## ALLADI RAMAKRISHNAN## Research Publications- (with H. J. Bhabha) "The mean-square deviation of the number
of electrons and quanta in cascade theory",
*Proc. Indian Acad. Sci.***32**(1950), 141-153. - "Stochastic processes relating to particles distributed in
a continuous infinity of states",
*Proc. Cambridge Phil Soc.*,**46**(1950), 595-602. - "A note on the size frequency distribution of penetrating showers",
*Proc. Phys. Soc. London*,**63A**(1950), 861-863. - "Stochastic processes and their applications to physical problems"
*PhD Thesis, Univ. Manchester*(1951). - "Some simple stochastic processes",
*J. Royal Stat. Soc.*,**13**(1951), 131-140. - "A note on Janossy's mathematical model of a nucleon cascade",
*Proc. Cambridge Phil. Soc.*,**48**(1952), 451-456. - "On an integral equation of Chandrasekhar and Munsch",
*Astrophysical J.*,**115**(1952), 141-144. - "Stochastic processes associated with random divisions of a line",
*Proc. Cambridge Phil. Soc.*,**49**(1953), 473-485. - (with P. M. Mathews) "A stochastic problem relating to counters",
*Phil. Mag.*,**44**(1953), 1122-1127. - (with P. M. Mathews) "Numerical work on the fluctuation problem
of electron cascades",
*Prog. Theor. Phys.***9**(1953), 679-681. - (with P. M. Mathews) "On a class of stochastic integro-differential
equations",
*Proc. Indian Acad. Sci,*Ser A**38**(1953), 450-466. - (with P. M. Mathews) "On the solution of an integral equation
of Chandrasekhar and Munsch",
*Astrophysical J.*.**119**(1954), 81-90. - "A stochastic model of a fluctuating density field",
*Astrophysical J.*,**119**(1954), 443-455. - "A stochastic model of a fluctuating density field - II"
*Astrophysical J.*,**119**(1954), 682-685. - "On the molecular distribution functions of a one dimensional
fluid - I",
*Phil. Mag.*,**45**(1954), 401-410. - "On counters with random dead time"
*Phil. Mag.*,**45**(1954), 1050-1052. - (with P. M. Mathews) "On the molecular distribution functions of a
one dimensional fluid - II",
*Phil. Mag.*,**45**(1954), 1053-1058. - (with P. M. Mathews) "Studies in the stochastic problem of
electron-photon cascades",
*Prog. in Theor. Phys.*,**11**(1954), 95-117. - (with S. K. Srinivasan) "Two simple stochastic models of cascade
multiplication",
*Prog. in Theor. Phys.*,**11**(1954), 595-603. - "On stellar statistics"
*Astrophysical J.*,**122**(1955), 24-31. - "Inverse probability and evolutionary Markov stochastic processes",
*Proc. Indian Acad. Sci.*,**41**(1955), 145-153. (Read at the Annual Meeting of the Academy in Belgaum, Dec 1954.) - (with S. K. Srinivasan) "Fluctuations in the number of photons in an
electron-photon cascade",
*Prog. in Theor. Phys.*,**13**(1955), 93-99. - (with P. M. Mathews) "Straggling of the range of fast particles
as a stochastic process",
*Proc. Indian Acad. Sci.*,**41**(1955), 202-209. (Read at the Annual Meeting of the Academy in Belgaum, Dec 1954.) - "Phenomenological interpretation of the integrals of a class
of random functions",
*Proc. Koninkl. Netherlands Akad.***58**(=*Indag. Math.*,**17**) (1955), 470-482. - "Phenomenological interpretation of the integrals of a class of
random functions - II",
*Proc. Koninkl. Netherlands Akad.***58**(=*Indag. Math.*,**17**) (1955), 634-645. - (with S. K. Srinivasan) "Correlation problems in the study of
brightness of the Milky Way",
*Astrophysical J.*,**123**(1956), 479-485. - "Processes represented as integrals of a class of random functions",
