Contact

All Stories

  1. Working Principle of an Infrared Search and Track (IRST) System

    Article • March 2026, Wiley

    Dr. Chinnaraji Annamalai

  2. Generalized Rational-Form Finite Sum Identities and Derivations within the Annamalai Combinatorial System for Stochastic Network Optimization

    Article • March 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  3. Generalized Closed-Form Finite Sum Identities and Derivations within the Annamalai Combinatorial System for Stochastic Network Optimization

    Article • February 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  4. A Methodological Framework for the Negative Binomial Theorem via Combinatorial Geometric Series and Generating Functions

    Article • February 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  5. Combinatorial Geometric Series and Generating Function: A Methodological Advance for the Negative Binomial Theorem

    Article • February 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  6. Integrating Annamalai Combinatorial Systems into the Foundations of Artificial Intelligence

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  7. Comparative Analysis of Stochastic Modeling and Computational Efficiency in Poisson Binomial and Annamalai Frameworks

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  8. Comparative Analysis of Stochastic Modeling and Computational Efficiency in Poisson Binomial and Annamalai Frameworks

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  9. A Generating Function Approach to Finite Sum Identities in the Annamalai Combinatorial System

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  10. Combinatorial Proof of Figurate Number Identities via the Cauchy Product

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  11. The Unified Properties of the Annamalai Coefficient in Combinatorial Analysis

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  12. Proving the Sum of Finite Combinatorial Geometric Series by Mathematical Induction

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  13. A Derivation of Finite Sum Identity of Combinatorial Geometric Series

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  14. Proof of Finite Sum Identity of Combinatorial Geometric Series

    Article • January 2026, Cambridge University Press

    Dr. Chinnaraji Annamalai

  15. Optimizing Deep Learning Architectures via the Log-Annamalai Probability Mass Function and Generating Functions

    Article • January 2026, Elsevier

    Dr. Chinnaraji Annamalai

  16. Accelerating Real-Time Network Analytics with Log-Annamalai Negative Binomial Distribution on FPGAs

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  17. Annamalai Combinatorial System

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  18. Combinatorial System: Binomial Coefficients and Generating Functions for Combinatorial Geometric Series

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  19. Combinatorial System: Binomial Coefficients, CGS and Generating Functions

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  20. Leveraging the Annamalai Coefficient for Optimized Stochastic Modeling in High-Dimensional Network Traffic

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  21. Recursive Relationships and Closed-Form Expressions in Annamalai’s Combinatorial System: A Framework for Large-Scale Data and Stochastic Modeling

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  22. Annamalai’s Combinatorial System and Generating Functions

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  23. Combinatorial Geometric Series and Negative Binomial Theorem: A Methodological Advance

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  24. Combinatorial Geometric Series and Negative Binomial Theorem: A Methodological Advance

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  25. Combinatorial Geometric Series and Negative Binomial Theorem: A Methodological Advance

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  26. Annamalai's Binomial Coefficient, Identities, and Generating Functions

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  27. Combinatorial Geometric Series and Generating Functions

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  28. Combinatorial System: Coefficients, Identities, and Generating Functions

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  29. Combinatorial System: Coefficients, Identities, and Generating Functions

    Article • December 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  30. A Novel Derivation of Relativistic Energy-Momentum Relation

    Article • October 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  31. Deriving the Accurate Mass-Energy Equivalence from the Energy-Momentum Relation

    Article • October 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  32. Derivation of Relativistic Momentum corresponding to Classical Momentum

    Article • October 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  33. Dirac’s Equation of Relativistic Energy-Momentum: A Compressive Derivation

    Article • October 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  34. Analysis of Mass-Energy Equivalence in Chemical vs. Nuclear Reactions

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  35. The Misconception of Relativistic Mass: A Modern Perspective on Mass and Energy in Special Relativity

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  36. The Spherical Gravitational Well Within a Cube

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  37. The Absence of Straight Lines: A Comparative Analysis of Gravity from Newtonian Physics to Einstein's Spacetime Curvature

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  38. The Conservation of Mass-Energy in the Expanding Cosmos

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  39. The Interplay of Mass and Energy: A Modern Relativistic Perspective

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  40. The Role of Gravity in Cosmic Stability

    Article • September 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  41. The Einstein’s Kinetic Energy: Is it valid?

