This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

The effect of molecules intersystem crossing (Kisc) on characteristics
(energy and duration) of a Passive Q- switched Laser Pulse has been
studied by mathematical description (rate equations model) for
temporal performance of which was used as a saturable absorber
material (passive switch) with laser. The study shows that the energy
and duration pulse are decreasing while the molecules intersystem
crossing into saturable absorber energy levels is increasing.

The extract of fig fruit has shown significant medical usefulness in various fields. The entrance of nanotechnology into the field of medicinal and pharmacology has shown remarkable advantages. Plants contain diverse molecules thatcan reduce metals, and provide a safe, eco-friendly approach for synthesizing nanoparticles. Iron oxide nanoparticles (IONPs) have been reported to possess an antimicrobial effect against some strains of bacteria and moulds. We have aimed to synthesize IONPs from fig fruit extract and investigate the influence of fig extract and IONPs in wound healing of mice. UV-Vis spectroscopy, X-ray diffraction (XRD), and field emission scanning electron microscopy were used to characterize the IONPs that were produced

Background: Venous leg ulcers (VLUs) affect 1-3% of the population and impose substantial pain-related morbidity, yet vascular pain remains underrecognized in clinical practice and research. Objectives: This narrative review synthesizes current evidence on the pathophysiology, clinical manifestations, and management strategies for VLU-associated pain. Methods: A comprehensive literature search was conducted across PubMed/MEDLINE, Scopus, Embase, and Web of Science (January 2015-July 2025) following SANRA guidelines. Search terms included "vascular pain", "venous leg ulcer", "chronic venous disease" and related terminology. Studies addressing pathophysiology, clinical characteristics, diagnostic approaches, and therapeutic interventi

The main object of this article is to study and introduce a subclass of meromorphic univalent functions with fixed second positive defined by q-differed operator. Coefficient bounds, distortion and Growth theorems, and various are  the obtained results.

An essential tool for studying the web is its ability to show how energy moves through an ecosystem. Understanding and elucidating the relationship between species variety and their placement within the inclusive trophic dynamics is also beneficial. A food web ecological model with prey and two rival predators under fear and wind flow conditions is developed in this article. The boundedness and positivity of the system’s solution are established mathematically. The stability and existence constraints of the system’s equilibria are examined. The proposed system’s persistence limitations are established. Additionally, the bifurcation analysis of every potential equilibrium is examined using the Sotomayor theorem. To describe the

The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil