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EN
Every human needs the ability to solve problems. In early childhood education, the development of this skill can and should be implemented by solving text tasks. Meanwhile, according to a variety of analyses, a significant number of students are unable to solve these tasks. This is most likely the result of insufficient mathematical competencies of teachers in early school education and related teaching errors, mainly involving calculating exercises and solving tasks according to patterns. At the same time, students who are in fact unable to solve tasks but only limit themselves to the use of learned patterns, in non-standard task situations (not practiced at school) do quite well.
EN
Coping with pain plays a very important role in human life and it may differ depending on the personality characteristics of patients such as their level of optimism. The aim of this study was therefore to determine whether the coping strategies for to cervical spine pain amongof office workers were determined by gender, the locus of pain control orand an optimistic attributional style. 30 office workers (Females = 15, Males = 15) took part in the experiment. The age of the participants was for females (M and for =43; SD=5.,9) and for males (M=44.,9; SD=4.,9. The subjects were asked to fill out 4 questionnaires: (CSQ), (BPCQ), (ASQ), a 10-grade visual analogue scale (VAS) and an original questionnaire. The study revealed that most of the office workers declare the ability to copeing with pain. Women were significantly more focused on emotions as a pain coping strategy than were the males participants. It was also shown that the internal locus of pain control significantly correlates with coping focused on problem solving. Participants characterized by anwith optimistic attributableional style used task oriented strategies more often than did the pessimists. There were no significant differences in the level of perceived pain between optimists and pessimists. It was foundind that there are statistically significant differences in coping with pain coping according to gender. Women were significantly more focused on emotions as a pain coping strategy than were the males participants. A high level of optimism may have a significant impact on the reduction of emotion - oriented strategies such as catastrophising by switching on more beneficial strategies to cope with pain by the individual. There are no significant differences in the level of perceived pain between pessimists and optimists.
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Content available remote Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge
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EN
Discrete tomography deals with the reconstruction of discrete sets with given projections relative to a limited number of directions, modeling the situation where a material is studied through x-rays and we desire to reconstruct an image representing the scanned object. In many cases it would be interesting to consider the projections to be related to more than one distinguishable type of cell, called atoms or colors, as in the case of a scan involving materials of different densities, as a bone and a muscle. Unfortunately the general n-color problem with n > 1 is NP-complete, but in this paper we show how several polynomial reconstruction algorithms can be defined by assuming some prior knowledge on the set to be rebuilt. In detail, we study the cases where the union of the colors form a set without switches, a convex polyomino or a convex 8-connected set. We describe some efficient reconstruction algorithms and in a case we give a sufficient condition for uniqueness.
PL
RESEARCH OBJECTIVE: The article attempts to explain the benefits that may result from the use of case studies developed by students as a teaching method applied in entrepreneurial pedagogy. THE RESEARCH PROBLEM AND METHODS: The main research problem concerns the effectiveness of using case studies created by students as a teaching method in entrepreneurial pedagogy. The article provides an overview of selected literature and presents the authors’ experience in applying student-developed case studies. THE PROCESS OF ARGUMENTATION: In the first part of the article, the most important entrepreneurial skills and competences are discussed. Subsequently, the importance of using activating methods is presented, with particular emphasis on the case study. In the second part, the use of the case study developed by students was analyzed and evaluated. Finally, the conclusions and recommendations are presented. RESEARCH RESULTS: The literature analysis indicates the importance of methods that foster students’ active involvement, including case studies, in entrepreneurial pedagogy. The analysis of case studies developed by students showed their strong commitment to the assignment. Students had to gain knowledge of the operation of enterprises and the processes that take place in them.In addition, the task required students to be familiar with methods and tools that support creative thinking and problem-solving skills. CONCLUSIONS, INNOVATIONS, AND RECOMMENDATIONS: Based on the analysis of literature and student-developed case studies, it seems that the discussed method is an effective teaching method that increases students’ commitment to the assignment and supports the development of entrepreneurial attitudes and skills. Furthermore, this method provides a range of benefits that give the teacher great freedom in choosing the issues and scope of case studies created by students.
