Concordia College was an educational institution of the Lutheran Church–Missouri Synod (LCMS) whose main purpose was to prepare men to enter one of the synod's seminaries. It was founded as a German-style gymnasium (i.e., a combined high school and junior college) in Perry County, Missouri, in 1839. It was moved to St. Louis, Missouri, in 1847, and ultimately to Fort Wayne, Indiana, in 1861. In 1935, the high school department of the school was separated from the junior college to form Concordia Lutheran High School. Concordia College was closed in 1957 when the LCMS opened Concordia Senior College on a new campus in Fort Wayne..The former campus was purchased by the Indiana Institute of Technology.e.
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.
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.
In this study, the Ulam stability of quantum equations on time scales that alternate between two quanta is considered. We show that linear equations of first order with constant coefficient or of Euler type are Ulam stable across large regions of the complex plane, and give the best Ulam constants for those regions. We also show, however, that linear equations of first order of period-1 type are not Ulam stable for any parameter value in the complex plane. This is due to the importance of pre-positioning the non-autonomous term for Ulam stability.
