scholarly journals Introducing Complex Numbers into Basic Growth Functions (4) : Hypothetic Appearance of Exponential Function with Base e from the Complex Representation of '0+(-1)+1'

10.5109/4596 ◽  
2004 ◽  
Vol 49 (2) ◽  
pp. 349-353
Author(s):  
Masataka Shimojo ◽  
Kentarou Ikeda ◽  
Reiko Ishiwaka ◽  
Hiroyuki Sato ◽  
Yoki Asano ◽  
...  
Keyword(s):  
Exponential Function ◽  
Complex Representation ◽  
Complex Numbers ◽  
Growth Functions

scholarly journals Beschreibung des Wachstums weiblicher Rinder verschiedener Rassen

1999 ◽  
Vol 42 (4) ◽  
pp. 335-346
Author(s):  
H.-D. Matthes ◽  
P. E. Rudolph
Keyword(s):  
Exponential Function ◽  
Adult Animal ◽  
Natural Growth ◽  
Growth Functions ◽  
Weight Data

Abstract. Title ofthe paper: Description on the growth of female cows of different race Continuously won weight data from the birth up to the adult animal of female cows of the races Charolais, Fleckvieh and Uckermärker were used for the determination of best fitted functions with respect to some' optimum functions from different growth-functions like exponential-, Gompertz-, logisfic-, Bertalanffy-, tanhand Janoschek-function. The four-parametric Richards- and Janoschek-function describe the natural growth (monthly increases) most exact. The exponential-function is also suitable for the describtion of the weight-development.

Simultaneous approximation of numbers connected with the exponential function

1978 ◽  
Vol 25 (4) ◽  
pp. 466-478 ◽  
Author(s):  
Michel Waldschmidt
Keyword(s):  
Lower Bounds ◽  
Exponential Function ◽  
Complex Number ◽  
Simultaneous Approximation ◽  
Complex Numbers ◽  
Linear Forms In Logarithms ◽  
Algebraic Numbers ◽  
Linear Forms

AbstractWe give several results concerning the simultaneous approximation of certain complex numbers. For instance, we give lower bounds for |a–ξo |+ | ea – ξ1 |, where a is any non-zero complex number, and ξ are two algebraic numbers. We also improve the estimate of the so-called Franklin Schneider theorem concerning | b – ξ | + | a – ξ | + | ab – ξ. We deduce these results from an estimate for linear forms in logarithms.

scholarly journals Exponential forms and path integrals for complex numbers inndimensions

2001 ◽  
Vol 25 (7) ◽  
pp. 429-450 ◽  
Author(s):  
Silviu Olariu
Keyword(s):  
Exponential Function ◽  
Complex Number ◽  
Path Integrals ◽  
Complex Numbers ◽  
Complex Polynomials ◽  
Hyperbolic Sine ◽  
Complex Functions ◽  
Geometric Variables ◽  
Sine And Cosine Functions ◽  
Cosine Functions

Two distinct systems of commutative complex numbers inndimensions are described, of polar and planar types. Exponential forms ofn-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and this leads to the concept of residue for path integrals ofn-complex functions. The exponential function of ann-complex number is expanded in terms of functions called in this paper cosexponential functions, which are generalizations tondimensions of the circular and hyperbolic sine and cosine functions. The factorization ofn-complex polynomials is discussed.

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