Production Rules Research Articles

Система поддержки принятия решений при выборе типа кожухотрубчатого теплообменника

The article discusses the development of an ontology for the subject area using a shell-and-tube heat exchanger as an example. This ontology enables the selection of the type of heat exchanger (fixed tube sheets, compensator, U-shaped tubes) based on the coolant (ammonia, methanol), heat exchange process conditions (pressure, temperature), and the geometric parameters of the heat exchanger (device diameter). The ontology is designed for use in the hardware design phase of chemical-engineering systems. A functional model is presented that outlines the key stages and information flows in the hardware design of chemical-engineering systems. Each design stage utilises an information model, converting the input information flow into an output one. The article describes an information model for selecting the type of heat exchanger, represented by production rules, which includes operators for determining the material of the heat exchanger elements based on the coolant, material-specific design, and the type of heat exchanger. A prototype of the described information model is implemented in the Protégé ontology editor. The ontology and an example query for determining the type of heat exchanger for a given coolant and heat exchange process parameters are provided. The data for creating the ontology are sourced from regulatory design documents. The article concludes that an ontological approach is feasible for creating "smart" design documents, including standards and technical specifications comprehensible to both humans and computers.

Fate of stringy noninvertible symmetries

Noninvertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of noninvertible gauge symmetries? In theories with gravity we find a new form of noninvertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy noninvertible gauge symmetries appear in standard examples such as non-Abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of noninvertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate noninvertible symmetries have implications for swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the distance conjecture, and can sometimes explain the existence of slightly subextremal states which fill in the gaps in the sublattice weak gravity conjecture. Published by the American Physical Society 2024

Adaptive Management of Multi-Scenario Projects in Cybersecurity: Models and Algorithms for Decision-Making

In recent years, cybersecurity management has increasingly required advanced methodologies capable of handling complex, evolving threat landscapes. Scenario network-based approaches have emerged as effective strategies for managing uncertainty and adaptability in cybersecurity projects. This article introduces a scenario network-based approach for managing cybersecurity projects, utilizing fuzzy linguistic models and a Takagi–Sugeno–Kanga fuzzy neural network. Drawing upon L. Zadeh’s theory of linguistic variables, the methodology integrates expert analysis, linguistic variables, and a continuous genetic algorithm to predict membership function parameters. Fuzzy production rules are employed for decision-making, while the Mamdani fuzzy inference algorithm enhances interpretability. This approach enables multi-scenario planning and adaptability across multi-stage cybersecurity projects. Preliminary results from a research prototype of an intelligent expert system—designed to analyze project stages and adaptively construct project trajectories—suggest the proposed approach is effective. In computational experiments, the use of fuzzy procedures resulted in an over 25% reduction in errors compared to traditional methods, particularly in adjusting project scenarios from pessimistic to baseline projections. While promising, this approach requires further testing across diverse cybersecurity contexts. Future studies will aim to refine scenario adaptation and optimize system response in high-risk project environments.

Energy-consistent discretization of viscous dissipation with application to natural convection flow

A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and by requiring that continuous identities like the product rule are mimicked discretely. The proposed viscous dissipation function has a quadratic, strictly dissipative form, for both simplified (constant viscosity) stress tensors and general stress tensors. The proposed expression is not only useful in evaluating energy budgets in turbulent flows, but also in natural convection flows, where it appears in the internal energy equation and is responsible for viscous heating. The viscous dissipation function is such that a consistent total energy balance is obtained: the ‘implied’ presence as sink in the kinetic energy equation is exactly balanced by explicitly adding it as source term in the internal energy equation.Numerical experiments of Rayleigh–Bénard convection (RBC) and Rayleigh–Taylor instabilities confirm that with the proposed dissipation function, the energy exchange between kinetic and internal energy is exactly preserved. The experiments show furthermore that viscous dissipation does not affect the critical Rayleigh number at which instabilities form, but it does significantly impact the development of instabilities once they occur. Consequently, the value of the Nusselt number on the cold plate becomes larger than on the hot plate, with the difference increasing with increasing Gebhart number. Finally, 3D simulations of turbulent RBC show that energy balances are exactly satisfied even for very coarse grids. Therefore, the proposed discretization also forms an excellent starting point for testing sub-grid scale models and is a useful tool to assess energy budgets in any turbulence simulation, with or without the presence of natural convection.

