Review of Intelligence for Additive and Subtractive Manufacturing: Current Status and Future Prospects.

Additive manufacturing (AM), an enabler of Industry 4.0, recently opened limitless possibilities in various sectors covering personal, industrial, medical, aviation and even extra-terrestrial applications. Although significant research thrust is prevalent on this topic, a detailed review covering the impact, status, and prospects of artificial intelligence (AI) in the manufacturing sector has been ignored in the literature.

Mathematical Study of a Resource-Based Diffusion Model with Gilpin-Ayala Growth and Harvesting.

This paper focuses on a Gilpin-Ayala growth model with spatial diffusion and Neumann boundary condition to study single species population distribution. In our heterogeneous model, we assume that the diffusive spread of population is proportional to the gradient of population per unit resource, rather than the population density itself. We investigate global well-posedness of the mathematical model, determine conditions on harvesting rate for which non-trivial equilibrium states exist and examine their global stability.

Nonlinear two-point boundary value problems: applications to a cholera epidemic model.

This paper is concerned primarily with constructive mathematical analysis of a general system of nonlinear two-point boundary value problem when an empirically constructed candidate for an approximate solution () satisfies verifiable conditions. A local analysis in a neighbour- hood of a assures the existence and uniqueness of solutions and, at the same time, provides error bounds for approximate solutions. Applying this method to a cholera epidemic model, we obtain an analytical approximation of the steady-state solution with rigorous error bounds that also displays dependence on a parameter.

Divergent expansion, Borel summability and three-dimensional Navier-Stokes equation.

We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and show how the IE approach can give rise to local existence proofs.