*Proc. Koninkl. Netherlands Akad.***59**(=*Indag. Math.*,**18**) (1956), 121-127. - (with P. M. Mathews) "Stochastic processes associated with a
symmetric oscillatory Poisson process",
*Proc. Indian Acad. Sci.*,**43A**(1956), 84-98. - (with S. K. Srinivasan) "A new approach to cascade theory",
*Proc. Indian Acad. Sci.*, Ser. A.**44**(1956), 263-273. - "A physical approach to stochastic processes",
*Proc. Indian Acad. Sci.*Ser A,**44**(1956), 428-450. - (with S. K. Srinivasan) "Stochastic integrals associated with
point processes" (in French),
*Publ. Inst. Stat. Univ. Paris*,**5**(1956), 95-106. - (with R. Vasudevan) "On the distribution of visible stars",
*Astrophysical J.*,**126**(1957), 573-578. - "Ergodic properties of some simple stochastic processes",
*Z. angew. Math. Mech.*,**37**(1957), 336-344. (Read at the GAMM Conference in May 1956 in Stuttgart.) - (with S. K. Srinivasan) "A note on cascade theory with ionisation
loss",
*Proc. Indian Acad. Sci.*, Ser. A**45**(1957), 133-138. - (with N. R. Ranganathan, S. K. Srinivasan and R. Vasudevan)
"Multiple processes in electron-photon cascades",
*Proc. Indian Acad. Sci.*, Ser. A,**45**(1957), 311-326. - (with S. K. Srinivasan) "On age distribution in population growth",
*Bull. Math. Biophys.*,**20**(1958), 289-303. - "Theoretical physics in the USA",
*Current Sci.***27**(1958), 469-471. - "Ambigenous stochastic processes",
*Z. angew Math. Mech*,**39**(1959), 389-390. - (with N. R. Ranganathan and S. K. Srinivasan) "Meson production
in nucleon-nucleon collisions",
*Nucl. Phys.*,**10**(1959), 160-165. - (with N. R. Ranganathan, S. K. Srinivasan and K. Venkatesan)
"Photo-mesons from polarized nucleons"
*Proc. Indian Acad. Sci. Ser. A***49**(1959), 302-306. - (with N. R. Ranganathan and S. K. Srinivasan) "A note on the
interaction between nucleon and anti-nucleon",
*Proc. Indian Acad. Sci.*,**50**(1959), 91-94. - "Probability and stochastic processes" in
*Handbuch der Physik*(S. Flugge, Ed)**III/2**(1959), Springer-Verlag, Berlin (1959), 524-651. - (with N. R. Ranganathan, S. K. Srinivasan, and R. Vasudevan)
"A note on dispersion relations",
*Nuclear Phys.*,**15**(1960), 516-518. - "Perturbation expansions and kernel functions associated with single
particle wave functions" in
*Studies in Theor. Phys., Proc. 1959 Mussoorie Summer School***1**(1960), 1-14. - "Quantum mechanics of the photon" in
*Studies in Theor. Phys., Proc. 1959 Mussoorie Summer School***1**(1960), 15-18. - "Applications of the theory of stochastic processes to physical
problems", in
*Studies in Theor. Phys., Proc. 1959 Mussoorie Summer School***2**(1960), 239-253. - (with R. Vasudevan) "A physical approach to some limiting
stochastic operation",
*J. Indian Math. Soc.***IV**(Golden Jubilee Volume, 1960), 458-477. (work done at Institute for Advanced Study in 1957-58; paper read by AR at Int'l Congress of Math., Edinburgh, 1958) - (with A. P. Balachandran and N. R. Ranganathan) "Some remarks on
the structure of elementary particle interactions",
*Proc. Indian Acad. Sci.*,**52**(1960), 1-11. - (with T. K. Radha and R. Thunga) "On the decomposition of the
Feynman propagator"
*Proc. Indian Acad. Sci.*, Ser. A,**52**(1960), 228-239. - (with P. Rajagopal and R. Vasudevan) "Ambigenous stochastic
processes",
*J. Math. Analysis and Appl.*,**1**(1960), 145-162. (Read by AR at the GAMM Conf., Hanover in May 1959) - (with. T. K. Radha) "Correlation problems in evolutionary stochastic
