Integration Rules Research Articles

(Δ∇)∇-Pachpatte Dynamic Inequalities Associated with Leibniz Integral Rule on Time Scales with Applications

We prove some new dynamic inequalities of the Gronwall–Bellman–Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations.

Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow

Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow

Some Generalizations of (∇∇)Δ–Gronwall–Bellman–Pachpatte Dynamic Inequalities on Time Scales with Application

As a new usage of Leibniz integral rule on time scales, we proved some new extensions of dynamic Gronwall–Pachpatte-type inequalities on time scales. Our results extend some existing results in the literature. Some integral and discrete inequalities are obtained as special cases of the main results. The inequalities proved here can be used in the analysis as handy tools to study the stability, boundedness, existence, uniqueness and oscillation behavior for some kinds of partial dynamic equations on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.

Mega Mergers in the Seeds & Agro-chem Industry

The Seeds and Agro-Chem Industry today is a tightly knit oligopoly with only a handful of global players. Following a detailed assessment, the European Commission recently conditionally cleared three major transactions in the already highly concentrated sector - Chem China and Syngenta, Dow and Du Pont, Bayer and Monsanto – reducing the number of effective global players from six-to-four. Even though the Commission’s decisions are laudatory in terms of their economic assessment of the impact of the transactions on product, price and innovation competition, these merger approvals suggest the following gap in EU Merger Control. Taking pride in its more economic approach, the EU Merger Control in its current form neglects the need to integrate the most fundamental principles of EU law. These principles can neither be easily quantified nor put in a straitjacket of ‘cost/benefit’ or ‘efficiency’ analysis. This article accordingly calls for the need to go back to the Treaty articles and examine how EU Merger Control can effectively meet the larger policy objectives as enshrined in the Treaty articles, such as Article 11 TFEU’s ‘environmental integration rule’, while simultaneously retaining the impression of being based in sound principles of competition law and economics. Incorporation of the principle of sustainable development alongside the well-defined economic principles well aligns with an integrated and holistic approach to policy-making. The approach suggested may lead to a multiciplty of objectives – meaning that if such an approach is indeed adopted, the EU Merger Control may well need to look beyond the narrow construct of ‘efficiency’ and ‘consumer welfare’. A failure to take account of these larger objectives, however, may ironically thwart the EU Merger Control from achieving the very fundamental objective it seemingly aspires to achieve that is ‘consumer welfare’! Consumers being numerous and geographically dispersed experience the collective action problem. In the Bayer/Monsanto merger, despite this typical collective active problem, the Commission received over 55,000 emails, letters and postcards and an uncountable number of tweets on the social networking site Twitter. The citizens, who are also consumers, in their complaints requested the Commission to prohibit the transaction, as they saw the proposed merger being detrimental to ‘human health, food safety, consumer protection, the environment and the climate’. The Commission’s response to these complaints was that even though the said concerns were significant - they nonetheless could not form the basis of merger assessment, which needs to be limited to competition issues. As for the issues raised, in the opinion of the Commission, other areas of law such as those dealing with the regulatory system for pesticides and the consumer protection law could well address these other concerns. The dilemma confronting the Commission was whether to assess these transactions within the current framework grounded in well-defined scientific principles of economics (and increasingly econometrics) or in the alternative take account of some qualitative non-price considerations. The Commission evidently resorted to the former option. A decision otherwise would have been subject to intense economic criticism just like the GE/Honeywell decision, wherein the Commission proposed a very novel theory of ‘Archimedean Leveraging’, and prohibited the proposed merger. This means that for a truly effective competition policy and EU Merger Control in particular, the authorities need to ‘re-think, re-design and re-frame’ the notion of competition policy as a ‘system of inter-locking processes’ in the Raworth’s ‘doughnut’. For such a sustainability-driven thinking on innovation, that re-directs the ‘consumption choices available to consumers’ within the sustainable ‘safe and just space for humanity’, there is a visible need to think and reflect upon the ‘double limit of planetary boundaries’ and incorporate it in the everyday philosophy of competition policy.
 

