Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more ...

A smooth intersection Y of two quadrics in $$\mathbb {P}^{2g+1}$$ has Hodge level 1. We show that such varieties have a multiplicative Chow–Künneth decomposition, the sense Shen–Vial. As consequence, certain tautological subring Chow ring powers injects into cohomology.

Andrew V. Sutherland A key ingredient to improving the efficiency of elliptic curve primality proving (and many other algorithms) is the ability to directly construct an elliptic curve E/Fq with a specified number of rational points, rather than generating curves at random until a suitable curve is found. To do this we need to develop the theory of complex multiplication. Recall from Lecture 7 ...

Given a natural number n, Waring’s problem asks for the minimum natural number sn such that every natural number can be represented as the sum of sn nth powers of integers. In this paper, we will answer this question for the case n = 2. To do this, we will examine the properties of two rings, one of which is a subring of the complex numbers, the other of which is a subring of the quaternions. T...