Examples of Nebuchadnezzar I in the following topics:
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- The Kassite Dynasty ruled Babylonia following the fall of Hammurabi and was succeeded by the Second Dynasty of Isin, during which time the Babylonians experienced military success and cultural upheavals under Nebuchadnezzar.
- Later in his reign, he went to war with Assyria and had some initial success before suffering defeat at the hands of the Assyrian king Ashur-Dan I.
- Nebuchadnezzar I (1124-1103 BCE) was the most famous ruler of the Second Dynasty of Isin.
- The earliest of three extant economic texts is dated to Nebuchadnezzar's eighth year; in addition to two kudurrus and a stone memorial tablet, they form the only existing commercial records.
- Some initial success in these conflicts gave way to catastrophic defeat at the hands of Tiglath-pileser I, who annexed huge swathes of Babylonian territory, thereby further expanding the Assyrian Empire.
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- Neo-Babylonian art and architecture reached its zenith under King Nebuchadnezzar II, who ruled from 604–562 BC and was a great patron of urban development, bent on rebuilding all of Babylonia's cities to reflect their former glory.
- It was Nebuchadnezzar II's vision and sponsorship that turned Babylon into the immense and beautiful city of legend.
- It was also during this period that Nebuchadnezzar supposedly built the Hanging Gardens of Babylon, although there is no definitive archeological evidence to establish their precise location.
- It was constructed in 575 BC by order of Nebuchadnezzar II, using glazed brick with alternating rows of bas-relief dragons and aurochs.
- Describe the artistic and architectural accomplishments of King Nebuchadnezzar II, including the city of Babylon
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- With the recovery of Babylonian independence, a new era of architectural activity ensued, and Nebuchadnezzar II (604–561 BCE) made Babylon into one of the wonders of the ancient world.
- Nebuchadnezzar II ordered the complete reconstruction of the imperial grounds, including rebuilding the Etemenanki ziggurat and the construction of the Ishtar Gate—the most spectacular of eight gates that ringed the perimeter of Babylon.
- Nebuchadnezzar is also credited with the construction of the Hanging Gardens of Babylon (one of the seven wonders of the ancient world), said to have been built for his homesick wife Amyitis.
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- On either 10 or 11 June 323 BCE, Alexander died in the palace of Nebuchadnezzar II, in Babylon, at age 32.
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- $\displaystyle A \equiv \frac{E_f}{E_i} \sim \frac{4}{3} \langle \gamma^2 \rangle = 16 \left ( \frac{kT}{mc^2} \right )^2.$
- The probability that a photon will scatter as it passes through a medium is simply $\tau_{es}$ if the optical depth is low, and the probability that it will undergo $k$ scatterings $p_k \sim \tau_{es}^k$ and its energy after $k$ scatterings is $E_k=A^k E_i$, so we have
- $\displaystyle I(E_k) = I(E_i) \exp \left ( \frac{\ln\tau_{es} \ln\frac{E_k}{E_i}}{\ln A} \right ) = I(E_i) \left ( \frac{E_k}{E_i} \right )^{-\alpha}$
- $\displaystyle P = \int_{E_i}^{A^{1/2}mc^2} I(E_k) dE_k = I(E_i) E_i \left [ \int_1^{A^{1/2} mc^2/E_i} x^{-\alpha} dx \right ].$
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- $\left( \mathbf{v}_i \mathbf{v}_i ^T \right) \mathbf{x} = (\mathbf{v}_i ^T \mathbf{x}) \mathbf{v}_i $
- For the operator $\mathbf{v}_i \mathbf{v}_i ^T $ this is obviously true since $\mathbf{v}_i ^T \mathbf{v}_i = 1$ .
- $\displaystyle{\sum _ {i=1} ^ m \mathbf{v}_i \mathbf{v}_i ^T = V V^ T = I . }$
- $\displaystyle{\sum _ {i=1} ^ r \mathbf{v}_i \mathbf{v}_i ^T = V_r V_r ^ T }$
- $\displaystyle{\sum _ {i=r+1} ^ m \mathbf{v}_i \mathbf{v}_i ^T = V_0 V_0 ^T}$
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- $\displaystyle
\begin{aligned}
b&=
\frac{1}{n} \sum_{i=1}^{n} y_{1} - m \frac{1}{n} \sum_{i=1}^{n} x_{i} \\
&= \left (\bar{y} - m \bar{x} \right)
\end{aligned}$
- Let $\bar{y}$, pronounced $y$-bar, represent the mean (or average) $y$ value of all the data points: $\bar y =\frac{1}{n}\sum_{i=1}^{n} y_{i}$.
- Respectively $\bar{x}$, pronounced $x$-bar, is the mean (or average) $x$ value of all the data points: $\bar x=\frac{1}{n}\sum_{i=1}^{n} x_{i}$.
- $\displaystyle
\begin{aligned}
\sum_{i=1}^{n}x_{i}y_{i}&=0+0+1+4+3+10+15+24\\&=57
\end{aligned}
$$\displaystyle
\begin{aligned}
\sum_{i=1}^{n}x_{i}&=-1+0+1+2+3+4+5+6\\&=20
\end{aligned}$$\displaystyle
\begin{aligned}
\sum_{i=1}^{n}y_{i}&=0+0+1+2+1+2.5+3+4\\&=13.5
\end{aligned}$
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- In what follows, it is useful to keep in mind the powers of the imaginary unit $i$:
- $(2+3i)^4=2^4+4\cdot 2^3\cdot 3i -6\cdot 2^2\cdot 3^2 -4\cdot 2 \cdot 3^3 i +3^4 $
- Suppose you wanted to compute $(1+i)^3$.
- Suppose you wanted to compute $(2+i)^5$.
- $(2+i)^5 =2^5 + 5\cdot 2^4 i + 10\cdot 2^3 i^2 + 10\cdot 2^2 i^3 + 5\cdot 2 \cdot i^4 + i^5$