In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.

In this paper, two-dimensional cubature error bounds are developed. It is assumed that the function to be integrated is analytic, and that the domain of integration is contained in [—1, 1] X [—1, 1]. Tables of error constants for several cubature rules and domains of integration are included.

Let α be an irrational and φ : N → R be a function decreasing to zero. For any α with a given Diophantine type, we show some sharp estimations for the Hausdorff dimension of the set Eφ(α) := {y ∈ R : ‖nα− y‖ < φ(n) for infinitely many n}, where ‖ · ‖ denotes the distance to the nearest integer.

As semiconductor technology advances, the size of the transistors is shrinking. This technology has reached a point where the potential of transient errors is becoming significant even for combinational logic. Previous efforts to detect such errors have used a general approach applied to the entire circuit. In this project, the error detection efforts are tailored to the specifics of the target...

We describe several established error of fit (EOF) functions for use in the least square fitting of ellipses, and introduce a further four new EOFs. Four measures are given for assessing the suitability of such EOFs, quantifying their linearity, curvature bias, asymmetry, and overall goodness. These measures enable a better understanding to be gained of the individual merits of the EOF functions.

In this paper, based on the relationship between logic functions and quantum error correcting codes(QECCs), we unify the construction of QECCs via graphs, projectors and logic functions. A construction of QECCs over a prime field Fp is given, and one of the results given by Ref[8] can be viewed as a corollary of one theorem in this paper. With the help of Boolean functions, we give a clear proo...

The sign-rank of a real matrix M is the least rank of a matrix R in which every entry has the same sign as the corresponding entry of M.We determine the sign-rank of every matrix of the form M = [ D(|x ∧ y|) ]x,y, where D : {0, 1, . . . , n} → {−1,+1} is given and x and y range over {0, 1}n . Specifically, we prove that the sign-rank of M equals 22̃(k), where k is the number of times D changes s...

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We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f . In a reflexive Banach space X, we...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.