Search results for " Lower"

Upper bounds for the zeros of ultraspherical polynomials

1990

AbstractFor k = 1, 2, …, [n2] let xnk(λ) denote the Kth positive zero in decreasing order of the ultraspherical polynomial Pn(λ)(x). We establish upper bounds for xnk(λ). All the bounds become exact when λ = 0 and, in some cases (see case (iii) of Theorem 3.1), also when λ = 1. As a consequence of our results, we obtain for the largest zero xn1(λ)0.. We point out that our results remain useful for large values of λ. Numerical examples show that our upper bounds are quite sharp.

Mapping Posidonia oceanica lower limit combining high resolution instruments (SSS and MBS)

2014

Coherence Checking and Propagation of Lower Probability Bounds

2003

In this paper we use imprecise probabilities, based on a concept of generalized coherence (g-coherence), for the management of uncertain knowledge and vague information. We face the problem of reducing the computational difficulties in g-coherence checking and propagation of lower conditional probability bounds. We examine a procedure, based on linear systems with a reduced number of unknowns, for the checking of g-coherence. We propose an iterative algorithm to determine the reduced linear systems. Based on the same ideas, we give an algorithm for the propagation of lower probability bounds. We also give some theoretical results that allow, by suitably modifying our algorithms, the g-coher…

Quantum Property Testing for Bounded-Degree Graphs

2011

We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion, we also prove an Omega(N^(1/4)) quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph s…

“Selling” chronic pain: physiotherapists’ lived experiences of communicating the diagnosis of chronic nonspecific lower back pain to their patients

2019

Introduction: Chronic nonspecific lower back pain (CNSLBP) is a common musculoskeletal condition which can be a source of significant distress and disability for patients. Approaches to managing CNSLBP have been explored in healthcare literature, as has the importance of communication in physiotherapy practice. However, no previous studies have explored clinicians’ experiences of communicating their understanding of this diagnosis to their patients. Methods: A qualitative research design, using hermeneutic phenomenological methodology, was employed. Five participants were purposively recruited for the research and data collected via semi-structured interviews. Interpretative phenomenologica…

A note on the Schur multiplier of a nilpotent Lie algebra

2011

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.

A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient

2019

Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where $c_{\lambda}$ depends on a parameter $\lambda \in \mathbb R$, the coefficients $c_{\lambda}$ and $h$ belong to $L^q(\Omega)$ with $q>N/2$ and $\mu \in L^{\infty}(\Omega)$. Under suitable assumptions, but without imposing a sign condition on any of these coefficients, we obtain an a priori upper bound on the solutions. Our proof relies on a new boundary weak Harnack inequality. This inequality, which is of independent interest, is established in the gener…

Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems

2005

In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K is any separately Holder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in \cite{CCS} some applications of Devroye inequality to statistical properties of this class…

Global fixed point proof of time-dependent density-functional theory

2011

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point question for potentials on a given time-interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as wel…

On the slope of hyperelliptic fibrations with positive relative irregularity

2016

Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $\lambda_f$ of $f$. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of $\lambda_f$ as an increasing function of $q_f$ in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if $\lambda_f<4$.