Division Problems Research Articles

Tauberian theorems for smooth functions that never vanish

It is well known that if a function has slow growth in the ordinary sense, then it has slow growth in the Cesàro sense. The converse holds if special extra conditions are assumed; results of this form are called Tauberian Theorems. In this paper, we use techniques from generalized functions to investigate this phenomenon, with particular emphasis on the space of multipliers of Schwartz functions. We then apply our results to study series of delta functions and the division problem for tempered distributions.

On existence of truthful fair cake cutting mechanisms

We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation to receive a better allocation. A (direct-revelation) mechanism takes agents' reported valuations as input and outputs an allocation that satisfies a given fairness requirement. A natural and fundamental open problem, first raised by Chen, Lai, Parkes, and Procaccia [1] and subsequently raised in reference [2–7], etc., is whether there exists a deterministic, truthful, and envy-free (or even proportional) cake cutting mechanism. In this paper, we resolve this open problem by proving that there does not exist a deterministic, truthful and proportional cake cutting mechanism, even in the special case where all of the following hold:•there are only two agents;•each agent's valuation is a piecewise-constant function;•each agent is hungry: each agent has a strictly positive value on any part of the cake. The impossibility result extends to the case where the mechanism is allowed to leave some part of the cake unallocated.We also present a truthful and envy-free mechanism when each agent's valuation is piecewise-constant and monotone. However, if we require Pareto-optimality, we show that truthful is incompatible with approximate proportionality for any positive approximation ratio even for piecewise-constant and monotone value density functions.To circumvent the main impossibility result, we aim to design mechanisms that possess a certain degree of truthfulness. Motivated by the kind of truthfulness possessed by the classical I-cut-you-choose protocol, we propose a weaker notion of truthfulness, the proportional risk-averse truthfulness. We show that the well-known moving-knife (Dubins-Spanier) procedure and Even-Paz algorithm do not have this truthful property. We propose a mechanism that is proportionally risk-averse truthful and envy-free, and a mechanism that is proportionally risk-averse truthful that always outputs allocations with connected pieces.

Evaluation of the iterative method of task distribution in a swarm of unmanned aerial vehicles in a clustered field of targets

The purpose of this article is to evaluate the performance of the developed iterative method for distributing tasks in a swarm of UAVs in a clustered target field. This article presents an iterative method for distributing tasks among agents of a swarm of unmanned aerial vehicles (UAVs) in a clustered target field, when the number of tasks significantly exceeds the number of agents. The main tasks solved by UAVs are surveillance and reconnaissance, detection of dangerous objects or places of emergency, search for victims, etc. The efficiency of solving the problems listed above is achieved by the simultaneous use of a group of UAVs, the elements (agents) of which can carry out the tasks of inspecting and scanning various areas in parallel. At the same time, the number of tasks can significantly exceed the number of UAV swarm agents. To organize the work of a swarm of UAVs in this case, it is necessary to solve the problem of labor division, considering the conditions of the problem. The results showed the high efficiency of the proposed task distribution method according to the criterion of minimizing the travel distance of agents.

Solution of Repeating Non-Terminating Problem in Division

Abstract: This article discusses the drawbacks of decimal theory in terms of repeating and non-terminating problems that may not give complete real results. This problem of decimal theory has persisted from its discovery to the present day. For this problem a theory has been developed in this research which proves to be better for repeating and never ending problem which is called L-Sign theory. The data which does not give hundred present absolute real result by decimal division method like 10/3, 5/11, 22/7[approximation of π(Pi)] and many more like these can be divided by this new L-Sign method to get absolute real result, the result obtained will be absolute real value of the given data. Mathematical operations can be easily performed with other numbers of the obtained results. Apart from this, the reality of these results has been checked by different methods.

Study on Composition Analysis and Identification of Ancient Glass Products

In this paper, an entropy-TOPSIS model is established to analyze and identify the composition of ancient glass products, which solves the relationship between the type, decoration, colour of glass and the surface weathering of glass cultural relics; The multivariate linear regression model is established, which solves the problem of statistical law of weathering chemical composition content on the surface of cultural relics samples. A random forest classification model based on an ant colony algorithm is established to solve the problem of determining the importance of chemical composition, and a K-means clustering model is established to solve the problem of sub-class division within the group; A grey correlation analysis model was established to solve the problem of the correlation between the chemical composition of the same type of glass.