    Article • April 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  42. Derivation of the Einstein’s Mass-Energy Equation from the Newton’s Second Law of Motion

    Article • March 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  43. The Einstein’s Mass-Energy Equivalence and the Relativistic Mass and Energy derived from the Newton’s Second Law of Motion

    Article • March 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  44. The Einstein’s Mass-Energy Equation: Kinetic Energy (½mv^2), Potential Energy (mgh), and Work done (mas)

    Article • March 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  45. Derivation of the Einstein’s Mass-Energy Equation (Sum of Kinetic Energy and Rest mass Energy) using Classical Mechanics

    Article • March 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  46. The Einstein’s Mass-Energy Equivalence relating to Total Energy

    Article • February 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  47. The Network of Cosmic Systems keeps the Universe as Stable

    Article • February 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  48. The Universe with its Systems is Stable

    Article • February 2025, Cambridge University Press

    Dr. Chinnaraji Annamalai

  49. Derivation of Relativistic Momentum Corresponding to Classical Momentum

    Article • January 2025, Elsevier

    Dr. Chinnaraji Annamalai

  50. Combinatorial System: Coefficients, Identities, and Generating Functions

    Article • January 2025, Elsevier

    Dr. Chinnaraji Annamalai

  51. Novel Method to compute the Sum of Geometric Series on Real Numbers

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  52. Novel Technique to compute the Sum of Geometric Series on Fraction

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  53. Computing the Sum of Geometric Series based on Algebraic Expression

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  54. New Method to compute the Sum of Geometric Series on Fractional Numbers

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  55. Computation of Novel Binomial Series and Theorems using Bivariable Geometric Series based on Algebraic Expression

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  56. Computation of the Sum of Geometric Series on Numerical Expression

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  57. Computation of Novel Binomial Series and Theorems using Multivariable Geometric Series

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  58. Computation of Geometric Series on Numerical Expansions

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  59. Computation of Novel Binomial Series using Bivariable Geometric Series

    Article • November 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  60. The Gaussian Integral for the Normal Distribution in Machine Leaning

    Article • October 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  61. Computation of Geometric Series on Relation between Dirichlet Eta Function and Riemann Zeta Function

    Article • October 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  62. Sum of Series involving Anna Iota Function and Riemann Zeta Function

    Article • September 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  63. Computation of Analog Theorems for the Annamalai Iota Function

    Article • September 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  64. Computation of Analog Theorems for the Dirichlet Eta Function

    Article • September 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  65. Computation of the Riemann Zeta Function equal to the Harmonic Series

    Article • September 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  66. Computation of Analog Theorem for Dirichlet Eta Function and Riemann Zeta Function

    Article • September 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  67. Application of Geometric Series and Maclaurin Series Relating to Taylor Series

    Article • August 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  68. Computer Program in C Programing Language for Calculating the Value of Euler Product equal to the Riemann Zeta Function

    Article • August 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  69. Product of Geometric Series on Prime Numbers is equal to Sum of Natural Numbers

    Article • August 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  70. Riemann Zeta Function and Dirichlet Eta Function relating to Alternative Harmonic Series

    Article • August 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  71. The main reason why the Euler product is not equal to the Riemann Zeta function

    Article • August 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  72. Disproof of the Euler Product equal to the Riemann Zeta Function   

    Article • July 2024, Institute of Electrical & Electronics Engineers (IEEE)

    Dr. Chinnaraji Annamalai

  73. Representation of the Euler Product for the Riemann Zeta Function

    Article • July 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  74. Computation of the Riemann Zeta Function for deriving the Euler Product

    Article • July 2024, Institute of Electrical & Electronics Engineers (IEEE)

    Dr. Chinnaraji Annamalai

  75. A Simple Proof of the Euler Product for the Riemann Zeta Function

    Article • July 2024, Institute of Electrical & Electronics Engineers (IEEE)

    Dr. Chinnaraji Annamalai

  76. New Mathematical Model for Quadratics

    Article • March 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  77. TCP/IP and Cellular Networks of GSM

    Article • February 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  78. Energy of the Object in Motion

    Article • February 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  79. Equations of the Energy-Work Relation: Right and Wrong

    Article • February 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  80. Error Correction in the Equations of Energy-Work Relation

    Article • February 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  81. Upper Limits for Velocity, Momentum, and Energy of Motion

    Article • January 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  82. Variations on the Equations of Energy-Work Relation

    Article • January 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  83. Energy-Force Relation

    Article • January 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  84. Einstein’s Special Theory of Relativity: A New Mass-Energy Equation

    Article • January 2024, Cambridge University Press

    Dr. Chinnaraji Annamalai

  85. Computation of the Euler Product Representation for the Riemann Zeta Function

    Article • January 2024, Elsevier

    Dr. Chinnaraji Annamalai

  86. Einstein’s Special Theory of Relativity: A New Mass-Energy Equivalence

    Article • SSRN Electronic Journal, January 2024, Elsevier

    Dr. Chinnaraji Annamalai

  87. Energy of the Object in Motion

    Article • SSRN Electronic Journal, January 2024, Elsevier

    Dr. Chinnaraji Annamalai

  88. New Mathematical Model for Quadratics

    Article • SSRN Electronic Journal, January 2024, Elsevier

    Dr. Chinnaraji Annamalai

  89. TCP/IP and Cellular Networks of GSM

    Article • SSRN Electronic Journal, January 2024, Elsevier

    Dr. Chinnaraji Annamalai

  90. A Different Perspective for Geometric Series with Binomial Coefficients

    Article • Kırklareli Üniversitesi Mühendislik ve Fen Bilimleri Dergisi, December 2023, Kirklareli Universitesi Muhendislik ve Fen Bilimleri Dergisi

