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Recall that a group G is called cyclic if there is an element a in G such that G is equal to a to the power of n where n is integers. Such an element a is called a generator of G. If a subset H of a group G is itself a group under the operation of G, we say that H is a subgroup of G. Moreover, an integer a has a multiplicative inverse modulo n if and only if a and n are relatively prime. So, for each n>1, we define U(n) to be the set of all positive integers less than n and relatively prime to n. Then U(n) is a group under multiplication modulo n. In this article, we will using Python determine all generator of the group U(n). The result of our study shows that by using Python, for any group of U(n), we can get all their generator quickly and easily. [ABSTRACT FROM AUTHOR]

Reconfigurable architectures targeting neural networks are an attractive option. They allow multiple neural networks of different types to be hosted on the same hardware, in parallel or sequence. Reconfigurability also grants the ability to morph into different micro-architectures to meet varying power-performance constraints. In this context, the need for a reconfigurable non-linear computational unit has not been widely researched. In this work, we present a formal and comprehensive method to select the optimal fixed-point representation to achieve the highest accuracy against the floating-point implementation benchmark. We also present a novel design of an optimised reconfigurable arithmetic unit for calculating non-linear functions. The unit can be dynamically configured to calculate the sigmoid, hyperbolic tangent, and exponential function using the same underlying hardware. We compare our work with the state-of-the-art and show that our unit can calculate all three functions without loss of accuracy. [ABSTRACT FROM AUTHOR]

In this work, we consider the system of hyperbolic equations with unbounded coefficients defined on a strip. Unique solvability of this system in the space of continuous and bounded functions is proved. The differential properties of its solution are received. [ABSTRACT FROM AUTHOR]

In this type functional variable method has been used to private type of nonlinear fractional differential equations. The main property of the method demonstrate in its flexibility and ability to solve nonlinear equations accurately, efficiency and conveniently. The fractional derivatives are described in the modified Riemann-Liouville sense. Three examples, are presented to show the application of the present technique. As a result, periodic and hyperbolic solutions are obtained. [ABSTRACT FROM AUTHOR]