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pro vyhledávání: '"Shinohara, Kazunori"'
Autor:
Shinohara, Kazunori
Publikováno v:
Applied Mathematical Sciences, Vol. 15, 2021, no. 9, 399-469
The exact solutions of both the cubic Duffing equation and cubic-quintic Duffing equation are presented by using only leaf functions. In previous studies, exact solutions of the cubic Duffing equation have been proposed using functions that integrate
Externí odkaz:
http://arxiv.org/abs/2102.02641
Autor:
Shinohara, Kazunori
Publikováno v:
CMES Computer Modeling in Engineering & Sciences, Vol.126, No.1, 2021, pp.275-292
A lemniscate is a curve defined by two foci, F1 and F2. If the distance between the focal points of F1 - F2 is 2a (a: constant), then any point P on the lemniscate curve satisfy the equation PF1 PF2 = a^2. Jacob Bernoulli first described the lemnisca
Externí odkaz:
http://arxiv.org/abs/2006.15529
Autor:
Shinohara, Kazunori
Publikováno v:
CMES Computer Modeling in Engineering & Sciences, Vol.123, No.2, 2020 ,pp.441-473
Addition formulas exist in trigonometric functions. Double-angle and half-angle formulas can be derived from these formulas. Moreover, the relation equation between the trigonometric function and the hyperbolic function can be derived using an imagin
Externí odkaz:
http://arxiv.org/abs/1902.10305
Autor:
Shinohara, Kazunori
Publikováno v:
Applied Mathematical Sciences, Vol. 13, 2019, no. 3, 103-123
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common to lineari
Externí odkaz:
http://arxiv.org/abs/1901.04297
Autor:
Shinohara, Kazunori
Publikováno v:
CMES: Computer Modeling in Engineering & Sciences, Vol.118, No.3, 2019 ,pp.599-647
According to the wave power rule, the second derivative of a function with respect to the variable t is equal to negative n times the function raised to the power of 2n-1. Solving the ordinary differential equations numerically results in waves appea
Externí odkaz:
http://arxiv.org/abs/1901.00606
Autor:
Shinohara, Kazunori
Publikováno v:
CMES: Computer Modeling in Engineering & Sciences, Vol.115,No.2,pp.149-215,2018
Exact solutions with the initial conditions are presented in the cubic duffing equation. These exact solutions are expressed in terms of the leaf function and the trigonometric function. The leaf functions: $r=sleaf_n(t) $ or $ r=cleaf_n(t)$ satisfy
Externí odkaz:
http://arxiv.org/abs/1709.04088
Autor:
Shinohara, Kazunori
Publikováno v:
Applied Mathematical Sciences, Vol. 11, 2017, no. 52, 2561 - 2577
The second derivative of a function r(t) with respect to a variable t is equal to -n times the function raised to the 2n-1 power of r(t); using this definition, an ordinary differential equation is constructed. Graphs with the horizontal axis as the
Externí odkaz:
http://arxiv.org/abs/1707.01282
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Additional file 3: Supplementary Table 1. P-values of univariate logistic regression analysis between confounders and outcomes Supplementary Table 2. Embryonic outcomes stratified by the ovarian stimulation method Supplementary Table 3. Pregnancy out
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10b295dd70cc4c89e6cebb3a8b1b59c7