In this paper we investigate the infinite convergent sum T = ∑∞ n=0 P (n) Q(n) , where P (x) ∈ Q[x], Q(x) ∈ Q[x] and Q(x) has only simple rational zeros. N. Saradha and R. Tijdeman have obtained sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 3. In this paper we give sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 4...

Consider the minimal β-shift containing the shift space generated by a given Sturmian word. In this paper we characterize such β and investigate their combinatorial, dynamical and measure-theoretical properties and prove that such β are transcendental numbers.

Throughout this paper L will be an algebraically closed field and K an algebraically closed subfield such that the transcendence rank of L over K is at least 3. In [4] we considered the pregeometry G(L/K) = (L,clK), where, for Y a subset of L, the closure clK( Y) is the algebraic closure in L of the subfield generated by K and Y. In this paper we shall be concerned mainly with the geometry G(L/...

The reduced Witt rings of certain formally real fields are computed here in terms of some basic arithmetic invariants of the fields. For some fields, including the rational function field in one variable over the rational numbers and the rational function field in two variables over the real numbers, this is done by computing the image of the total signature map on the Witt ring. For a wider cl...

We introduce a class of analytic functions of number theoretic interest, namely stammering functions. It has been recently proved that these functions take transcendental values at some algebraic points. In the present paper, we establish a general transcendence criterion that extends these results. Another aim is to underline the main difficulties arising from the use of the Schmidt Subspace T...

Through making references to some inter-disciplinary and cross-cultural studies of “Transcendence” as well the usage relevant terms in contemporary Confucianism Christianity, especially concepts “transcendence” “immanence” (which is translated sometimes nèi zài Chinese), this study attempts challenge prevalent stereotypes Christianity Confucianism. With special historical Christian-Confucian di...

Feminine language for God has been largely absent within Christianity. However, a focus on feminine aspects of the divine can help Christians reclaim characteristics of God that get lost in a religion where language of God the Father is pervasive. This paper addresses the use of Mother as a metaphor for God and its implications for a therapeutic context. The current conversation around parental...