PL EN


Preferences help
enabled [disable] Abstract
Number of results
2020 | 148 | 60-71
Article title

Complexification of operational infinity

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
It is demonstrated here by examples that infinitesimal descending infinity is formwise analogous to the Cauchy integral formula. Hence the concept of total, twin operational infinity is represented by complex formula combining the real neverending ascending infinity and the imaginary infinitesimal descending infinity, each depicted in separate abstract spaces that appear as dual reciprocal, though.
Year
Volume
148
Pages
60-71
Physical description
Contributors
author
  • Science/Mathematics Education Department, Southern University and A&M College, Baton Rouge, LA 70813, USA
References
  • [1] Czajko J. Unrestricted division by zero as multiplication by the – reciprocal to zero – infinity. World Scientific News 145 (2020) 180-197
  • [2] Czajko J. New product differentiation rule for paired scalar reciprocal functions. World Scientific News 144 (2020) 358-371
  • [3] Czajko J. Pairing of infinitesimal descending complex singularity with infinitely ascending, real domain singularity, World Scientific News 144 (2020) 56-69
  • [4] Okumura H., Saitoh S. & Matsuura T. Relations of 0 and ∞. JTSS J. Tech. Soc. Sci. 1(1) (2017) 70-77 see p.74.
  • [5] Matsuura T. & Saitoh S. Matrices and division by zero z/0=0. Adv. Lin. Alg. Matrix Theor. 6 (2016) 51-58
  • [6] Saitoh S. Mysterious properties of the point at infinity. [Manuscript distributed by prof. Saburou Saitoh dated as of Dec-29-2017, see pp.1,4, therein].
  • [7] Needham T. Visual Complex Analysis. Oxford: Clarendon Press, 2001, p.141ff.
  • [8] Sussman G.J. & Wisdom J. with Farr W. Functional differential geometry. Cambridge, MA: The MIT Press, 2013, p.19.
  • [9] Saff E.B. & Snider A.D. Fundamentals of complex analysis with applications to engineering and science. Third edition. Pearson Education, [no publication date], pp.60,382.
  • [10] Biswal C.P. Complex analysis. Delhi: PHI Learning, 2015, p.24.
  • [11] Matthews J.H. & Howell R.W. Complex analysis for mathematics and engineering. New Delhi: Jones and Bartlett, 2011, p.91.
  • [12] Fisher S.D. Complex variables. Mineola, NY: Dover, 1999, p.28.
  • [13] McGehee O.C. An introduction to complex analysis. New York: Wiley, 2000, p.93.
  • [14] Greenleaf F.P. Introduction to complex variables. Philadelphia: Saunders, 1972, pp.209,482.
  • [15] Stewart I. & Tall D. Complex analysis. (The hitchhiker’s guide to the plane). Cambridge: Cambridge Univ. Press, 1996, p.224f.
  • [16] Norton R.E. Complex analysis for scientists and engineers. An introduction. Oxford: Oxford Univ. Press, 2010, p.159f.
  • [17] Boas R.P. Invitation to complex analysis. Washington, DC: MAA, 2010, p.3.
  • [18] Bray C. Multivariable calculus. Lexington, KY, 2009, p.185.
  • [19] Ames W.F. Nonlinear partial equations in engineering. New York: Academic Press, 1965, p.411ff.
  • [20] Ahlfors L.V. Complex analysis. An introduction to the theory of analytic functions of one complex variable. New York: McGraw-Hill, 1966, p.76.
  • [21] Rudin W. Real and complex analysis. New Delhi: McGraw-Hill, 2006, p.18f.
  • [22] Maurin K. Analysis II: Integration, distributions, holomorphic functions, tensor and harmonic analysis. Dordrecht: Reidel, 1980, pp.65,726.
  • [23] Cheng E. Beyond infinity. An expedition to the outer limits of mathematics. New York: Basic Books, 2017, p.13ff.
  • [24] Gelbaum B.R. Modern real and complex analysis. New York: Wiley, 1995, p.367.
  • [25] Greene R.E. & Krantz S.G. Function theory of one complex variable. New York: Wiley, 1997, p.486.
  • [26] Andersson M. Topics in complex analysis. New York: Springer, 1997, p.8.
  • [27] Flanigan F.J. Complex variables. Harmonic and analytic functions. New York: Dover, 1983, p.158ff.
  • [28] Volkovyskii L.I., Lunts G.L. & Aramanovich I.G. A collection of problems on complex analysis. New York: Dover, 1991, p68ff.
