Integration Rules Research Articles

A comparative study of Filon-type rules for oscillatory integrals

Our aim is to answer the following question: "Among the Filon-type methods for computing oscillatory integrals, which one is the most efficient in practice?". We first discuss why we should seek the answer among the family of Filon-Clenshaw-Curtis rules. A theoretical analysis accompanied by a set of numerical experiments reveals that the plain Filon-Clenshaw-Curtis rules reach a given accuracy faster than the (adaptive) extended Filon-Clenshaw-Curtis rules. The comparison is based on the CPU run-time for certain wave numbers (medium and large).

An efficient numerical scheme to solve generalized Abel’s integral equations with delay arguments utilizing locally supported RBFs

Hereditary effects are commonly observed in diverse scientific domains such as engineering, economics, biology, mathematics, and physics. In the model of atomic irradiation of solids with unbounded cross-sectional areas, determining the average number of atoms displaced has been achieved through delay systems that incorporate the consideration of past states. In this study, we employ the discrete collocation method using local radial basis functions to numerically solve Abel-type integral equations with a delay argument. This method balances accuracy, efficiency, and flexibility and is well-suited for complex practical problems as it requires less memory and computational volume compared to its global counterpart. Instead of approximating the solution at all points of the domain, the method considers a set of nodes in the neighborhood of a certain point. As a result, the method can be readily implemented on a standard personal computer without requiring high-end specifications. To calculate the singular integrals the nonuniform composite Gauss–Legendre numerical integration rule is employed. We discuss the error analysis and convergence rate of the offered scheme and test it with several numerical examples. The results obtained are also consistent with the theoretical error analysis expectations.

Numerical analysis of COVID-19 model with Caputo fractional order derivative

This paper focuses on the numerical solutions of a six-compartment fractional model with Caputo derivative. In this model, we obtain non-negative and bounded solutions, equilibrium points, and the basic reproduction number and analyze the stability of disease free equilibrium point. The existence and uniqueness of the solution are proven by employing the Picard–Lindelof approach and fixed point theory. The product–integral trapezoidal rule is employed to simulate the system of FODEs (fractional ordinary differential equations). The numerical results are presented in the form of graphs for each compartment. Finally, the sensitivity of the most important parameter (β) and its impact on COVID-19 dynamics and the basic reproduction number are reported.

Translating Educational and Cultural Literacy Works under Berne, Ius Cogens, and Linguistic Genocide

The lack of works for educational and cultural literacy purposes in their own languages threatens the cultural survival of many vulnerable minority and indigenous groups worldwide. Translation could satisfy related access needs. A strict reading of international copyright law, however, does not facilitate the translation of works into other languages. Yet, it is often forgotten that, in accordance with the integration rule of treaty interpretation, the Berne Convention, and other relevant international intellectual property instruments, would have to be read in the light of internationally protected linguistic human rights in education and for cultural literacy. This mechanism could go some way towards assisting the easier translation of (parts of) works for the stated purposes into other languages. The argument made in this article, however, is that a harmonious reading of existing international copyright law with international human rights law cannot go as far as to sufficiently resolve the access needs of vulnerable groups speaking an endangered language, insofar as translated texts are concerned. In fact, it is contended that the existing regulation of translation under international copyright law is so inimical to the survival of vulnerable groups and their languages that it must be held to promote cultural or linguistic genocide. For that reason, the relevant copyright rules must be considered to conflict with ius cogens, that is, peremptory norms of international law, and to be void in their application to neglected languages. The article makes suggestions as to how countries could design national copyright law regulating translation rights and limitations and exceptions in a way that facilitates translation generally, and into neglected languages specifically. These suggestions are based on a reappraisal of the true character of translation, which must be seen to be highly transformative in nature and resulting in the creation of autonomous new works.

Educația și conștientizarea etică a tehnologiilor IA și folosirea lor în mediul academic

The essay aims to contribute to discussions about the implementation of AI-based technologies in education, through a perspective that will stimulate the advance of ethical research and will overcome the classic “pro” or “con” controversy. We will explore here, albeit not exhaustively (given the dimensions of this paper), aspects of learning that should be integrated into the analysis of how we evaluate AI technologies and design rules of academic integrity. We will review some directions for the development of AI technologies for education, the risks and benefits presented so far in the specialized literature, and we will endorse the idea that education and “ethical awareness” are basic presuppositions for the success of any model of academic integrity. The conclusion will focus on the importance of adopting in the respective fields principles that are more relevant to the reality in which we live and that do not arbitrarily circumscribe the field, inevitably leading to the success of some underground models, opposed to integrity. Conversely, it would support those principles that foster the advancement of ethical research by integrating all aspects that affect the academic field, on the model: knowledge enables improvements and adjustments.

