Mathematical Principles Research Articles

Transient hygrothermal response of an infinite solid cylinder with internal heat generation

This paper aims to study the effect of internal heat generation in a transient infinitely long solid cylinder subjected to hygrothermal loadings. The linear dependence theory of moisture and temperature is derived, based on Dufour and Soret effect. The meticulous solutions of temperature, moisture, and thermal stresses are procured by using the Hankel transform technique. The influence of the internal heat source on the radial aspect is examined for coupled and uncoupled cases. In the present study, the composite material T300/5208 is considered and the coupled and uncoupled cases are analyzed. The results obtained are computed numerically and illustrated graphically. The study presented here is purely hypothetical and entirely based on mathematical principles.

Objects Camouflage Possibilities Analysis in the Modern Military Conflicts Conditions

The article analyses the methods of camouflage used in modern military conflicts. The article gives a historical overview of camouflage of military equipment and personnel since the beginning of the twentieth century. The mathematical and physical principles that should be taken into account in the manufacture of camouflage nets are discussed, the requirement for which is the difficulty in recognising and differentiating between an artificial surface and real terrain. The mathematical model of a camouflage net pattern is a fractal, a self-similar scale-invariant object of noninteger topological dimension. From the point of view of physics, the fractal dimension is a statistical value that demonstrates how densely a fractal fills a space. This means, in particular, that by dividing a photo of a real surface into cells and then counting the number of black cells in relation to all of them (in the simplest case of a photo of a winter forest, for example), you can find out the average indicator of the landscape's scale similarity, which can be reproduced on a camouflage grid. In the context of active military operations caused by russian aggression, for effective camouflage, it is proposed to use the concepts and methods of fractal geometry in the manufacture of camouflage means, in particular camouflage nets, to maximise the imitation of natural landscapes and structures that will not be easy to recognise.

Cognitive Neural Computation Modeling of Human Brain Information Storage and Extraction Based on Intelligent Computing

With the development of neurological and brain science, human beings have more understanding of the memory mechanism of the brain. Therefore, using the memory mechanism of the brain to store and retrieve images is one of the most popular research fields in the world. Memory is an important part of the human cognitive system, and it is the basis for the realization of higher-level cognitive activities. Human perception and memory are closely related. If people lose the ability to perceive, then people’s memory function will not be able to display. The current storage and extraction of brain information are mostly based on mathematical principles, without considering the memory mechanism in the brain, so the correctness and effectiveness of these methods are not high. Therefore, this study adopts an intelligent algorithm based on PCNN to denoise, segment, identify, and retrieve images. On this basis, a new learning method is adopted. This method can realize online incremental learning and can realize the storage of brain image data without predetermining the size and structure of the network. And when necessary, the information is extracted or not based on the distance between the detected versus the stored data. The test shows that when the number of images is 25, the present technique has an accuracy of 100% and the time required is 2345 s. Compared with the median filtering method, the efficiency of the present technique is greater.

A novel detection and defense mechanism against false data injection attack in smart grids

AbstractAs the next generation of green power system, smart grids have gradually enhanced the operation efficiency of power system. Meanwhile, the application of communication and intelligent technologies make the power grid more vulnerable to the emerging cyber‐physical attacks, such as the false data injection attack (FDIA). Particularly, the deception property of the FDIA on the output measurement estimation can fool the current security mechanism without triggering an alarm. Motivated by this problem, this paper aims at developing a novel detection and recovery mechanism against FDIA in smart grid. Based on the established state space grid model derived from the three‐phase sinusoidal voltage equations, an improved principal component analysis (PCA)‐based detection method is proposed. By introducing the mathematical transformation principle method, the detection performance such as detection rate and false positive rate can be improved. To keep the stable running of power system, a genetic optimization algorithm‐based linear quadratic regulator (LQR) defense method is developed. In addition, to improve the response performance to external attacks, an artificial intelligence method named genetic optimization algorithm is introduced to optimize the robust performance of the proposed defense method. Finally, the simulation results on the IEEE 6‐bus and 118‐bus grid system demonstrate the superiority of the proposed genetic algorithm optimization‐based LQR defense method.

