In this paper we show some very interesting properties of weak Chebyshev subspaces and use them to simplify Pinkus's characterization of Asubspaces of C[a, b]. As a consequence we obtain that if the metric projection PG from C[a, b] onto a finite-dimensional subspace G has a continuous selection and elements of G have no common zeros on (a, b), then G is an /4-subspace.

This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a non-commutative space.

‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules‎. ‎We investigate the relations between frames and $ ast $-frames‎. ‎Some properties of $ ast $-frames in Hilbert pro-$ C^* $-modules are studied‎. ‎Also‎, ‎we show that there exist two differences between $ ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ ...

the combination of flexural frame and shear wall is one of the suitable systems to apply in reinforced concrete buildings. the deflections of flexural frame become limited due to the high stiffness of wall and the interaction of these systems. tall buildings even higher than fifty stories can be designed by using frame- wall systems. with respect to special behavior of flexural frame or shear w...

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of nonnormality. Associated with a desired se...

1.2. Primer on Connections. Recall from Peng’s talk that a connection on P → X can be thought of in three ways: (1) As a field of horizontal subspaces: TpP = HpP⊕VpP , where V P = ker (π∗). (Note that Vp ∼= g, and Hp ∼= Tπ(p)X). (2) As a g-valued 1-form A ∈ ΩX (g) which is invariant w.r.t. the induced G-action on ΩX (g). (3) Given a representation of G on W , as a vector bundle connection on th...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

An equiangular tight frame (ETF) is a sequence of vectors in Hilbert space that achieves equality the Welch bound and so has minimal coherence. More generally, an equichordal fusion (ECTFF) equi-dimensional subspaces Conway, Hardin Sloane’s simplex bound. Every ECTFF type optimal Grassmannian code, is, packing space. We construct ECTFFs by exploiting new relationships between known ETFs. Harmon...

For a natural number c, c-arrangement is an arrangement of dimension c subspaces satisfying the following condition: sum any subset has multiple c. Matroids arising as normalized rank functions c-arrangements are also known multilinear matroids. We prove that it algorithmically undecidable whether there exists such given matroid representation, or equivalently multilinear. It follows certain pr...