We construct a topological charge of gauge field configurations on a fuzzy S2×S2 by using a Dirac operator satisfying the Ginsparg-Wilson relation. The topological charge defined on the fuzzy S2×S2 can be interpreted as a noncommutative (or matrix) generalization of the 2nd Chern character on S2 × S2. We further calculate the number of chiral zero modes of the Dirac operator in topologically no...

Theorem 1. Let M be a compact manifold, E and F be two (smooth) vector bundles over M , and P : C∞(M ;E) → C∞(M ;F ) be a differential operator (with smooth coefficients) of order n. Assume that P is elliptic, in the sense defined in the next section. Then: 1. The operator P (or rather its relevant extension) is Fredholm W n 2 (M ;E)→ L(M ;F ). Here W n 2 is a Sobolev space (introduced below). ...

In the previous papers, we studied the ’t Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere, and showed they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provide a meaning of the projecti...

The bio operons of Citrobacter freundii and Escherichia coli K-12 (strain C600) were isolated by screening lambda banks for complementation of E. coli bio mutants. These were compared with the previously isolated bio operon of Salmonella typhimurium and previous data on E. coli K-12. The restriction maps of the operon are very different in the three species, but no difference in gene order was ...

Pullulanase plays an important role in specific hydrolysis of branch points in amylopectin and is generally employed as an important enzyme in starch-processing industry. So far, however, the production level of pullulanase is still somewhat low from wide-type strains and even heterologous expression systems. Here the gene encoding Bacillus naganoensis pullulanase was amplified and cloned. For ...

The aim of this short note is to reconsider and to extend a former result of K. Mochizuki [Moc76], [MN96] on the existence of the scattering operator for wave equations with small dissipative terms. Contrary to the approach used by Mochizuki we construct the wave operator explicitly in terms of the parametrix construction obtained by a (simplified) diagonalization procedure, cf. [Yag97]. The me...

and Applied Analysis 3 Definition 2.1. Let E be a real Banach space. A nonempty closed convex set P ⊂ E is called a cone of E if it satisfies the following two conditions: 1 x ∈ P, σ > 0 implies σx ∈ P ; 2 x ∈ P,−x ∈ P implies x θ. Definition 2.2. An operator is called completely continuous if it is continuous and maps bounded sets into precompact sets. Let E be a real Banach space, E∗ the dual...

Let X be a space of homogeneous type in the sense of Coifman and Weiss and D a collection of balls in X . The authors introduce the localized atomic Hardy space H q D (X ) with p ∈ (0, 1] and q ∈ [1,∞] ∩ (p,∞], the localized Morrey-Campanato space E p D (X ) and the localized Morrey-Campanato-BLO space Ẽ p D (X ) with α ∈ R and p ∈ (0,∞) and establish their basic properties including H q D (X )...

Let C(R) be the space of functions on R whose m derivatives are Lipschitz 1. For E ⊂ R, let C(E) be the space of all restrictions to E of functions in C(R). We show that there exists a bounded linear operator T : C(E)→ C(R) such that, for any f ∈ C(E), we have Tf = f on E.

For the numerical treatment of Hammerstein equations by variational methods which has been considered by Hertling, we establish the stability in the sense of Mikhlin, Stetter and Tucker. Introduction. If one uses a variational method for the numerical treatment of Hammerstein equations, one obtains a nonlinear algebraic system of equations. In order to investigate the stability of the computing...