1. SOBOLEV SPACES AND WEAK FORMULATIONS Let Ω be a bounded Lipschitz domain in R. We introduce the Sobolev spaces H(curl ; Ω) = {v ∈ L(Ω), curlv ∈ L(Ω)}, H(div; Ω) = {v ∈ L(Ω),div v ∈ L(Ω)} The vector fields (E,H) belong to H(curl ; Ω) while the flux (D,B) in H(div; Ω). We shall use the unified notation H(d; Ω) with d = grad , curl , or div. Note that H(grad ; Ω) is the familiar H(Ω) space. The...

This paper presents H∞ control problem for input-delayed systems. A neutral system approach is considered to the design of PD controller for input delay systems in presence of uncertain time-invariant delay. Using this approach, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed coeff...

This paper deals with the study of Birkhoff--James orthogonality a linear operator to subspace operators defined between arbitrary Banach spaces. In case domain space is reflexive and finite dimensional we obtain complete characterization. For spaces, same under some additional conditions. an Hilbert H, also L(H), both respect norm as well numerical radius norm.

We present a spectrum-level version of the norm map in equivariant homotopy theory based on the algebraic construction in the 1997 paper by Greenlees and May. We show that this new norm map is the same as the construction in the 2009 paper by Hill, Hopkins and Ravenel. Our comparison of the two norm maps gives a conceptual understanding of the choices inherent in the definition of the multiplic...

The problem of inflation has been of central concern to American policymakers since the mid 1960s. Of particular concern has been the rise in the core, or sustained, inflation rate from below the 2 percent level in the early 1960s to near the double-digit level by the late 1970s. Since 1981 a rapid disinflation has occurred, bringing the current inflation rate down to below 5 percent. The recen...

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...

Recently, a new deterministic characterization of the H 2 norm has been proposed, using a new norm (DD . DD Wg ), based on (approximate) set membership modeling of white noise. The main result shows that under mild conditions, for a xxed system the gap between the H 2 and g norms can be made arbitrarily small. Motivated by these results it has been argued that the DD . Wg norm provides a useful...

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...