Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant. In this work, we introduce a model which allows for non-homogeneous behaviour in both cases. In particular, we outline a censoring mechanism based on a non-homogeneous alternating renewal process in which interval generation is assumed to be time-dependent, and we propose a Markov point process model for the underlying occurrence time distribution. We prove the existence of this process and derive the conditional distribution of the occurrence times given the intervals. We provide a framework within which the process can be accurately modelled, and subsequently compare our model to the homogeneous approach through a number of illustrative examples.

In this study, the glass forming ability, thermal stability, and room-temperature mechanical behavior of a high Zr-containing Zr71Cu11Ni10.5Al7Ti0.5 bulk glassy alloy were investigated. The glassy alloy exhibits a high glass-forming ability with a critical casting diameter of 5 mm using copper mold injection casting, and its critical cooling rate is estimated to be smaller than 40 K/s. A small kinetic fragility index m of 32 indicates its good thermodynamic stability and glass-forming ability. Compressive tests indicate that the glassy alloy displays a significant average plastic strain of 12.3%, a high fracture strength of 1592 MPa, and Young's modulus of 74.5 GPa. The good ductility is attributed to the introduction of more free volume and local compositional inhomogeneity with increasing Zr addition. This finding may provide useful guidelines for the development of novel high Zr-containing glassy alloys.

Inhomogeneity may lead to premature failure and operationally determines the lifetime estimation of thick weld joints. Considerable novelty of this paper was the achievement of the microstructural and mechanical inhomogeneity, especially along the thickness direction, in the narrow-gap weld seam of thick gas metal arc (GMA) welded Al–Zn–Mg alloy plates. The microstructure of the weld seam was investigated by means of optical metallography, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy dispersive spectrum (EDS), after which the phase composition was ascertained according to the x-ray diffraction (XRD) analysis and selected area diffraction analysis by TEM (TEM-SAD). The generation of intergranular short rod-shaped MgZn2 particles changed the distribution of precipitates on the grain boundary with intragranular ellipsoidal MgZn2 particles simultaneously formed as the strengthening phase, which rendered preferable mechanical performances to the bottom layer of the weld seam. The above conclusion was farther affirmed by micro fractography and EDS test results on the fractured surface of the tensile samples. In addition, the effect of following weld passes on the microstructure and micro hardness profile of the finished weld pass was investigated.

In the present paper the propagation of torsional surface waves is discussed in an inhomogeneous elastic layer lying over a fluid saturated porous half space. The inhomogeneity in rigidity and density in the inhomogeneous layer plays an important role in the propagation of torsional surface waves. The presence of fluid in the pores diminishes the velocity. Further, it is seen that if the layer becomes homogeneous and the porous half space is replaced by a homogeneous half space, the velocity of the torsional surface waves coincides with that of Love wave. The effect of inhomogeneity factors and porosity factor on the phase velocity of torsional surface wave is delimitated by means of graphs.

We consider linear elliptic systems which arisein coupled elastic continuum mechanical models. In these systems, the straintensor ε P := sym (P -1∇u) is redefined to include amatrix valued inhomogeneity P(x) which cannot be described by a spacedependent fourth order elasticity tensor. Such systems arise naturally ingeometrically exact plasticity or in problems with eigenstresses.The tensor field P induces a structural change of the elasticity equations. Forsuch a model the FETI-DP method is formulated and a convergence estimateis provided for the special case that P -T = ∇ψ is a gradient.It is shown that the condition number depends only quadratic-logarithmicallyon the number of unknowns of each subdomain. Thedependence of the constants of the bound on P is highlighted. Numericalexamples confirm our theoretical findings. Promising results are also obtainedfor settings which are not covered by our theoretical estimates.

