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...

We extend earlier examples provided by Schoen, Nori and Bloch to show that when a surface has the property that the kernel of its Albanese map is non-zero over the field of complex numbers, this kernel is non-zero over a field of transcendence degree one. This says that the conjecture of Bloch and Beilinson that this kernel is zero for varieties over number fields is precise in the sense that i...

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Healing aims to restore the wholeness of persons by restoring the unity of mind and body disrupted by disease. Transcendence promotes healing by altering or cultivating beliefs that can modulate the body's response to pain or make sense of pain. This in turn can produce an emotional response that enables people to cope with chronic or terminal illness. I explain transcendence in terms of a moni...

Let A be a commutative R–algebra of finite transcendence degree d ∈ N. We investigate the relationship between the subring of (geometrically) bounded elements H(A) := {a ∈ A | ∃ν ∈ N : |a| ≤ ν on SperA} and the subring of arithmetically bounded elements H (A) := {a ∈ A | ∃ν ∈ N : ν + a and ν − a are sums of squares in A}. Obviously, H ′(A) ⊆ H(A). In 1991, Schmüdgen proved the remarkable theore...

We characterize the principal differential ideals of a polynomial ring in n indeterminates with coefficients in the ring of differential polynomials in n indeterminates and derivation given by a “general” element of Lie(GLn) and use this characterization to construct a generic Picard-Vessiot extension for GLn. In the case when the differential base field has finite transcendence degree over its...

In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational invariants a transcendence basis in terms of Schofield’s determinantal semi-invariants. We also show that the moduli space of modules over a regular irreducib...