In this paper, we discuss the properties of curves of the form y3 = f(x) over a given field K of characteristic different from 3. If f(x) satisfies certain properties, then the Jacobian of such a curve is isomorphic to the ideal class group of the maximal order in the corresponding function field. We seek to make this connection concrete and then use it to develop an explicit arithmetic for the...

In this paper, we will study a partial sum modulus distribution for specific natural number set using dynamically sliding window. Then construct cubic equation from and formula to calculate zero. go through some applications of Cubic the basic algebraic concepts explain numbers.
 
 First part in interduce sums numbers dynamic window as parameter explore distribution. As simpler way st...

A “function field version” of Voronoi’s algorithm can be used to compute the fundamental unit of a purely cubic complex congruence function field of characteristic at least 5. This is accomplished by generating a sequence of minima in the maximal order of the field. The number of mimima computed is the period of the field. Generally, the period is very large — it is proportional to the regulato...

By introducing a symmetric pair of time instants, a modification of the cubic phase (CP) function, named as the quartic phase (QP) function, is proposed to estimate the quadratic FM signal. The performance in terms of estimate bias and variance is presented via the first-order permutation principle. Two extensions are presented for multiple components and the cubic FM signals. Both theoretical ...

This paper proposes an algorithm for generating irreducible cubic trinomials in the form x + ax + b, b ∈ Fp, where a is a certain fixed non-zero element in the prime field Fp. The proposed algorithm needs a certain irreducible cubic trinomial over Fp to be previously given as a generator; however, the proposed algorithm can generate irreducible cubic polynomials one after another by changing a ...

in today's globalization, an effective integration of production and distribution plans into a unified framework is crucial for attaining competitive advantage. this paper addresses an integrated multi-product and multi-time period production/distribution planning problem for a two-echelon supply chain subject to the real-world variables and constraints. it is assumed that all transportations a...