In this paper we introduce Lévy-driven Cox point processes (LCPs) as Cox point processes with driving intensity function Λ defined by a kernel smoothing of a Lévy basis (an independently scattered, infinitely divisible random measure). We also consider log Lévy-driven Cox point processes (LLCPs) with Λ equal to the exponential of such a kernel smoothing. Special cases are shot noise Cox processes, log Gaussian Cox processes, and log shot noise Cox processes. We study the theoretical properties of Lévy-based Cox processes, including moment properties described by nth-order product densities, mixing properties, specification of inhomogeneity, and spatio-temporal extensions.

This report examines the recommendations of The International Commission for Radiation Units and Measurements, ICRU 50 and a typical interpretation of them. It hypothesises that there is a small identifiable group of patients that may be at risk of long term damage due to current radiotherapy treatment to the breast.

The report emphasises the variation in dose obtained when the whole volume of the irradiated breast is considered. The dose distribution beyond the central contour and the effect of lung density is analysed. Even if three-dimensional planning and inhomogeneity correction factors are not available, consideration must be given to their significance.

This report acknowledges that the ICRU reference point is a much-needed method of comparing radiotherapy treatments between hospitals, but points out that it was not intended to be a means of determining dosimetry, despite the suggestion that it may be advantageous if its relative dose is 100%.

The report concludes that there should be greater awareness and attention paid to the recommendation that heterogeneity should be within +7 and −5% of the prescribed dose.

In this article, the secondary electron-emission properties of both vertically and laterally inhomogeneous samples are discussed. To study the effect of surface coverage, the total electron-emission yield of tungsten and niobium samples was measured as a function of primary electron energy and oxide thickness. A method is suggested to avoid charging difficulties during AES measurements of samples that consist of both metal and various insulator parts.

The local Nash inequality is introduced as a natural extension of the classical Nash inequality yielding a space-homogeneous upper heat kernel estimate. The local Nash inequality contains local information of the heat kernel and is a necessary condition for the space-inhomogeneous heat kernel estimate involving the volume of balls like the one obtained by Li and Yau for a complete Riemannian manifold with non-negative Ricci curvature. Under the volume doubling property, the local Nash inequality combined with the exit time estimate is shown to be equivalent to a sub-Gaussian off-diagonal upper estimate of the heat kernel allowing space-inhomogeneity.

A new class of models for inhomogeneous spatial point processes is introduced. These locally scaled point processes are modifications of homogeneous template point processes, having the property that regions with different intensities differ only by a scale factor. This is achieved by replacing volume measures used in the density with locally scaled analogues defined by a location-dependent scaling function. The new approach is particularly appealing for modelling inhomogeneous Markov point processes. Distance-interaction and shot noise weighted Markov point processes are discussed in detail. It is shown that the locally scaled versions are again Markov and that locally the Papangelou conditional intensity of the new process behaves like that of a global scaling of the homogeneous process. Approximations are suggested that simplify calculation of the density, for example, in simulation. For sequential point processes, an alternative and simpler definition of local scaling is proposed.

Based on the weight function theory and Hutchinson's technique, the analytic form of the toughness change near a crack-tip is derived. The inhomogeneity toughening is treated as an average quantity calculated from the mean-field approach. The solutions are suitable for the composite materials with moderate concentration as compared with Hutchinson's lowest order formula. The composite has the more toughened property if the matrix owns the higher value of the Poisson ratio. The composite with thin-disc inclusions obtains the highest toughening and that with spheres always provides the least effective one. For the microcrack toughening, the variations of the crack shape do not significantly affect the toughness change if the Budiansky and O'Connell crack density parameter is used. The explicit forms for three types of the void toughening and two types of the microcrack toughening are also shown.

There are many indications for the existence of dense cold clumps in Wolf-Rayet (WR) atmospheres, expanding outwards from the stellar core (e.g., Cherepaschuck et al. 1984, St-Louis et al. 1993). Based on this, we consider a clump model for WR model atmospheres. The main features of the model are described. The mechanism of clump structure formation is outlined. The clump model is used for calculating emission line profiles.