On dynamic inequalities in two independent variables on time scales and their applications for boundary value problems

Our work is based on the multiple inequalities illustrated by Boudeliou and Khalaf in 2015. With the help of the Leibniz integral rule on time scales, we generalize a number of those inequalities to a general time scale. Besides that, in order to obtain some new inequalities as special cases, we also extend our inequalities to discrete, quantum, and continuous calculus. These inequalities may be of use in the analysis of some kinds of partial dynamic equations on time scales and their applications in environmental phenomena, physical and engineering sciences described by partial differential equations.

The finite difference method for the fourth‐order partial integro‐differential equations with the multi‐term weakly singular kernel

This paper is concerned with an efficient numerical method for a class of fourth‐order partial integro‐differential equations (PIDEs) with weakly singular kernel. Due to the presence of the weakly singular kernel, the exact solution has singularity near the initial time . The proposed method is constructed on the graded meshes, which can achieve the second‐order convergence in time for weakly singular solutions. The product integral rule of the Riemann–Liouville fractional integral with the generalized time‐stepping is used for the time discretization, and the standard central difference formula is used for the space discretization. The stability and convergence of the method are proved, and the optimal error estimates in the discrete ‐norm and ‐norm are obtained. Numerical results show the effectiveness of the proposed method. Further, by the extrapolation method, we improve the convergence order in space and time to four order, respectively.

Scaled lattice rules for integration on ℝ^{𝕕} achieving higher-order convergence with error analysis in terms of orthogonal projections onto periodic spaces

We introduce a new method to approximate integrals∫Rdf(x)dx\int _{\mathbb {R}^d} f(\boldsymbol {x}) \,\mathrm {d}\boldsymbol {x}which simply scales lattice rules from the unit cube[0,1]d[0,1]^dto properly sized boxes onRd\mathbb {R}^d, hereby achieving higher-order convergence that matches the smoothness of the integrand functionffin a certain Sobolev space of dominating mixed smoothness. Our method only assumes that we can evaluate the integrand functionffand does not assume a particular density nor the ability to sample from it. In particular, for the theoretical analysis we show a new result that the method of adding Bernoulli polynomials to a function to make it “periodic” on a box without changing its integral value over the box is equivalent to an orthogonal projection from a well chosen Sobolev space of dominating mixed smoothness to an associated periodic Sobolev space of the same dominating mixed smoothness, which we call a Korobov space. We note that the Bernoulli polynomial method is often not used because of its excessive computational complexity and also here we only make use of it in our theoretical analysis. We show that our new method of applying scaled lattice rules to increasing boxes can be interpreted as orthogonal projections with decreasing projection error. Such a method would not work on the unit cube since then the committed error caused by non-periodicity of the integrand would be constant, but for integration on the Euclidean space we can use the certain decay towards zero when the boxes grow. Hence we can bound the truncation error as well as the projection error and show higher-order convergence in applying scaled lattice rules for integration on Euclidean space. We illustrate our theoretical analysis by numerical experiments which confirm our findings.

Multi-Period EOQ Model for Multi-Generation Technology Products With Short Product Life Cycles

In this paper, the multi-period EOQ model is developed for the technology products that have multiple generations co-existing in the market, with each of them having a very short product life cycle. The paper first develops the framework for computation of inventory-related costs and then minimizes the total replenishment costs using random search technique and approximating the non-linear expressions while using Simpson’s Rule for integration. The paper also provides numerical illustrations and establishes a few important theorems that relate the EOQ to the innovation of diffusions. It is found that the total replenishment cost curve, drawn on the EOQ axis in the case of technology generations is convex to the origin. Since the objective function is highly non-linear, the genetic algorithm has been used to find the solution to the problem. The study also suggests that the faster diffusion of the next generations has a conflicting effect on the EOQ of the first generation in the case of pooled and non-pooled logistics.

On the Ayed-Kuo stochastic integration for anticipating integrands

In this article, we prove new results for the anticipating stochastic integral introduced by Ayed and Kuo. We present an existence criterion for the integral, a Fubini’s theorem, a Leibniz integral rule, and an alternative definition for a class of integrands.

