A well-known open problem of Muckenhoupt–Wheeden says that any Calderón–Zygmund singular integral operator T is of weak type (1,1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat “dual” problem: sup λ>0 λw { x ∈Rn : |Tf (x)| Mw > λ } ≤ c ∫

The inverse velocity problem is fundamental to robot position control. The weighted, three-point velocity approach offers a solution to the inverse velocity problem in robot manipulation. The theory applies to redundant robots, to robots with less than or equal six degrees-of-freedom, and to robots in singular configurations. The method always yields solutions, provided the three velocity node ...

For the fractional integration operators of any positive order on the half-line and on a bounded interval we explicitly present a singular value decomposition, thereby considering these operators as acting on and into spaces of functions square integrable with appropriate weights. The results obtained amount to an interpretation of properties of systems of orthogonal polynomials.

In this paper we develop computational techniques with enhanced accuracy for two frequency-weighted model reduction approaches, namely, balanced truncation, and singular perturbation approximation. New stability-enforcing choices of the frequency-weighted grammians can guarantee the stability of reduced models for two-sided frequency weights. Several numerical examples show the effectiveness of...

The structured singular value framework is applied to a distillation benchmark problem formulated for the 1991 IEEE Conference on decision and control (CDC). A two degree of freedom controller, which satisfies all control objectives of the CDC problem, is designed using -synthesis. The design methodology is presented and special attention is paid to the approximation of given control objectives...

Asymptotic expressions are derived for the singular value decompositon of a matrix some of whose columns approach zero. Expressions are also derived for the QR factorization of a matrix some of whose rows approach zero. The expressions give insight into the method of weights for approximating the solutions of constrained least squares problems.

A generalization with singular weights of Moore-Penrose generalized inverses of closed range operators in Hilbert spaces is studied using the notion of compatibility of subspaces and positive operators. ∗Partially supported by CONICET (PIP 2083/00), UBACYT I030 and ANPCYT (PICT03-9521)

Singular sources mining is essential in many applications like sensor fusion or dataset analysis. A singular source of information provides pieces of evidence that are significantly different from the majority of the other sources. In the Dempster-Shafer theory, the pieces of evidence collected by a source are summarized by basic belief assignments (bbas). In this article, we propose to mine si...

A method for making weighted linear combinations of the spectra acquired by a phased-array coil is described. Unlike most previous combination methods, no special reference points in the data are chosen to represent the coil weights. Instead, all the data points are used, which results in optimal signal-to-noise ratio more reliable estimation. The method uses singular value decomposition to ide...

Introduction Let G be a simply connected and connected semisimple group over an algebraically closed field k of characteristic p > 0. T ⊂ G is a maximal torus and R is the root system relative to T . X(T ) is the weight lattice. Let B ⊃ T be a Borel subgroup corresponding to the negative roots R− = R. Denote by Gr the r-th Frobenius kernel of G. The socle and radical structures of the cohomolog...