The stability radius of a matrix polynomial P (λ) relative to an open region Ω of the complex plane and its relation to the numerical range of P (λ) are investigated. Using an expression of the stability radius in terms of λ on the boundary of Ω and ‖P (λ)−1‖2, a lower bound is obtained. This bound for the stability radius involves the distances of Ω to the connected components of the numerical...

K 0 form factor at order p 6 of chiral perturbation theory Abstract This paper describes the calculation of the electromagnetic form factor of the K 0 meson at order p 6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p 4 result achieved by Gasser and Leutwyler. On the one hand, at order p 6 the chiral expansion contains 1-and 2-loop diagrams which ...

A decreasing radius k-nearest neighbor search algorithm for the mapping-based indexing schemes is presented. We implement the algorithm in the Pyramid technique and the iMinMax(θ), respectively. The Pyramid technique divides d-dimensional data space into 2d pyramids, and the iMinMax(θ) divides the data points into d partitions. Given a query point q, we initialize the radius of a range query to...

We prove versions of various standard inequalities in which the dependence of the constant on the metric is explicit. 1 Technical results Definition. Let (M, g) be a smooth Riemannian n-manifold and let x ∈ M . Given Q > 1, k ∈ N, and p > n, the (Q, k, p)-harmonic radius at x, rH(Q, k, p)(x), is the supremum of reals r such that, on the geodesic ball Bx(r) of center x and radius r, there is a h...

This article considers three types of analytic functions based on their infinite product representation. The radius the k-parabolic starlikeness these classes is studied. optimal parameter values for starlike are determined in unit disk. Several examples provided that include special such as Bessel, Struve, Lommel, and q-Bessel functions.

In this paper, we study some extremal problems of three kinds of spectral radii of k-uniform hypergraphs (the adjacency spectral radius, the signless Laplacian spectral radius and the incidence Q-spectral radius). We call a connected and acyclic k-uniform hypergraph a supertree. We introduce the operation of “moving edges” for hypergraphs, together with the two special cases of this operation: ...

Let ‎X be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎Cartesian decomposition ‎‎X = A + i ‎B‎‎‎‎‎, ‎where ‎‎A ‎and ‎‎B ‎are ‎‎‎n ‎‎times n‎ ‎Hermitian ‎matrices. ‎It ‎is ‎known ‎that ‎‎$Vert X Vert_p^2 ‎leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎Vert . Vert_p$ ‎is ‎the ‎Schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎In this paper‎, this inequality and some of its improvements ...