    Dr. Chinnaraji Annamalai

  91. Einstein’s Special Theory of Relativity: A New Mass-Energy Equation

    Article • December 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  92. Upper Limits for Relativistic Energy and Momentum

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  93. Upper Limits for Relativistic Energy and Momentum

    Article • December 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  94. Upper Limit for the Energy of Motion

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  95. Upper Limit for the Energy of Motion

    Article • December 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  96. A New Mass-Energy Equivalence from Lorentz Factor and Energy of Motion

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  97. Mass-Energy Equivalence: Light Energy

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  98. A New Mass-Energy Equivalence from Lorentz Factor and Energy of Motion

    Article • December 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  99. Binomial Series without Binomial Coefficients

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  100. Energy-Momentum Equivalence

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  101. Energy-Work Equivalence

    Article • December 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  102. Momentum-Velocity Equivalence

    Article • November 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  103. Computation of Mass-Energy Equation from Lorentz Factor and Kinetic Energy

    Article • November 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  104. Binomial Geometric Series for Computational Application

    Article • November 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  105. Novel Binomial Series without Binomial Coefficients

    Article • November 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  106. Computation of Mass-Energy Equation from Lorentz Factor and Kinetic Energy

    Article • November 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  107. A Computational Comparison of Novel and Traditional Binomial Series

    Article • November 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  108. Novel Binomial Series without Binomial Coefficients

    Article • November 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  109. Binomial Geometric Series for Computational Application

    Article • November 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  110. A Novel Computational Approach to Binomial Coefficients in Discrete System

    Article • October 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  111. Lorentz Factor and Time Dilation on the Special Theory of Relativity

    Article • October 2023, Institute of Electrical & Electronics Engineers (IEEE)

    Dr. Chinnaraji Annamalai

  112. Lorentz Factor and Time Dilation on the Special Theory of Relativity

    Article • October 2023, Institute of Electrical & Electronics Engineers (IEEE)

    Dr. Chinnaraji Annamalai

  113. Computational Technique for Geometric Series with Radicals

    Article • October 2023, Institute of Electrical & Electronics Engineers (IEEE)

    Dr. Chinnaraji Annamalai

  114. Binomial Geometric Series

    Article • October 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  115. Geometric Progression-Based Binomial Series for Computing Application

    Article • October 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  116. Computational Technique for Geometric Series with Radicals

    Article • October 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  117. Lorentz Factor and Time Dilation on the Special Theory of Relativity

    Article • October 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  118. Binomial Geometric Series

    Article • October 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  119. Geometric Progression-Based Binomial Series for Computing Application

    Article • October 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  120. A Generalized Computational Method for Multi-Ordered Geometric Series

    Article • September 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  121. New Approach to Geometric Series for Computational Applications

    Article • September 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  122. Computation of Geometric Series: A New Approach

    Article • September 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  123. A Novel Approach to Computation of Multiple Geometric Series

    Article • September 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  124. New Approach to Geometric Series for Computational Applications

    Article • September 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  125. A New Perspective on Geometric Series for Computing Applications

    Article • September 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  126. A New Perspective on Geometric Series for Computing Applications

    Article • August 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  127. Novel Geometric Series for Application of Computing Science

    Article • August 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  128. Novel Geometric Series for Application of Cryptography

    Article • August 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  129. Novel Geometric Series for Application of Cryptography

    Article • August 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  130. Novel Geometric Series for Application of Computational Science

    Article • August 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  131. An Alternative Method for the Gamma Function derived from Natural Logarithm and Pi Function

    Article • The Journal of Engineering and Exact Sciences, June 2023, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  132. Mass-Energy Equivalence: Light Energy

    Article • June 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  133. The Einstein’s Mass-Energy Equivalence and the Relativistic Mass and Momentum derived from the Newton’s Second Law of Motion

    Article • June 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  134. Mass-Energy Equivalence: Light Energy

    Article • June 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  135. Mass-Energy Equivalence derived from Newtonian mechanics

    Article • The Journal of Engineering and Exact Sciences, June 2023, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  136. Einstein’s Mass-Energy Equivalence is not applicable to Photon Energy

    Article • June 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  137. A Mathematical Approach to the Momentum Equations of Massless Photon and Particle with Relativistic Mass

    Article • June 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  138. The Einstein’s Mass-Energy Equivalence and the Relativistic Mass and Momentum derived from the Newton’s Second Law of Motion

    Article • June 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  139. Mass-Energy Equivalence derived from Work and Kinetic Energy

    Article • June 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  140. Work done by Time is equal to Einstein’s Mass-Energy Equivalence

    Article • June 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  141. Mathematical Approach to the Momentum Equations of Massless Photon and Particle with Relativistic Mass

    Article • June 2023, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  142. A Mathematical Approach to the Momentum Equations of Massless Photon and Particle with Relativistic Mass

