Various normwise relative condition numbers that measure the sensitivity of Bott– Duffin inverse and the solution of constrained linear systems are characterized. The sensitivity of condition number itself is then investigated. Finally, upper bounds are derived for the sensitivity of componentwise condition numbers. 2002 Elsevier Science Inc. All rights reserved.

Algae preparations are commonly used in alternative medicine. We examined the effects of algae extracts on normal hematopoietic cells and leukemia cells. Ethanol extracts were prepared of Dunaliella salina (Dun), Astaxanthin (Ast), Spirulina platensis (Spir), and Aphanizomenon flos-aquae (AFA). Cell viability effects were completed by Annexin staining. Ast and AFA inhibited HL-60 and MV-4-11 wh...

The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete varieties. In addition, our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions. This class ...

We completely characterize real Bott manifolds up to diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism betwe...

A real Bott manifold is the total space of a sequence of RP 1 bundles starting with a point, where each RP 1 bundle is the projectivization of a Whitney sum of two real line bundles. A real Bott manifold is a real toric manifold which admits a flat riemannian metric. An upper triangular (0, 1) matrix with zero diagonal entries uniquely determines such a sequence of RP 1 bundles but different ma...

Multidrug resistance is a major cause of chemotherapy failure. Recent studies indicate that drug resistance can be rapidly induced by some soluble factors, such as cytokines, chemokines, growth factors, and cell adhesion factors in the tumor microenvironment. Osteopontin (OPN), an extracellular matrix protein, has a functional arginine-glycine-aspartic acid (RGD) domain for binding to integrin....

We study a matrix that arises from singular form of the Woodbury identity. present generalized inverse and pseudo-determinant identities for this matrix, which have direct applications Gaussian process regression, specifically its likelihood representation precision matrix. extend definition to Bott-Duffin covariance preserving properties related conditional independence, precision, marginal pr...

Part 1. Vector Bundles and Bott Periodicity 2 1. Families of Vector Spaces and Vector Bundles: 8/27/15 2 2. Homotopies of Vector Bundles: 9/1/15 5 3. Abelian Group Completions and K(X): 9/3/15 8 4. Bott’s Theorem: 9/8/15 12 5. The K-theory of X × S2: 9/10/15 15 6. The K-theory of the Spheres: 9/15/15 18 7. Division Algebras Over R: 9/17/15 22 8. The Splitting Principle: 9/22/15 25 9. Flag Manif...

<p style='text-indent:20px;'>We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using theory of integrable systems, any admissible Morse-Bott be realized as flow. This interpreted an inverse problem Arnold's structure theorem and yields a corollary topological c...