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The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating.

To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method.

Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident.

The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

This paper aims to explore the optimization process involved in the aircraft maintenance allocation and packing problem. The aircraft industry misses a part of the optimization potential while developing maintenance plans. This research provides the modeling foundation for the missing part considering the failure behavior of components, costs involved with all maintenance tasks and opportunity costs.

The study models the cost-effectiveness of support against the availability to come up with an optimization problem. The mathematical problem was solved with an exact algorithm. Experiments were performed with real field and synthetically generated data, to validate the correctness of the model and its potential to provide more accurate and better engineered maintenance plans.

The solution procedure provided excellent results by enhancing the overall arrangement of the tasks, resulting in higher availability rates and a substantial decrease in total maintenance costs. In terms of situational awareness, it provides the user with the flexibility to better manage resource constraints while still achieving optimal results.

This is an innovative research providing a state-of-the-art mathematical model and an algorithm for efficiently solving a task allocation and packing problem by incorporating components’ due flight time, failure probability, task relationships, smart allocation of common preparation tasks, operational profile and resource limitations.

When establishing a mathematical model to simulate solid mechanics, considering realistic geometries, special tools are needed to translate measured data, possibly with noise, into idealized geometrical entities. As an engineering application, wheel-rail contact interactions are fundamental in the dynamic modeling of railway vehicles. Many approaches used to solve the contact problem require a continuous parametric description of the geometries involved. However, measured wheel and rail profiles are often available as sets of discrete points. A reconstruction method is needed to transform discrete data into a continuous geometry.

The authors present an approximation method based on optimization to solve the problem of fitting a set of points with an arc spline. It consists of an initial guess based on a curvature function estimated from the data, followed by a least-squares optimization to improve the approximation. The authors also present a segmentation scheme that allows the method to increment the number of segments of the spline, trying to keep it at a minimal value, to satisfy a given error tolerance.

The paper provides a better understanding of arc splines and how they can be deformed. Examples with parametric curves and slightly noisy data from realistic wheel and rail profiles show that the approach is successful.

The developed methods have theoretical value. Furthermore, they have practical value since the approximation approach is better suited to deal with the reconstruction of wheel/rail profiles than interpolation, which most methods use to some degree.

Research has shown that for young adults, marital attitudes (e.g., desire, importance, and expectation) are associated with relationship quality. However, how this association plays out for young adults of color is less known. Additionally, the influence of skin tone perception on the relationship between marital attitudes and relationship quality remains understudied. To explore these associations, the authors examined African American and Latinx young adults (N = 57, M_age = 20.71 years, SD = 1.28; 75.4% female) attending a Midwestern university. Exploratory results indicated that marital expectations were positively associated with relationship quality in that young adults who expected to marry one day, reported greater relationship satisfaction, commitment, and intimacy in their current relationships. Additionally, skin tone perception moderated the association between marital attitudes and relationship quality in two ways (i.e., between expectations and satisfaction and between importance and intimacy). Collectively, findings suggest that differing levels of marital attitudes and skin tone perception contributes to young adults’ perceptions of relationship quality. Considering these psychological factors of attitudes, skin tone perception, and relationship quality, together with systemic racial/ethnic discrimination, the authors discuss future research and practice considerations.