Let jν,k denote the k-th positive zero of the Bessel function Jν(x). In this paper, we prove that for ν > 0 and k = 1, 2, 3, . . . , ν − ak 21/3 ν < jν,k < ν − ak 21/3 ν + 3 20 ak 21/3 ν1/3 . These bounds coincide with the first few terms of the well-known asymptotic expansion jν,k ∼ ν − ak 21/3 ν + 3 20 ak 21/3 ν1/3 + · · · as ν →∞, k being fixed, where ak is the k-th negative zero of the Airy...

Let Mn be the set of n × n complex matrices, and for every A ∈ Mn, let Sp(A) denote the spectrum of A. For various types of products A1 ∗ · · · ∗ Ak on Mn, it is shown that a mapping φ : Mn → Mn satisfying Sp(A1 ∗ · · · ∗ Ak) = Sp(φ(A1) ∗ · · · ∗ φ(Ak)) for all A1, . . . , Ak ∈ Mn has the form X → ξS−1XS or A → ξS−1XtS for some invertible S ∈ Mn and scalar ξ. The result covers the special cases...

Software architectural knowledge (AK) is the integrated representation of the software architecture (SA) of a software-intensive system, the architectural design decisions, and the external context/environment. AK annotation using AK conceptual model is used to recover formal AK from SA documentation, including architecture design as well as the design decisions, rationale, context, and other f...

The adjusting mechanism is an important part of aero engine, and the wear degradation clearance widely present in its hinges. In this work, with hinge analyzed by dynamic simulation depth predicted precisely using a model. Based on that, sequential reliability analysis motion accuracy carried out. order to avoid expensive computational cost simulation, adaptive radial-based importance sampling ...

We give two proofs of a representation theorem for those totally finite signed Radon measures on an infinite power K of a compact Hausdorff space K (with its product topology) with the property of invariance under permutation of coordinates, in terms of powers of Radon probability measures on K. This is essentially a version of de Finetti’s theorem on exchangeable sequences of random variables....

A classical theorem of Pick gives a criterion for interpolation by analytic functions in the open unit disc D subject to an H∞-norm bound. This result has substantial generalizations in two different directions. On the one hand, one can replace H∞ by the multiplier algebras of certain Hilbert function spaces, some of them having no connection with analyticity [Ag1, Ag2]. On the other hand, one ...

In multicellular organisms p53 maintains genomic integrity through activation of DNA repair, and apoptosis. EBNA3C can down regulate p53 transcriptional activity. Aurora kinase (AK) B phosphorylates p53, which leads to degradation of p53. Aberrant expression of AK-B is a hallmark of numerous human cancers. Therefore changes in the activities of p53 due to AK-B and EBNA3C expression is important...

acanthamoeba keratitis (ak) is a sight-threating infection of the cornea that mostly affects contact lens wearers. until now, ak treatment remains very difficult due to the existence of a highly resistant cyst stage in the life cycle of acanthamoeba which is extremely resistant to most of the available anti-amoebic compounds. moreover, current treatment of ak is usually based in the combination...

Let k and n be positive integers, n > k. Define r(n, k) to be the minimum positive value of | √ a1 + · · ·+ √ ak − √ b1 − · · · − p bk| where a1, a2, · · · , ak, b1, b2, · · · , bk are positive integers no larger than n. It is important to find a tight bound for r(n, k), in connection to the sum-of-square-roots problem, a famous open problem in computational geometry. The current best lower bou...