Books

 

 

The Euler System for the Algebraic Number Theory & Mathematical Models In Pollution

 

The Algorithmic Solution of the Original Euclidean Fermat's Last Theorem

 

Several "Star" Problems In Analytic Number Theory

 

The Paratrigonometry

 

 

Papers

 

  1. with H.Hasse, Putting last digits first yields multiple, Rendiconti di Matematica (1) vol.8, serie VI.,(1975).

  2.  

  3. n-Dimensional Fibonacci numbers and their applications, The Fibonacci quarterly, Vol.21, No.4 (1983), 285-301.

  4.  

  5. An algorithm in a complex field and its applications to the calculation of units (ACF), Pacific J.of Math., Vol.110, No.1 (1984), 21-40.

  6.  

  7. Some new combinatorial identities derived from units in algebraic number fields, Discrete Mathematics, 54 (1985), 133-141.

  8.  

  9. Diophantine Equations and Identities, Internat.J.Math. & Math.Sci., Vol.8.No.4 (1985), 755-777.

  10.  

  11. Approximation of irrationals, Internat.J.Math.and Math.Sci., Vol.8.No.2 (1985), 303-320.

  12.  

  13. Trigonometric Identities, Internat.J.Math. & Math.Sci.Vol.9.No.4 (1986), 705-714.

  14.  

  15. Pythagorean Triangle of equal areas, Internat.J.Math. & Math.Sci.Vol.11.No. 4 (1988), 769-780.

  16.  

  17. More units from the periodicity of an algorithm, Bul.Numb.Theory, Vol.XII (1988), 81-89.

  18.  

  19. Halter-Koch units from the periodicity of (AFC) Algorithm, Bul.Numb.Theory, Vol.XIII (1989), 73-80.

  20.  

  21. Hermite's problem from the periodicity of (ACF) algorithm, Bul.Numb.Theory, Vol.XIV (1990), 57-67.

     

  22. The periodicity of an algorithm over the complex number field (ACF) and the solution of the Hermite problem, The Math.heritage of C.F.Gauss, 43-52, 1991.

     

  23. Hilbert's demand for the disclosure of units in algebraic number fields, Bul.Numb.Theory, vol.XVI (1992), 149-163.

  24.  

  25. With M.Gerlach, Fibonacci Triples and Pythagorean triangles of equal areas, Bul.Numb.Theory, Vol.XVI (1992), 7-14.

  26.  

  27. Baica's General Euclidean algorithm (BGEA) and the solution of Fermat's Last Theorem (FLT), Notes on number theory and discrete mathematics (NNTDM), 1 (1995), 3 (120-134).

  28.  

  29. More explanations about Baica's proof of Fermat's Last Theorem, NNTDM 2 (1996), 15-19.

  30.  

  31. The Euclidean character of Fermat's Last Theorem, NNTDM 2 (1996), 1, 20,23.

  32.  

  33. Baica's solution of Fermat's Last Theorem in Euclidean, models and algorithms the transition from abstract to applied mathematics, Analele Universitatii "Eftimie Murgu", Resita, Fascicola III, Anul III (1996), 267-278.

  34.  

  35. Baica's General Euclidean Algorithm (BGEA) restricted periodicity an N-dimensional equivalent of Euler-Lagrange theorem from quadratics, Scientific Bulletin of the "Politehnica" University of Timisoara, Romania, Tom 42 (56)2 Math. & Physics (1997), 18-23.

  36.  

  37. Baica's General Euclidean Algorithm (BGEA) and sums of some infinite series, Scientific Bulletin of the "Politehnica" University of Timisoara, Romania, Tom 43 (57), 1 Math. & Physics (1998), 54-61.

  38.  

  39. Some infinite series and sums from (BGEA), Scientific Bulletin of the "Politehnica" University of Timisoara, Romania, Tom 43 (57), 2 Math. & Physics (1998), 8-15.

  40.  

