In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evo...

We then define the Pfaffian transformation of (a0, a1, a2, ...) to be the sequence of Pfaffians (Pf(A0), P f(A1), P f(A2), ...), where the Pfaffian of a skew-symmetric matrix is the positive or negative square root of its determinant. (For a precise definition of the Pfaffian, see section 2.) The Pfaffian transformation is thus a function from sequences to sequences. We begin by observing the e...

A certain functional–difference equation that Runyon encountered when analyzing a queuing system was solved in a combined effort of Morrison, Carlitz, and Riordan. We simplify that analysis by exclusively using generating functions, in particular the kernel method, and the Lagrange inversion formula.

The 321,hexagon–avoiding (321–hex) permutations were introduced and studied by Billey and Warrington in [4] as a class of elements of Sn whose Kazhdan– Lusztig and Poincaré polynomials and the singular loci of whose Schubert varieties have certain fairly simple and explicit descriptions. This paper provides a 7–term linear recurrence relation leading to an explicit enumeration of the 321–hex pe...

Let E be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let P = (x1/z 2 1 , y1/z 3 1) be a rational point of infinite order on E, where x1, y1, z1 are coprime integers. We show that the integer sequence (zn)n>1 defined by nP = (xn/z 2 n, yn/z 3 n) for all n > 1 does not eventually coincide with (un2)n>1 for any choice of linear recurrence sequence (un)n>1 with...

Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation an+1 = Aan + Ban−1, by means of algebraic equations in two variables of degree n ∈ N . We do this, as far as we know, like it has never been formalized before. I’d like to precise that the work was develop without the support of any well-kn...

The 321,hexagon–avoiding (321–hex) permutations were introduced and studied by Billey and Warrington in [4] as a class of elements of Sn whose Kazhdan– Lusztig and Poincaré polynomials and the singular loci of whose Schubert varieties have certain fairly simple and explicit descriptions. This paper provides a 7–term linear recurrence relation leading to an explicit enumeration of the 321–hex pe...