Some notes on the trapezoidal rule for Fourier type integrals

This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the number of nodes can be a priori selected. The analysis is also used to design an automatic integrator that can be employed without any knowledge of the function involved in the problem. Several numerical examples, which confirm the reliability of this strategy, are reported.

Data-Augmented Numerical Integration in State Prediction: Rule Selection

This paper deals with the state prediction of nonlinear stochastic dynamic systems. The emphasis is laid on a solution to the integral Chapman-Kolmogorov equation by a deterministic-integration-rule-based point-mass method. A novel concept of reliable data-augmented, i.e., mathematics- and data-informed, integration rule is developed to enhance the point-mass state predictor, where the trained neural network (representing data contribution) is used for the selection of the best integration rule from a set of available rules (representing mathematics contribution). The proposed approach combining the best properties of the standard mathematics-informed and novel data-informed rules is thoroughly discussed.

The ethical aspect of public administration under special regime and sustainable development

Standards of ethical conduct for public servants encompass all aspects of public administration. Standards of ethical conduct for public servants under special legal regimes act as a measure of the rule of law, impartiality, and integrity. They are guarantees of the rationality and efficiency of public administration. The article aims to determine the content and features of applying standards of ethical conduct for public servants under special legal regimes, particularly the legal regime of martial law. The methodological framework of this study encompasses general and special methods, methods of scientific cognition, system analysis, formal-logical, structural-logical, and dialectical methods, and numerous empirical methods. The article substantiates that the legal regime of martial law has entailed increased corruption risks and determines their objective (impossibility of electronic declaration, expended list of admissible gifts) and subjective (involvement of public servants in the collection, receipt, and distribution of charitable and humanitarian assistance) reasons. The above should be compensated by means of raising standards of ethical conduct. Conclusions make a stand for the inadmissibility of disregarding the rules of ethical conduct by public servants and deny any justification for their violation under the legal regime of martial law

Values of academic integrity in higher medical education.

Aim: The aim is to identify features of theoretical and empirical research of academic integrity as characteristics of the educational environment of medical higher education institution (hereinafter - HEI). Materials and Methods: A complex of general scientific methods: logical-analytical, dialectical, theoretical-logical, comparative analysis, formalization and generalization, as well as quantitative sociological methods for collecting, processing and analyzing information. The object of the pilot empirical study were domestic medical students of full-time education at the Bogomolets NMU (N=472) and scientific and pedagogical staff who provide teaching of fundamental, specialized and socio-humanitarian disciplines at the university (N=153). Results: The values of academic integrity are the moral guideline that reveals the latest ethical demands of society and regulates the educational and scientific activities of all participants in the educational process. Opinions on the primary responsibility for compliance with the rules of academic integrity of a student differ between the surveyed scientific and pedagogical staff and students (p=0.000): the vast majority of the surveyed scientific and pedagogical staff tend to evenly divide the responsibility between a teacher and a student, and the majority of students-respondents noted that the student bears the primary responsibility. Conclusions: Commitment to the principles of integrity motivates both students and teaching staff to act in an academic manner. Therefore, the creation of a methodology for studying the phenomenon of academic integrity in medical higher education institution through the study of attitude of the subjects of educational process to basic values is promising.

Construction of new fractional inequalities via generalized $ n $-fractional polynomial $ s $-type convexity

<p>This paper focuses on introducing and investigating the class of generalized $ n $-fractional polynomial $ s $-type convex functions within the framework of fractional calculus. Relationships between the novel class of functions and other kinds of convex functions are given. New integral inequalities of Hermite-Hadamard and Ostrowski-type are established for our novel generalized class of convex functions. Using some identities and fractional operators, new refinements of Ostrowski-type inequalities are presented for generalized $ n $-fractional polynomial $ s $-type convex functions. Some special cases of the newly obtained results are discussed. It has been presented that, under some certain conditions, the class of generalized $ n $-fractional polynomial $ s $-type convex functions reduces to a novel class of convex functions. It is interesting that, our results for particular cases recaptures the Riemann-Liouville fractional integral inequalities and quadrature rules. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes, and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.</p>

Некоторые формулы дробного интегрирования от одной функции Фокса с пятью параметрами

The study obtained Riemann – Liouville and Erdelyi – Kober formulas for fractional integration of five-parameter special Fox function. The paper gives an integral representation of the function under consideration in terms of the Mellin – Barnes integral, conditions for absolute convergence, and asymptotic expansions both for large and small values of the argument. We obtained the formulas proved, using the above integral representation and known power rules for integration. For partial parameters, we got some well-known elementary and special functions.