SPECIFICS OF IMPLEMENTATION OF THE ASYMMETRIC ENCRYPTION ALGORITHM ON ELLIPTIC CURVES

The use of information technologies has become an integral part of the modern world, and the internet has played a vital role in facilitating access to various services, from ordering food to obtaining government services. However, with the increased reliance on the internet, the issue of information protection has become more pressing than ever. In the wake of the COVID-19 pandemic, remote work and online learning have become the norm, which has further emphasized the need for robust information protection mechanisms. One of the primary ways of ensuring information security is through the use of cryptographic algorithms. These algorithms have been in use for several decades and have provided an effective means of protecting sensitive information. However, with the exponential growth of computing power, the demands on these algorithms have increased, and some of them have become outdated and are no longer secure enough. As a result, there is a pressing need for the development of new cryptographic algorithms that use more complex mathematical principles to provide a higher level of security. One such class of algorithms that has gained popularity in recent years is elliptic curve cryptography. These algorithms use the principles of elliptic curves to provide greater security while using relatively fewer system resources. Elliptic curve cryptography has several advantages over other cryptographic algorithms. Firstly, it provides a higher level of security with shorter key lengths, making it ideal for use in devices with limited processing power and memory. Additionally, it offers greater resistance to attacks by quantum computers, which are expected to become more prevalent in the future. Moreover, elliptic curve cryptography has found applications in several areas, including secure communication protocols, digital signatures, and key exchange algorithms. These algorithms are part of the TLS protocol, which is used by the HTTPS protocol to ensure secure transmission of information over the Internet. The continuous development and integration of cryptographic algorithms into various information systems will be crucial for protecting against cyber threats in the future.

Classical consequences of constructive systems.

This is a survey of formal axiomatic systems for the three main varieties of constructive analysis, in a common language and with intuitionistic logic, which are as nearly as possible compatible with classical analysis and with one another. Classically sound consequences of principles of intuitionistic mathematics are emphasized. Compatibility with classical analysis is of two kinds. On the one hand, Bishop's constructive mathematics and a very substantial part of intuitionistic analysis are classically correct, sharing with constructive recursive mathematics a neutral subsystem adequate for recursive function theory and elementary real analysis. On the otherhand, each constructive system considered here is separately consistent with the negative interpretation of each of its classically sound subsystems, establishing internal compatibility with the classical context it is intended to refine. A possibly new criterion for the transposability of unique existential quantifiers and a recent theorem of Vafeiadou on the internal compatibility of classical and intuitionistic analysis are included. This article is part of the theme issue 'Modern perspectives in Proof Theory'.

Algorithmic Color Methods of Media Arts

The paper describes a framework for systematically exploring the RGB color model (RGB color cube) for generating color palettes based on six algorithmic methods divided into two categories: Primitive and Derivative. The Primitive method is comprised of the RGB Linear method, the RGB Planar method, and the RGB Cuboid method. The Derivative method includes the RGB Multi-Linear method, the RGB Multi-Planar method, and the RGB Multi-Cuboid method. On a practical level, the goal of the paper is to introduce a systems approach to the notion of creating and applying algorithms to create a variety of color combinations and palettes in the field of Media Arts. The framework was implemented as a color design approach to the process of producing color palettes in the context of Media Arts while exploring the intersection of mathematical principles of geometry, color, and code. An investigation was conducted into how algorithmic color palettes generated from the methods correlate to culture, history, and other artistic practices. An application of the methodology and a discussion about how the framework can continue to evolve and be applied to other research areas and fields of applications, such as digital color literacy education, are presented.

The Use of ICT and the Realistic Mathematics Education on Learning Functions to Develop Algebraic Thinking Skills

The concept of function has evolved into one of the most fundamental principles in modern mathematics, influencing practically every area. However, it proved to be one of the most difficult ideas to grasp in mathematics. The concept of function is frequently taught without any connection to real-life situations. Students must work with problem scenarios that happen in a variety of contexts that are relevant to their everyday lives or make sense to them in order to gain authentic comprehension. This is consistent with the RME's properties. The unwillingness to highlight the visual element of the notion is one of the major roadblocks in learning functions. Using ICT and an RME approach to learning functions as an alternative to overcome these barriers could be a viable option. ICT and RME can help students learn mathematical principles in function content by providing a clearer visual experience. The purpose of this study is to investigate how ICT and RME can be used to improve learning function and increase algebraic thinking skills. This study conducted in a classroom of 29 junior high school students at the eighth grade. Design research methodology was used in this study by conducting three phases: preliminary design, teaching experiment, and retrospective analysis.

