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File:Hurricane Hattie radar 30 Oct 1961 - cropped.jpg From Wikipedia, the free encyclopedia Jump to navigation Jump to search File File history File usage Global file usage Size of this preview: 574 × 599 pixels. Other resolutions: 230 × 240 pixels | 460 × 480 pixels | 575 × 600 pixels | 736 × 768 pixels | 981 × 1,024 pixels | 2,912 × 3,040 pixels. Original file ‎ (2,912 × 3,040 pixels, file size: 2.5 MB, MIME type: image/jpeg ) This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. Summary Description Hurricane Hattie radar 30 Oct 1961 - cropped.jpg English: Radar image of Hurricane Hattie at peak intensity prior to making landfall on the British Honduras. (Cropped version) Date 30 October 1961 Source This file was derived from: Hurricane Hattie radar 30 Oct 1961.jpg:  ...

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2 3 $underline{text{p-adic numbers and p-adic power series}}:$ If $ a,X in mathbb{Q}$ , then when the binomial expression $f(X)=(1+X)^a in mathbb{Q} $ both in p-adic field $mathbb{Q}_p$ and real field $mathbb{R}$ ? Answer: For example let $X=frac{7}{9}$ and $a=frac{1}{2}$ , we see $f(frac{7}{9})=(1+frac{7}{9})^{frac{1}{2}}=left(frac{16}{9} right)^{frac{1}{2}}=pm frac{4}{3}$ and fix the prime $p=7$ . Thus in $mathbb{Q}_7$ as well as in $mathbb{R}$ , the number $frac{16}{9}$ has square $ pm frac{4}{3}$ . But in $ mathbb{Q}_7$ , the square root $ pm frac{4}{3} equiv 1 (mod 7)$ . Thus in $mathbb{R}$ the value of $f(frac{7}{9})= frac{4}{3} in mathbb{Q} $ and in $ mathbb{Q}_7$ the value of $f(frac{7}{9})=1 (mod 7) in mathbb{Q}$ . Thus in this case $f(X)=(1+X)^a$ gives rational value both in $mathbb{...