General Considerations and Perspectives on New Artificial Intelligence (AI) Systems. Influence of AI Systems in the Area of Criminal Liability for Breaches of Integrity Rules in Public Office

Artificial intelligence systems are being used in various areas such as e-commerce, e-government and e-advertising, mainly because of their efficiency and ability to provide fast access to services. However, AI uses a massive amount of data, raising concerns about the privacy and control of this data held by large corporations or government entities. Although there are some risks associated with AI, such as discrimination in AI algorithms and over-reliance on technology, there are also many benefits to be gained from using these systems: automating administrative processes, providing assistance and support to citizens, data analysis and personalised decision-making etc. To maximise benefits and minimise risks, responsible control and management of AI data and systems is required. The integration of artificial intelligence in e-government and in the detection of breaches of the integrity of public functions may prove useful, but it must be accompanied by measures to ensure respect for human rights, data protection, discrimination and the avoidance of violations.

The Mists of Time: Intertemporality and Self-determination's Territorial Integrity rule in the ICJ's Chagos Advisory Opinion

The Mists of Time: Intertemporality and Self-determination's Territorial Integrity rule in the ICJ's Chagos Advisory Opinion

Efficient implementation on accuracy improvement of the two-dimensional node-to-segment contact approach for explicit dynamic analysis

The penalty-method-based node-to-segment (NTS) approach is widely employed in the explicit dynamic analysis owing to its computational efficiency and implementation simplicity. However, the classical approach does not pass the contact patch test and results in severe inaccuracies. This study attempts the accuracy enhancement of an explicit dynamic contact analysis with minimum efficiency loss using the NTS algorithm with the modified area regularization technique (NTS-mAR). The computational procedure is compared to an allied modified penalty-method-based NTS approach, i.e., the virtual node-to-segment algorithm passing the patch test (VTS-PPT). Then, an extension to an explicit dynamic analysis framework is attempted, wherein the speed of the contact force calculation significantly influences the overall computational efficiency. The cost of the remaining computation was minimized by employing a lumped mass matrix and a one-point integration rule for the internal force. Elastoplasticity was considered to extend its application. The accuracy improvement compared to the classical one-pass NTS approach was similar for the modified approaches. The VTS-PPT approach requires more than twice the cost of contact force estimation compared with the classical one-pass NTS approach. In contrast, NTS-mAR approach induces a cost increase from 6 to 36% that of classical one-pass NTS approaches. For the given examples, the NTS-mAR approach is beneficial when an improvement in accuracy is desired with minimum efficiency loss.

A Practical Data Extraction, Cleaning, and Integration Method for Structural Condition Assessment of Highway Bridges

The success of regional bridge condition assessment, a crucial component of systematic maintenance strategies, relies heavily on comprehensive, well-structured regional bridge databases. This study proposes the data extraction, cleaning, and integration method for the construction of such databases. First, this research proposes an extraction method tailored for unstructured data often present in inspection reports. Additionally, this paper meticulously outlines a cleaning procedure designed to rectify two distinct categories of typical errors that are present within the inspection data. Subsequently, this study takes a holistic approach by establishing integration rules that harmonize data from various sources, including inspection records, monitoring data, traffic statistics, as well as design and construction blueprints. The architectural framework of the regional bridge information database is then meticulously laid out. To validate and demonstrate the effectiveness of the method, this study applies them to a set of representative highway bridges situated within Shandong Province. The results show that this approach can be used to successfully establish a functional regional bridge database. The database plays a pivotal role in harnessing the latent potential of an extensive range of multi-source information and propels the field of bridge condition assessment forward by providing a solid basis for informed decision making and strategic planning in the realm of infrastructure maintenance.

