Abstract The main objective of this paper is to establish some new Hermite–Hadamard type inequalities involving k -Riemann–Liouville fractional integrals. Using the convexity differentiable functions related have been proved, which deep connection with known results. At end, applications obtained results in error estimations quadrature formulas are also considered.

One of the unfulfilled aims of the authors of the preceding paper [W. Parry and M. Pollicott. An analogue of Bauer’s theorem for closed orbits of skew products. Ergod. Th. & Dynam. Sys. 28 (2008), 535–546] was to find a dynamical analogue of Artin reciprocity. In this addendum, we present one such version, suggested by work of Sunada. 0. Introduction In algebraic number theory, one of the most ...

The fractional weak discrepancy of a poset P , written wdF (P ), is the least k such that some f : P → R satisfies f(y)− f(x) ≥ 1 for x ≺ y and |f(y)− f(x)| ≤ k for x‖y. We determine the minimal forbidden subposets for the property wdF (P ) ≤ k when k is an integer.

We introduce a fractional version of the illumination problem of Gohberg, Markus, Boltyanski and Hadwiger, according to which every convex body in R is illuminated by at most 2 directions. We say that a weighted set of points on Sd−1 illuminates a convex body K if for each boundary point of K, the total weight of those directions that illuminate K at that point is at least one. We define the fr...

We determine the exact minimum `-degree threshold for perfect matchings in kuniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than 12 ( n k−` ) . This extends our previous results that determine the minimum `-degree thresholds for perfect matchings in k-uniform hypergraphs for all ` > k/2 and provides two new (exact) thresholds: (k, `) =...

Admissiblê sl(2|1; C) k Characters and Parafermions. Abstract The branching functions of the affine superalgebrâ sl(2|1; C) k characters into characters of the subalgebrâ sl(2; C) k are calculated for fractional levels k = 1 u − 1, u ∈ N. They involve rational torus A u(u−1) and Z u−1 parafermion characters.

The K = 4 fractional superstring Fock space is constructed in terms of Z4 parafermions and free bosons. The bosonization of the Z4 parafermion theory and the generalized commutation relations satisfied by the modes of various parafermion fields are reviewed. In this preliminary analysis, we describe a Fock space which is simply a tensor product of Z4 parafermion and free boson Fock spaces. It i...