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1
EN
China’s manufacturing industry faces the dual imperatives of supporting economic growth while reducing emissions to achieve national carbon neutrality targets. This study analyses the potential for decarbonisation across manufacturing sub-sectors. Using factor analysis and fuzzy comprehensive evaluation, it assesses industries based on foundational advantages, growth prospects, and sustainability. The results rank sub-sectors and identify promising areas like eco-friendly equipment and agricultural processing. However, carbon-intensive industries require urgent transformation. To optimise China’s industrial structure for low-carbon development, coordinated efforts across policy, industry, and enterprise are needed. Supportive regulations, industrial integration, and technology adoption can incentivise green manufacturing. By strategically promoting circular economy models, China can enhance quality and efficiency, convert waste into value, and contribute to global climate action. This study provides insights into aligning manufacturing growth with carbon neutrality in the new economic era.
EN
Performance appraisal in human resource management is a function that evaluates employees’ knowledge, skills, and abilities in executing their job. To assess this appraisal, the employees’ key performance index (KPI) can be used. Recently, office politics has been indicated as an activity that may ruin employee-employer relationships and turn the office ecosystem unharmonious. The influence of organizational politics must be avoided during the performance appraisal process. This work depicted practical knowledge and theoretical gaps of the previous studies. Among them are leniency, straightness and stereotype behavior errors. This research was conducted to assess dimensions of organizational politics as one more error in the employee’s performance appraisal. The presented study considered a questionnaire directed to 274 officers and clerical staffs who were selected randomly through proportionate stratified sampling method in one of the Malaysian government financial sectors located in Kuala Lumpur, Malaysia. In total 271 questionnaires were returned and used in this study. This work employed Questionnaire of Political Considerations in Performance Appraisal by using robust statistical techniques for testing and validating the results. This study has successfully extracted three reliable dimensions of politics in performance appraisal, namely acquiring benefit, human relations, and control. In addition, this work developed a new conceptual model together with a dynamic and practical recommendation for top management in this field used to avoid the extant error factors.
EN
One of major challenge in a sustainable growth, which organizations face is a slow adoption of the digital transformation. This research work presents the reasons that lead to the slow digitization process in medical device SMEs in southern Germany. In addition, by developing the conceptual model, this work highlights the effect of these improper implementations on SME's business performances and financial situation. The researchers applied correlational research design methodology, with simple random sampling techniques along with empirical and statistical study with primary data collection. The main study variables are SME’s financial situation, SMEs organizational performance, and medical digitization rules. The study demonstrated the negative impact of delayed digital mechanisms in terms of businesses and financial performances.The extra transparency restrictions that add burdens for SMEs, and the lack of training for the employees, which in overall add more difficulties for adopting innovation and digital transformation are other factors negatively affecting the studied process.
EN
Rapid urbanization has resulted in a slew of issues, including urban transportation, in most emerging countries' cities. Public transportation provides transportation for the community and plays an important role in the daily lives of the city's citizens, particularly the urban poor, by reducing travel costs and providing job opportunities. Thus, evaluating public bus service performance from the perspective of users is critical for identifying service operators' strengths and deficiencies. Consequently, the primary goal of this research is to determine the level of consumer satisfaction with public bus service in the city and identify the most important factors that influence satisfaction. Hence, a survey was carried out between December and January 2020. Stratified sampling approaches were used to obtain data from 500 travelers. Factor analysis and customer satisfaction index were used to analyze the data collected. Lastly, the findings show that users were quietly satisfied (0.54) with the quality of the bus services supplied in the city. Moreover, travelers were better satisfied with attributes that related to availability (0.64) and less satisfied with attributes under timeliness (0.50) and security (0.48). Therefore, service operators and other concerned stakeholders should give urgent attention to attributes under timeliness and security to enhance users’ satisfaction in the provision of bus service in the city.
EN
The results of this investigation show that Azerbaijan industries and agricultural sector provide considerable anthropogenic impact on the environment of Caucasus. The use of moss biomonitoring technique and neutron activation analysis (NAA) is a first attempt to study heavy metal atmospheric deposition in Azerbaijan, a country different relief and climate. The study was undertaken in the summer of 2015 of atmospheric deposition of man-made heavy metal pollutants in the area of mining and processing plant in Gadabay and Dashkasan mininig district. At the same time samples were collected from the Goygol State Reserve in the Lesser Caucasus not far from the city of Ganja. A total 85 moss samples (predominantly Pleurozium schreberi) collected in both environmentally contrast area. Elemental determination was carried out by epithermal neutron activation analysis (ENAA) at the reactor IBR-2 of Joint Institute for Nuclear Research (FLNP JINR). For the first time 44 elemental concentrations were determined (Na, Mg, Al, Si, Cl, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Br, Rb, Sr, Mo, Ag, Cd, In, Sb, I, Cs, Ba, La, Ce, Nd, Sm, Eu, Tb, Tm, Yb, Hf, Ta, W, Au, Th, U). Multivariate statistical analysis of the analytical results obtained will make it possible to identify the main sources of pollution and to assess the role of long-range transport of pollutants.