Unsupervised learning of stationary and switching dynamical system models from Poisson observations

Objective. Investigating neural population dynamics underlying behavior requires learning accurate models of the recorded spiking activity, which can be modeled with a Poisson observation distribution. Switching dynamical system models can offer both explanatory power and interpretability by piecing together successive regimes of simpler dynamics to capture more complex ones. However, in many cases, reliable regime labels are not available, thus demanding accurate unsupervised learning methods for Poisson observations. Existing learning methods, however, rely on inference of latent states in neural activity using the Laplace approximation, which may not capture the broader properties of densities and may lead to inaccurate learning. Thus, there is a need for new inference methods that can enable accurate model learning. Approach. To achieve accurate model learning, we derive a novel inference method based on deterministic sampling for Poisson observations called the Poisson Cubature Filter (PCF) and embed it in an unsupervised learning framework. This method takes a minimum mean squared error approach to estimation. Terms that are difficult to find analytically for Poisson observations are approximated in a novel way with deterministic sampling based on numerical integration and cubature rules. Main results. PCF enabled accurate unsupervised learning in both stationary and switching dynamical systems and largely outperformed prior Laplace approximation-based learning methods in both simulations and motor cortical spiking data recorded during a reaching task. These improvements were larger for smaller data sizes, showing that PCF-based learning was more data efficient and enabled more reliable regime identification. In experimental data and unsupervised with respect to behavior, PCF-based learning uncovered interpretable behavior-relevant regimes unlike prior learning methods. Significance. The developed unsupervised learning methods for switching dynamical systems can accurately uncover latent regimes and states in population spiking activity, with important applications in both basic neuroscience and neurotechnology.

Novel Definitions of α-Fractional Integral and Derivative of the Functions

An α-fractional integral and derivative of real function have been introduced in new definitions and then, they compared with the existing definitions. According to the properties of these definitions, the formulas demonstrate that they are most significant and suitable in fractional integrals and derivatives. The definitions of α-fractional derivative and integral coincide with the existing definitions for the polynomials for 0 ≤ α < 1. Furthermore, if α = 1, the proposed definitions and the usual definition of integer derivative and integral are identical. Some of the properties of the new definitions are discussed and proved, as well, we have introduced some applications in the α- fractional derivatives and integrals. Moreover, α-power series and α–rule of integration by parts have been proposed and implemented in this study.

Interpositional auxiliary components in the structure of a multi-topic scientific discourse

The article aims to study the presence/absence of references (interpositional auxiliary components) in the structure of a multi-topic scientific discourse. Today, the problem of compliance with the rules of academic integrity, which is caused by free access to a large amount of information and the often dishonesty of researchers, has become particularly noticeable. That is why it became necessary to control the presence of references to quotations and the author's ideas and the need to prepare them correctly. The purpose of the article is to analyze the presence of quotations as the main type of a reported speech in a scientific style, and to define the use of dominant methods of designing references to the sources. The goal determined the following task: to group randomly selected articles on various topics for analysis; to analyze the presence/absence of references in the texts; to characterize the methods of formatting the list of references; find out the productivity of different types of references; formulate conclusions and outline the research perspective. The article uses descriptive, comparative methods of contextual analysis and reception of quantitative calculations. The research material became 24 scientific articles, randomly selected from collections of scientific works published on the boundary of 2020 s, and conditionally divided into six blocks: "human sciences"; "sciences about the state"; "education sciences"; "sciences of nature"; "social sciences"; "technical sciences". It was found that the most productive model, according to which references to the paper of a certain author is formed in multidisciplinary scientific articles, is the construction «number of the work in the list of used literature» (261 fixations). It must be said that the construction can be seen in all blocks of research, and is more often traced in works on the technical sciences, state and social, episodically - in articles on the humanities.

Numerical analysis of temporal second‐order accurate scheme for the abstract Volterra integrodifferential equation

In this paper, a second‐order accurate scheme is considered for the temporal discretization of the abstract Volterra integrodifferential equation with a weakly singular kernel. The time discrete scheme is constructed by the Crank–Nicolson method for approximating the time derivative and product integration (PI) rule for approximating the integral term. The proposed scheme employs a graded mesh for time to compensate for the singular behavior of the exact solution at . Under the suitable assumptions, the stability and convergence are established by the energy argument, and the error is of order , where is the parameter for the time grids. Numerical experiments validate the theoretical estimate.

Gaussian rule for integrals involving Bessel functions

Gaussian rule for integrals involving Bessel functions