The Profound Nature of Derivatives and Integration: A Comprehensive Examination

This article delves into the fundamental concepts of derivatives and integration, two core principles of calculus that govern a wide range of mathematical and real-world applications. Derivatives, which measure the rate of change of a function, and integration, which calculates accumulation and areas under curves, are essential tools in fields such as physics, economics, engineering, and finance. The article offers a detailed exploration of their mathematical definitions, key properties—including linearity, the product and chain rules, and the Fundamental Theorem of Calculus—and the diverse techniques used in integration. The practical applications of these concepts are also examined, with special emphasis on their role in modeling dynamic systems, optimizing processes, and solving real-world problems such as motion analysis, financial modeling, and economic optimization. Through in-depth discussion and examples, this comprehensive article bridges the theoretical underpinnings of derivatives and integration with their vast and critical uses in various scientific and economic disciplines.

Misconceptions and Errors Among Grade 12 Students When Learning Differentiation Rules: A Case Study

t is an established fact that some grade 12 students learning differentiation in calculus are found struggling with the rule of differentiation and these rules include power rule, quotient rule, chain rule and product rule. Because of these, some students came up with some misconceptions which eventually resulted to the students having multiple errors when learning rules of differentiation. The reason associated with these common errors are not far from their failure to model some prerequisite knowledge in the laws of logarithm into their learning of the laws of differentiation. And this has resulted to the poor performance of some students in mathematics (calculus) since calculus carries about 40% in the overall grade in mathematics as a subject at grade 12 level. On this note, this paper presents an analysis of students’ errors and misconceptions in learning differentiation rule. The study was conducted among grade 12 students preparing for NSC examination in a high school in Limpopo province in South Africa. And the data was initially collected using 35 test scripts of grade 12 on the topic of differentiation and differentiation rule. A qualitative approach was considered, and the data collected was analysed, focusing on product rules, quotient rules and chain rules and the errors committed. The result of the study indicated that some grade 12 students make some errors and misconceptions in differentiation rules. And these were because of poor conceptual understanding, poor mathematics language understanding, and some other error. It was confirmed that the results of this study highlight the common mistakes and errors students make when learning differentiation rules, and these errors are; conceptual, systemic, language, and generalization errors.

Notational production rules in the Muisca culture iconography, Colombia

Notational production rules in the Muisca culture iconography, Colombia

Far from home

After the disappearance of the Linear Pottery culture (LBK) in the area now known as the Polish Lowlands, we observe a heterogeneous cultural situation. The Late Band Pottery culture (LBPC) and the Stroke-Ornamented Ware culture (SBK) are distinguished here. Generally, none of these communities used grog (ground potsherds, ‘chamotte’) as the main type of clay temper. However, there are exceptions to these production rules. In this article, the presented pottery materials from sites in the Polish Lowlands allow us to conclude that grog temper was important for some of these communities. An attempt to interpret the addition of fragments of other vessels to the pottery clay does not point to the technical advantages of the chamotte itself, but rather to its symbolic meaning – the use of fragments of burned vessels to produce new forms. A great deal of ethnographic data justifies this approach, which is sometimes used in archaeological interpretations. The proposed hypothesis allows us to consider an alternative concept of the origin of some post-LBK communities in the Polish Lowlands.

Features of the information and control system of the car's hybrid power plants

Abstract. Problem. Until now, a number of features of IBS power plants of electric and hybrid cars remain unexplored. The applied IIUS analysis and synthesis methods do not pay enough attention to the multi-criteria nature of the arising optimization tasks. Management adaptation methods to changingexternal operating conditions are insufficiently effective. These circumstances do not allow to fully reveal the potential possibilities of IISD power plants of electric and hybrid cars. This determines the relevance of improvement and development of new methods of modeling and optimization of IIUS control of power plants of electric and hybrid cars based on modern theory of automatic control, vector optimization, neural network and neuro-fuzzy adaptive methodology. A methodology for the construction of IIUS invariant to various power plants of electric and hybrid cars has been developed for operational management of modes according to quality, energy and other criteria. Results. The mathematicalsupport of the "Recovery" mode differs from classical problems of optimal control in that it allows changing the parameters of the control power plant, its model type, limit values for control influences, and phase coordinates. Originality. The core of the IICS GSU software is a knowledge base, in which procedural knowledge is presented in the form of frames that implement the algorithmic support of IICS GSU. The knowledge base has a stratified, hierarchical structure that reflects an integrated graph of the synthesis technology of the ZOU solution. The content of the frames of the knowledge base ensures the search for a solution to the ZOU problem in the state space. Frames contain slots that hold not only specific data but also the names of procedures that process them according to a given algorithm. Some frames contain slots filled with product rules. During the creation of the knowledge base of the research prototype, work was carried out on the unification of frame names, which makes it possible to quickly build the knowledge bases of working prototypes. Knowledge frames are a set of classes developed in a visual programming environment. Practical value. The resulting optimal program is worked out using simulation modeling modules, which include direct modeling of systems in multiple states of operation, and if it satisfies the specified requirements, the resulting data is converted into a file containing optimal control influences, which is stored in the database.