  • [29] Miller K.S. An introduction to advanced complex calculus. New York: Dover, 1970, p.80ff.
  • [30] Walker P.L. An introduction to complex analysis. New York: Wiley, 1974, pp.22,31.
  • [31] O’Neil P.V. Advanced engineering mathematics. Pacific Grove, CA: Thompson, 2003, p.1092ff.
  • [32] Watson G.N. Complex integration & Cauchy’s theorem. Mineola, NY: Dover, 2012, pp.31,46.
  • [33] Page A. Mathematical analysis and techniques II. Oxford: Oxford Univ. Press, 1974, p.226.
  • [34] Heins M. Selected topics in the classical theory of functions of a complex variable. Mineola, NY: Dover, 2015, p.135ff.
  • [35] Nevanlinna R. & Paatero V. Introduction to complex analysis. Providence, RI: AMS Chelsea Publishing, 2007, p.131ff.
  • [36] Paliouras J.D. & Meadows D.S. Complex variables for scientists and engineers. Mineola, NY: Dover, 2014, p.211ff.
  • [37] Ablowitz M.J. & Fokas A.S. Complex variables: Introduction and applications. Cambridge: Cambridge Univ. Press, 2017, pp.50,91ff.
  • [38] Weisstein E.W. Cauchy integral formula. Wolfram: MathWorld.
  • [39] Zill D.G. & Shanahan P.D. A first course in complex analysis with applications. Boston: Jones and Bartlett Publishers, 2009, p.246ff.
  • [40] Ash R.B. & Novinger W.P. Complex variables. Mineola, NY: Dover, 2004, p.84.
  • [41] Derrick W.R. Complex analysis and applications. Belmont, CA: Wadsworth, 1984, p.103.
  • [42] Nehari Z. Conformal mapping. New York: Dover, 1975, p.90.
  • [43] Ponnusamy S. & Silverman H. Complex variables with applications. Boston: Birkhäuser, 2006, p.236.
  • [44] Ahlfors L.V. & Sario L. Riemann surfaces. Princeton, NJ: Princeton Univ. Press, 1960, p.16.
  • [45] Junghenn H.D. A course in real analysis. Boca Raton, FL: CRC Press, 2015, p.495.
  • [46] Krantz S.G. Handbook of complex variables. Boston: Birkhäuser, 1999, p.133.
  • [47] Carrier G.F., Krook M. & Pearson C.E. Functions of a complex variable. Theory and technique. Philadelphia: SIAM, 2005, p.40.
  • [48] Marsden J.E. Basic complex analysis. San Francisco: W.H. Freeman, 1973, p.88ff.
  • [49] Wunsch A.D. Complex variables with applications. Reading, MA: Addison-Wesley, 1994, pp.375ff,378ff.
  • [50] Levinson N. & Redheffer R.M. Complex variables. San Francisco: Holden-Day, 1970, pp.133ff,263ff.
  • [51] Dwight H.B. Tables of integrals and other mathematical data. New York; Macmillan, 1961, p.20.
  • [52] Czajko J. Quaternionic division by zero is implemented as multiplication by infinity in 4D hyperspace. World Scientific News 94(2) (2018) 190-216
  • [53] Czajko J. Operational constraints on dimension of space imply both spacetime and timespace. Int. Lett. Chem. Phys. Astron. 36 (2014) 220-235.
  • [54] Gellert W. et al (Eds.), The VNR concise encyclopedia of mathematics. Second edition. New York: Van Nostrand Reinhold, 1989, p.704f.
  • [55] Iyanaga S. & Kawada Y. (Eds.) Encyclopedic dictionary of mathematics 1: A-M. Cambridge, MA: The MIT Press, 1980, p.28,604f.
  • [56] Andrews L.C. & Phillips R.L. Mathematical techniques for engineers and scientists. New Delhi: Prentice-Hall, 2006, p.226ff.
  • [57] Wright J.E. Invariants of quadratic differential forms. Mineola, NY: Dover, 2013, p.22.
  • [58] Tribble A.C. Princeton guide to advanced physics. Princeton, NJ: Princeton Univ. Press, 1996, p.24ff.
  • [59] Euler L. Elements of algebra. Amazon/CreateSpace, 2015, p.50.
  • [60] MacLane S. Mathematical models of space. Am. Math. Month. 68 (1980) 184-191, see p.191.
  • [61] Godement R. Cours d’Algèbre. Paris : Hermann, 1966, p.21.
  • [62] Czajko J. Dual reciprocal scalar potentials paired via differential operators in Frenet frames make the operators to act simultaneously in each of two paired 3D reciprocal spaces. World Scientific News 137 (2019) 96-118
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-d3ff9ea0-49cf-4769-be79-306c015b0230
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.