Given (M,Ω) a calibrated Riemannian manifold with a parallel calibration of rank m, and M an immersed orientable submanifold with parallel mean curvature H we prove that if cos θ is bounded away from zero, where θ is the Ω-angle of M , and if M has zero Cheeger constant, then M is minimal. In the particular case M is complete with Ricc ≥ 0 we may replace the boundedness condition on cos θ by co...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing “if θ is true then, normally, φ is true” be said to follow from a given set of items of such information. Many answers to this question have been proposed but...

Every mode of a quantized boson (photon) field is described as a quantum harmonic oscillator. In this description one meets the quantum phase problem, which has been reviewed in the paper [1]. Using the photon annihilation and creation operators â and â†, respectively, which obey the boson commutation relation [â, â†] = 1̂, with 1̂ an identity operator, the number operator is expressed as n̂ = â†â...

It is shown that the closure of the set of Fourier coefficients of the Bernoulli convolution μθ parameterized by a Pisot number θ, is countable. Combined with results of Salem and Sarnak, this proves that for every fixed θ > 1 the spectrum of the convolution operator f 7→ μθ ∗ f in L(S) (where S is the circle group) is countable and is the same for all p ∈ (1,∞), namely, {μ̂θ(n) : n ∈ Z}. Our re...

The Sharma–Mittal entropies generalize the celebrated Shannon, Rényi and Tsallis entropies. We report a closed-form formula for the Sharma–Mittal entropies and relative entropies for arbitrary exponential family distributions. We explicitly instantiate the formula for the case of the multivariate Gaussian distributions and discuss on its estimation. Q1 Q2 PACS numbers: 03.65.Ta, 03.67.−a (Some ...

We show that the application of Regge phenomenology to SU(4) meson multiplets leads to a new Gell-Mann–Okubo mass-mixing angle formula in the SU(3) sector, 3m 2 1 + cos 2 θ m 2 0 + sin 2 θ m 2 0 ′ + √ 2 sin 2θ m 2 0 − m 2 0 ′ = 4m 2 1/2 , where m 1 , m 1/2 , m 0 , m 0 ′ are the masses of the isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet states, respectively, and θ i...

We study a model of "elastic" lattice polymer in which a fixed number of monomers m is hosted by a self-avoiding walk with fluctuating length l . We show that the stored length density ρm≡1-/m scales asymptotically for large m as ρm=ρ∞(1-θ/m+…) , where θ is the polymer entropic exponent, so that θ can be determined from the analysis of ρm. We perform simulations for elastic lattice polymer l...

Write Θ for the stable character associated to a finite dimensional representation E of a connected real reductive group G. Let M be the centralizer of a maximal torus T , and denote by ΦM (γ,Θ ) Arthur’s extension of |D M (γ)| 1 2Θ(γ) to T (R). In this paper we give a simple explicit expression for ΦM (γ,Θ ), when γ is elliptic in G.