Isac G.'s 0 - Epi families of mappings, topological degree, and PDF

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Extra info for 0 - Epi families of mappings, topological degree, and optimization

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A picture message uses paint or chalk on a canvas. An electronic message involves movement of electrons. No matter how the message is transmitted, understanding it requires interpretation and reconstruction of what is received to reveal what the sender intended to convey; namely, the information. Until the message is interpreted by the receiver, the information remains hidden. It is coded in and represented by the physical changes—variations and arrangements of pressure, color, inkspots, electrical voltage, electromagnetic waves, light patterns, and so forth—that are involved in the actual transmission of the message.

In contrast, if the set of allowable symbols is limited to 0 and 1 (the binary or base-2 digits), then the chance of successfully interpreting even a poor message increases. Combining binary digits (or bits) in large groups can be used to represent information of any desired complexity. A string of eight bits is known Analog and Digital Each piano key generates a distinct, digital “message” of sound. But the music of a complex piano tune is analog because the listener hears a blending of notes, continuously changing melody, and layered harmonies.

The flagpole forms a right angle with level ground. Suppose the flagpole casts a shadow of 20 feet. See part (a) of the figure on the following page. The 20-foot shadow and the flagpole itself form two legs of a right triangle. The triangle’s hypotenuse is formed by the line of sight extending from the end of the shadow (Point E) upwards toward the Sun. The angle of elevation of the Sun has one ray extending along the horizontal toward the bottom of the pole, and the other extending toward the Sun.

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0 - Epi families of mappings, topological degree, and optimization by Isac G.


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