    Article • June 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  143. Einstein’s Mass-Energy Equivalence and Relativistic Mass derived from Newton’s Second Law of Motion

    Article • May 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  144. The Einstein’s Mass-Energy Equivalence and the Relativistic Mass and Momentum derived from the Newton’s Second Law of Motion

    Article • May 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  145. Relation between Kinetic Energy and Mass-Energy Equivalence

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  146. Relation between Kinetic Energy and Relativistic Mass-Energy

    Article • May 2023, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  147. Einstein’s Mass-Energy Equivalence and the Relativistic Mass and Momentum derived from the Newton’s Second Law of Motion

    Article • May 2023, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  148. The Einstein’s Mass-Energy Equivalence and the Relativistic Mass and Momentum derived from the Newton’s Second Law of Motion

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  149. A Solution for Algebraic Equations x^2+1=0 and x^2-1=0 is √(-1)

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  150. The Starting Point of Complex Number

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  151. A Theorem on the Imaginary Number √(-1)

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  152. Biosystems and Ghosts

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  153. Speed of Massless Object is equal to the Speed of Light

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  154. An Alternative Method for the Gamma Function derived from Natural Logarithm and Pi Function

    Article • May 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  155. Speed of Matter is less than Speed of Light

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  156. E=mc^2 : Mass-Energy Equivalence

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  157. An Alternative Method for the Gamma Function derived from Natural Logarithm and Pi Function

    Article • May 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  158. Geometric Series with Binomial Coefficients: A New Approach

    Article • May 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  159. Gamma Function derived from Natural Logarithm and Pi Function

    Article • May 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  160. Geometric Series with Binomial Coefficients: A New Approach

    Article • April 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  161. Proof of Gamma Function using Natural Logarithm and Pi Function

    Article • April 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  162. A Simple Proof of Pi Value and Euler’s Identity

    Article • April 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  163. Factorial Theorem for Computation of Factorials to Positive Real Numbers

    Article • April 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  164. Gamma Function derived from Factorial Function based-Pi Function

    Article • April 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  165. Gamma Function derived from Natural Logarithm and Pi Function

    Article • April 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  166. Factorial Theorem for Computing the Factorial of Positive Real Number

    Article • April 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  167. Review on the Gamma Function and Error Correction

    Article • April 2023, Cambridge University Press

    Dr. Chinnaraji Annamalai

  168. Analysis of Factorial Function for Non-Negative Real Numbers

    Article • April 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  169. Review on the Gamma Function and Error Correction

    Article • March 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  170. Factorials: Difference between 0! and 1!

    Article • March 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  171. Vector Space on the Binomial Coefficients in Combinatorial Geometric Series

    Article • The Journal of Engineering and Exact Sciences, March 2023, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  172. Theorem on the Binomial Coefficient for Positive Real Number

    Article • March 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  173. Factorial Theorem: An Alternative to Gamma Function

    Article • March 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  174. Binomial Coefficients and Factorials for Non-Negative Real Numbers

    Article • March 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  175. Real Numbers with Binomial Coefficients of Geometric Series

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  176. Finite and Infinite Geometric Series with Binomial Coefficients

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  177. Combinatorial Geometric Series: Infinite Series with Binomial Coefficients

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  178. Computation of Binomial Coefficient with Real Number

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  179. Annamalai Series

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  180. Summation of Combinatorial Geometric Series

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  181. Fourier Series with Binomial Coefficients of Combinatorial Geometric Series

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  182. Trigonometric Equations and Series by Combinatorial Geometric Series

    Article • February 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  183. Application of combinatorial Algebraic Equations in Computing and Cybersecurity

    Article • January 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  184. Computation of Algebraic Equations of Combinatorial Geometric Series

    Article • January 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  185. Method for solving the Algebraic Equations of Combinatorial Geometric Series

    Article • January 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  186. Analysis of Combinatorial Binomial Coefficients and Series

    Article • January 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  187. System of Novel Binomial Coefficients and Series

    Article • January 2023, Center for Open Science

    Dr. Chinnaraji Annamalai

  188. A Computational Comparison of Novel and Traditional Binomial Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  189. A Novel Approach to Computation of Multiple Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  190. A Novel Mass-Energy Equation from Lorentz Factor and Energy of Motion

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  191. A Simple Proof of Pi Value and Euler’s Identity

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  192. A Theorem on the Imaginary Number √(-1)

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  193. Analysis of Combinatorial Binomial Coefficients and Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  194. Annamalai Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  195. Binomial Coefficients and Factorials for Non-Negative Real Numbers

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  196. Combinatorial Geometric Series: Infinite Series with Binomial Coefficients

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  197. Computation of Algebraic Equations of Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  198. Computation of Algebraic Expressions and Geometric Series with Radicals

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  199. Computation of Binomial Coefficient with Real Number

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  200. E=mc^2 : Mass-Energy Equivalence

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  201. Factorial Theorem: An Alternative to Gamma Function

