We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi–Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.

In this paper, we first give a new definition of Ω-Dedekind complete Riesz space (E,≤) in the frame vector metric (Ω,ρ,E) and investigate relation between Dedekind our concept. Moreover, introduce contraction so called α-vector proximal mapping. Then, prove certain best proximity point theorems for such mappings spaces where is space. Thus, time, acquire results on spaces. As result, generalize...

A Dedekind category (locally complete division allegory) D is a category satisfying the following:

In this paper we will study the number-theoretical properties of the expression v1 nkal rcka,, d(p; a I . . . . . an) = ( 1) n/2 ~ cot cot (1) k=l P P and of related finite trigonometric sums. In Eq. (I), p is a positive integer, a~ . . . . . a, are integers prime to p, and n is even (for n odd the sum is clearly equal to zero). There are two reasons for being interested in sums of this type. F...

Let K be a number field and p be a prime number. When we factor (p) = pOK into prime ideals, say (p) = p1 1 · · · p eg g , we refer to the data of the ei’s, the exponents fi in the norms Npi = p fi , and g (the number of pi’s), as the “shape” of the factorization of (p). (What we are leaving out of this is explicit information about generators for the ideals pi.) Similarly, if a monic polynomia...