The Impact of Institutional Governance on Perceived Organizational Reputation in the Jordanian Public Sector

This paper aims to identify the impact of institutional governance on perceived organizational reputation in the Jordanian public sector. A quantitative approach was adopted through designing a questionnaire which was distributed to 600 employees in 6 governmental institutions. A total of 556 valid questionnaires were retrieved in the first stage and 97 questionnaires (items) were removed in the second SEM stage, so that 459 questionnaires were subject to analysis. In light of the data analysis, the study revealed a number of findings. Most notably, there is a significant impact of justice and rule of law, integrity and work ethics and social responsibility upon perceived organizational reputation in the Jordanian public sector. Justice and rule of law came first (79%), then, integrity and work ethics (65%), followed by social responsibility (61%). This means the endeavor of Jordanian public sector organizations towards adherence to laws and resorting to them in their functions, operations and services. Also, this result reflects the level of awareness of the importance of justice as a core value and an essential input in building a good organizational reputation for Jordanian public-sector organizations. This paper provides evidence from the public sector employees and concludes the impact of institutional governance factors on organizational reputation, which has not been researched enough previously in the public-sector context. These are important factors underlying organizational reputation and trust from the users of public services. Finally, new insights have been provided into the organizational reputation theory in the public sector.

EC-tractability of multivariate approximation in Hermite spaces for the standard information class

In this paper, we study exponential tractability of multivariate approximation problem for Hermite spaces of analytic functions over [Formula: see text] in the worst case setting. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. The considered algorithms based on tensor products of Gauss–Hermite rules for multivariate integration are constructive and use the class [Formula: see text] of only function evaluations. We give matching necessary and sufficient conditions for notions of EC-quasi-polynomial tractability and EC-uniform weak tractability in terms of two weight parameters of the problem.

Efficient Implementation of Multi-Port Frequency Dependent Network Equivalents for Electromagnetic Transient Studies using Norton Equivalent Circuits

Power system electromagnetic transient studies require that a small part of the electrical network be modelled in detail. The rest of the system is represented by a network equivalent taking into account the frequency dependence of the system components (FDNE). With the purpose of getting a FDNE, this paper presents a procedure for including high-order rational models in EMTP-type simulation programs based on Norton equivalent circuits. This approach has the advantage of using few conductance branches compared to those obtained by fitting any particular circuit structure.In relation to the work carried out, this paper presents the following issues: a) a procedure for calculating the admittance matrix of the rest of the system as a function of frequency b) this matrix is synthesized in the form of multi-terminal π-equivalent circuits, whose branches are fitted by rational functions in the pole-residue form c) each partial fraction is converted into a differential equation in time domain. The trapezoidal rule of integration is applied to that differential equation, resulting in a conductance in parallel with a history term current source. Considering all the partial fractions corresponding to a branch, a Norton equivalent circuit is obtained for that branch.This paper also shows how the procedure is implemented in three different ways in an EMTP-type program, along with the validation of such approach through simulations in an electric utility 500 kV transmission system.

The EU Common Regional Market Proposals for the Western Balkans

The EU and the Western Balkans in 2020 launched a regional economic integration initiative entitled ‘The Western Balkans Common Regional Market’, aimed at economically integrating the Western Balkans based on the EU Single Market rules by 2025. The economic integration initiative has been met with challenges, and this contribution provides an assessment of EU-led initiatives to promote economic integration within the Western Balkans between 2014 and 2021, analysing some of the challenges to ensuring that the Western Balkans Common Regional Market is operational by 2025. The contribution conceptualises the mode of governance approach used by the EU in engaging with the Western Balkans since 2014 and suggests that it is largely based on soft law. The contribution finds that the action plan for establishing a regional common market is flawed, as it has not taken on board the high level of corruption and the lack of rule of law in the Western Balkans. The contribution provides new insights into the nature of corruption taking place in the Western Balkans and argues that corruption and the lack of the rule of law could be a major barrier for the proper function of the regional common market. Western Balkans, Berlin Process, Common Market, Open Balkan, Corruption, Rule of Law, Economic Integration, European Neighbourhood and Enlargement Policy

Статистичне оцінювання якості освітньої програми “Економічна аналітика та статистика”, рівня задоволеності навчанням та факторів, що їх визначають