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  202. Finite and Infinite Geometric Series with Binomial Coefficients

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  203. Fourier Series with Binomial Coefficients of Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  204. Lorentz Factor and Time Dilation on the Special Theory of Relativity

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  205. Method for Solving the Algebraic Equations of Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  206. Novel Geometric Series for Application of Cryptography

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  207. Real Numbers with Binomial Coefficients of Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  208. Review on the Gamma Function and Error Correction

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  209. Summation of Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  210. System of Novel Binomial Coefficients and Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  211. Theorem on the Binomial Coefficient for Positive Real Number

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  212. Trigonometric Equations and Series by Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  213. Upper Limits for Velocity, Momentum, and Energy of Motion

    Article • SSRN Electronic Journal, January 2023, Elsevier

    Dr. Chinnaraji Annamalai

  214. Skew Field on the Binomial Coefficients in Combinatorial Geometric Series

    Article • The Journal of Engineering and Exact Sciences, November 2022, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  215. Novel Multinomial Expansion and Theorem

    Article • November 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  216. Construction of Novel Binomial Theorem

    Article • November 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  217. Annamalai’s Binomial Expansion

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  218. Algorithmic Approach for Computation of Binomial Expansions

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  219. Computation and Analysis of Combinatorial Geometric Series and Binomial Series

    Article • October 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  220. Abelian Group on the Binomial Coefficients in Combinatorial Geometric Series

    Article • The Journal of Engineering and Exact Sciences, October 2022, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  221. Computation for the Summation of Binomial Series and Combinatorial Geometric Series

    Article • October 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  222. Two Different and Equal Coefficients of Combinatorial Geometric Series

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  223. Lemma on the Binomial Coefficients of Combinatorial Geometric Series

    Article • The Journal of Engineering and Exact Sciences, October 2022, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  224. Computation and Summation of Binomial Series and Combinatorial Geometric Series

    Article • October 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  225. Computation and Summation of Binomial Series and Combinatorial Geometric Progression

    Article • October 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  226. Computation and Analysis of Binomial Series

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  227. Computational Analysis of Binomial Series

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  228. A Theorem on Binomial Series

    Article • October 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  229. Sum of Binomial Coefficients and its Lemma

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  230. Theorems on Binomial Series

    Article • October 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  231. The Root of a Binomial Coefficient is equal to the Sum of its Leaves

    Article • October 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  232. Binomial Coefficient: Root, Predecessor, Successor, and Leaf

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  233. Lemma on Combinatorial Geometric Series with Binomial Coefficients

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  234. Combinatorial and Multinomial Coefficients and its Computing Techniques for Machine Learning and Cybersecurity

    Article • The Journal of Engineering and Exact Sciences, September 2022, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  235. Ring Field and Vector Space on Combinatorial Geometric Series and Binomial Coefficients

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  236. Sum of Successive Partitions of Binomial Coefficient

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  237. Alternative to the Binomial Series or Binomial Theorem

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  238. Computation and Calculus for Combinatorial Geometric Series and Binomial Identities and Expansions

    Article • The Journal of Engineering and Exact Sciences, September 2022, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  239. Computation and Calculus for Combinatorial Geometric Series and Binomial Identities and Expansions

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  240. Sum of Successive Partitions of Binomial Coefficient

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  241. Scalar and Vector Space of Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  242. Commutative Ring and Field on the Binomial Coefficients of Combinatorial Geometric Series

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  243. Construction and Analysis of Binomial Coefficients

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  244. Binomial Coefficients of Combinatorial Geometric Series: System of Natural Numbers

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  245. Real and Complex Numbers of Binomial Coefficients in Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  246. Combinatorial Geometric Series: Vector Space

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  247. Commutative Division Ring and Skew Field on the Binomial Coefficients of Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  248. Sum of Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  249. Abelian Group on the Binomial Coefficients of Combinatorial Geometric Series

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  250. Abelian Group on the Binomial Coefficients of Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  251. Generalized Methods to prove the Factorial and Multinomial Theorems for Machine Leaning and Cybersecurity

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  252. A Theorem on the Binomial Coefficients of Combinatorial Geometric Series and Some Solutions on Partitions of the Binomial Coefficients

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  253. Partition of Multinomial Coefficient

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  254. Computation of Binomial, Factorial and Multinomial Theorems for Machine Leaning and Cybersecurity

    Article • September 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  255. Successive Partition Method for Binomial Coefficient in Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  256. A Generalized Method for proving the Theorem derived from the Binomial Coefficients in Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  257. Theorems on the Binomial Coefficients for Combinatorial Geometric Series

    Article • September 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  258. Computation of Factorial and Multinomial Theorems for Machine Leaning and Cybersecurity

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  259. Computation of Multinomial and Factorial Theorems for Cryptography and Machine Learning

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  260. Binomial Theorem on the Coefficients for Combinatorial Geometric Series

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  261. Computation of Combinatorial Geometric Series and its Combinatorial Identities for Cryptographic Algorithm and Machine Learning

