Full text
... This enables us to solve not only the problem of the lumped network mentioned above, but a special question of the theory of the distributed networks (e.g., transmission lines) can also be solved. If we want to describe the pair of transmission lines having resistance r0 and shunt-admittance 1//?0 ( ...
... This enables us to solve not only the problem of the lumped network mentioned above, but a special question of the theory of the distributed networks (e.g., transmission lines) can also be solved. If we want to describe the pair of transmission lines having resistance r0 and shunt-admittance 1//?0 ( ...
Full text
... 2. If a0 = (0,0,..., 0,1), then the Ducci sequence a0, a1? ... is called the basic Ducci sequence and the resulting cycle the basic Ducci cycle. From now on, a^ will always denote a tuple in the basic Ducci sequence.. 3. The period (also referred to as the length) of the basic Ducci cycle is denoted ...
... 2. If a0 = (0,0,..., 0,1), then the Ducci sequence a0, a1? ... is called the basic Ducci sequence and the resulting cycle the basic Ducci cycle. From now on, a^ will always denote a tuple in the basic Ducci sequence.. 3. The period (also referred to as the length) of the basic Ducci cycle is denoted ...
Inequality Problem Solutions
... (x + 1/x)3 + (x3 + 1/x3 ) Now, using difference of squares, the above is precisely ((x + 1/x)3 + (x3 + 1/x3 ))((x + 1/x)3 − (x3 + 1/x3 )) (x + 1/x)3 + (x3 + 1/x3 ) ...
... (x + 1/x)3 + (x3 + 1/x3 ) Now, using difference of squares, the above is precisely ((x + 1/x)3 + (x3 + 1/x3 ))((x + 1/x)3 − (x3 + 1/x3 )) (x + 1/x)3 + (x3 + 1/x3 ) ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.