In today’s changing world, training of specialists in any sphere requires a constant active search on the part of educational service providers for the development of relevant competencies of students of higher education, to ensure the correspondence of educational training to the modern needs of practice. That is why any educational program needs not only an internal but also an external audit aimed at its improvement. Understanding the factors that determine the quality of the program by chance is the basis not only for building a sustainable and competitive system of training specialists, but also for its successful practical implementation. Such a system should be based on providing feedback to students. One of the forms of such communication is a survey of students and graduates regarding the quality of the educational program and the level of satisfaction with education to find the factors that determine them. To achieve this goal, an expert questionnaire was developed, which includes three blocks of questions regarding the completeness of the program itself, its implementation in the educational process and in practice. A list of questionnaire questions is proposed, which potentially outline the range of problems of student training and possible ways to solve them.
 To evaluate the quality of the educational program in different blocks of disciplines, its main advantages and disadvantages, comparative diagrams of factors that influenced the decision-making regarding admission were constructed. Considerable attention is paid to the comparative analysis of the distribution of grades depending on the educational level of training: bachelors, masters, graduates.
 The implementation of the program in the educational process is considered in detail, namely: the level of teaching disciplines, their methodical support, and the evaluation system. The observance of the rules of academic integrity by teachers and students studying in the educational program and the organization of the educational process are analyzed separately. Questions were also asked that were supposed to reveal the need to implement certain actions to become a good specialist.
 Special attention is paid to the retrospective evaluation of the educational program, which is a generalized measure of its quality, because it summarizes the respondents’ answers to the important question: “If you had the information, you now have about studying in this program at the university before entering, would you choose it?”. For this purpose, the authors proposed an approach to the analysis of the level of satisfaction with education using binary output models. The change in the probability of the outcome variables when the predictors change, and the reliability of the models were also evaluated. The capabilities of binary output models in confirming analytical assumptions are shown.
 Proposals have been put forward regarding the possibilities of improving students’ attitudes towards the educational program and eliminating existing shortcomings.

Geometry and sizing optimization of steel gable frames with tapered members

Steel gable frames with tapered members are often used to cover large-span spaces. To save material, the members of these frames are often considered I-shaped with linearly tapered webs. However, more savings in the material may be obtained if the design of structures is optimized. Many attempts have been made to optimize the size of these kinds of frames. Since optimizing the geometry may result in more savings, in this research, besides optimizing the sectional properties of tapered members, the height of the crown of frames has been considered as a design variable and optimized. The optimality criteria (OC) algorithm is used to find the optimal design. The Leibnitz integral rule has been employed to overcome the difficulties that arise when doing sensitivity analysis of non-prismatic members. This research shows that: a) the use of the OC algorithm provides less weight design than the meta-heuristic algorithms. b) Considering the geometry variables makes the structure more optimal.

Adaptive Quasi-Monte Carlo Finite Element Methods for Parametric Elliptic PDEs

We introduce novel adaptive methods to approximate moments of solutions of partial differential Equations (PDEs) with uncertain parametric inputs. A typical problem in Uncertainty Quantification is the approximation of the expected values of quantities of interest of the solution, which requires the efficient numerical approximation of high-dimensional integrals. We perform this task by a class of deterministic quasi-Monte Carlo integration rules derived from Polynomial lattices, that allows to control a-posteriori the integration error without querying the governing PDE and does not incur the curse of dimensionality. Based on an abstract formulation of adaptive finite element methods (AFEM) for deterministic problems, we infer convergence of the combined adaptive algorithms in the parameter and physical space. We propose a selection of examples of PDEs admissible for these algorithms. Finally, we present numerical evidence of convergence for a model diffusion PDE.