A combination of FDM, EWM, and GRA to measure performance in higher vocational college: An empirical case from China

Given the problems of unclear division of evaluation factors, inadequate utilization of objective data and unreasonable distribution of weight in college performance measurement, this study extracts relevant indicators and quantitative data from the survey report of administrational institutions, and constructs a comprehensive performance measurement model based on the integration of fuzzy Delphi method (FDM), Entropy weight method (EWM), and grey relational analysis (GRA). The study seeks to identify differences in measurement analysis by comparing the weights, the performance and the rankings of the alternatives about higher vocational colleges in Zhejiang province. Finally, the results show the following: (1) by FDM, 33 indicators about colleges' performance are selected to form the evaluation system of the college’s performance, (2) the indicators' weights are obtained through EWM and GRA, and a nonparametric test shows that there is no significant difference between the two types of weights, (3) the grey relational degrees of the alternatives are obtained and ranked on the basis of comprehensive evaluation model. By nonparametric test, there is a significant difference between the two types of relational degrees. On the contrary, no significant difference is found in the ranking of relational degrees, (4) based on the analysis results, this study further compares the performance of alternatives in different forms. There are significant differences between the performance of public colleges and private colleges, while no significant differences are observed between the performance of vocational colleges in Hangzhou and non-Hangzhou. Given the reliability and validity of the model, the comprehensive measurement model provides a relatively objective reference for college governance and administrational institutions, and also becomes an effective tool of colleges' evaluation to assist and improve the management practice in educational institutions.

Cutting a Cake Fairly for Groups Revisited

Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a singleton. We also establish an analogous existence result for chore division, and show that the result does not hold for a mixed cake.

Искусственное разделение единого административного правонарушения лицензионных требований в сфере управления многоквартирными домами

The paper deals with the problem of qualification and artificial division of a single administrative offense related to the presence of a debt to the public utilities suppliers by a managing company amounting double average monthly accrual when implementing the entrepreneurial activities on the management of apartment buildings with a gross violation of license requirements. The paper reveals the elements of administrative offense provided by part 3 of Art. 14.1.3 of the Code of the Russian Federation on Administrative Offenses. The author pays the particular attention to the analysis of small, but critically important judicial practice. Often the positions of regional courts contradict the positions of the RF Supreme Court and the general principles of administrative law. A problem of artificial division of a single offense into several independent ones was identified, since the disposition of part 3 of Art. 14.1.3 of the Code of the Russian Federation on Administrative Offenses is formulated inaccurately. Failure to fulfill the obligation for timely mutual settlements with a resource supplying organization may be erroneously qualified as several offenses, depending on the number of suppliers to whom the debt arose, and depending on the period of occurrence of such debt. Such an approach to law enforcement is found among the prosecution and housing supervision authorities. This problem leads to the repeated application of administrative punishment, when a single offense is qualified as several. The study identified general regularities in the approaches of superior courts, starting from the cassation level. These regularities allow determining the more precise conditions for qualifying gross violations of license requirements in the sphere of housing and utilities infrastructure in accordance with part 3 of Article 14.1.3 of the Code of the Russian Federation on Administrative Offenses.

Kindergarten Curriculum Implementation in the Context of High-Quality Development

In the context of high-quality development in China, it is the trend of the times for preschool education to move towards high-quality development. High-quality development of curriculum is a prerequisite for high-quality development of preschool education. To improve the quality of kindergarten curriculum, the problem of extreme division between free play and direct instruction in the implementation of kindergarten curriculum in China must be solved. Therefore, this paper introduces a new concept of curriculum implementation—guided play, which can deeply integrate play and teaching and promote deep learning in young children's play. As the introduction of guided play in our curriculum implementation still faces challenges, recommendations are made from three perspectives: the state, kindergartens and teachers, in order to improve the problems of kindergarten curriculum implementation and enhance the quality of the curriculum.

A Quantitative Model of the Multisubject Quality Responsibility of Construction Projects Based on an IPSO

In order to solve the problem of the quantitative division of multisubject quality responsibility in construction project quality disputes, this article proposes a quantitative model of multisubject quality responsibility division in construction projects based on an improved particle swarm optimization (IPSO). First, this article proposes a set of classification guidelines for quality risk behaviors based on the theory of organizational behavior. Through these, the interconnections between different types of risk behaviors and quality defects were explored. Following this, this article explored potential laws among 84 practical judicial cases from China using the IPSO. The category coefficients of the three types of quality risk behaviors, namely, technical defects, management violations, and irregularities, were obtained in this analysis. This article also deduced the mathematical expression of the division of engineering quality responsibility using fuzzy mathematical theory and established a multisubject quality responsibility quantitative model. It was then simulated and applied in four practical judicial cases. The simulation results revealed that the multisubject quality responsibility quantitative model based on quality risk behavior has good applicability.

