应用与计算数学杂志

The problem of free convection boundary layer flow of nanofluids over a non-linear stretching sheet in the presence of a magnetic field parameter and a suction parameter is investigated numerically. The underlying non-linear partial differential equations with associated boundary conditions are solved numerically using the spectral relaxation method. Present results agree with the previously published work in the absence of magnetic field, thermal radiation and suction. The physics of the problem is well explored for the embedded material parameters through tables and graphs. The effects of various physical parameters are analyzed in details. It is found that thermal radiation greatly effects the velocity and temperature distributions in the boundary layer.

The application of mathematical and computer modelling methods transcends disciplinary boundaries, revolutionizing how we understand, predict, and optimize complex systems across a myriad of fields. These methods provide a powerful lens through which we can dissect intricate phenomena, simulate real-world scenarios, and unravel the hidden patterns that underlie natural and artificial processes. In engineering, mathematical modelling enables the design and analysis of innovative structures, systems, and technologies, guiding the creation of efficient and resilient solutions. Similarly, in the physical sciences, mathematical models facilitate the exploration of fundamental principles, aiding in the discovery of new materials, the prediction of physical behaviour, and the advancement of scientific knowledge. In the realm of economics and finance, mathematical and computer modeming offer insights into market dynamics, risk assessment, and investment strategies, contributing to informed decision-making in a globally interconnected financial landscape. Environmental science leverages these methods to simulate ecological interactions, forecast climate trends, and design sustainable policies for resource management and conservation. Moreover, in the life sciences, mathematical modelling unravels the complexities of biological systems, enabling the study of disease spread, drug interactions, and genetic evolution, ultimately driving breakthroughs in healthcare and medicine.

A Residual Classes based mathematical model emerges as a sophisticated and powerful framework for assessing the reliability of computer systems, transcending conventional paradigms by offering a dynamic and comprehensive perspective on system robustness. Rooted in modular arithmetic and congruence theory, this model elegantly represents the intricate interplay of components within a computer system by partitioning its state space into distinct residue classes, each encapsulating a unique configuration of component states. This partitioning facilitates the characterization of system reliability through residual class transformations, enabling the modelling of fault propagation, error recovery, and fault tolerance mechanisms with remarkable clarity. The essence of this model lies in its ability to capture the nuanced interactions between various components and their responses to internal and external influences. By assigning residue classes to different states, such as functional, degraded, or failed, and defining congruence relations that map these classes onto each other, the model effectively simulates the flow of system behaviour over time. This allows for the analysis of fault scenarios, the evaluation of system performance under stress, and the prediction of reliability metrics under diverse conditions.

Utilizing a Brain Computer Interface (BCI) as a transformative tool in mitigating math anxiety represents a pioneering approach that has the potential to revolutionize the way individuals perceive and engage with mathematical concepts. Math anxiety, a psychological phenomenon characterized by heightened levels of stress, fear, and apprehension towards mathematics, often hinders learning, problem-solving, and overall academic performance. The integration of BCI technology offers a multifaceted avenue to address this issue by directly interfacing with the human brain and reconfiguring cognitive and emotional responses associated with mathematical activities. BCI technology, which enables direct communication between the brain and external devices, holds promise in reducing math anxiety through several key mechanisms. By detecting and analysing neural activity patterns, BCIs can provide real-time feedback to individuals during mathematical tasks, facilitating enhanced selfawareness and emotional regulation. Through neuro feedback mechanisms, users can gain insights into their cognitive states, allowing them to identify and modify detrimental thought patterns and emotional reactions that contribute to math anxiety.

An AI translator fundamentally transforms the way computers handle mathematical tasks, ushering in a new era of computational efficiency and accuracy. By leveraging advanced machine learning algorithms and neural networks, an AI translator has the remarkable ability to decipher complex mathematical expressions, equations, and calculations across various domains. This technology enables computers to swiftly and accurately interpret intricate mathematical concepts, transcending language barriers and streamlining the process of computation. The AI translator's prowess lies in its capacity to bridge the gap between human-generated mathematical notations and the digital language of computers. It comprehends and dissects mathematical symbols, functions, and operations, effectively translating them into a format that computational systems can readily understand and manipulate. This transformative capability has profound implications for a myriad of fields, from scientific research and engineering to finance and data analysis, where mathematical precision is paramount.

This article presents and develops one of Isaac Newton's most significant discoveries and traces its application in computer graphics and 3D modelling. Newton was the first scientist to introduce the concept of limit, which is used in modern mathematical analysis and differential geometry. Newton's theory was further developed in this study. A new boundary method is presented, which finds application in geometry, physics, and computer graphics. Using the new approach, it is possible to draw a regular polygon. Subsequently, it can be used to construct more complex geometric objects, such as prism and pyramids. Based on the primitives: triangle, quadrilateral, cube, circle, sphere, cylinder (prism), cone, etc., arbitrary 3D models can be constructed. This article presents new authors mathematical software called StereoMV, which enables the export of 3D stereometry objects in files with the extension .obj. The generated 3D objects can be imported into a 3D modelling program like Blender. On their basis, using a variety of techniques, arbitrary and more complex models other than those of stereometry can be recreated. Thanks to the new method, it is possible to use a 3D library and, from there, visualization through virtual reality systems. This is the most significant contribution of the proposed boundary method. With the traditional programming approach using trigonometry, this is a difficult task to make it. The application of this innovative way of modelling can be added to a wide variety of projects, such as a 3D serious extreme game involved in the analysis of cardiac data.