for all x, y ∈ X and all natural numbers n, where φn : [0,∞)→ [0,∞) and limn→∞φn = φ, uniformly on any bounded interval [0,b]. Suppose that φ is upper semicontinuous and that φ(t) < t for all t > 0. Furthermore, suppose that there exists a positive integer n∗ such that φn∗ is upper semicontinuous and φn∗(0)= 0. If there exists x0 ∈ X which has a bounded orbit O(x0)= {x0,Tx0,T2x0, . . .}, then T...

It is proved that any static system that is spacetime-geodesically complete at infinity, and whose spacelike-topology outside a compact set is that of R minus a ball, is asymptotically flat. The matter is assumed compactly supported and no energy condition is required. A similar (though stronger) result applies to black holes too. This allows us to state a large generalisation of the uniqueness...

where κ(t) is the curvature of C given as a function of the arclength t and l the length of C. See also McClure and Vitale [7] and for asymptotic formulae for approximation with respect to the Hausdorff metric in higher dimensions R. Schneider [8],[9] and P.M. Gruber [5]. In this article we extend the asymptotic formulae (1) by deriving the second terms in the asymptotic expansions of δ(C,P i n...

Background: The Health & Safety Executive’s (HSE) Indicator Tool offers a measure of exposure to psychosocial work conditions that may be linked to stress-related outcomes. The HSE recommends that Indicator Tool data should be used as a basis for discussions concerned with the identification of psychosocial work conditions that might warrant prioritisation for intervention. However, operational...

in this paper, a new formula is applied for the calculation of gravity anomalies from a cylinder model representing a geological body. compared to conventional methods, this new development allows the cylinder to be freely oriented in space. 38 gravity forward models are produced each of which anomaly attributes are calculated. then a linear relationship is established between attributes and so...

Attempts to unify Gravity Theory and Quantum Field (QFT) under Loop (LQG), are diverse; a dividing line between classical quantum is sought with Schrödinger cat-state experiments. A Primordial Theory-based alternative presented, gravity-based harmonic oscillator developed. With theory applied at micro-scales gravity meso- macro-scales, this scale-gap contributes the conceptual problems associat...

The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossin...

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The effective response of a periodic fibre reinforced material to SH wave propagation is studied using the method of asymptotic homogenization, complex variable theory and multipole expansions. The quasi-static limit of the effective properties is calculated when the wavelength is much longer than the defining lengthscale of the microstructure. The method developed allows the determination of t...

Abstract. When a spacetime takes Bondi radiating metric, and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy-momentum is the past limit of the Bondi energy-momentum. We also derive a formula relating the ADM energy-momentum of any asymptotically flat spacelike hypersurface to the Bondi energy-momentum of any nu...