Let the discrete group G act properly and isometrically on the Riemannian manifold X. Let C0(X, δ) be the section algebra of a smooth locally trivial G-equivariant bundle of elementary C∗-algebras representing an element δ of the Brauer group BrG(X). Then C0(X, δ ) ⋊ G is KK-theoretically Poincaré dual to ( C0(X, δ)⊗̂C0(X)Cτ (X) ) ⋊ G, where δ is the inverse of δ in the Brauer group. We deduce t...

Recently, a previous contributor showed how the delta-wye conversion may be applied to find the equivalent capacitance of five capacitors arranged in a bridge configuration. In fact, that contributor gave an algorithm for this purpose which showed that the equivalent capacitance depends upon all five capacitors. However, in this paper, we point out that there is a special case where the equival...

The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem (Newman’s Inequality in Lp[a, b] for [a, b] ⊂ (0,∞)). Let Λ := (λj) ∞ j=0 be an increasing sequence of nonnegative real numbers. Suppose λ0 = 0 and there exists a δ > 0 so that λj ≥ δj for each j. Suppose 0 < a < b and 1 ≤ p ≤ ∞. Then there exists a constant c(a, b, δ) depending only on a, ...

I describe a general formalism for galaxy biasing [20] and its application to measurements of β (≡ Ω/b), e.g., via direct comparisons of light and mass and via redshift distortions. The linear and deterministic relation g = bδ between the density fluctuation fields of galaxies g and mass δ is replaced by the conditional distribution P (g|δ) of these as random fields, smoothed at a given scale a...

The new siderophore tsukubachelin B (1) was isolated from the iron-deficient culture medium of the newly isolated strain Streptomyces sp. TM-74. The chemical structure of tsukubachelin B (1) was established via interpretation of 2D nuclear magnetic resonance and electrospray ionization-mass spectroscopic data. The structure of tsukubachelin B (1) comprises 6 mol of amino acids, including 2 mol ...

Denote points in Euclidean n-space, Rn, by x = (x1, . . . ,xn) and let E and ∂E denote the closure and boundary of E ⊆Rn, respectively. Let 〈x, y〉 denote the standard inner product in Rn, |x| = 〈x,x〉1/2, and set B(x,r)= {y ∈Rn : |y− x| < r} whenever x ∈Rn, r > 0. Define k-dimensional Hausdorffmeasure, 1≤ k ≤ n, in Rn as follows: for fixed δ > 0 and E ⊆Rn, let L(δ)= {B(xi,ri)} be such that E ⊆ ⋃...

Let A, B ⊆ Z be finite, nonempty subsets with minA = minB = 0, and let δ(A,B) = n 1 if A ⊆ B, 0 otherwise. If maxB ≤ maxA ≤ |A|+ |B| − 3 and (1) |A+B| ≤ |A|+ 2|B| − 3− δ(A,B), then we show A + B contains an arithmetic progression with difference 1 and length |A|+ |B| − 1. As a corollary, if (1) holds, max(B) ≤ max(A) and either gcd(A) = 1 or else gcd(A+ B) = 1 and |A+B| ≤ 2|A|+ |B| − 3, then A+...

We present an updated theoretical prediction of ǫ/ǫ, using the next-to-leading ∆S = 1 effective hamiltonian and lattice QCD matrix elements. The CP violating phase is costrained by using both the experimental values of ǫ and xd, assuming the theoretical determination of fB. Predictions of cos δ and sin 2β are also obtained in this way. For ǫ/ǫ, our estimate is ǫ/ǫ = (2.8± 2.4)× 10. We repeat th...

In this paper, optimal convex combination bounds of centroidal and harmonic means for weighted geometric mean of logarithmic and identric means are proved. We find the greatest value λ(α) and the least value Δ(α) for each α ∈ (0,1) such that the double inequality: λC(a,b)+(1−λ)H(a,b) < Lα (a,b)I1−α (a,b) < ΔC(a,b)+(1−Δ)H(a,b) holds for all a,b > 0 with a = b. Here, C(a,b), H(a,b) , L(a,b) and I...

We develop algorithms for computing Craig interpolants for first-order formulas over real numbers with a wide range of nonlinear functions, including transcendental functions and differential equations. We transform proof traces from δ-complete decision procedures into interpolants that consist of Boolean combinations of linear constraints. The algorithms are guaranteed to find the interpolants...