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  262. Multinomial-based Factorial Theorem on the Binomial Coefficients for Combinatorial Geometric Series

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  263. Binomial Identities on the Coefficients for Combinatorial Geometric Series

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  264. Binomial Coefficients and Identities in Combinatorial Geometric Series

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  265. Computation of Combinatorial Geometric Series and its Combinatorial Identities for Machine Learning and Cybersecurity

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  266. Combinatorial Techniques and Multinomial Theorems with Factorials for Machine Learning and Cybersecurity

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  267. Multinomial Computation and Factorial Theorems for Artificial Intelligence and Cybersecurity

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  268. Factorials, Integers, Binomial Coefficient and Factorial Theorem

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  269. Binomial Coefficients and Identities in Combinatorial Geometric Series

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  270. Computation Method for Combinatorial Geometric Series and its Applications

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  271. Multinomial Computation and Factorial Theorems for Cryptographic Algorithm and Machine Learning

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  272. Factorials, Integers and Multinomial Coefficients and its Computing Techniques for Machine Learning and Cybersecurity

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  273. Combinatorial Theorems in Factorials with Multinomial Computation

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  274. Factorials, Integers, and Factorial Theorems for Computing and Cryptography

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  275. Factorial, Integers, and Multinomials for Algorithms

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  276. Computational and Numerical Methods for Combinatorial Geometric Series and its Applications

    Article • August 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  277. Computation of Geometric Series with Negative Exponents

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  278. Computation of Derivative of Geometric Series without Differentiation

    Article • August 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  279. Computational Method for Combinatorial Geometric Series and Binomial Theorems

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  280. New Idea to compute the Geometric Series and its Derivative

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  281. Computing Method for Combinatorial Geometric Series and Binomial Expansion

    Article • July 2022, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  282. Numerical Method and Computation for Combinatorial Geometric Series and Binomial Theorems

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  283. Computing Method for Combinatorial Geometric Series and Binomial Expansion

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  284. A Theorem on the Annamalai’s Binomial Identities

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  285. Computing Method for Combinatorial Geometric Series and Binomial Expansion

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  286. Combinatorial Geometric Series and Binomial Theorems

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  287. Calculus and Computation for Geometric Series with Binomial Coefficients

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  288. Computational Method and Calculus for the Summation of Geometric Series and Binomial Expansions

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  289. Combinatorial Geometric Series

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  290. Computation of Summations of Annamalai’s Binomial Expansions

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  291. Computational Techniques and Calculus for the Summation of Geometric Series and Binomial Expansions

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  292. Computation and Calculus for the Summation of Geometric Series and Binomial Expansions

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  293. Computation Method for the Summation of Series of Binomial Expansions and Geometric Series with its Derivatives

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  294. Computational Technique and Differential Calculus for the Summation of Geometric Series and Binomial Expansions

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  295. Combinatorial and Algorithmic Technique for Computation of Binomial Expansions and Geometric Series with its Derivatives

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  296. Computation and Numerical Method for Summations of Binomial and Geometric Series

    Article • July 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  297. Differential Calculus for the Summation of Geometric Series with Binomial Expansions

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  298. Algorithmic Technique for Computation of Binomial Expansions and Geometric Series of Multiples of Powers of Two

    Article • July 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  299. Algorithmic and Numerical Techniques for Computation of Binomial and Geometric Series

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  300. Computation for the Summation of Binomial Expansions and Geometric Series of Multiples of Powers of Two

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  301. Computation for the Summation of Integers and Geometric Progression of Powers of Two

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  302. Numerical Computational Method for Computation of Binomial Expansions and Geometric Series

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  303. Computation Method for Summation of Binomial Expansions equal to Sum of Geometric Series with Exponents of Two

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  304. Computational Method for Summation of Binomial Expansions equal to Sum of Geometric Series with Exponents of 2

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  305. Computation and combinatorial Techniques for Binomial Coefficients and Geometric Series

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  306. Computing Method for Binomial Expansions and Geometric Series

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  307. Computing Method for Sum of Geometric Series and Binomial Expansions

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  308. Sum of the Summations of Binomial Expansions with Geometric Series

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  309. Computation of Geometric Series in Different Ways

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  310. Computing Method for the Summation of Series of Binomial Coefficients

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  311. Factorials, Integers and Mathematical and Binomial Techniques for Machine Learning and Cybersecurity

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  312. A novel computational technique for the geometric progression of powers of two

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  313. Sum of the Summation of Binomial Expansions with Optimized Binomial Coefficient

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  314. Combinatorial Techniques for Binomial Expansions with Multiples of 2

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  315. Factorials and Integers for Applications in Computing and Cryptography

    Article • June 2022, Cambridge University Press

    Dr. Chinnaraji Annamalai

  316. My New Idea for Optimized Combinatorial Techniques

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  317. Extension of Binomial Series with Optimized Binomial Coefficient