processes",
*Proc. Cambridge Phil. Soc.*,**57**(1961), 843-847. - (with A. P. Balachandran, N. G. Deshpande, and N. R. Ranganathan)
"On an isobaric spin scheme for leptons and leptonic decays of strange
particles",
*Nucl. Phys.*,**26**(1961), 52-56. - (with R. Vasudevan) "A physical approach to limiting stochastic
operations",
*J. Indian Math. Soc. (N.S)***24**(1961), 457-477. - (with G. Bhamathi and S. Indumathi) "A limiting process in
quantum electrodynamics",
*Proc. Indian Acad. Sci. Ser A*,**53**(1961), 206-213. - (with V. Devanathan and G. Ramachandran) "A time dependent approach
to rearrangement collosions",
*Il Nuovo Cimento*,**21**(1961), 145-154. - (with S. K. Srinivasan) "A note on electron photon showers",
*Nucl. Phys.*,**25**{1961), 152-154. - (with G. Bhamathi, S. Indumathi, T. K. Radha, and R. Thunga)
"Some consequences of spin
*3/2*for Ξ",*Il Nuovo Cimento*,**22**(1961), 604-609. - (with V. Devanathan and G. Ramachandran) "Elastic photo production
of nuetral pions from dueterium",
*Nucl. Phys.*,**24**(1961), 163-168. - (with N. R. Ranganathan) "Stochastic models in quantum mechanics"
*J. Math. Analysis and Appl.*,**3**(1961), 261-294. (Presented by AR at the Conference on Elementary Particles, Trieste 1960) - (with K. Venkatesan) "Some new stochastic aspects in cascade theory",
*in Proc. 7-th Annual Cosmic Ray Symposium, Chandigarh*(1961), 59-61. - (with T. K. Radha) "Essay on symmetries"
*Lectures at the Kodaikanal Summer School*,**2**(1961), 1-77. - (with N. R. Ranganathan) "Stochastic methods in quantum mechanics",
*J. Math. Analysis and Appl.*,**3**(1961), 261-294. - (with T. K. Radha and R. Thunga) "The physical basis of quantum field
theory",
*J. Math. Analysis and Appl.*,**4**(1962), 494-526. - (with T. K. Radha and R. Thunga) "On the concept of virtual states",
*J. Math. Analysis and Appl.*,**5**(1962), 225-236. - (with G. Ramachandran) "Magnetic bremsstrahlung in nucleon-electron
collisions",
*Rand Corporation Preprint*, Los Angeles (1962). - "New perspectives on the Dirac Hamiltonian and the Feynman propagator",
*in High Energy Phys. and Fundamental Particles*, Gordon and Breach, NY (1962), 665-672. - "A new form of the Feynman propagator",
*J. Math. Phys, Sci.*,**1**(1967), 57-64. - (with A. P. Balachandran and K. Raman) "Low energy
*K*-nucleon scattering",^{+}*Il Nuovo Cimento*,**24**(1962), 369-378. - (with V. Devanathan and K. Venkatesan) "On the scattering of pions
by dueterons",
*Nucl. Phys.*,**29**(1962), 680-686. - (with T. K. Radha and R. Thunga) "Possible resonances in Ξ
_{p}reactions",*Nucl. Phys.*,**29**(1962), 517-523. - (with A. P. Balachandran) "Partial wave dispersion relations for
Λ-nucleon scattering",
*Il Nuovo Cimento*,**24**(1962), 980-999. - (with A. P. Balachandran, T. K. Radha, and R. Thunga) "On the
*Y*resonances",^{*}*Il Nuovo Cimento*,**24**(1962), 1006-1012. - (with A. P. Balachandran, T. K. Radha, and R. Thunga) "On the spin
and parity of
*Y*resonances",^{*}*Il Nuovo Cimento*,**25**(1962), 723-729. - (with A. P. Balachandran, T. K. Radha, and R. Thunga) "Photo
production of pions and Λ-hyperons",
*Il Nuovo Cimento*,**25**(1962), 939-942. - (with G. Bhamathi, S. Indumathi, T. K. Radha, and R. Thunga)
"Dispersion analysis of Ξ
*production in*KN collisions"*Nucl. Phys.*,**37**(1962), 585-593. - (with T. K. Radha, K. Raman, and R. Thunga) "Quantum numbers and