EVALUATION OF PANCASILA EDUCATION AMONG HEALTH STUDENT DURING COVID-19 PANDEMIC IN GRESIK CITY

This study aims to evaluate the knowledge of health students in Pancasila education with online teaching methods, namely zoom meeting and SPADA (Online Learning System). Health students are prospective health workers who will later be involved in the health profession. With humanitarian responsibilities that will be borne in the future, health students need to have cognitive abilities in the field of citizenship so that they can perform their professional performance in accordance with the integrity and applicable rules. The method used is semi-experimental by conducting two different learning methods on 116 health students at the University of Muhammadiyah Gresik. This research was conducted in januari - februari 2022. The results of this study indicate that the knowledge of health students related to pancasila education is in the good category. In addition, the results of this study indicate that there is no difference in Pancasila knowledge between health students using the Zoom Meeting and SPADA online learning methods.

Symbolic-numeric integration of univariate expressions based on sparse regression

The majority of computer algebra systems (CAS) support symbolic integration using a combination of heuristic algebraic and rule-based (integration table) methods. In this paper, we present a hybrid (symbolic-numeric) method to calculate the indefinite integrals of univariate expressions. Our method is broadly similar to the Risch-Norman algorithm. The primary motivation for this work is to add symbolic integration functionality to a modern CAS (the symbolic manipulation packages of SciML, the Scientific Machine Learning ecosystem of the Julia programming language), which is designed for numerical and machine learning applications. The symbolic part of our method is based on the combination of candidate terms generation (ansatz generation using a methodology borrowed from the Homotopy operators theory) combined with rule-based expression transformations provided by the underlying CAS. The numeric part uses sparse regression, a component of the Sparse Identification of Nonlinear Dynamics (SINDy) technique, to find the coefficients of the candidate terms. We show that this system can solve a large variety of common integration problems using only a few dozen basic integration rules.

Brand Potential User Identification Algorithm Based on Sentiment Analysis.

This paper firstly compares the current research status of text sentiment analysis and potential customer identification, and introduces the process of building sentiment dictionaries and feature selection, feature screening, and common classification algorithms in text analysis. Secondly, around the most used tool for sentiment analysis, sentiment dictionary, the sentiment polarity discriminative rules of sentiment words are studied. In response to the shortcomings of using a single recognition algorithm in the current process of building sentiment dictionaries, an improved integration rule is designed and an automatic construction method for domain sentiment dictionaries in the social media environment is proposed. Then, this paper analyzes the sentiment topic information existing in user-generated content and adds the domain sentiment lexicon to the joint sentiment topic model as a posteriori information to extract the sentiment topic features, based on which the feature engineering study of potential customer identification is conducted and the feature set is constructed. In addition, a sample resampling method and a diverse integration framework for unbalanced data are designed to work together for the prospect identification task under data skewing in response to the category imbalance in real data. Finally, an experimental study is conducted using a social media text corpus to validate the proposed method in this paper. The proposed domain sentiment lexicon construction method and the joint domain sentiment topic-based lead identification method show good performance in different control group experiments. This paper provides an in-depth study on the construction of domain sentiment lexicon and imbalance classification in theory and provides solutions for companies to discover potential customers in practice, which has certain theoretical significance and practical value.

Prospective interpreters and translators' training: theoretical and practical disciplines online

The system of higher education in Ukraine has been changing offering new distance learning solutions to all the participants of the educational process, lecturers and students. In higher educational establishments worldwide (Australia, Asia, North and South America, Europe), professors have been using different online platforms to teach students theoretical and practical disciplines according to the syllabus. Special attention is paid to the prospective translators and interpreters' preparation as their high quality education requires powerful theoretical and practical input. Online platforms Google Classroom and MyEnglishLab can be adjusted to the interpreters and translators' needs providing a wide range of functional learning tools for the professional preparation of pre-service specialists. According to the criteria of selection of educational online platforms for prospective interpreters and translators' preparation are the following: easy access to the online platform and user-friendly navigation, a possibility to create content, a possibility of bilateral communication, a possibility of computer-aided assessment and observance of academic integrity rules, both online platforms are suitable for theoretical input and practical skills that the students should acquire during their university studies. However, as for prospective translators and interpreters, it is recommended to use Google Classroom for teaching theoretical disciplines such as "Comparative Linguistics", "The History of the English Language", "Introduction to Translation Studies". While MyEnglishLab platform is suitable for covering practical courses developed by Pearson company. Meanwhile English practice for pre-service interpreters and translators' preparation is possible at the abovementioned platform as well.