In this paper, we discuss the properties of the hyperfibonacci numbers F [r] n and hyperlucas numbers L [r] n . We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that {F [r] n }n≥1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.

This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $...

in this paper, we discuss the equivalent conditions of pretopological and topological $l$-fuzzy q-convergence structures and define $t_{0},~t_{1},~t_{2}$-separation axioms in $l$-fuzzy q-convergence space. {furthermore, $l$-ordered q-convergence structure is introduced and its relation with $l$-fuzzy q-convergence structure is studied in a categorical sense}.

We break the convexity bound in the t–aspect for L–functions attached to cuspforms f for GL2(k) over arbitrary number fields k. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twists L(s, f ⊗χ) by grossencharacters χ, from our previous paper [Di-Ga]. §0. Introduction In many instances, for cuspidal automorphic forms f on r...

Most of arithmetically significant Dirichlet series such as the Riemann zeta-function ζ(s), Dirichlet L-functions, and Hecke L-functions associated with various cusp forms satisfy Riemannian functional equations connecting values at s = σ + it and 1 − s of respective functions. Essentially best possible estimates for these functions near the line σ = 1 and σ = 0 can usually be deduced from the ...

Parametric linear constant and gain-scheduled control systems design are studied for a class of linear parameter varying (LPV) systems and piecewise linear (PL) systems based on stabilization via convexity restrictions. Specifically, the maximum row sum (matrix) norm is utilized to obtain a computationally attractive state space method for the scheduling of simple linear controllers under incom...

A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which balls around nodes are convex, and those...