EN
RESEARCH OBJECTIVE: The article attempts to explain the benefits that may result from the use of case studies developed by students as a teaching method applied in entrepreneurial pedagogy. THE RESEARCH PROBLEM AND METHODS: The main research problem concerns the effectiveness of using case studies created by students as a teaching method in entrepreneurial pedagogy. The article provides an overview of selected literature and presents the authors’ experience in applying student-developed case studies. THE PROCESS OF ARGUMENTATION: In the first part of the article, the most important entrepreneurial skills and competences are discussed. Subsequently, the importance of using activating methods is presented, with particular emphasis on the case study. In the second part, the use of the case study developed by students was analyzed and evaluated. Finally, the conclusions and recommendations are presented. RESEARCH RESULTS: The literature analysis indicates the importance of methods that foster students’ active involvement, including case studies, in entrepreneurial pedagogy. The analysis of case studies developed by students showed their strong commitment to the assignment. Students had to gain knowledge of the operation of enterprises and the processes that take place in them. In addition, the task required students to be familiar with methods and tools that support creative thinking and problem-solving skills. CONCLUSIONS, INNOVATIONS, AND RECOMMENDATIONS: Based on the analysis of literature and student-developed case studies, it seems that the discussed method is an effective teaching method that increases students’ commitment to the assignment and supports the development of entrepreneurial attitudes and skills. Furthermore, this method provides a range of benefits that give the teacher great freedom in choosing the issues and scope of case studies created by students. The results of the analysis permit concluding that student-developed case studies can be commonly used and allow developing a wide range of students entrepreneurial skills.  
PL
The paper presents the comments relating to the role of tasks in theprocess of teaching and learning of mathematics in the context of educationof students studying to become teachers. In the considerations part, referencewas made to the fragments of undergraduate and postgraduate works, madeat seminars of didactics of mathematics.
EN
Complaints management process is very important from the point of view of each company, particularly production companies. Claims both internal and external generate costs, which the companies must face. To identify properly the source of the problems formation all sorts of methods and tools of quality management can be used. This will indicate in an unambiguous manner the cause of the problem and help to take corrective and preventive actions in effective way.
PL
Proces rozwiązywania problemów reklamacyjnych jest bardzo istotny z punktu widzenia każdego przedsiębiorstwa, a w szczególności przedsiębiorstwa o charakterze produkcyjnym. Reklamacje zarówno wewnętrzne, jak i zewnętrzne generują koszty, z którymi przedsiębiorstwo musi się zmierzyć. Aby prawidłowo zidentyfikować źródło powstawania problemów można posłużyć się różnego rodzaju metodami oraz narzędziami zarządzania jakością, które w jednoznaczny sposób pozwolą wskazać przyczyny problemu oraz podjąć skuteczne działania korygujące i zapobiegawcze.
PL
Identyfikacja i analiza zależności przyczynowo-skutkowych jest ważną częścią opisu sytuacji problemowej. Podstawowymi trudnościami występującymi w modelowaniu takich zależności są liczność i złożoność zjawisk, jakie należy uwzględnić oraz ograniczona przewidywalność zamierzonych wyników. W artykule przedstawiono ogólny model struktury zależności przyczynowo-skutkowych oraz sposoby dekompozycji i upraszczania złożoności w celu utworzenia modeli formalnych, mających zastosowanie w komputerowych symulacjach badawczych.
EN
Identifying and analyzing cause-and-effect relationships is an important part of the problem description. The basic difficulties involved in modeling such dependencies are the multiplicity and complexity of the phenomena to be taken into account and the limited predictability of the intended results. The article presents the general model of causal relationship structure and the ways of decomposition and simplification of complexity in order to create formal models applied in computer simulation tests.
EN
This study was aimed to identify the relationship between problem solving skills, metacognitive awareness, and mathematics achievement as well as to identify the role of metacognitive awareness as a mediator. This study involved a total of 333 Form Four students from ten secondary schools in Malaysia. Data were collected using questionnaires, while information about mathematics achievement was provided by the school management. Data were analyzed using the Structural Equation Modeling (SEM) technique. Results indicated that all variables correlated significantly with each other, while path analysis revealed the mediation effect of metacognitive awareness between problem solving skills and mathematics achievement. The findings suggest the importance of problem solving skills in influencing secondary school students’ mathematics achievement through the development of metacognitive awareness.
