of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an err...
The Young operator inequality is represented for λ∈[0,1] as follows A 1-λ B≥A# 1-λ B for positive invertible operators A and B with 0 M Tominaga - 《Scientiae Mathematicae Japonicae》 被引量: 135发表: 2002年 Optimal young's inequality and its converse: a simple proof We give a...
2)via the spectrum of some Toeplitz operators on the Hardy spaceH^{2}. Second, we give examples to show that Shimorin’s condition for the shift operator fails on theI_{a
Then a natural aim could be to find how further these estimations can arrive and, moreover, to study what happens outside the log-concave case. In this paper we can prove that, in a right neighbourhood of 0, there exists a linear lower bound for the cumulative distribution function of σ...
The purpose of this article is to prove three major sharp estimates for fully bubbling solution (see (1.7) below) to general SU(n+1) Toda systems: 1. All fully bubbling solutions are approximated by a sequence of global solutions with sharp error; 2. The gradient of certain functions must...
Invertible condition of quantum Fisher information matrix for a mixed qubitQuantumOpticsEstimating multiparamter simultaneously as precise as possible is an important goal of quantum metrology. As a first step to this end, here we give a condition determining whether two arbitrary parameters can be ...
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ever, a single graph is insufficient to accurately model the relationships between both the systems and their schemas. We present below a set of representational models for large-scale semantic systems which will then be used throughout the rest of this paper. We model information parties as ...
First, for the population case, we establish a sufficient and almost necessary condition for the reference dictionary $\\mathbf D_0$ to be locally identifiable, i.e., a local minimum of the expected $l_1$-norm objective function. Our condition covers both sparse and dense cases of the ...
Let M be any closed subspace of a Hilbert space H. Then (a) There is a unique orthogonal projection P on H with M=Ran(P), M⊥=Nul(P), and H=M⊕M⊥. (b) For each x∈H, its projection yo=P(x) is the unique point in M whose difference from x is orthogonal to M: x−...