This paper presents a numerical method for solving a nonlinear age-structured population model based on a set of piecewise constant orthogonal functions. The block-pulse functions (BPFs) method is applied to determine the numerical solution of a non-classic type of partial differential equation with an integral boundary condition. BPFs duo to the simple structure can efficiently approximate the solution of systems with local or non-local boundary conditions. Numerical results reveal the accuracy of the proposed method even for the long term simulations.

Introduction: the presence of anti-CCP is an important prognostic tool for rheumatoid arthritis (RA), but its relationship with the activity of the disease and functional capacity is still being investigated. Objectives: to study the relationship between anti-CCP and the indices of disease activity, functional capacity and structural damage, by means of conventional radiography (CR) and magnetic resonance imaging (MRI), in stabilized RA. Methods: cross-sectional study of RA patients with one to 10 years of disease. The participants were subjected to clinical evaluation with anti-CCP screening. Disease activity was assessed by means of the Clinical Disease Activity Index (CDAI) and functional capacity by means of the Health Assessment Questionnaire (HAQ). CR was analyzed by the Sharp van der Heijde index (SmvH) and MRI by the Rheumatoid Arthritis Magnetic Resonance Image Scoring System (RAMRIS). Results: 56 patients were evaluated, with median (IIq) of 55 (47.5–60.0) years, 50 (89.3%) were female among whom 37 (66.1%) were positive for anti-CCP. The median (IIq) of CDAI, HAQ, SmvH and RAMRIS were 14.75 (5.42–24.97), 1.06 (0.28–1.75), 2 (0–8) and 15 (7–35), respectively. There was no association between anti-CCP and CDAI, HAQ, SmvH and RAMRIS. Conclusion: our results did not establish the association of anti-CCP with the severity of the disease. So far, we cannot corroborate the anti-CCP as a prognostic tool in RA established.

Water splitting has gained significant attention as a means to produce clean and sustainable hydrogen fuel through the electrochemical or photoelectrochemical decomposition of water. Efficient and cost-effective water splitting requires the development of highly active and stable catalysts for the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER). Carbon nanomaterials, including carbon nanotubes, graphene, and carbon nanofibers, etc., have emerged as promising candidates for catalyzing these reactions due to their unique properties, such as high surface area, excellent electrical conductivity, and chemical stability. This review article provides an overview of recent advancements in the utilization of carbon nanomaterials as catalysts or catalyst supports for the OER and HER in water splitting. It discusses various strategies employed to enhance the catalytic activity and stability of carbon nanomaterials, such as surface functionalization, hybridization with other active materials, and optimization of nanostructure and morphology. The influence of carbon nanomaterial properties, such as defect density, doping, and surface chemistry, on electrochemical performance is also explored. Furthermore, the article highlights the challenges and opportunities in the field, including scalability, long-term stability, and integration of carbon nanomaterials into practical water splitting devices. Overall, carbon nanomaterials show great potential for advancing the field of water splitting and enabling the realization of efficient and sustainable hydrogen production.

Functions are the core of algebra, and the teaching of function concepts is also the main task of high school mathematics Students' learning of functions and their concepts shifts from understanding specific quantitative relationships to understanding abstract quantitative relationships The monotonicity of functions, as the property of the first function that students learn in high school, lays a certain foundation for learning function related knowledge in the future.

Based on 898 English documents and 363 Chinese documents citing the Rising of Network Society, it studied that the knowledge contribution of citation content analysis and citation context analysis methods, and the knowledge contribution of Chinese and foreign quotations to human geography. The study found that “mobile space” is the most quoted theoretical view in domestic and foreign literature, and the proportion of domestic research is significantly higher than foreign research; the focus of domestic and foreign research focuses on the external spatial form and its transformation, while foreign research pays more attention on the internal spatial dynamics of network society and three types of knowledge contributions, reflecting the influence of “network social theory” on human geography. Among them, critical references reveal the shortcomings of “network social theory” point out the abstraction of “spatial duality” the importance of local space, and the limitations of research data, methods, and time background, which provides new enlightenment for the future application and innovation of “network social theory” in the field of human geography.