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Content available remote The Quotient Space Theory of Problem Solving
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EN
The paper introduces a framework of quotient space theory of problem solving. In the theory, a problem (or problem space) is represented as a triplet, including the universe, its structure and attributes. The problem spaces with different grain sizes can be represented by a set of quotient spaces. Given a problem, the construction of its quotient spaces is discussed. Based on the model, the computational complexity of hierarchical problem solving and the information combination are also dealt with. The model can also be extended to the fuzzy granular world.
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Content available remote Problem-Solving Skills of High School Students Exercising Regularly in Sport Teams
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EN
In this article, the effect of regular sport activities on the problem-solving approaches performed by high school students when they encountered said problem was analyzed. Six hundred male high school students participated in the study (Mage=15.45 years, age range: 14-17 years). The Problem-Solving Inventory (PSI) was used to evaluate students’ problem-solving solutions. Student-athletes were selected from the students who took charge in school teams, exercised for 6 days a week, provided that this exercise did not exceed 1 h 30 min, and who also participated in competitions. Mann-Whitney U test, which is nonparametrictest, was used to examine two samples (athlete, & non-athlete) and Kruskal-Wallis one-way analysis was used to make intergroup (branches of sport) examinations. According to the findings that were obtained, a significant difference was found among selfconfident approach values of athlete and non-athlete students (U=45.0, p=0.008). A significant difference was observed among assessor approach values of athlete and non-athlete students (U=46.2, p=0.033). The students who did sports regularly were more self-confident than those who did not do sports regularly and were of the same age when they encountered a problem, and student-athletes evaluated the phase of solving the problem and results that they obtained more carefully than those who did not do sport regularly and were of the same age. Student-athletes believed that they would solve the problem that they encountered. Further, student athletes preferred using a systematic method while solving a problem and making a decision more often than those who were not athletes and were of the same age.
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EN
The volumes of reactions in solution are usually ignored in problem solving. Neglection of reaction volumes may lead to errors on the order of 1 % in the final result. Calculation of the volume of neutralization reaction based on the specific densities of solutions from chemical tables is demonstrated.
EN
This paper underlines the need for unification of knowledge that illuminates the phenomena and processes in different worlds as is also exemplified by one of the missions of Systems Science. Many of the important problems faced by humanity today are very complex and do not have solutions in the isolated islands of knowledge. As the complexity of these problems is accentuated by their stretching across several diverse disciplines, even teams with deep expertise in the respective fields find the problems quite challenging. The imminent need is to focus on Transdisciplinarity- discovering hidden connections between and establishing a common platform for people from diverse disciplines for a holistic understanding of the problem at hand. Despite the challenges in the task of linking diverse fields there are examples in human history which raise hope as they have clearly benefited our understanding and enriched our civilization. The author discusses two such examples from human history: (1) Philosophy-Mathematics (-Genetics) (2) Various Branches of Physical Sciences. The author then points to the need for further Unity of Knowledge especially between Natural and Social Sciences to enable us to handle complex current problems. The author pins his hope for success in efforts in this direction despite the challenges because of his belief that all branches of knowledge are siblings since they all evolved from a common source- the human intellect. Therefore, there must be some kind of "Genetic Connections" between all of them. It is the responsibility of the human mind itself to unify all its diverse children, each grown to great depths of specialization in isolation, into an "integrated family of knowledge members".
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Content available remote Monitoring Changes in Dynamic Multiset Systems
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EN
Models of biological systems expressed as multiset rewriting systems can be very complex, impeding the analysis of their behaviour. In this paper we propose a practical solution to this problem, in the form of change monitors, i.e. computational instruments which synchronise with the model and record its behaviour. Change monitors play the role of passive observers. Since change monitors can automatically identify specific behaviours generated by the model under investigation, it is sufficient to focus only on the output produced by the monitors (instead of examining the dynamics of the initial model).