decay models of resonances"
*Rand Corp. Preprint*, Los Angeles (1962) - "An unconventional view of perturbation expansions",
*in Proc. Seminar on Unified Theories of Elem. Particles, Univ. Rochester, D. Lurie and N. Mukunda, Eds.*(1963), 411-421. - (with V. Devanathan and K. Venkatesan) "A note on the use of
Wick's theorem",
*J. Math. Analysis and Appl.*,**8**(1964), 345-349. - (with K. Raman and R. K. Umergee) "Isobar production in
nucleon-nucleon scattering",
*Nuclear Phys.*,**60**(1964), 401-426. - (with K. Raman and R. K. Umergee) "Isobar production in
nucleon-nucleon scattering - II, Polarization effects",
*Nuclear Phys.*,**66**(1965), 609-631. - (with S. K. Srinivasan and R. Vasudevan) "Some new mathematical
features in cascade theory",
*J. Math. Analysis and Appl.*,**11**(1965), 278-289. (Presented at the Int'l Conf. on Cosmic Rays,**5**(1964), TIFR, Bombay, 458-501.) - (with T. S. Shankara and K. Venkatesan) "Sensitivity of the vector
coupling constant to
*mu*-nuetrino mass and T-invariance",*Il Nuovo Cimento*,**37**(1965), 1046-1048. - (with R. Vasudevan and S. K. Srinivasan) "Scattering phase shifts
in stochastic fields",
*Z. fur Phys.*,**196**(1966), 112-122. - "Fundamental multiplets" in
*Symp. in Theor. Phys. and Maths., Alladi Ramakrishnan Ed.***5**Plenum Press, NY (1967), 85-92. - "New perspectives on the Dirac Hamiltonian and the Feynman propagator",
in
*High energy physics and fundamental particles*(1967), Gordon and Breach, New York, 665-672. (Presented at the Theoretical Physics Institute, University of Colorado, Boulder, 1967.) - (with S. K. Srinivasan and R. Vasudevan) "Angular correlations in the
brightness of the Milky Way",
*J. Math. Phys. Sci.*,**1**(1967), 75-84. - "Some new topological features in Feynman graphs",
*J. Math. Analysis and Appl.*,**17**(1967), 68-91. - "A new form of the Feynman propagator",
*J. Math. Phys. Sci*,**1**(1967), 57-64. - "L-matrix hierarchy and the higher dimensional Dirac Hamiltonian",
*J. Math. Phys. Sci*,**1**(1967), 190-193. - (with S. K. Srinivasan and R. Vasudevan) "Multiple product densities",
*J. Math. Phs. Sci.***1**(1967), 275-279. - "Graphical representation of CPT",
*J. Math. Analysis and Appl.*,**17**(1967), 147-150. - (with I. V. V. Raghavacharyulu) "A new combinatorial feature of
Feynman graphs",
*J. Math. Analysis and Appl.***18**(1967), 175-181. - "The Dirac Hamiltonian as a member of a hierarchy of matrices",
*J. Math. Analysis and Appl.***20**(1967), 9-16. - "Helicity and energy as members of a hierarchy of eigenvalues",
*J. Math. Analysis and Appl.*,**20**(1967), 397-401. - "Symmetry operations on a hierarchy of matrices",
*J. Math. Analysis and Appl.*,**21**(1968), 39-42. - "On the relationship between L-matrix hierarchy and Cartan spinors",
*J. Math. Analysis and Appl.*,**22**(1968), 570-576. - (with. P. S. Chandrasekharan, N. R. Ranganathan, and R. Vasudevan)
"A generalization of the L-Matrix hierarchy",
*J. Math. Analysis and Appl.*,**23**(1968), 10-14. - "L-Matrices, quaternions and propagators",
*J. Math. Analysis and Appl.*,**23**(1968), 250-253. - (with I. V. V. Raghavacharyulu) "A note on the representation of
Dirac groups",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed),**8**(1968), Plenum Press, NY, 25-32. - "Should we revise our notions about spin and parity in relativistic
quantum theory?"