Explosive percolation in finite dimensions

Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [], we demonstrated that the correct critical behaviors of EP in infinite dimensions (complete graph) can be accurately extracted using the event-based method, with finite-size scaling behaviors still described by the standard finite-size scaling theory. We perform an extensive simulation of EPs on hypercubic lattices ranging from dimensions d=2 to 6, and find that the critical behaviors consistently obey the standard finite-size scaling theory. Consequently, we obtain a high-precision determination of the percolation thresholds and critical exponents, revealing that EPs governed by the product and sum rules belong to different universality classes. Remarkably, despite the mean of the dynamic pseudocritical point TL deviating from the infinite-lattice criticality by a distance determined by the d-dependent correlation-length exponent, TL follows a normal (Gaussian) distribution across all dimensions, with a standard deviation proportional to 1/V, where V denotes the system volume. A theoretical argument associated with the central-limit theorem is further proposed to understand the probability distribution of TL. These findings offer a comprehensive understanding of critical behaviors in EPs across various dimensions, revealing a different dimension-dependence compared to standard bond percolation. Published by the American Physical Society 2024

Probability Threshold Optimization for Classification of COVID-19 Patients with Higher Mortality Risk: A Case Study from the North-Eastern Region in North Macedonia

Research goal: The goal of this research is to identify, compare and demonstrate some available methodological approaches which are sufficient to draw the optimal probability threshold, particularly in the case of classification of infected patients with increased risk of dying from COVID-19. The presented methodologies generate identical results if the purpose of classification is to maximize the prognosis accuracy from the point of sensitivity. Sample: As part of the whole population, the sample counts 1013 patients from the north-eastern region of the Republic of North Macedonia. Methodology: The general methodological frame used to calculate and forecast the probabilities of death outcome from COVID-19 is the binary logistic regression. In extension, we applied the rules of maximum sum and maximum product as well as the so-called Youden Index for the purpose of optimization of the probability threshold. The principals of the ROC curve in addition with the Index of Union was also helpful for the same purpose. Prognosis accuracy was evaluated through the status of patient according to the rules of “golden standard” in which sensitivity, specificity and the general accuracy of prognosis play a crucial role. Results: Accordingly, the results from the research indicate that the optimal probability threshold or “cut-off” point that provides maximal accuracy, particularly from the perspective of sensitivity in the prognosis is 0,1. In that point, the coefficient of sensitivity (the percentage of true positively predicted death cases in respect to all death cases from the sample) is measured 85,71%. Conclusion: The applied methodological approaches offer scientifically sound foundations in the context of mortality risk evaluation and classification of COVID-19 patients. Then targeted patients will be subject of precaution with strict measures, protocols and more aggressive treatment in order to minimize the chances of death outcome.

Matching and Rewriting Rules in Object-Oriented Databases

Graph query languages such as Cypher are widely adopted to match and retrieve data in a graph representation, due to their ability to retrieve and transform information. Even though the most natural way to match and transform information is through rewriting rules, those are scarcely or partially adopted in graph query languages. Their inability to do so has a major impact on the subsequent way the information is structured, as it might then appear more natural to provide major constraints over the data representation to fix the way the information should be represented. On the other hand, recent works are starting to move towards the opposite direction, as the provision of a truly general semistructured model (GSM) allows to both represent all the available data formats (Network-Based, Relational, and Semistructured) as well as support a holistic query language expressing all major queries in such languages. In this paper, we show that the usage of GSM enables the definition of a general rewriting mechanism which can be expressed in current graph query languages only at the cost of adhering the query to the specificity of the underlying data representation. We formalise the proposed query language in terms declarative graph rewriting mechanisms described as a set of production rules L→R while both providing restriction to the characterisation of L, and extending it to support structural graph nesting operations, useful to aggregate similar information around an entry-point of interest. We further achieve our declarative requirements by determining the order in which the data should be rewritten and multiple rules should be applied while ensuring the application of such updates on the GSM database is persisted in subsequent rewriting calls. We discuss how GSM, by fully supporting index-based data representation, allows for a better physical model implementation leveraging the benefits of columnar database storage. Preliminary benchmarks show the scalability of this proposed implementation in comparison with state-of-the-art implementations.

