The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivar...

In this Letter we show the existence of bidifferential structures on finite Hopf algebras, which arise from quantum groups at roots of unity.

meister eckhart is one of the christian mystics that christian orthodoxy and catholic church accused his thoughts in medieval ages and named him heretic. most important themes that disparate the theism of eckhart from his christian predecessors are belief to godhead beyond god, denial of possibility of knowing god, innovations about trinity, belief to apophatic theology and etc. he defended of ...

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.

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...

We prove some general results on the existence of partitions of unity in Sobolev type spaces on various innnite dimensional manifolds. As special cases we obtain in particular, (continuous) partitions of unity a) in the Malliavin test functions on an abstract Wiener space; b) in the rst order Sobolev space on pinned and free loop spaces; c) in the rst order Sobolev spaces associated with revers...

one of the consequences of accepting personal unity of existence as well as the philosophical rule of “al-wahid” is wujud-e munbasit (the extended existence). sayyid haydar amuli explains origination of multiplicity from the one on the basis of wujud-e munbasit. according to him the first emanation from being is universal and extendedand contains all degrees of contingent world. by depicting of...

according to abū al-barakāt baghdādī, time and place are a priori conditions of motion; moreover, against the peripatetic philosophers, for whom time is the measure of motion, he holds that time is the measure of existence. nevertheless, he believes that we can define motion on the basis of our intuitive non-scientific concept of time and, by so doing, we can resolve the apparent circularity of...