<caption><image_83>The image shows a hand holding a black pen and writing on a whiteboard. The whiteboard has a mathematical equation written on it in black ink. The equation is written in Korean and appears to be a mathematical problem. The hand is holding the pen in a way that suggests that the person is writing on the whiteboard with precision. The background of the image is plain white.</caption><transcript><audio_84>and of course you have an omega squared common so the omega has no contribution to the magnitude i mean it does not affect the the nature of the mag what what affects the what makes the numerator and denominator different</transcript><transcript><audio_85>is the factors 1 plus omega square and 1 minus omega squared indeed when sigma is greater than 0 then 1 plus omega squared is bound to be greater than 1 minus omega square that is very easy to see</transcript><transcript><audio_86>and nothing changes if you add omega square to both sides so numerator is greater so numerator by denominator</transcript><video><caption><image_87>The image is a whiteboard with a mathematical equation written on it. The equation is written in black marker and is written on a white background. The equations are written in a neat and organized manner, with each equation having its own set of numbers and symbols. 

On the top left corner of the whiteboard, there is a logo of the Indian government of India, which is a shield with the emblem of the state of India in the top right corner. Below the logo, there are two lines of text, one for the equation and the other for the number of the equation.

In the center of the image, the equation "1-2" is written with a plus sign, indicating that it is a mathematical problem. On the right side of the board, there appears to be a list of mathematical equations, with the first line representing the equation, the second line representing a number, and the third line representing two numbers. The text on the board reads "CDEEP IT BOMB 1".

Overall, the image appears to have been taken in a classroom or classroom setting, as there are no other students present in the image.</caption><caption><image_88>The image is a screenshot of a whiteboard with a hand holding a black marker. On the whiteboard, there are several mathematical equations written in black ink. The equations are written in a neat and organized manner, with some of them overlapping each other. The background of the image is white, and there is a logo on the top right corner that reads "COEP" and a logo of a company or organization on the bottom left corner. The image appears to be a screenshot from a video or presentation.</caption></video><transcript><audio_89>for sigma greater than zero sigma plus 1 the whole squared must be greater than sigma 1 minus sigma in that case the numerator is strictly greater than the denominator</transcript> and of course you have an omega squared common so the omega has no contribution to the magnitude i mean it does not affect the the nature of the mag what what affects the what makes the numerator and denominator different is the factors 1 plus omega square and 1 minus omega squared indeed when sigma is greater than 0 then 1 plus omega squared is bound to be greater than 1 minus omega square that is very easy to see and nothing changes if you add omega square to both sides so numerator is greater so numerator by denominator for sigma greater than zero sigma plus 1 the whole squared must be greater than sigma 1 minus sigma in that case the numerator is strictly greater than the denominator
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