UNITY is a simple programming logic to reason about distributed systems. It is especially attractive because of its elegant axiomatical style. Since its power is limited, people introduce variants to extends it with various new functionalities. However, in the axiomatical style it is easy to make a mistake: a seemingly very logical new inference rule may turn out to be unsound. Formal verificat...

Dear Madam, There are many perspectives from different standing points with distinguished context of truths in nursing. Some philosophers might hold multiple truths, and others hold only one truth. However, truth in nursing is assumed in the eye of beholder, which means multiple perspectives are appropriate for knowledge development in nursing. There are no less than nine different philosophica...

A hermeneutical substructure for the reading of historical texts in mathematics classroom is described. It organized according to four transcendentals unity, truth, beauty and goodness, each which considered internally –with respect text itself – externally with both its relations mathematical thought general other cultural manifestations. Lead questions are provided category as also details re...

In this article, the relation between crisis, dying, and apocalypse is examined from vantage point of Franz Rosenzweig’s philosophy revelation. Following suggestion that truth—for finite temporal beings like us—can only be found in time, article suggests there exists an intrinsic truth death. Truth not or even primarily logical mathematical according to Rosenzweig. reality our lives implies esc...

The main result of this paper gives necessary and sufficient conditions for the ^-primary part S(K)P of the Schur group S (K) to be induced from S (F)p for any subfield F of K where K is contained in Q (εn), under the restriction that εp2 is not in K if p > 2 and n is odd if p~2, where εn is a primitive nth root of unity. Moreover we completely answer the question: "When is SiQiεn + ε-)) induce...

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity of elliptic curves over F .

In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite ...

We deal with the unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths a; b + m; c; a + m; b; c + m, where an equilateral triangle of side length m has been removed from the center. We give closed formulas for the plain enumeration and for a certain (?1)-enumeration of these lozenge tilings. In the case that a = b = c, we also provide closed formulas for certain...