Modelling the removal efficiency of hydrogen sulfide from biogas in a biofilter using multiple linear regression and support vector machines

The main goal of this study is to create a statistical and intelligent model that can forecast the removal efficiency of hydrogen sulfide (H2S) in a fixed bed biofilter. The majority of conventional models employ mathematical principles that necessitate highly technical infrastructure, extremely detailed information on the biofiltration mechanism, and estimation of model input parameters. However, in this study, Multiple Linear Regression and Support Vector Machine methodology were used to reduce the reliance on experimental data. Experimental research was done to determine the effects of three factors on H2S removal efficiency, including the moisture content of the compost used as the biofilter bed, the empty bed residence time in the reactor, and the H2S concentration in the biogas stream input to the biofilter. Experimental findings demonstrated that the biofilter with a moisture content of 6%, and empty bed residence time of 60 s was capable of removing up to 75% of H2S from a biogas stream with H2S inlet concentration of 70 ppm(v). With a Coefficient of Determination between 0.98 and 0.99, the proposed models show excellent ability to predict the H2S removal efficiency. Compared to a Multiple Linear Regression based model, test results from a Support Vector Machine based model showed better agreement with experimental data.

Effect of Structured Training Workshop on Nurses’ Drug Dosage Calculation Competence at Tertiary Care Hospitals of Faisalabad

Background: Drug administration is a major component of patient care provided by nurses at hospitals. Appropriate drug administration ensures patient safety, as incorrect or unsafe administration can result in adverse patient health and hospital outcomes. Drug dosage calculation errors are the most common, threatening patient safety, lengthening patients' hospital stay and increasing associated costs worldwide. Aim: To evaluate the effectiveness of structured training workshop at enhancing nurses’ competence in drug dosage calculations. Methods: One group pre-test post-test quasi-experimental study was conducted on a convenient sample of 73 staff nurses working at public tertiary care hospitals of Faisalabad, Pakistan. Staff nurses aged 21-60 years who provide direct patient care, were included in the study.The study duration spanned over 04 months from July to October 2020. A structured questionnaire was used for the pre-test and post-test competency level of nurses in drug dosage calculations. The study intervention consisted of a structured training workshop focusing on basic mathematical skills for drug dosage calculation using the correct mathematical formula for unit conversions and linking the correct dose to the patient case scenario. SPSS version 26 was used for with-in group analysis employing t-test statistics. Results: Pre-test results revealed common errors in the application of basic mathematical principles for drug concentration unit conversions and complex calculations involving patient-age, weight and other variables.Post-test results demonstrated a significant improvement in level of competence of participant nurses in this regard, indicated by significant difference (p-value 0.000). Structured training workshop was found effective in enhancing nurses’ competency level in drug dosage calculations. Practical implication Conclusion: Structured training improved nurses' ability to identify drug calculation errors, understand the use of the correct formula, and calculate drug dosage accurately. This study emphasizes the importance of structured education and training of nurses aimed at reducing medication errors and improving patient health and hospital outcomes. Keywords: Competence; Drug dosage calculation; Nurses; Quasi experimental study; Pakistan; Workshop.

SPECIFICS OF IMPLEMENTATION OF THE ASYMMETRIC ENCRYPTION ALGORITHM ON ELLIPTIC CURVES

The modern world is inextricably linked with information technologies. Every year, the Internet expands, and thousands of sites that provide various services have been created. With a stable Internet connection, you can solve most of life's problems without leaving home – from ordering dinner to receiving government services. Nowadays, when educational institutions and businesses have been forced to switch to a remote form of work due to the pandemic, the issue of information protection is more pressing than ever. There are many cryptographic algorithms that have protected our information on the Internet for decades, but as computing power grows, so do the demands on such algorithms. Some of them have not coped with the challenge of time and are no longer used, which is why there is a need to develop new algorithms that use more complex mathematical principles and provide a higher level of security. And there is a whole class of algorithms that use the principles of elliptic curves to provide greater security with relatively lower use of system resources.

Optimisation Models for Pathway Activity Inference in Cancer.

