In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

One trivial zero phenomenon for p-adic analytic function is considered. We then prove that the first derivative of this function is essentially the Kummer class associated with p. 1. Introduction. In this paper we always fix an odd prime p > 2. For n ≥ 1, fix a p n th primitive root of unity ζ p n such that ζ

In this note, we calculate all the basic invariants of the number field K = Q(3 √ 5, ω), where ω = (−1 + √ −3)/2 is a primitive cube root of unity. Here is the notation for the fields and Galois groups to be used. Let

The quintuple identity has a long history and, as Berndt [5] points out, it is difficult to assign priority to it. It seems that a proof of the identity was first published in H. A. Schwartz’s book in 1893 [19]. Watson gave a proof in 1929 in his work on the RogersRamanujan continued fractions [20]. Since then, various proofs have appeared. To name a few, Carlitz and Subbarao gave a simple proo...

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.

We must mention that the assumption that we are dealing with a Cartan matrix of finite type and a root of unity appears only at the very end (see Chapter 4). We need these assumptions in order to compare our representations with the conventional definition of the category C. All previous results are valid in more general assumptions. In particular a Cartan matrix could be arbitrary and a deform...

Broadly speaking, the Holy Quran as the most sublime heavenly message is a book of human life. Since, the Life Creator, the sender of this holy book, is the Creator of human body and mind. Human mental activity starts from about 16 weeks of fetal life with the blow of divine spirit into the fetus. At this point, we observe the beginning of mental and psychological activities and the emergence o...

because of using principles such as principality, unity, gradation of existence and concomitance between existence and unity, along with an exhaustive understanding of ibn sina's philosophical principle about our knowledge of unity and multiplicity, mulla sadra believed new philosophical-aesthetical principles such as principality, unity and gradation of beauty, though he didn't use t...

unity is one of the most important social issues in the holy religion of islam. unity makes possible entanglement from dependencies, success in settling social issues, and firmness in confronting conspiracies and invasions. since islam is a religion of kindness and brotherhood, it invites its followers to engage in being united, which will, however, never be achieved without resolving conflicts...