  41. with M.Cardu, Regarding a global methodology to estimate the energy-ecologic efficiency of thermopower plants, Energy Conversion & Management, 40 (1999) 71-87.

  42.  

  43. with M.Cardu, Regarding a new variant methodology to estimate globaly the ecologic impact of thermopower plants, Energy Conversion & Management, 40 (1999)1569-1575.

  44.  

  45. The Euler System for the Algebraic Number Theory, Scientific Bulletin of the "Politehnica" University of Timisoara, Romania, Tom 44 (58), 2 Math. & Physics (1999)15-24.

  46.  

  47. with M.Cardu, Regarding the energy ecologic efficiency of desulphurization and denox systems and installations in thermopower plants, Energy Conversion & Management 41 (2000) 1155-1164. 

  48.  

  49. Baica's General Euclidean Algorithm (BGEA) the only Algorithmic explicit solution of Hilbert's tenth problem, The PAMM's periodical Bulletins for Applied and Computer Mathematics .BAM - 743/2000XCII-A, 121-128.

  50.  

  51. Baica's Euclidean solution of Fermat's Last Theorem (FLT), Italian Journal of pure and applied Mathematics, No.7 (2000), 151-156.

  52.  

  53. A BOOK titled:"The Euler System for the Algebraic Number Theory," MB-15/PAMM (2000) 175 pages.

  54.  

  55. with M.Cardu, Application of the methodology to estimate the energy-ecologic efficiency of fluidized bed boilers, Energy Conversion & Management 42 (2001), 867-876.

  56.  

  57. A BOOK titled:"The Algorithmic Solution of the original Euclidean Fermat's Last Theorem," MB-21/PAMM (2001) 92 pages.

  58.  

  59. Solution of Goldbach's Conjecture, Italian Journal of pure and applied Mathematics N.9 (2001), 187-200.

  60.  

  61. The Elliptical Fermat's Last Theorem (ELFLT) and the original Euclidean Fermat's Last Theorem (ELFT), Scientific Bulletin of the "Politehnica" University, Timisoara, Romania, Tom 46 (60), 1 Math. & Physics (2001), 5-12.

  62.  

  63. With M.Cardu, A seismic version regarding a methodology to estimate globally the energy-ecologic efficiency of Thermopower Plants (TPP-s), Energy Conversion and Management 42 (2001), 1317-1325.

  64.  

  65. Algorithmic Solution of the original Euclidean Fermat's Last Theorem (EFLT), The PAMM's Periodical Bulletins for Applied and Computer Mathematics, BAM-1841/2001 (XCVI-A), 29-36.

  66.  

  67. Solution of Goldbach's Conjecture, The PAMM's Periodical Bulletins for Applied and Computer Mathematics, BAM-1842/2001 (XCVI-A), 39-42.

  68.  

  69. With M. Cardu, Gas Turbine Installations with divided expansion, Energy Conversion & Management, 43 (2002), 1747-1756.

  70.  

  71. With M.Cardu, A new global estimation of the atmospheric pollution due to the Thermopower Plants. Scientific Bulletin of the Politehnica" University Timisoara, Romania, Mechanical Section, Tom47 (61) (2002), 41-44.

  72.  

  73. Clarifications of the Author's Previous Paper on Goldbach's Conjecture, Scientific Bulletin of the "Politehnica"University, Timisoara, Romania, Tom 47 (61), 1 Math. & Physics (2002), 20-34.

  74.  

  75. A cyclotomic field to derive some trigonometric identities, The PAMM's Periodical Bulletins for Applied and Computer Mathematics, BAM 2036-CI/2002, 9-14.

  76.  

  77. With M.Cardu, Elements of Polygonal Trigonometry, Scientific Bulletin of the "Polytehnica" Timisoara, Romania, Tom 47 (61), 2 Math. & Physics (2002), 7-13.

  78.  