With advances in high-throughput technologies, there has been an enormous increase in data related to profiling the activity of molecules in disease. While such data provide more comprehensive information on cellular actions, their large volume and complexity pose difficulty in accurate classification of disease phenotypes. Therefore, novel modelling methods that can improve accuracy while offering interpretable means of analysis are required. Biological pathways can be used to incorporate a priori knowledge of biological interactions to decrease data dimensionality and increase the biological interpretability of machine learning models. A mathematical optimisation model is proposed for pathway activity inference towards precise disease phenotype prediction and is applied to RNA-Seq datasets. The model is based on mixed-integer linear programming (MILP) mathematical optimisation principles and infers pathway activity as the linear combination of pathway member gene expression, multiplying expression values with model-determined gene weights that are optimised to maximise discrimination of phenotype classes and minimise incorrect sample allocation. The model is evaluated on the transcriptome of breast and colorectal cancer, and exhibits solution results of good optimality as well as good prediction performance on related cancer subtypes. Two baseline pathway activity inference methods and three advanced methods are used for comparison. Sample prediction accuracy, robustness against noise expression data, and survival analysis suggest competitive prediction performance of our model while providing interpretability and insight on key pathways and genes. Overall, our work demonstrates that the flexible nature of mathematical programming lends itself well to developing efficient computational strategies for pathway activity inference and disease subtype prediction.

Modeling facial perception in group context from a serial perception perspective.

By utilizing statistical properties and summary statistics, the visual system can efficiently integrate perception of spatially and temporally adjacent stimuli into perception of a given target. For instance, perception of a target face can either be biased positively toward previous faces (e.g. the serial dependence effect) or be biased negatively by surrounding faces in the same trial/space (e.g. spatial ensemble averaging). However, both aspects were investigated separately. As spatial and temporal processing share the same purpose to reduce redundancy in visual processing, if one statistical processing occurs, would the statistical processing in the other domain still exist or be discarded? We investigated this question by exploring whether serial dependence of face perception (of attractiveness and averageness) survives when the changed face perception in the group context occurs. The results of Markov Chain modeling and conventional methods suggested that serial dependence (the temporal aspect) co-occurs with changed face perception in the group context (the spatial aspect). We also utilized the Hidden Markov modeling, as a new mathematical method, to model statistical processing from both domains. The results confirmed the co-occurrence of temporal effect and changed face perception in the group context for both attractiveness and averageness, suggesting potentially different spatial and temporal compression mechanisms in high-level vision. Further modeling and cluster analysis further revealed that the detailed computation of spatially and temporally adjacent faces in the attractiveness and averageness processing were similar yet different among different individuals. This work builds a bridge to understanding mathematical principles underlying changed face perception in the group context from the serial perspective.

Neural network based formation of cognitive maps of semantic spaces and the putative emergence of abstract concepts

How do we make sense of the input from our sensory organs, and put the perceived information into context of our past experiences? The hippocampal-entorhinal complex plays a major role in the organization of memory and thought. The formation of and navigation in cognitive maps of arbitrary mental spaces via place and grid cells can serve as a representation of memories and experiences and their relations to each other. The multi-scale successor representation is proposed to be the mathematical principle underlying place and grid cell computations. Here, we present a neural network, which learns a cognitive map of a semantic space based on 32 different animal species encoded as feature vectors. The neural network successfully learns the similarities between different animal species, and constructs a cognitive map of ‘animal space’ based on the principle of successor representations with an accuracy of around 30% which is near to the theoretical maximum regarding the fact that all animal species have more than one possible successor, i.e. nearest neighbor in feature space. Furthermore, a hierarchical structure, i.e. different scales of cognitive maps, can be modeled based on multi-scale successor representations. We find that, in fine-grained cognitive maps, the animal vectors are evenly distributed in feature space. In contrast, in coarse-grained maps, animal vectors are highly clustered according to their biological class, i.e. amphibians, mammals and insects. This could be a putative mechanism enabling the emergence of new, abstract semantic concepts. Finally, even completely new or incomplete input can be represented by interpolation of the representations from the cognitive map with remarkable high accuracy of up to 95%. We conclude that the successor representation can serve as a weighted pointer to past memories and experiences, and may therefore be a crucial building block to include prior knowledge, and to derive context knowledge from novel input. Thus, our model provides a new tool to complement contemporary deep learning approaches on the road towards artificial general intelligence.