A new fractional derivative extending classical concepts: Theory and applications

In this paper, a novel general definition for the fractional derivative and fractional integral based on an undefined kernel function is introduced. For 0<α≤1, this definition aligns with classical interpretations and is applicable for calculating the derivative in an open negative interval I⊆[a,+∞),a∈R. Additionally, when α=1, the definition coincides with the classical derivative. Fundamental properties of the fractional integral and derivative, including the product rule, quotient rule, chain rule, Rolle’s theorem, and the mean value theorem, are derived. These properties are illustrated through various applications to demonstrate their applicability. Furthermore, some applications of solving fractional nonlinear systems of integro-differential equations using framelets are presented.

Bandwidth modulation and pulse characterization of passively Q-switched erbium-doped fiber laser

We demonstrate the modulation of laser bandwidth by utilizing an ultranarrow tunable bandpass filter (UNTBF) in a passively Q-switched erbium-doped fiber laser. The passive Q-switch mechanism is enabled by using carbon nanotubes as saturable absorber at a Q-switched threshold of 35.5 mW. Based on spectral filtering effect introduced by the UNTBF, the 3 dB laser bandwidth can be tuned from 0.016 nm to 0.478 nm at a fixed pump power of 75.9 mW. The corresponding pulse behavior for each different bandwidth is characterized, and the results reveals that the pulse width can be as well tuned from 7.8 to 2.6 μs against the laser bandwidth, which agrees with the rule of time-bandwidth product. Correspondingly, the pulse repetition rate and the pulse energy vary from 16.23 kHz to 26.16 kHz and from 0.67 to 1.03 μJ respectively across the laser bandwidth. Further investigation of the pulse performance is performed against the pump power increment up to 107.2 mW. To the best of our knowledge, this is the first demonstration of spectrum bandwidth modulation in a passively Q-switched fiber laser, which can be useful for fully exploiting the possibilities of Q-switched pulse applications.

On some $$\Sigma ^{B}_{0}$$-formulae generalizing counting principles over $$V^{0}$$

AbstractWe formalize various counting principles and compare their strengths over $$V^{0}$$ V 0 . In particular, we conjecture the following mutual independence between: a uniform version of modular counting principles and the pigeonhole principle for injections, a version of the oddtown theorem and modular counting principles of modulus p, where p is any natural number which is not a power of 2, and a version of Fisher’s inequality and modular counting principles. Then, we give sufficient conditions to prove them. We give a variation of the notion of PHP-tree and k-evaluation to show that any Frege proof of the pigeonhole principle for injections admitting the uniform counting principle as an axiom scheme cannot have o(n)-evaluations. As for the remaining two, we utilize well-known notions of p-tree and k-evaluation and reduce the problems to the existence of certain families of polynomials witnessing violations of the corresponding combinatorial principles with low-degree Nullstellensatz proofs from the violation of the modular counting principle in concern.

High Throughput Variant Libraries and Machine Learning Yield Design Rules for Retron Gene Editors.

The bacterial retron reverse transcriptase system has served as an intracellular factory for single-stranded DNA in many biotechnological applications. In these technologies, a natural retron non-coding RNA (ncRNA) is modified to encode a template for the production of custom DNA sequences by reverse transcription. The efficiency of reverse transcription is a major limiting step for retron technologies, but we lack systematic knowledge of how to improve or maintain reverse transcription efficiency while changing the retron sequence for custom DNA production. Here, we test thousands of different modifications to the retron-Eco1 ncRNA and measure DNA production in pooled variant library experiments, identifying regions of the ncRNA that are tolerant and intolerant to modification. We apply this new information to a specific application: the use of the retron to produce a precise genome editing donor in combination with a CRISPR-Cas9 RNA-guided nuclease (an editron). We use high-throughput libraries in S. cerevisiae to additionally define design rules for editrons. We extend our new knowledge of retron DNA production and editron design rules to human genome editing to achieve the highest efficiency retron-Eco1 editrons to date.

