Examples of yamato-e in the following topics:
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- These imports not only changed the subject matter of painting, but they also modified the use of color; the bright colors of Yamato-e yielded to the monochromes of painting in the Chinese manner of Sui-boku-ga (水) or Sumi-e (墨).
- The foremost painter of the new Sumi-e style was Sesshū Tōyō (1420–1506), a Rinzai priest who traveled to China in 1468-69 and studied contemporary Ming painting.
- The Sumi-e style was highly influenced by calligraphy, using the same tools and style as well as its Zen philosophy.
- Distinguish the techniques of the Yamato-e, Sumi-e, Sansuiga, and Shigajiku styles of Japanese Zen Ink painting.
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- Subject matter and style were often borrowed from Heian period traditions of Yamato-e, with elements from Muromachi ink paintings, Chinese Ming dynasty flower-and-bird paintings, and Momoyama period Kanō school developments.
- Sōtatsu also pursued the same classical Yamato-e genre as Kōetsu, but he pioneered a new technique with bold outlines and striking color schemes.
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- Dating from about 1130, the Genji Monogatari Emaki, a famous illustrated Tale of Genji, represents the earliest surviving yamato-e handscroll, and is considered one of the high points of Japanese painting.
- Emaki also serve as some of the earliest and greatest examples of the otoko-e ("men's pictures") and onna-e ("women's pictures") styles of painting.
- Onna-e, epitomized by the Tale of Genji handscroll, typically deals with court life, particularly the court ladies, and with romantic themes.
- Otoko-e, on the other hand, often recorded historical events, particularly battles.
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- It depicts the descent of the Amida Buddha and is one of the first examples of Yamato-e, a classical style of Japanese painting inspired by Tang dynasty paintings and fully developed by the late Heian period.
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- The classic yamato-e style of Japanese painting, which gained significance in the Heian period, was continued throughout this era.
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- It followed the Yayoi period in Japanese history; the Kofun and the subsequent Asuka periods are sometimes referred to collectively as the Yamato period.
- Kofun burial mounds on Tanegashima and two very old Shinto shrines on Yakushima suggest that these islands were the southern boundaries of the Yamato state.
- Its northernmost extent was as far north as Tainai in the modern Niigata Prefecture, where mounds have been excavated associated with a person with close links to the Yamato kingdom.
- The trend of the keyhole kofun first spread from Yamato to Kawachi (where very large kofun such as Daisenryō Kofun exist) and then throughout the country (with the exception of the Tōhoku region) in the 5th century.
- Keyhole kofun disappeared later in the 6th century, probably because of the drastic reformation which took place in the Yamato court; records suggest the introduction of Buddhism at this time.
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- $\displaystyle I'(E',\mu') = F_0 \left (\frac{E'}{E}\right)^2 \delta (E-E_0)\\ \displaystyle = F_0 \left (\frac{E'}{E_0}\right)^2 \delta (\gamma E' (1+\beta\mu') -E_0) \\ \displaystyle = \frac{F_0}{\gamma\beta E'} \left (\frac{E'}{E_0}\right)^2 \delta \left (\mu' - \frac{E_0-\gamma E'}{\gamma\beta E'} \right )$
- where we have assumed that $E_f'=E'$.
- $\displaystyle j'(E_f') = \frac{N' \sigma_T E_f' F_0}{2 E_0^2 \gamma \beta}~\text{ if }~ \frac{E_0}{\gamma (1+\beta)} < E_f' < \frac{E_0}{\gamma(1-\beta)}$
- $\displaystyle j(E_f,\mu_f) = \frac{E_f}{E_f'} j'(E_f') \\ \displaystyle = \frac{N \sigma_T E_f F_0}{2 E_0^2 \gamma^2 \beta} \\ \displaystyle ~~\text{ if }~ \frac{E_0}{\gamma (1+\beta)(1-\beta \mu_f)} < E_f < \frac{E_0}{\gamma(1-\beta)(1-\beta \mu_f)} \nonumber$
- $\displaystyle \frac{d E}{dV dt dE_f} = 4 \pi E_f j(E_f) \\ \displaystyle = \frac{3}{4} c \sigma_T C \int d E \left ( \frac{E_f}{E} \right ) v(E) \int_{\gamma_1}^{\gamma_2} d \gamma \gamma^{-p-2} f \left ( \frac{E_f}{4\gamma^2 E} \right ) \\ \displaystyle = 3\sigma_T c C 2^{p-2} E_f^{-(p-1)/2} \times \\ \displaystyle \nonumber ~~~\int d E E^{(p-1)/2} v(E) \int_{x_1}^{x_2} x^{(p-1)/2} f(x) dx$
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- $\displaystyle \int_{-\infty}^{\infty} |E(t)|^2 dt = 2\pi \int_{-\infty}^{\infty} |{\hat E}(\omega)|^2 d \omega.$
- $\displaystyle \int_{-\infty}^{\infty} |E(t)|^2 dt = \int_{-\infty}^{\infty} d t \int_{-\infty}^{\infty} {\hat E}(\omega') e^{-i\omega' t} d \omega'.
- \int_{-\infty}^{\infty} {\hat E}^*(\omega) e^{i\omega t} d \omega \\ \displaystyle = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} d t d\omega' d \omega {\hat E}(\omega') {\hat E}^*(\omega) e^{-i\omega' t} e^{i\omega t} $
- The integral over time is simply Fourier transform of $2\pi e^{-i\omega' t}$ which we know,
- $\displaystyle \int_{-\infty}^{\infty} |E(t)|^2 dt = 2\pi \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} d\omega' d \omega {\hat E}(\omega') {\hat E}^*(\omega) \delta (\omega -\omega') \\ \displaystyle = 2 \pi \int_{-\infty}^{\infty} d \omega {\hat E}(\omega) {\hat E}^*(\omega) =2 \pi \int_{-\infty}^{\infty} |{\hat E}(\omega)|^2 d \omega$
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- First, we determine the derivative of $e^{x}$ using the definition of the derivative:
- Since $e^{x}$ does not depend on $h$, it is constant as $h$ goes to $0$.
- Therefore $\ln(e^x) = x$ and $e^{\ln x} = x$.
- Let's consider the example of $\int e^{x}dx$.
- Since $e^{x} = (e^{x})'$ we can integrate both sides to get:
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- The Shōwa regime thus preached racial superiority and racialist theories, based on sacred nature of the Yamato-damashii.