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  318. Factorial of Sum of Two Nonnegative Integers Is Equal to Multiple of the Product of Factorial of the Two Nonnegative Integers

    Article • June 2022, MDPI AG

    Dr. Chinnaraji Annamalai

  319. Analysis of the Relationship between Factorials and Integers

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  320. Factorial of Sum of Two nonnegative Integers is equal to Multiple of the Product of Factorial of the Two Nonnegative Integers

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  321. Factorial of Sum of Nonnegative Integers for Computing and Algorithms

    Article • June 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  322. Application of Factorial and Binomial identities in Communications, Information and Cybersecurity

    Article • May 2022, Springer Science + Business Media

    Dr. Chinnaraji Annamalai

  323. Intuitionistic Fuzzy sets and Combinatorial Techniques in Computation and Weather Analysis

    Article • May 2022, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  324. Intuitionistic Fuzzy sets and Combinatorial Techniques in Computation and Weather Analysis

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  325. Computation of Sum of Optimized Binomial Coefficients and Application in Computational Science and Engineering

    Article • May 2022, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  326. Computation of Sum of Optimized Binomial Coefficients and Application in Computational Science and Engineering

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  327. Application of Factorial and Binomial identities in Communication and Cybersecurity

    Article • May 2022, Springer Science + Business Media

    Dr. Chinnaraji Annamalai

  328. Application of Factorial and Binomial identities in Cybersecurity and Communications

    Article • May 2022, Springer Science + Business Media

    Dr. Chinnaraji Annamalai

  329. Computation of Binomial Expansions and Application in Science and Engineering

    Article • May 2022, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  330. Application of Factorial and Binomial identities in Computing and Cybersecurity

    Article • May 2022, Springer Science + Business Media

    Dr. Chinnaraji Annamalai

  331. Sum of Summations of Annamalai’s Binomial Expansions

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  332. Application of Factorial and Binomial identities in Computing and Cybersecurity

    Article • May 2022, Springer Science + Business Media

    Dr. Chinnaraji Annamalai

  333. Relation between the Results of Binomial Expansions with Multiple of 2

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  334. A Binomial Expansion equal to Multiple of 2 with Non-Negative Exponents

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  335. Combinatorial Theorem for Multiple of Two with Exponents

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  336. Application of Factorial and Binomial identities in Cybersecurity

    Article • May 2022, Open Engineering Inc

    Dr. Chinnaraji Annamalai

  337. Application of Factorial and Binomial identities in Cybersecurity

    Article • May 2022, Springer Science + Business Media

    Dr. Chinnaraji Annamalai

  338. Application of Annamalai’s Factorial and Binomial identities in Cybersecurity

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  339. Differentiation and Integration of Annamalai’s Binomial Expansion

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  340. Theorems based on Annamalai’s Binomial Coefficient and Identity

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  341. Ascending and Descending Orders of Annamalai’s Binomial Coefficient

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  342. Binomial Distribution with Optimized Combination of Combinatorics

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  343. Intuitionistic fuzzy sets: new approach and applications

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  344. The Einstein’s Mass-Energy  Equivalence and the Relativistic Mass and Momentum derived from the Newton’s  Second Law of Motion                      

    Article • May 2022, Wiley

    Dr. Chinnaraji Annamalai

  345. A Model of Iterative Computations for Recursive Summability

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  346. Applications of exponential decay and geometric series in effective medicine dosage

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  347. Computational modelling for the formation of geometric series using Annamalai computing method

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  348. Novel Computing Technique in Combinatorics

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  349. Optimized Computing Technique for Combination in Combinatorics

    Article • May 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  350. Analysis and Computation of Extended Geometric Series and Summability

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  351. Annamalai’s Binomial Identity and Theorem

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  352. Computation of multiple binomial Series based on geometric series

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  353. Sum of Geometric Series with Negative Exponents

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  354. Series and Summations on Binomial Coefficients of Optimized Combination

    Article • The Journal of Engineering and Exact Sciences, April 2022, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai

  355. Summations of Single Terms and Successive Terms of Geometric Series

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  356. Multiple summations of a geometric series and its binomial series

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  357. Comparison between Optimized and Traditional Combinations of Combinatorics

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  358. Novel Binomial Series and its Summations

    Article • April 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  359. Combinatorial Relation of Optimized Combination with Permutation

    Article • March 2022, Center for Open Science

    Dr. Chinnaraji Annamalai

  360. A Binomial Expansion Equal to Multiple of 2 with Non-Negative Exponents

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  361. A Generalized Method for Proving the Theorem derived from the Binomial Coefficients in Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  362. A Theorem on Binomial Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  363. A Theorem on Successive Partitions of Binomial Coefficient

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  364. A Theorem on the Annamalai’s Binomial Identities

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  365. A Theorem on the Binomial Coefficients of Combinatorial Geometric Series and Some Solutions on Partitions of the Binomial Coefficients

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  366. Abelian Group on the Binomial Coefficients of Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  367. Algorithmic Approach for Computation of Binomial Expansions