*J. Math. Phys. Sci.*,**3**(1969), 213-219. - (with P. S. Chandrasekharan and T. S. Santhanam) "On representations
of generalised Clifford algebras",
*J. Math. Phys. Sci.*,**3**(1969), 301-313. - "Symmetries associated with roots of the unit matrix",
*J. Math. Phys. Sci.*,**3**(1969), 317-318. - "Generalized helicity matrices"
*J. Math. Analysis and Appl.*,**26**(1969), 88-91. - (with P. S. Chandrasekharan, T. S. Santhanam, and A. Sundaram)
"Helicity matrices for generalized Clifford algebra",
*J. Math. Analysis and Appl.*,**26**(1969), 275-278. - (with P. S. Chandrasekharan, N. R. Ranganathan, T. S. Santhanam,
and R. Vasudevan) "The generalized Clifford algebra and the unitary
groups",
*J. Math. Analysis and Appl.*,**27**(1969), 164-170. - (with P. S. Chandrasekharan, N. R. Ranganathan, T. S. Santhanam,
and R. Vasudevan) "Idempotent matrices from a generalized Clifford
algebra",
*J. Math. Analysis and Appl.*,**27**(1969), 563-564. - (with P. S. Chandrasekharan, N. R. Ranganathan, and R. Vasudevan)
"Kemmer algebra from generalized Clifford elements",
*J. Math. Analysis and Appl.*,**28**(1969), 108-110. - "On the algebra of L-matrices",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed.),**9**(1969), Plenum Press, NY, 73-78. - "L-matrices and propagators with imaginary parameters",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed.)**9**(1969), Plenum Press, NY, 79-84. - (with R. Vasudevan) "A hierarchy of idempotent matrices",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed.),**9**(1969), Plenum Press, NY, 85-88. - (with P. S. Chandrasekharan and R. Vasudevan) "Representation of
para-Fermi rings and generalized Clifford algebra",
*J. Math. Analysis and Appl.***31**(1970), 1-5. - "On the composition of generalized helicity matrices",
*J. Math. Analysis and Appl.*,**31**(1970), 254-258. - (with R. Vasudevan) "On generalized idempotent matrices",
*J. Math. Analysis and Appl.*,**32**(1970), 414-423. - "New generalizations of Pauli matrices",
*in Proc. Int'l Conf. on Symmetries and Quark Models, Wayne State Univ. 1969*, Gordon and Breach, NY (1970), 133-138. - "Unitary generalization of Pauli matrices",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed.),**10**(1970), Plenum Press, NY, 51-57. - (with I. V. V. Raghavacharyulu) "Generalized Clifford basis and
infinitesimal generators of the unitary group",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed.),**10**(1970), Plenum Press, NY, 59-62. - (with P. S. Chandrasekharan and T. S. Santhanam) "L-matrices and the
fundamental theorem of spinor theory",
*in Symposia on Theor. Phys. and Math.*(Alladi Ramakrishnan, Ed.),**10**(1970), Plenum Press, NY, 63-68. - "Stochastic theory of evolutionary processes (1937-71)" in
*Stochastic Point Processes, Proc. IBM Conf. on Point Processes*, (J. Lewis Ed), Interscience, John Wiley (1971), 533-548. - "A new approach to quantum numbers in elementary particle physics",
*in Proc. Rutherford Centennial Conf., Christchurch*(1971), 150-156. - (with P. S. Chandrasekharan and R. Vasudevan) "Algebras derived
from polynomial conditions",
*J. Math. Analysis and Appl.*,**35**(1971), 131-134. - (with P. S. Chandrasekharan and R. Vasudevan) "Para-Fermi operators
and special unitary algebras",
*J. Math. Analysis and Appl.*,**35**(1971), 249-254. - "The weak interaction Hamiltonian in L-Matrix theory",
*J. Math. Analysis and Appl.*,**37**(1972), 432-434. - "On the shell structure of an L-Matrix",
*J. Math. Analysis and Appl.*,**38**(1972), 106-108. - "A matrix decomposition theorem",
*J. Math. Analysis and Appl.*,**40**(1972), 36-38. - "Einstein - a natural completion of Newton",
*J. Math. Analysis and Appl.*,**42**(1973), 377-380. - "The generalized Gell-Mann - Nishijima relation", in
*Proc. Conf. on Nucl. Phys., MATSCIENCE Report***78**, (1973) 1-4. - (with R. Jaganathan) "A new approach to matrix theory or many facets
of the matrix decomposition theorem", in
*Topics in Numerical Analysis, Proc. 1974 Int'l Conf. on Numerical Analysis, Dublin*(J. H. Miller Ed.)**133**(1976), 133-139. - "New concepts in matrix theory"
*J. Math. Analysis and Appl.*,**60**(1977), 255-258. - "Unnoticed symmetries in Einstein's special relativity",
*J. Math. Analysis and Appl.*,**63**(1978), 335-338. - "Lorentz to Gell-Mann - can the masters be retouched?"