14
Content available remote Antimatter as a Frontier of Tractability in Membrane Computing
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EN
It is well known that the polynomial complexity class of recognizer P systems with active membranes without polarizations, without dissolution and with division for elementary and nonelementary membranes is exactly the complexity class P (see [9], Theorem 2). In this paper, we prove that if such a P systems model is endowed with antimatter and annihilation rules, then NP problems can be solved, even without non-elementary membrane division. In this way, antimatter is shown to be a frontier of tractability in Membrane Computing.
15
Content available remote Iterating Transducers
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EN
We discuss simple functional transductions defined by invertible Mealy automata under iteration and in particular the question when the orbit relation defined by iteration is rational. We identify a class of these automata that has relatively complicated orbits, yet some of them are still orbit rational and discuss a number of decision problems associated with these devices.
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Content available remote Twelve Years of QBF Evaluations : QSAT Is PSPACE-Hard and It Shows
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EN
Twelve years have elapsed since the first Quantified Boolean Formulas (QBFs) evaluation was held as an event linked to SAT conferences. During this period, researchers have striven to propose new algorithms and tools to solve challenging formulas, with evaluations periodically trying to assess the current state of the art. In this paper, we present an experimental account of solvers and formulas with the aim to understand the progress in the QBF arena across these years. Unlike typical evaluations, the analysis is not confined to the snapshot of submitted solvers and formulas, but rather we consider several tools that were proposed over the last decade, and we run them on different formulas from previous QBF evaluations. The main contributions of our analysis, which are also the messages we would like to pass along to the research community, are: (i) many formulas that turned out to be difficult to solve in past evaluations, remain still challenging after twelve years, (ii) there is no single solver which can significantly outperform all the others, unless specific categories of formulas are considered, and (iii) effectiveness of preprocessing depends both on the coupled solver and the structure of the formula.
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Content available remote The Structure of Elementary Strategies for Gene Assembly in Ciliates
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EN
We consider in this paper the assembly of micronuclear genes in stichotrichous ciliates to their macronuclear form. We represent the micronuclear genes and all their intermediate forms from micro- to macro- as signed permutations, where integer i stands for the i-th MDS of the macronuclear gene and i stands for the inverted form of that MDS; the macronuclear assembled gene is represented as the sorted permutation 1 2 : : : n, while its micronuclear form is an arbitrary signed permutation. We focus on the elementary gene assembly model consisting of two operations on signed permutations: eh (elementary hairpin inverting) and ed (elementary double recombination); gene assembly is modeled in this framework as a permutation sorting process. The general problem we investigate is to give a characterization of all signed permutations that can be sorted by the elementary operations. We make progress towards a full solution for this problem by relating sequences of eh and ed operations applicable to a given permutation to paths in the dependency graph associated to that permutation.
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Content available remote A Function Elimination Method for Checking Satisfiability of Arithmetical Logics
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EN
We study function elimination for Arithmetical Logics. We propose a method allowing substitution of functions occurring in a given formula with functions with less arity. We prove the correctness of the method and we use it to show the decidability of the satisfiability problem for two classes of formulas allowing linear and polynomial terms.
20
Content available remote Verification of Scenarios in Petri Nets Using Compact Tokenflows
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EN
In this paper we tackle the problem of verifying whether a scenario is executable in a Petri net. In contrast to sequentially ordered runs, a scenario includes both information about dependencies and independencies of events. Consequently, a scenario allows a precise and intuitive specification of a run of a concurrent or distributed system. In this paper we consider Petri nets with arc weights, namely marked place/transition-nets (p/t-nets) and p/t-nets with inhibitor arcs (pti-nets). A scenario of a p/t-net is a labelled partial order (lpo). A scenario of a pti-net is a labelled stratified order structure (lso). Accordingly, the question is either whether a given lpo is in the language of a given p/t-net or whether an lso is in the language of a given pti-net. Different approaches exist to define the partial language of a Petri net. Each definition yields a different verification algorithm, but existing algorithms perform quite poorly in terms of runtime for most examples. We introduce a new compact characterization of the partial language of a Petri net. This characterization is optimized with respect to the verification problem. The paper is a revised and extended version of the conference paper [10].
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