  79. Some Trigonometric Identities, The PAM's Periodical Bulletins for Applied and Computer Mathematics, BAM-2048/2002 (CII), 1-4.

  80.  

  81. With M.Cardu, About the Ecological aspects of Dual fuel combustion in Thermopower Plants, Energy Conversion & Management 44 (2003), 1773-1786.

  82.  

  83. With M.Cardu, On the relation between Atmospheric pollution due to the Thermopower Plants and the Characteristics of their fuels, Energy Conversion & Management 44 (2003) 1419-1431.

  84.  

  85. Today's status of the Fermat's Last Theorem, Scientific Bulletin of the "Politehnica" University of Timisoara, Romania--Transactions on Mathematics & Physics--Tom 48 (62), 2 (2003)--ISSN 1224-6069 (1-12).

  86.  

  87. With M. Cardu, Regarding the general character of the Polygonal Trigonometry, Scientific Bulletin of the "Politehnica" University of Timisoara, Romania--Transactions on Mathematics & Physics--Tom 48 (62), 1 (2003)--ISSN 1224-6069 (1-6).

  88.  

  89. With A.Peretti, Baica's Contributions to the Solution of the Binary Goldbach Problem, Timisoara Research Centre of the Romanian Academy and "Politehnica"University of Timisoara, Department of Mathematics Prosidings of the tenth Symposium of Mathematics and its Applications (Nov.6-9, 2003).

  90.  

  91. With A. Peretti, The Binary Goldbach Problem, Scientific Bulletin of the "Politehnica"University of Timisoara, Romania--Transactions on Mathematics & Physics--Tom 49 (63), 1, 2004. (Also available in an abridged format.)

  92.  

  93. Baica, Malvina &  Cardu, Mircea, The Hydrogen-Ideal Energy Vector from the Ecological Point of View, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Conference on Pollution Generated by Thermo Power Plants (TPPs), Mechanics, Nov. 2004.

  94.  

  95. With M.Cardu, Regarding the relation between the NOx content and CO content in thermo power plants flue gases, Energy Conversion & Management 46 (2005) 47-59.

  96.  

  97. Baica, Malvina & Peretti, Aldo, The fundamental solution of the equation X^2-DY^2=1,The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania Transactions on Mathematics and Physics, (2005), Tom 50(64), No.2, p.2-9.

  98.  

  99. Baica, Malvina & Cardu, Mircea, Periodic Transtrigonometric Functions, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mechanics, Proceedings of the XI-th International Conference on Vibration Engineering.(2005)

  100.  

  101. Baica, Malvina & Cardu, Mircea, A Global Energy-Ecologic and Synthetic approach of the problem of thermo power plants gaseous pollutant emissions, EMERG I (book on selected papers), Romanian Academy of Sciences (2005), p.233-248.

  102.  

  103. Baica, Malvina & Peretti, Aldo, a BOOK titled : Several “Star” problems in Analytic Number Theory,Monographical Booklets in Applied & Computer Mathematics.MB-31 (2005)/PAMM-Budapest University of Technology and Economics (BUTE), 115 pages.

  104.  

  105. Baica, Malvina & Cardu, Mircea, Nuclear power plants for peak loads in power systems, using the hydrogen as energy agent, Academie Roumaine, Revue Roumaine des Sciences Techniques, Serie Electrotechnique et Energetigue, Tome 51 (2006), No.1, p.97-109.

  106.  

  107. Baica, Malvina& Peretti, Aldo, An Abridged Method to derive asymptotic formula for Goldbach Decomposition, The PAM-CIX/2006, Nr. 2270.

  108.  

  109. Baica, Malvina & Cardu, Mircea, The Infratrigonometry, an inferior order neighborhood domain of Transtrigonometry, The Scientific Bulletin of the “ Politehnica” University of Timisoara, Romania, Transactions on Mathematics and Physics, Tom 51(65), 1, 2006, p. 16-21.

  110.  

