This paper is a study of applications of the Lambert W function to solve delay differential equation models that arise in economics and finance. The Lambert W function, one of the mathematical special functions, is a basis of an effective technique to examine the stability and the dynamical regimes, especially cyclical one. The introduction to the Lambert W function is presented, showing its analytical properties. To demonstrate the method at work two economic models are chosen. First, the model of economic growth with a production delay and second, the market price model with supply dependent on a delayed price. In the Solow model of economic growth with a delay, the conditions are derived to determine how the interaction of the delay and the population growth rate can lead to the appearance of cyclical behavior in the economy and possibly the switch in stability near the steady state, and emergence of constant fluctuations and growth cycles, in consequence. Second, in the model of market price, similarly to the Solow model with a delay, exact conditions for the emergence of fluctuations and possible stability switch are constructed.

Operator splitting decoupled energy stable numerical schemes for phase field grain growth models

Global well-posedness of a nonlinear Fokker-Planck type model of grain growth

Atomistically-informed modeling of void growth in spallation of FCC metals

Storage stability of purple glutinous rice: Kinetic modeling of Penicillium citrinum growth and citrinin production under variable temperature and water activity.

An invariant-region-preserving scheme for a convection-reaction-Cahn–Hilliard multiphase model of biofilm growth in slow sand filters

A fluxomic model of microalgae photoautotrophic growth for application in industrial photobioreactors

The increasing frequency of extreme weather events, such as heatwaves and heavy rainfall, attributed to climate change, has considerably escalated the multifaceted threat of mycotoxins to agricultural productivity, food security, and public health. This review comprehensively examines the effect of climate change on fungal growth dynamics, mycotoxin production, and exposure patterns. Central to this effect is the phenomenon of niche transition within fungal communities, marked by the expansion of the thermal tolerance of traditional toxigenic species and the emergence of novel thermotolerant fungi via cross-regional migration. In addition, climate change drives the regional migration of mycotoxins and promotes the emergence of "novel" and "masked" mycotoxins by altering substrate effects. Furthermore, climate-driven environmental stress may activate previously silent secondary metabolic gene clusters (or hidden gene clusters) by affecting the regulatory network and epigenetic mechanisms of fungi, thereby reshaping metabolic pathways and inducing differential expression of genes related to toxin synthesis, resulting in a surge in mycotoxin exposure. This review also evaluates current global mycotoxin exposure trends and critically analyzes the limitations of prevailing fungal growth and mycotoxin prediction models, which often fail to explain the nonlinear effects of climate variables. Ultimately, this review underscores the pressing need to redefine the mycotoxin risk framework and develop mechanistic information prediction tools tailored to climate change, thereby warning of new risks associated with global warming.

This fundamental research was conducted with the aim of explaining and deriving a coherent developmental psychology model from the perspective of Islam, with a specific focus on educational psychology. In the contemporary era—where Western educational systems face numerous challenges such as identity crises, loss of meaning, and the weakening of the family institution—the reinterpretation and systematization of educational models based on authentic Islamic texts emerge as both a scientific and cultural necessity. The research method employed was a library-based approach combined with deductive and ijtihādī analysis of original Islamic religious sources (the Qur’an, the Prophetic Sunnah, and the traditions of the Ahl al-Bayt), examined in interaction with contemporary findings in developmental psychology. The results indicate that Islam, by presenting two classifications that appear distinct but are in fact deeply complementary—one detailed, practical, and educational (the three developmental stages of ages 0–7, 7–14, and 14–21), and the other holistic, philosophical, and ontological (the stages of first weakness, strength, and second weakness)—offers a comprehensive and multidimensional representation of the human growth and development process. This article argues, through an ijtihādī approach, that the unique and golden developmental period from birth to age 21, formed under purposeful parental nurturing, functions not only as the foundation of an individual’s personality but also as the primary determinant of the quality of one’s transition into the stage of strength (youth and middle adulthood), and even of the lived experience of the stage of second weakness (old age). Within this model, rational education is presented and explained as the core and backbone of the harmonious and integrated development of a child’s other existential dimensions—emotional, social, moral, and physical. Ultimately, the study proposes an “Integrated Islamic Growth Model,” which can serve as a foundation for theorization and practice in the domain of Islamic education.

Trajectories of sport exhaustion, cynicism and inadequacy among adolescent student-athletes: A three-year longitudinal study of social influences in the Finnish dual career context.

The profiled parameter estimation method for dynamic systems applied to the calibration of dynamic crop growth models

Joint developmental trajectory of school bullying victimization, perpetration and bystander behavior and the mental health in adulthood among sexually and gender diverse youth.

Bicultural acceptance attitude and school adjustment in multicultural adolescents in South Korea: A latent growth model approach

Blister growth model in plate-type fuel elements under irradiation conditions

Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage

Examining bullying perpetration and parent-adolescent conflict in Chinese adolescents: A parallel latent class growth modeling approach.

Prenatal exposure to heavy metals and the trajectory of autistic traits in childhood.

A second-order time-accurate, linear fully decoupled unconditional energy stabilization finite element method for tumor growth model

The similarities and differences of multiple chronic diseases risk factors across depressive symptoms trajectories among middle-aged and older Chinese adults: A 10-year longitudinal cohort study.

Regional development represents a fundamental pillar of economic growth, territorial cohesion, and sustainable resource management. As Georgia continues to navigate economic and political transitions, spatial-territorial planning emerges as a strategic tool for fostering balanced regional development and minimizing socio-economic disparities. This study examines the role of functional spatial planning in regional economic sustainability by conducting a comparative analysis of planning methodologies implemented in four EU member states—Germany, France, the Netherlands, and Sweden. The research explores the theoretical underpinnings of spatial zoning, evaluates the effectiveness of various land-use planning strategies, and assesses economic incentives for regional development. Additionally, the study integrates qualitative methods, including expert interviews and stakeholder surveys, to provide policy recommendations tailored to Georgia’s specific development context. The findings suggest that adopting an integrated spatial planning framework, leveraging data-driven land-use modeling, and implementing sustainability-oriented economic incentives can significantly enhance Georgia’s regional economic resilience. This research was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) [grant number: YS-24-308]