Let K be an algebraically closed field, X a smooth projective variety over K and f : X → X a dominant regular morphism. Let N (X) be the group of algebraic cycles modulo numerical equivalence. Let χ(f) be the spectral radius of the pullback f∗ : H∗(X,Ql) → H ∗(X,Ql) on l-adic cohomology groups, and λ(f) the spectral radius of the pullback f∗ : N∗(X) → N∗(X). We prove in this paper, by using con...

In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius using convex functions. Applications of the new results include obtaining forms that generalize and extend some well known in literature, with application newly defined generalized radius. We emphasize approach followed article different fro...

We give a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties. Both finiteand infinitedimensional aspects are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems. 1. DEFINITION, BOUNDS, AND EVALUATION Let H be a Hilbert space over the complex fie...

The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...

We present a method for obtaining atmospheric temperature, pressure, and number density profiles for small bodies through inversion of light curves recorded during stellar occultations. This method avoids the assumption that the atmospheric scale height is small compared with the radius of the body, and it includes the variation of gravitational acceleration with radius. First we derive the int...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions. Keywords—Spectral norm, Numerical radius, Spectral radius, Ratios