*Proc. Tamil Nadu Acad. Sci.***1**(1978), 29-33. - "A new concept in special relativity - exterior relative velocity",
*Proc. Tamil Nadu Acad. Sci.***1**(1978) 67- - "A new look at matrix operations"
*in Proc. Oberwolfach Conf. on Math. Phys. Dec. 1977*(Methoden und Verfahren der Mathematischen Physik - B. Brosowski and E. Martenson, Eds.), Peter Lang Publ. (1978), 49-53. - "New facets and new concepts in the special theory of relativity",
*in Proc. Oberwolfach Conf. on Math. Phys. Dec. 1977*(Methoden und Verfahren der Mathematischen Physik - B. Brosowski and E. Martenson, eds.), Peter Lang Publ. (1978), 55-61. - "Approach to stationarity in stochastic processes",
*Proc. Tamil Nadu Acad. Sci.***2**(1979), 189-190. - "On the generalization of the Gellmann-Nishijima relation",
in
*Symmetries in Science*(B. Gruber and R. S. Millman, Eds.), Plenum Publ. Corp. (1980), 323-325. - "Mathematical features of evolutionary stochastic processes",
*Methods of Operations Research*,**36**(1980), 239-240. - "A new concept in probability theory",
*J. Math. Analysis and Appl.*,**83**(1981), 408-410. - "Duality in stochastic processes",
*J. Math. Analysis and Appl.*,**84**(1981), 483-485. - "Further unnoticed symmetries in special relativity",
*J. Math. Analysis and Appl.*,**94**(1983), 237-241. - "Tantalizing asymmetries in special relativity",
*J. Math. Analysis and Appl.*,**110**(1985), 222-224. - "Decomposition of intervals in special relativity",
*J. Math. Analysis and Appl.*,**110**(1985), 225-226. - "A reflection principle",
*Phys. Education*,**30**(1995), 204-205. - "A remarkable unnoticed theorem in special relativity",
*J. Math. Analysis and Appl.*,**213**(1997), 155-159. - "Theorem on non-simultaneity - extension to an external observer",
*J. Math. Analysis and Appl.*,**213**(1997), 354-356. - "Cubic and general extensions of the Lorentz transformation",
*J. Math. Analysis and Appl.*,**229**(1999), 88-92. - "A new Rod approach to the special theory of relativity",
*J. Math. Analysis and Appl.*,**249**(2000), 243-251. (Special Millennium issue dedicated to Richard Bellman)
## Books/Monographs/Handbuch articles
- "Probability and stochastic processes", in
*Handbuch der Physik*,**3**(1959) Springer Verlag, Berlin, 524-651. - "Elementary particles and cosmic rays", Pergamon Press, Oxford
(1962), 580 pp
- "L-Matrix theory or the grammar of Dirac matrices", Tata-McGraw Hill,
Bombay-New Delhi (1972)
- "Special relativity", East West Books, Madras, India (2005)
## Books edited
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