We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.

The need for us, as educators, to cultivate and encourage a climate of unity, harmony, and prosperity in educational and non-educational settings is pertinent. Conflict resolution in teaching and learning in educational settings, for example, is a feat that may be achieved via different methodological means. In this article, we provide an account of our teaching and research experiences in the ...

Based on an explicit representation of the Artin map for Kummer extensions, we present a method to compute arbitrary class fields. As in the proofs of the existence theorem, the problem is first reduced to the case where the field contains sufficiently many roots of unity. Using Kummer theory and an explicit version of the Artin reciprocity law we show how to compute class fields in this case. ...

from the point of view of the mystics, “creation” in its conventional meaning does not have a real existence and whatever observed in the universe is but the manifestation of the essence of divine unity. all creatures are “manifested” and the real “being” is exclusive to the divine essence. in religious terms, whatever manifested in the world of existence is “the face of allah”. on the other ha...

The chiral vertex operators for the minimal models are constructed and used to define a fusion product of representations. The existence of com-mutativity and associativity operations is proved. The matrix elements of the associativity operations are shown to be given in terms of the 6-j symbols of the weak quasitriangular quasi-Hopf algebra obtained by truncating U q (sl(2)) at roots of unity.

In Hegel’s philosophy, both truth and genuine freedom belong to the domain of Idea. Life, as it is categorized in Science Logic, first form stage Idea, therefore essential for a comprehension self-determination. this paper, I explore why what extent Life self-determining true. Considering Hegel considers be three fundamental features all life, explain how life with respect its organic unity, re...

We classify all the cocyclic Butson Hadamard matrices BH(n, p) of order n over the pth roots of unity for an odd prime p and np ≤ 100. That is, we compile a list of matrices such that any cocyclic BH(n, p) for these n, p is equivalent to exactly one element in the list. Our approach encompasses non-existence results and computational machinery for Butson and generalized Hadamard matrices that a...

This paper addresses robust H∞ control problems for nonlinear systems with parameter uncertainty. By using the technique of partition of unity, necessary and sufficient conditions for existence of strong robust H∞ dynamic compensators and static state feedback controllers are established in terms of nonlinear matrix inequality (NLMI) approach, respectively. These conditions reduce the robust H∞...