Concordia College (Indiana)

The Hyers-Ulam stability of a first-order nonlinear differential equation based on a generalized Richards growth model (also known as a Savageau growth model) is conditionally established based on the maximum size of the perturbation being not too large and the initial condition being not too small in terms of the carrying capacity and the powers involved. The Hyers-Ulam stability constants are determined explicitly and are shown to depend on the relative sizes of the power parameters in the model. Examples are provided of both stability and instability to illustrate the sharpness of our results. The main result is then applied to a tissue growth model. These results generalize known stability properties of the logistic equation and contribute to the theory of functional stability in nonlinear differential equations, with implications for population and biological models and related applications.

Recent studies have demonstrated that factors influencing perception, such as Gestalt grouping cues, can influence the storage of information in visual working memory (VWM). In some cases, stationary cues, such as stimulus similarity, lead to superior VWM performance. However, the neural correlates underlying these benefits to VWM performance remain unclear. One neural index, the contralateral delay activity (CDA), is an event-related potential that shows increased amplitude according to the number of items held in VWM and asymptotes at an individual's VWM capacity limit. Here, we applied the CDA to determine whether previously reported behavioral benefits supplied by similarity, proximity, and uniform connectedness were reflected as a neural savings such that the CDA amplitude was reduced when these cues were present. We implemented VWM change-detection tasks with arrays including similarity and proximity (Experiment 1); uniform connectedness (Experiments 2a and 2b); and similarity/proximity and uniform connectedness (Experiment 3). The results indicated that when there was a behavioral benefit to VWM, this was echoed by a reduction in CDA amplitude, which suggests more efficient processing. However, not all perceptual grouping cues provided a VWM benefit in the same measure (e.g., accuracy) or of the same magnitude. We also found unexpected interactions between cues. We observed a mixed bag of effects, suggesting that these powerful perceptual grouping benefits are not as predictable in VWM. The current findings indicate that when grouping cues produce behavioral benefits, there is a parallel reduction in the neural resources required to maintain grouped items within VWM.

This study uses an associated Riccati equation to study the Ulam stability of non-autonomous linear differential vector equations that model the damped linear oscillator. In particular, the best (minimal) Ulam constants for these non-autonomous linear differential vector equations are derived. These robust results apply to vector equations with solutions that blow up in finite time, as well as to vector equations with solutions that exist globally on $(-\infty,\infty)$. Illustrative, non-trivial examples are presented, highlighting the main results.

This study extends the application of photothermal spectroscopy to explore heat transfer dynamics in biological fluids, focusing on the examination of artificial vitreous humor (VH) models of human VH and an endogenous sample of cervine (deer) VH. The research integrates previously established methods for analyzing thermal lensing through photothermal deflection. By visualizing convective and conductive heat transfer processes in the artificial components of human VH, one gains insights into the dynamic behavior of heat transfer in the VH. Relevance extends to clinical cases where pathology requires replacement of endogenous VH with an artificial VH substitute. Several VH substitutes identified in the literature were chosen for this study based on their physical properties and relative abundance in the VH. Individual component fluids, and mixtures of these components, were analyzed at various concentrations based on their physiological concentration ranges in the human VH as they varied with age, sex, and certain disease states. By way of comparison to endogenous biological VH, a sample of VH obtained from a female white-tailed deer eye was analyzed, enhancing the understanding of heat transfer in artificial components of the VH compared to endogenous VH. There is a vast array of ophthalmological procedures that utilize an external heat source interacting with endogenous or artificial VH. The data found in this study will progress the understanding of heat transfer within artificial VH components in comparison to endogenous VH and contribute to the advancement of certain ophthalmological procedures.

In this article, we investigate the 3D additive-type functional equation. Next, we introduce the ternary hom-multiplier in ternary Banach algebras using the concepts of ternary homomorphisms and ternary multipliers. We first establish proof that solutions to the 3D additive-type functional equation are additive mappings. We further demonstrate that these solutions are C-linear mappings. The final portion of our work examines both the stability and hyperstability properties of the 3D additive-type functional equation, ternary hom-multiplier, and ternary Jordan hom-multiplier on ternary Banach algebras. Our analysis employs the fixed-point theorem using control functions developed by Gǎvruta and Rassias.