Unfold potential [Art - Engineering

Just like fashioning decorative shapes and figures using the Japanese art of folding paper, tracing when and where origami originated is complicated. But what cannot be disputed is its incredible influence in modern engineering. While styles of origami can be incredibly diverse, the art is rooted in mathematical principles that make it applicable to science and industry. The ability to fold two-dimensional structures into complex, yet compact three-dimensional shapes is especially valuable to space sciences and missions, where it pays to keep payloads small.

Unfold potential [Art - Engineering

Just like fashioning decorative shapes and figures using the Japanese art of folding paper, tracing when and where origami originated is complicated. But what cannot be disputed is its incredible influence in modern engineering. While styles of origami can be incredibly diverse, the art is rooted in mathematical principles that make it applicable to science and industry. The ability to fold two-dimensional structures into complex, yet compact three-dimensional shapes is especially valuable to space sciences and missions, where it pays to keep payloads small.

THE CONTENT OF MATHEMATICAL DEVELOPMENT OF PRESCHOOLERS

This topic deals with the problem of mathematical education of pre-schoolers. The content of mathematical development of children, its structure and approaches to the development of the content of mathematical development is given on the basis of program documents "From birth to school", "Childhood". Here is the implementation of the principles of mathematics, a personality-oriented approach, developing learning in the formation of mathematical representations of preschool children of older groups.

Children's understanding of length measurement using a ruler in preschool and primary education: A cross-national longitudinal study

Measuring length is a practice of everyday life and a mathematical principle shared across cultures. A cross-national and longitudinal study was designed to analyse the evolution of the strategies used by Spanish and Portuguese preschoolers and 1st graders when measuring length. The instruments were rulers designed to discriminate between the strategies demonstrated by young children in previous research, taking as variables the number of correct measurements and the strategy used to measure, and country as a covariate. Neither country nor age influenced correct measurements while the ruler used affected the strategy developed by the children. No significant differences were found in the strategies used from preschool to 1st grade, except for the ruler with numbered units and marks. Considering the sequence of sophistication of the strategies, our results reinforce the scaffolding role of discrete units for the understanding of length measurement towards the use of the standard ruler.

Research on Abstraction Ability under the Background of Mathematics Key Competencies in Junior High School in China

The abstraction ability in junior high school is an extension of the number sense, quantity sense, and symbolic awareness in primary school, and the foundation of mathematical abstraction in senior high school. Abstraction ability is one of the key competencies that junior high school students must have. This study used the China Knowledge Network(CNKI) as a data source to analyze previous research to find out the current situations, deficiencies, and gaps in this direction and found that: (1) Current domestic research on abstraction ability against the background of mathematics key competencies mainly focuses on the following five aspects: strategies for cultivating students' abstraction ability, development status of abstraction ability, evaluation dimension division of abstraction ability, specific manifestations of abstraction ability, influencing factors of students' abstraction ability. (2) The cultivation strategies of students' abstraction ability mainly focus on six aspects, and the researchers have given more comprehensive training suggestions. The previous research mainly investigated the situations of students' abstraction ability and teachers' teaching on the training of abstraction ability. Almost all of the evaluation dimension division of abstraction ability is based on students' mastery of mathematical concepts, principles, rules, and ways of thinking in different situations. There is less research on the specific manifestations and influencing factors of abstraction ability. (3) Based on current research, future research needs to adopt more scientific research tools, a more reasonable analysis framework, expand the research scope, increase validation research, and give more scientific suggestions. So that the research on the abstraction ability of junior high school students is more comprehensive, systematic, and profound.

Enigma Machine Structure and The Mathematical Principle of The Introduction and Self-experiment

The Enigma machine is a kind of advanced mechanical encryption system used by the Nazi German military during World War II, with the rotor structure as the main structure. Cryptographic machines generally take the form of a boxed structure. When encrypting a string of characters, the user enters the information into a machine or system and gets ciphertext. The original information can be obtained by reverse operation of the ciphertext. As the operator enters the message to be encrypted, a sequence of plain-length passwords can be recorded based on the sequence of letters lit up on the lamp board. This article will focus on the simple structure of the Enigma machine and the mathematics behind it, thus illustrating its importance and security in the history of human encryption. Then, to further explore the working principle of the Enigma machine and help to better understand its internal nature, the essay has provided a simple code that can realize the simple function of the Enigma, and also shows a simply equipped Enigma machine.