constant moment and other problems in classical mechanics.

40. The Buffon needle problem in N-dimensional space.

41. On the stability of equilibrium defined by a system of first-order differential equations and its relevance to biology.

42. Generalization of Guldin’s theorems.

43. The characteristic function of four stochastic algorithms.

44. The biological phenomenon of the struggle for existence, the stability of capitalist economics, and the prediction of Pareto’s law.

45. The aleatores.

46. G-metric spaces and G-normed groups. G-convergence of non-Cauchy sequences.

47. Biological applications of hereditary oscillations.

48. Relaxation oscillations in time series statistics.

49. The limits of life concentration.

50. The quantification of space and time in wave mechanics.

51. The quantification of mass, velocity, and the uncertainty of absolute rest in wave mechanics.

52. Cosmological consequences of the discontinuity theory of wave mechanics variables.

53. Calculation of the number of electrons and protons in the universe.

54. Calculation of the upper limit of the mass-radius ratio of material bodies and the density of the universe as a function of its radius.

55. The theory of the cosmological structure of the expanding universe.

56. Galaxy recession in the theory of the expanding universe. Variation of the ionization energy of cosmic rays over time.

57. The quantification of probability and physical impossibility in wave mechanics.

58. The dynamic solution of the one-body problem in relativity theory. Hypotheses about the origin of cosmic rays.

59. The string problem and the concept of waves.

60. The superposition principle and the integration of integro-differential equations with partial derivatives.

61. On the continuity equation in non-relativistic quantum mechanics.

62. The concept of mass and force in physics and the problem of natural geometry.

63. Stochastic interpretation of the law of supply and demand.

64. Evolution and methodology of physics.

65. New theory of the deflection of light rays and the redshift of spectral lines under the influence of a gravitational field.

66. Research on the shape and rotation of galaxies.

67. A new rank correlation criterion.

68. Contribution to the theory of electrical oscillations.

69. The mathematical theory of the stability of capitalist economics. The stochastic process of income distribution.

70. Applications of stochastic processes to demography, biometry, and electrodynamics.

71. The evolution of allele frequencies of Mendelian genes in a randomly mating population without selection or mutation.

72. Theoretical physics research with agronomic applications.

73. Stochastic processes of pest and contagious disease propagation.

74. Theoretical physics research with agronomic applications.

75. Research on the theory of linear oscillations with applications to electrotechnics.

76. Hereditary oscillations. Self-oscillations of bending-tension. The theory of pyroelectricity.

77. Statistical populations of random size.

78. A bidimensional stochastic process of contagion and a stable queue distribution.

79. A minimization problem in business economics.

80. A new abstract space of aleatores in economics and mathematical biology. The demographic-financial illusion.

81. Biophysical and noophysical metrology.

82. Mathematical models of biological phenomena. Statistical pathology.

83. Addition of isotropic random vectors in an n-dimensional space.

84. Essay on the axiomatization of probability calculus and distribution theory.

85. The inverse problem of integrating a random variable over a random interval.

86. The mathematical method in biology. XXVI Luso-Spanish Congress of the Association for the Advancement of Science. Porto 1962, invited paper. Current state of statistical applications in biology.

87. Reflections on teaching and research in statistics applied to physics and biology (1991), invited article.

88. Ortega y Gasset and the physics of his time (1983–84), invited article for the centenary of Ortega. He was invited to deliver two lectures in Santander: “Galileo seen by Ortega” and “Leibniz seen by Ortega.”

89. Operations research, economics, and agriculture (1968). Invited lecture at the Hispano-French Operations Research Conference, Valencia, May 1968. Includes original research.

90. Sociological mathematical models (1970).

91. N-dimensional random vectors and associated integral transforms (1968).

92. A theorem of relativistic statistical mechanics and Hilbert–Lobachevsky spaces (1985), invited article in honor of Sixto Ríos.

