Analytical Characterization - Amplitude Equations

Um salama Ahmed Abd Alla Elemam, Ahmed Abd Alla, Elemam — Mon, 11 May 2026 00:00:00 +0100

Our main focus in this CHAPTER is analyzing the simple patterns. Simple patterns are when the number of unknowns is less than or equal to one. All of these simple patterns are in 3D however, the variation of these patterns can happen in only one direction, such as stripes, or along two directions, such as hexagons. Others can be along three directions, such as a simple cube, body-cent red cubic, and face-cent red cubic. Each pattern demonstrates the stability of the system at certain values of the dependent parameter. In this chapter, our initial focus is on analyzing the amplitude equations and determining their equilibrium solutions. Once we have obtained the solutions for each pattern, we proceed to assess their stability using the Jacobian matrix. This step is necessary because the stable equilibria of a pattern can become unstable along modes that are not accounted for in the ODEs. Consequently, it is essential to examine the solutions of patterns, such as z-stripes, along other possible directions, such as the z-direction and w-direction. Even if the pattern amplitude is zero along certain directions, we still need to evaluate stability along those directions because perturbations along new directions may amplify. For instance, a mode such as w, which is not considered in the simplified system for the z-stripes pattern, can destabilize a striped pattern associated with wavevectors k1 and k1. Thus, conducting stability analysis using the Jacobian matrix is of utmost importance.

Toward the Development of a Comprehensive Couple-Based Parenting Program: A Reanalysis Focusing on the Low-Parenting Group-

Yoshiko Shimizu — Wed, 13 May 2026 00:00:00 +0100

This study, scheduled to commence in fiscal year 2026 under the Grant-in-Aid for Scientific Research (C) project entitled “Development of a Couple Parenting Program—Focusing on the Low-Performing Group,” aims to clarify the structural characteristics of couples classified within a low-performing parenting group. This objective will be achieved through a reanalysis of recent empirical data, with particular attention to changes observed before and after the intervention, as well as participants’ qualitative and quantitative feedback on the program. Based on these findings, the existing program will be redesigned to more effectively address individual needs, followed by the initiation of continuous, practice-based research. In the author’s previous research, which sought to promote awareness of “couple parenting,” defined as collaborative childrearing by both parents, an evaluation instrument (the Couple Parenting Awareness Scale) and accompanying program worksheets were developed to assess intervention effectiveness. However, the presence of a subgroup whose awareness scores remained low despite program participation became evident. The most recent survey was conducted between June and September 2025. Participants comprised 473 couples with preschool-aged children drawn from all 47 prefectures of Japan who provided informed consent. Assessments conducted before and after the intervention employed validated scales measuring “New Male Roles,” “Collaboration–Functionality,” and “Perception of Couple Parenting.” In addition, participants reported their impressions and emotional responses to the program using a dichotomous (yes/no) format, while open-ended responses were collected regarding the program worksheets. A total of 247 valid responses were obtained, yielding data from 494 individuals, including spouses. The mean age of husbands was 35.7 ± 4.1 years, and that of wives was 34.6 ± 3.8 years; the mean spousal age difference was 2.2 ± 2.8 years. The average duration of marriage was 8.1 ± 3.0 years, and the mean number of children per household was 1.7 ± 0.7. Regression analysis indicated that the factor most strongly associated with classification into the low-performing group was participants’ “approach to the initiative.” Specifically, the odds ratios were 3.086 for respondents who indicated that they were not able to tackle the program as a couple, and 8.900 for those who reported that they were not able to act while being mindful of the program content. The absence of these behavioral changes significantly increased the likelihood of belonging to the low-performing group. Furthermore, frequent experiences of negative emotions, such as irritation, anger, dissatisfaction, emptiness, and sadness, in relation to the program, along with high levels of domineering behavior (a negative dimension of collaboration functionality), were also identified as significant risk factors. Based on these results, a tailored intervention program specifically designed for individuals in the low-performing group will be developed, implemented, and systematically evaluated. Tip: Flow & Transition: To create an easy flow of ideas, transition words, such as, however, therefore, moreover, etc. can be used. This usage enhances coherence of ideas in the paragraph and the manuscript on the whole.

Applied Sciences Research Periodicals

Analytical Characterization - Amplitude Equations

Toward the Development of a Comprehensive Couple-Based Parenting Program: A Reanalysis Focusing on the Low-Parenting Group-