  111. Baica, Malvina & Cardu, Mircea, The Ultratrigonometry, a superior order adjacent domain of the Transtrigonometry, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mathematics and Physics, Tom51(65), 1, 2006, p. 29-35.

  112.  

  113. Baica, Malvina & Cardu, Mircea, The Paratrigonometry and some of its Specific Symmetries, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mathematics and Physics, Tom 51 (65), 2, 2006, p.1-11.

  114.  

  115. Baica, Malvina & Peretti, Aldo (2006), A Generalized Descartes (Goldbach) Binary Problem, The PAM’s Periodical Bulletins for applied and Computer Mathematics, BAM-CIX/2006,Nr.2274.

  116.  

  117. Baica, Malvina & Cardu, Mircea, Regarding the Paratrigonometric Equation of the Circle, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mathematics and Physics, Tom 52(66), 1, 2007, p.18-23.

  118.  

  119. Baica, Malvina & Cardu, Mircea, Some Developments of the fundamental Paratrigonometric Equation, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mathematics and Physics, Tom 52(66), 2, 2007,p.23-29.

  120.  

  121. Baica, Malvina, Some new non-classical Trigonometries, The Bulletin for Applied and Computer Mathematics (B A M)-CX/2007, Nr.2309.

  122.  

  123. Baica, Malvina & Cardu, Mircea, The application of the four Trigonometric Quadrants, The Scientific Bulletin of the “ Politehnica “ University of Timisoara, Romania, Transactions on Mathematics & Physics, Tom 53(67) 1, 2008.

  124.  

  125. Baica, Malvina & Cardu, Mircea, An Application case of the Paratrigonometric Polar Coordinates, The Scientific Bulletin of the “ Politehnica” Universityof Timisoara, Romania, Transactions on Mathematics & Physics, Tom 53(67), 2, 2008.

  126.  

  127. Baica, Malvina & Cardu, Mircea, Baica & Cardu  Paratrigonometric functions raised to some powers and their Applications, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mathematics & Physics, Tom 54(68), 1, 2009.

  128.  

  129. With M. Cardu, SONOX criterion application for ecological analysis of thermo power plants operation, Energy Conversion & Management 50 (2009) 304-308.

  130.  

  131. Baica, Malvina & Cardu, Mircea, Para trigonometric functions relative to the finite spirals as the basic trigonometric figures, The Scientific Bulletin of the “ Politehnica” University of Timisoara, Romania, Transactions on Mathematics & Physics, Tom 54(68), 2, 2009, 9 – 17.

  132.  

  133. Baica, Malvina & Cardu, Mircea, Possibilities to represent some symmetric functions by unified equations and some of their applications in the Para trigonometry, The Scientific Bulletin of the “Politehnica” University of Timisoara, Romania, Transactions on Mathematics & Physics, Tom 55(69), 1, 2010, 1 – 11.

  134.  

  135. Baica, Malvina & Cardu, Mircea, A simplified alternative to develop periodic functions in Trigonometric Fourier Series, The Scientific Bulletin of the “ Politehnica” University of Timisoara, Romania, Transactions on Mathematics & Physics, Tom 55(69), 2, 2010.

  136.  

  137. With Cardu, Mircea and Negrea, Virgiliu – Dan, Considerations regarding a Thermo-power installation having a Diesel Engine with Hydrogen combustion and Steam Turbine, Energy Conversion & Management, 51, 2010, 147 – 154.

  138.  

  139. Baica, Malvina & Cardu, Mircea, a BOOK titled: The Paratrigonometry – Nonconventional Trigonometry, The Academy of Technical Sciences of Romania, AGIR Publishing House Bucharest, Romania, 2010.

  140.  

  141. Baica, Malvina & Cardu, Mircea, Paratrigonometry, a Generalization of the Classical and Some New Non- Classical Trigonometries and its Application in Mechanics and Wave Theory, Transylvanian Journal of Mathematics and Mechanics, Volume 2, Number 1, June 2010.