Transformer oil electrical–thermal characteristics analysis and evaluation

Transformer oil plays the role of heat dissipation and insulation in power transformers, and its electrical and thermal characteristics are directly related to the stable operation of the transformer. At the same time, it is important to master the electric–thermal characteristics of transformer oil for transformer state evaluation, latent fault prediction, and maintenance planning. Based on this, the gas production rule and electrical characteristics of transformer oil under accelerated aging are studied in this paper. First, the experimental platform for power transformer aging is established to accelerate the aging of power transformers. Second, the accelerated aging transformer oil is taken as the research object, and the power frequency, DC, lightning, and gas chromatography are measured and analyzed. Finally, a transformer oil aging evaluation model is established, which takes into account four factors: carbon and oxygen gas factors in transformers, life loss factors calculated by hotspot temperature, hydrocarbon gas factors dissolved in transformer oil, and oil quality factors, and conducts aging evaluation. The conclusion shows that the T parameter proposed in this paper can effectively evaluate the quality of transformer oil. When T is less than or equal to 0.6, there is no aging of the oil. When T is greater than 0.6 and less than 1, the transformer oil has been aging, but it is not manifested. Those are parameters whose chromatography and breakdown voltage are not far beyond the IEEE standard. When T = 1, the aging of oil with significant changes in gas content and breakdown voltage can be observed. When T is greater than 1, the oil has undergone serious aging.

Design of a decision support system to form optimal technological processes for parts machining based on artificial intelligence methods

The object of this study is the process of designing a decision support system for automating the formation of technological processes (TPs) for machining parts of high-precision equipment for the aviation industry. The task of improving the efficiency of the optimization of the process of mechanical processing of parts through the use of a decision support system (DSS) and artificial intelligence methods, which, unlike known analytical approaches, allow describing processes and phenomena that do not have strict formalization, has been solved. DSS consists of three subsystems. The first is an information subsystem for the automated formation of the structure in the technological process of machining parts of high-precision equipment. The second is an information subsystem for optimizing parameters of TP operations by cutting, taking into account the accumulation of tool wear. The third is a subsystem of control and adjustment of operating parameters. In the process of conducting research, an approach was devised for designing optimal technological processes to machine parts of high-precision equipment. The task of designing the structure of technological processes was solved using production rules. The task of determining the optimal parameters of turning and milling operations was solved in a multi-criteria statement. The following objective functions were used: cost of the operation, specific energy consumption for the operation, and productivity of the operation. At the same time, the wear of the tool accumulated over time was taken into account. The solution was obtained by searching for the Pareto-optimal solution using genetic algorithms and artificial neural networks. As a result of the work of DSS, an optimal technological process for machining parts of high-precision equipment for the aviation industry was formed, which made it possible to reduce the production time of one part by 5 % and reduce the total cost of production of the part by 14 %

Problem-based Curriculum to Conceptually Develop the Multiplication Principle for Counting

Counting exercises are difficult (e.g., Batanero et al., 1997; Hadar &amp; Hadass, 1981). As a case in point, although multiplication is a relatively simple concept, students often use multiplication incorrectly on counting problems (Batanero et al., 1997). To address this issue, this paper develops a problem-based curriculum to help students learn about the multiplication principle (MP) for counting. In this paper, we outline the important mathematical issues and nuances associated with the MP in our proposed exercise set, and discuss how mathematics educators could implement this sequence of exercises to develop students’ conceptual understanding of the MP. We conclude by discussing how our exercise set aligns with a broader theory of learning – variation theory.

Integration of Control Strategies for Cleaning Based on Granular Computing

Cleaning control based on changes in cleaning loss rate and impurity rate has emerged as a hot topic in the research on intelligent control for rice and wheat combined harvesters. However, numerous operation parameters can lead to deviations beyond the normal range of cleaning loss rate and impurity rate. The impact of cleaning control parameters in rice and wheat combined harvesters on cleaning loss rate and impurity rate often tends to be contradictory. How to combine different contradictory cleaning control strategies to get a more widely used and better cleaning control strategy is a hot issue in the current cleaning control research. In this paper, the granularity of quotient space is introduced into the cleaning control based on operation parameters, and a cleaning control model based on granularity synthesis theory is proposed. This method first constructs a knowledge base for intelligent control of cleaning tailored to the cleaning loss rate and impurity rate using production rule representation, and considers that these control strategies constitute different quotient spaces, and then organizes these quotient spaces according to granularity synthesis theory to get the cleaning control strategy. The experimental results verify that the validity of the cleaning control based on granular computing is better than fuzzy control.