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140 Engineering
146 Information and computing sciences
1Convex inequality
1Directional derivative
1Hausdorff measure
1Lebesgue measure
1Liouville numbers
1Local and global error bounds
1Monte Carlo method
1Particle-in-cell method
1Particle–gas flow
1Polydispersion
1Radiative heat transfer
1Semi-infinite convex constraint systems
1Stability

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A continuous homomorphism of a thin set onto a fat set

- Chalebgwa, Taboka, Morris, Sidney

**Authors:**Chalebgwa, Taboka , Morris, Sidney**Date:**2022**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 106, no. 3 (2022), p. 500-503**Full Text:**false**Reviewed:****Description:**A thin set is defined to be an uncountable dense zero-dimensional subset of measure zero and Hausdorff measure zero of an Euclidean space. A fat set is defined to be an uncountable dense path-connected subset of an Euclidean space which has full measure, that is, its complement has measure zero. While there are well-known pathological maps of a set of measure zero, such as the Cantor set, onto an interval, we show that the standard addition on

- Chen, Jingling, Kumar, Apurv, Coventry, Joe, Lipiński, Wojciech

**Authors:**Chen, Jingling , Kumar, Apurv , Coventry, Joe , Lipiński, Wojciech**Date:**2022**Type:**Text , Journal article**Relation:**Applied Mathematical Modelling Vol. 110, no. (2022), p. 698-722**Full Text:**false**Reviewed:****Description:**Heat transfer in directly-irradiated high-temperature solid–gas flows laden with polydisperse particles is investigated using a novel transient three-dimensional computational fluid dynamics model. The model couples particle–gas hydrodynamics of solid–gas flows laden with polydisperse particles, radiative heat transfer in non-grey absorbing, emitting and anisotropically-scattering multi-component participating media, conduction heat transfer in the gas phase, and interfacial convection heat transfer. The multiphase particle-in-cell method is used to predict high-fidelity solid–gas flow characteristics, such as the local discrete particle size distribution, with increased computational efficiency by combining the advantages of both Eulerian and Lagrangian methods. The multi-component radiative transfer model is implemented using an advanced collision-based Monte Carlo ray-tracing method. The number of the prescribed discrete particle components is found to be the key parameter affecting the computational accuracy and efficiency, which primarily depends on the size distribution of the particles. For the model particle–gas flow featuring free-falling Gamma-distributed ceramic particles exposed to concentrated solar irradiation, the particle volume fraction, radiative, fluid flow and thermal characteristics appear to converge with the increasing number of the discrete particle components. Five particle components are sufficient to obtain physically meaningful results. A further increase in the number of the particle components only slightly increases the accuracy of the numerical predictions at the expense of a rapidly increasing computational time. For five particle components, the particle vertical velocity at the receiver exit for particles with the diameter of 43.4

Characterizations of stability of error bounds for convex inequality constraint systems

- Wei, Zhou, Théra, Michel, Yao, Jen-Chih

**Authors:**Wei, Zhou , Théra, Michel , Yao, Jen-Chih**Date:**2022**Type:**Text , Journal article**Relation:**Open Journal of Mathematical Optimization Vol. 3, no. (2022), p. 1-17**Full Text:****Reviewed:****Description:**In this paper, we mainly study error bounds for a single convex inequality and semi-infinite convex constraint systems, and give characterizations of stability of error bounds via directional derivatives. For a single convex inequality, it is proved that the stability of local error bounds under small perturbations is essentially equivalent to the non-zero minimum of the directional derivative at a reference point over the unit sphere, and the stability of global error bounds is proved to be equivalent to the strictly positive infimum of the directional derivatives, at all points in the boundary of the solution set, over the unit sphere as well as some mild constraint qualification. When these results are applied to semi-infinite convex constraint systems, characterizations of stability of local and global error bounds under small perturbations are also provided. In particular such stability of error bounds is proved to only require that all component functions in semi-infinite convex constraint systems have the same linear perturbation. Our work demonstrates that verifying the stability of error bounds for convex inequality constraint systems is, to some degree, equivalent to solving convex minimization problems (defined by directional derivatives) over the unit sphere. © Zhou Wei & Michel Théra & Jen-Chih Yao.

**Authors:**Wei, Zhou , Théra, Michel , Yao, Jen-Chih**Date:**2022**Type:**Text , Journal article**Relation:**Open Journal of Mathematical Optimization Vol. 3, no. (2022), p. 1-17**Full Text:****Reviewed:****Description:**In this paper, we mainly study error bounds for a single convex inequality and semi-infinite convex constraint systems, and give characterizations of stability of error bounds via directional derivatives. For a single convex inequality, it is proved that the stability of local error bounds under small perturbations is essentially equivalent to the non-zero minimum of the directional derivative at a reference point over the unit sphere, and the stability of global error bounds is proved to be equivalent to the strictly positive infimum of the directional derivatives, at all points in the boundary of the solution set, over the unit sphere as well as some mild constraint qualification. When these results are applied to semi-infinite convex constraint systems, characterizations of stability of local and global error bounds under small perturbations are also provided. In particular such stability of error bounds is proved to only require that all component functions in semi-infinite convex constraint systems have the same linear perturbation. Our work demonstrates that verifying the stability of error bounds for convex inequality constraint systems is, to some degree, equivalent to solving convex minimization problems (defined by directional derivatives) over the unit sphere. © Zhou Wei & Michel Théra & Jen-Chih Yao.

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