93. Functional equations in demography and characteristic functions of Markov chains (1968).

94. Updating dynamic programming (1968).

95. The semiring associated with a semigroup. Probabilistic spaces and algebras. G-complete spaces (1968).

96. The axioms of financial and actuarial mathematics and distributions (1969).

97. Integral convergence in quantum mechanics and the generalization of Hilbert spaces (1969).

98. Stochastic processes in radioactivity (1969).

99. Classes of topologies in probabilities and measures. Almost-probability algebras (1970).

100. Symmetric algebra and the stochastic processes of economics (1970).

101. Stochastic processes in cybernetics and dual statistical and deterministic theories (1970).

102. Continuous branching stochastic processes and differential equations between random variables (1970).

103. Equivalence between stochastic processes of order statistics and of radioactivity (1970).

104. Stochastic processes in cycles of nature and exchange (1970).

105. Message spaces in information and language theory (1971).

106. Fusion stochastic processes as duals to branching processes (1971).

107. Stochastic processes in genetics (1971).

108. The characteristic function as a criterion of stochastic convergence. New types of convergence (1972).

109. Stochastic processes in reliability, labor rationality, and the statistics of extreme values (1972).

110. An existence and uniqueness theorem for nonlinear integral equations in L (1973).

111. Fractional differential equations and fractional oscillations (1973).

112. The stochastic process of ionic recombination and a statistical theory of the logistic curve.

113. Stochastic processes of chemical equilibrium and a statistical theory of the law of mass action (1976).

114. New laws of rare events and stochastic processes of chemical equilibrium (1976).

115. Exact solutions of integral equations in rheology and viscoelasticity and their physical consequences (1978).

116. Differential and integral equations with random initial conditions (1978).

117. Finite difference equations and linear differential equations with random coefficients (1978).

118. On minimum principles in electrodynamics and classical and relativistic mechanics (1978).

119. Non-Riemannian spaces and the use of classical mechanics methods in relativity theory (1979).

120. The stochastic process of the provoking agent (1979).

121. Asymptotic behavior and invariant solutions of linear systems of differential and finite difference equations with random initial conditions. Stochastic control theory (1980).

122. Markov chains in random populations and generalized chain probabilities (1981).

123. Essay on a unified theory of the infinitely large, the infinitely small, and randomness, and the laws of large numbers (1982).

124. Variational principles and differential equations of relativistic system dynamics (1983).

125. Binomial and Bernoulli distributions with random probability. Central limit theorems (1983).

126. Some stochastic processes applicable to physics, epidemiology, and advertising (1983).

127. Some new theorems of relativistic statistical mechanics, analytical mechanics, and hydrodynamics (1984).

128. Stochastic coupling of linear systems of differential and finite difference equations and Markov chains. Diagonal functions (1984).

129. Chain probabilities in Hilbert spaces. Physical applications (1984).

130. Two- and three-dimensional stochastic processes of birth, death, and immigration with permanent trait acquisition (1985).

131. Hilbert–Lobachevsky spaces, pressure and mass of a relativistic gas, and relativistic matter waves (1986).

132. Some new results in electrodynamics and relativistic statistical mechanics (1988).

133. Essay on a unified theory of relativistic waves of matter and radiation. Fractal functions and fractal objects in mechanics and probability (1988).

134. Stochastic birth process with reproductive and non-reproductive individuals. Non-homogeneous linear and finite difference systems with random initial values. Relativistic modification of Bose–Einstein and Fermi–Dirac quantum statistics (1988).

135. VII International Congress on Mining and Metallurgy (1984, Barcelona). The impact of technological advances on science. The change in the unit of length and the theory of relativity (invited article).

136. Random vectors in Hilbert and Euclidean spaces (1976).

137. Integration of systems of linear differential equations with random initial values (1978).

138. A three-dimensional stochastic process of birth, death, and immigration (1979).

139. A correspondence principle between classical and relativistic mechanics (1981). Invited article.

140. Some aspects of scientific language (1973, Florence). Invited article. Simultaneously delivered a lecture at the Accademia della Crusca in Florence, the oldest (1583).