ФИНЛЯНДИЗАЦИЯ КАК КОНЦЕПЦИЯ НАУЧНОГО ИССЛЕДОВАНИЯ ВНЕШНЕЙ ПОЛИТИКИ И МЕЖДУНАРОДНЫХ ОТНОШЕНИЙ

The article is aimed at studying the main stages in the formation of the scientific concept of finlandization on the example of German studies of Anglo-American historiography, at determining its essential characteristics and the possibilities of using it in the modern research of foreign policy and international relations. The choice of the German case seems logical. The special role of the German issue in the system of Great Powers relations, its obvious dependence on the microclimate of the Soviet-American relations, the close proximity of West Germany to the borders of the socialist bloc, the painful problem of the German nation division – all this has significantly increased the risks of Soviet influence and theoretically turned the FRG into the most likely candidate for finlandization. Given the key importance of West Germany in the system of Euro-Atlantic security and economy, this prospect was perceived very painfully, the possible reorientation of the FRG was actively discussed in the academic circles in the USA and Great Britain. The formation of finlandization as a concept for the scientific study of foreign policy and international relations had basically been completed by the beginning of the 1990s. Today, it finds many followers and critics among scientists from different countries, which indicates its modern relevance.

Development of an information system for optimal division of training courses into modules

Currently, progress in world pedagogy is largely associated with the transition to a personality-oriented education, in which a student does not just master the amount of knowledge under the guidance of a teacher, but learns to independently extract and apply the knowledge gained in practice. At the same time, there is still an urgent problem of optimal division of educational material (courses) into modules and the output of information on the course or module. The solution to this problem is to create an information system that will allow the training course to be divided into modules of a given complexity, depending on the number of modules, the volume of material, and the number of terms. The purpose of this work is to increase the optimal grouping of sections of educational material into modules.

Socio-legal problems of division of jointly acquired property of spouses

To identify gaps in legislation when regulating the relations of spouses on the division of common property in court, as well as to formulate proposals for the modernization of legislation in the field of property relations of spouses. The following methods were used in the work: system, dialectical, comparative legal, analysis, and synthesis. Based on the identified gaps in the legislation, it is important to introduce the most expanded concept of "spouse's noteworthy interest" when departing from the equality of shares and the division of the common property of spouses. And we also suggest that the courts, when resolving such a category of cases, be guided not only by the fundamental principle of "equality of shares", but also apply the principle of "justice", which is most widely used in foreign countries with the Anglo-Saxon legal family. The study not only identified existing gaps in legislation but also conducted a comparative analysis with foreign regulation of the issue. It cannot be argued that family law is outdated. However, relations in society are subject to development, which should be considered by the legislator when reforming the regulatory framework. The article has a high value because it is an attempt to introduce recommendations on reforming family legislation in Russia based on comparison with foreign experience and will create the possibility of an individual approach to resolving cases in the sphere of property relations of spouses.

All sequential allotment rules are obviously strategy‐proof

For division problems with single‐peaked preferences, we show that all sequential allotment rules, a large subfamily of strategy‐proof and efficient rules, are also obviously strategy‐proof. Although obvious strategy‐proofness is, in general, more restrictive than strategy‐proofness, this is not the case in this setting.

『중용장구』 20장 해석에 대한 비교 고찰

Chapter 20 of Juongyongjanggu has been criticized not only for the problem of sentence division but also for the interpretation of the concepts contained in it. This paper compares and analyzes the interpretation of Ju-hee and Wang-buji related to the ‘three good ways’, ‘three knowledges, three practices’, and ‘three closer’ among the main concepts shown in Chapter 20. Ju-hee used the dual perspective of categorical interpretation and graded interpretation in connecting and interpreting the ‘three good ways’ and the ‘three knowledges, three practices’ according to a perspective on knowledge and practices. This causes the complexity of interpretation, which has become one of the important problems in the history of Juongyong interpretation. There are many people who raised questions about Ju-hee’s interpretation, but this paper examined Wang-buji’s opinion from a relatively perspective.
 In the interpretation of Chapter 20 of Jungyongjanggu, it is believed that the reason why Ju-hee interpreted it from two perspectives is to emphasize the character of knowledge and practice. On the other hand, Wang-buji rejects Ju-hee’s inter-pretation and provides his own interpretation by his ideological diagram that emphasizes the unity of knowledge and practice, and the priority of “practice” Although he accepts most of Ju-hee’s views in the interpretation of the Saseo, he is not following Ju-hee’s view in this matter.

Preservice Elementary Teachers Understanding of Fraction Multiplication and Division in Multiple Contexts

The present study examined preservice elementary teachers’ performance on the problems of multiplication and division of fractions and compared their performances and analyzed the misconceptions. An instrument including 11 fraction multiplication and division tasks was given and the task involved three contexts: making own story problem, computations, representing operation using visual model. The findings reported that among the three contexts, making a diagram was the most challenging task for both operations, and their division performance varied depending on the division problem types. The author suggests that specific emphasis with rich story problem with different whole(s) in fraction, carefully designed context with different types of division concept, and building fractional number sense can help both PSTs and students reduce misconceptions and enhance deeper understanding of fraction operations.

