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Published in Sergio Pizzini, Defects in Nanocrystals, 2020
Using a sum of the core-shell property terms and the BOLS correlation mechanism, the size-dependence function Q(R) of a generic property Q could be derived, that is uniquely a function of the number of the undercoordinated atoms at the shell structure Q(R)=Qb+∑i≤3Ni(qi−qb)
Dynamical systems approach of modelling
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
Consider a d-dimensional compact manifold Μ. For pairs (F, f), where F is a smooth (C2) vector field and f is a smooth function on Μ, it is a generic property that ΦF,f(Y):M→Rm≥2d+1
Thermoelastic wave propagation due to local thermal shock on the functionally graded media
Published in Journal of Thermal Stresses, 2022
Kushan Prasad Verma, Dipak Kumar Maiti
In the present study, the analyses have only been done on a two-dimensional half-space domain of the whole FGM medium. The ceramic and metal constituents and hence their properties in the FGM layer are considered to be graded across horizontal or vertical axes of the domain as a function of the power law. The schematic of the distribution of constituent materials along the x and y-axis of the domain is illustrated in Figure 1. The material properties like density (ρ), Lame’s constants (λ and μ), thermal expansion coefficient (α), thermal expansion modulus (β = 3λ + 2μ), specific heat (cv) and thermal conductivity (k) including the relaxation time (τ0) are considered to be the functions of position x in the body. The expressions of variation of a generic property, Peff as a function of position, x according to power-law (Tanigawa et al. [41]), is presented in Eq. (7). The terms n, Pc, and Pm denote the volume fraction index and properties of ceramic and metal, respectively.
Global C∞ integrability of quartic–linear polynomial differential systems
Published in Dynamical Systems, 2019
In order to analyze a family of planar polynomial differential systems depending on parameters, it is usual to begin detecting the elements of the family that satisfy some non-generic property (in our study the existence of a first integral). Next, the dynamical behaviour of these non-generic systems is studied. After that, if possible, some systems in the family are described as perturbations of this non-generic systems studied, and then, the dynamical behaviour of the perturbed systems can be analyzed. For instance, some non-generic systems present a continuum of periodic orbits. This is related with the centre problem and also with the existence of a C∞ or analytic first integral, see [12] and references therein. If we perturb a continuum of periodic orbits in a planar differential system, we can think about the number of limit cycles that persist under a perturbation, see [4].
Global aspects of the continuous reformulation for cardinality-constrained optimization problems
Published in Optimization, 2023
Let us discuss the consequences of Proposition 3.2 and Theorems 3.7, 3.10 for the regularized continuous reformulation from the global optimization perspective. We start by looking at the generic properties of . We recall that a generic property holds on an open and dense subset of defining functions f, h, and g with respect to the strong (or Whitney-) topology, cf. [5]. Especially, the following Proposition 3.12 suggests that the assumption of NDT5 is not restrictive.