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  368. Algorithmic Technique for Computation of Binomial Expansions and Geometric Series of Multiples of Powers of Two

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  369. Analysis of the Relationship between Integers and Factorial Functions

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  370. Annamalai's Binomial Identity and Theorem

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  371. Annamalai’s Binomial Expansion

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  372. Application of Factorial and Binomial identities inCybersecurity

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  373. Ascending and Descending Orders of Annamalai’s Binomial Coefficient

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  374. Binomial Coefficients and Identities in Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  375. Binomial Coefficients in Combinatorial Geometric Series and its Combinatorial Identities

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  376. Binomial Theorem on the Coefficients for Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  377. Combinatorial Relation of Optimized Combination with Permutation

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  378. Combinatorial Theorems in Factorials with Multinomial Computation

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  379. Comparison between Optimized and Traditional Combinations of Combinatorics

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  380. Computation Method for Combinatorial Geometric Series and its Applications

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  381. Computation and Analysis of Combinatorial Geometric Series and Binomial Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  382. Computation for the Summation of Binomial Expansions and Geometric Series of Multiples of Powers of Two

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  383. Computation for the Summation of Integers and Geometric Progression of Powers of Two

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  384. Computation of Derivative of Geometric Series without Differentiation

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  385. Computation of Factorial and Multinomial Theorems for Machine Leaning and Cybersecurity

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  386. Computation of Geometric Series with Negative Exponents

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  387. Computing Method for Combinatorial Geometric Series and Binomial Expansion

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  388. Construction of Novel Binomial Expansion

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  389. Differential Calculus for the Summation of Geometric Series with Binomial Expansions

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  390. Differentiation and Integration of Annamalai’s Binomial Expansion

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  391. Extension of Binomial Series with Optimized Binomial Coefficient

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  392. Factorial of Sum of Nonnegative Integers for Computing and Algorithms

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  393. Factorials, Integers and Mathematical and Binomial Techniques for Machine Learning and Cybersecurity

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  394. Factorials, Integers and Multinomial Coefficients and its Computing Techniques for Machine Learning and Cybersecurity

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  395. Factorials, Integers, Binomial Coefficient and Factorial Theorem

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  396. Factorials, Integers, and Factorial Theorems for Computing and Cryptography

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  397. Lemma on Combinatorial Geometric Series with Binomial Coefficients

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  398. Multinomial Theorem on the Binomial Coefficients for Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  399. Multinomial-based Factorial Theorem on the Binomial Coefficients for Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  400. Multiple Summations of a Geometric Series and Its Binomial Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  401. New Idea to Compute the Geometric Series and its Derivative

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  402. Novel Binomial Series and its Summations

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  403. Novel Multinomial Expansion and Theorem

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  404. Partition of Multinomial Coefficient

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  405. Successive Partition Method for Binomial Coefficient in Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  406. Sum of Geometric Series with Negative Exponents

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  407. Sum of Summations of Annamalai’s Binomial Expansions

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  408. Sum of the Summation of Binomial Expansions with Optimized Binomial Coefficient

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  409. Summation of Series of Binomial Coefficients

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  410. Summations of Single Terms and Successive Terms of Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  411. Theorems based on Annamalai’s Binomial Coefficient and Identity

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  412. Theorems on the Binomial Coefficients for Combinatorial Geometric Series

    Article • SSRN Electronic Journal, January 2022, Elsevier

    Dr. Chinnaraji Annamalai

  413. COMBINATORIAL TECHNIQUE FOR OPTIMIZING THE COMBINATION

    Article • The Journal of Engineering and Exact Sciences, June 2020, Universidade Federal de Vicosa

    Dr. Chinnaraji Annamalai, Prof. Vishnu Narayan Mishra

  414. Extension of ACM for Computing the Geometric Progression

    Article • Journal of Advances in Mathematics and Computer Science, April 2019, Sciencedomain International

    Dr. Chinnaraji Annamalai

  415. Computation of Series of Series Using Annamalai’s Computing Model

    Article • SSRN Electronic Journal, January 2019, Elsevier

    Dr. Chinnaraji Annamalai

  416. Annamalai’s Computing Model for Algorithmic Geometric Series and Its Mathematical Structures

    Article • Mathematics and Computer Science, January 2018, Science Publishing Group

    Dr. Chinnaraji Annamalai

  417. Algorithmic Computation of Annamalai’s Geometric Series and Summability

    Article • Mathematics and Computer Science, January 2018, Science Publishing Group

    Dr. Chinnaraji Annamalai

  418. Analysis and Modelling of Annamalai Computing Geometric Series and Summability

    Article • Mathematical Journal of Interdisciplinary Sciences, September 2017, Chitkara University Publications

    Dr. Chinnaraji Annamalai

  419. Applications of exponential decay and geometric series in effective medicine dosage

    Article • Advances in Bioscience and Biotechnology, January 2010, Scientific Research Publishing, Inc,

    Dr. Chinnaraji Annamalai