How Do University Students Get Relevant Information?

The web and learning have evolved parallel as technological changes have influenced teaching and learning processes. In this study, I intend to extend this parallel with two other dimensions, namely, human 1.0-3.0 and influencer 1.0-3.0. The concepts are closely related to how the online world became popular abroad and what their impact is on learning and education. Thus, the question, “what is the significance of social media, and of its latest, most popular actors, of the “work” of influencers (which can be interpreted as fake news) in the lives of students in higher education?”, is also a very pertinent issue to touch on. Its involvement in our lives is ever growing and very often influences our media literacy. This gives us even more reason to look into social media’s impact. However, our main goal is to find answers to the following questions:• What opportunities does the digital toolkit give to students? What kind of digital literacy do students think they need to thrive in the job market?• To what extent does the ICT literacy of pedagogical students differ from that of other students (lawyer, economics, doctor, technical)? What form of cognitive development is used for lifelong learning?• To what extent are students’ IT literacy influenced by cultural, material, and family capital?• How is information acquisition implemented in education? How conscious is the use of media among university students, and what is their critical attitude?• To what extent does online media penetrate the medium of formal-informal and non-formal learning? How does the influencer activity of professional opinion leaders help students to think critically and thoughtfully? The sample of the survey is made up of students from the University of Debrecen. From the results we can see, that university students behave differently in the online space, on social media platforms and on messengers than they would elsewhere, thus this affects how they get information. The current situation, the pandemic, clearly demonstrates that advanced digital competence is essential for a confident presence in the online space and advanced critical thinking. Problems of digital inequality and division have surfaced, and the constructed reality mediated by the media is becoming increasingly distorted. During this period, the relationship between the media and media consumers has changed greatly, and the interaction has intensified.

Envy-free division in the presence of a dragon

Following a novel approach, where the emphasis is on configuration spaces and equivariant topology, we prove several results addressing the envy-free division problem in the presence of an unpredictable (secretive, non-cooperative) player, called the dragon. There are two basic scenarios. (1) There are \(r-1\) players and a dragon. Once the “cake” is divided into r parts, the dragon makes his choice and grabs one of the pieces. After that, the players should be able to share the remaining pieces in an envy-free fashion. (2) There are \(r+1\) players who divide the cake into r pieces. A ferocious dragon comes and swallows one of the players. The players need to cut the cake in advance in such a way that no matter who is the unlucky player swallowed by the dragon, the remaining players can share the tiles in an envy-free manner. We emphasize that in both settings, some players may prefer to choose degenerate pieces of the cake. Moreover, the players construct in advance both a cut of the cake and a decision tree, allowing them to minimize the uncertainty of what pieces can be given to each of the players.

Recognition of Emotions in Speech Using Convolutional Neural Networks on Different Datasets

Artificial Neural Network (ANN) models, specifically Convolutional Neural Networks (CNN), were applied to extract emotions based on spectrograms and mel-spectrograms. This study uses spectrograms and mel-spectrograms to investigate which feature extraction method better represents emotions and how big the differences in efficiency are in this context. The conducted studies demonstrated that mel-spectrograms are a better-suited data type for training CNN-based speech emotion recognition (SER). The research experiments employed five popular datasets: Crowd-sourced Emotional Multimodal Actors Dataset (CREMA-D), Ryerson Audio-Visual Database of Emotional Speech and Song (RAVDESS), Surrey Audio-Visual Expressed Emotion (SAVEE), Toronto Emotional Speech Set (TESS), and The Interactive Emotional Dyadic Motion Capture (IEMOCAP). Six different classes of emotions were used: happiness, anger, sadness, fear, disgust, and neutral. However, some experiments were prepared to recognize just four emotions due to the characteristics of the IEMOCAP dataset. A comparison of classification efficiency on different datasets and an attempt to develop a universal model trained using all datasets were also performed. This approach brought an accuracy of 55.89% when recognizing four emotions. The most accurate model for six emotion recognition was trained and achieved 57.42% accuracy on a combination of four datasets (CREMA-D, RAVDESS, SAVEE, TESS). What is more, another study was developed that demonstrated that improper data division for training and test sets significantly influences the test accuracy of CNNs. Therefore, the problem of inappropriate data division between the training and test sets, which affected the results of studies known from the literature, was addressed extensively. The performed experiments employed the popular ResNet18 architecture to demonstrate the reliability of the research results and to show that these problems are not unique to the custom CNN architecture proposed in experiments. Subsequently, the label correctness of the CREMA-D dataset was studied through the employment of a prepared questionnaire.

A Study on the Implementation processes and Problems of Reverse Area Division to Form a Compact City

A Study on the Implementation processes and Problems of Reverse Area Division to Form a Compact City