6
Content available remote Expert evaluation of road infrastructure management
EN
A dense and modern road network determines the proper functioning of trade-in economically developed countries. The aim of this article is to assess the influence of individual road infrastructure components on their performance in terms of traffic flow. To obtain a complete and comprehensive description of the problem, a mixed method of quantitative data analysis was used based on available statistical databases including information on linear and nodal infrastructure operating in the European Union. In light of the problem under consideration, a multi-stage statistical analysis was conducted. Factor analysis and multiple linear regression were used to assess the heterogeneity of the data and estimate the parameters of the models to explain the various components of road infrastructure performance. In turn, based on the k-means classification analysis, groups of EU countries differing in road network performance were identified. The results indicated that the extracted road network factors contribute to improving the performance of road infrastructure in its various study areas.
PL
Gęsta i nowoczesna sieć drogowa warunkuje właściwe funkcjonowanie wymiany handlowej w krajach rozwiniętych gospodarczo. Celem pracy jest ocena wpływu poszczególnych składników infrastruktury drogowej na jej wydajność w aspekcie płynności ruchu przewozowego. Na potrzeby osiągnięcia kompletnego oraz kompleksowego opisu zagadnienia, w artykule zastosowano metodę mieszaną analizy danych ilościowych pozyskanych w oparciu o dostępne bazy statystyczne obejmujące informacje o infrastrukturze liniowej i punktowej funkcjonującej na terenie Unii Europejskiej. W świetle rozważanego problemu przeprowadzono wieloetapową analizę statystyczną. Do oceny heterogeniczności danych i do oszacowania parametrów modeli wyjaśniania poszczególnych składowych wydajności infrastruktury drogowej zastosowano analizę czynnikową oraz wielowymiarowej regresji liniowej. Z kolei w oparciu o przeprowadzoną analizę klasyfikacji metodą k-średnich zidentyfikowano grupy krajów unijnych różniące się wydajnością sieci drogowej. Wyniki wskazały, że wyodrębnione czynniki sieci drogowej przyczyniają się do poprawy wydajności infrastruktury drogowej w jej poszczególnych badanych obszarach.
EN
The paper regards a specific class of optimization criteria that possess features of probability. Therefore,constructing objective functionof optimization problem,the importance is attached to probability indices that show the probability of some criterial event or events to occur. Factor analysis has been taken for the main method of constructing objective function. Algorithm for constructing objective function of optimization is donefor criterion of minimization risk level in multimodaltransportations that demanded demonstration data. The application of factor analysis in classical problem solution was shown to givethe problem a more distinct analytical interpretation in solving it.
PL
Artykuł dotyczy szczególnej klasy kryteriów optymalizacyjnych, które posiadają cechy prawdopodobieństwa. W związku z tym, przy konstruowaniu funkcji celu problemu optymalizacyjnego pierwszorzędne znaczenie mają wskaźniki prawdopodobieństwa wystąpienia określonego zdarzenia lub zbioru zdarzeń. Jako główną metodę konstruowania takiej funkcji celu wybrano analizę czynnikową. Algorytm konstrukcji funkcji celu optymalizacji wykonano dla kryterium minimalizacji poziomu ryzyka w przewozach multimodalnych –w tym celu wykorzystano dane demonstracyjne. Wykazano, że zastosowanie analizy czynnikowej w klasycznym sformułowaniu problemu badawczego pozwala nadać mu bardziej wyrazistą interpretację analityczną w jego rozwiązywaniu.
EN
The paper regards a common transport problem with a non-classic optimization criterion to minimize transportation risks. It demonstrates that the risk parameters of the function could be found through the factor analysis method. Besides, considering that the problem contains several points of sending and delivering loads, the method is dealt with as a matrix. The research also regards the algorithm of matrix factor analysis application for determining parameters of the objective function for the problem to be solved. The survey results in a new method to construct the objective function for the optimization problem with probability parameters. It generally assists in suggesting a formal solution to such problems, foremost due to particular software.
PL
Artykuł dotyczy powszechnego problemu transportowego z nieklasycznym kryterium optymalizacji w celu zminimalizowania ryzyka transportowego. Wykazano, że parametry ryzyka takiej funkcji można wyznaczyć metodą analizy czynnikowej. Dodatkowo, ze względu na występowanie w zgłoszeniu problemu kilku punktów wysyłki i dostawy towarów, metoda ta jest prezentowana w postaci matrycy. W wyniku przepr owadzonych badań uzyskano nową metodę konstruowania funkcji celu dla postawionego problemu optymalizacji, której parametry mają charakter probabilistyczny. Pozwala to na ogólne sformalizowanie procesu rozwiązywania tego typu problemów – przede wszystkim przy pomocy specjalistycznego oprogramowania.
EN
Factor analysis is a standard statistical technique for reducing data dimensionality, which is widely used in sociology, psychology, and demography. Also, financial and insurance institutions commonly use such a technique for marketing research. In recent years, factor analysis has been used, at the beginning rather diffidently, to analyse selected problems of business management, e.g. to troubleshoot consumer and company communication. There are some literature reports about the successful use of factor analysis in managing a company area. Nevertheless, the literature seems to lack examples with successful use of the method with a clear explanation of its rather difficult application in the field of competitiveness or potential company boost. The modest popularity of such a powerful technique in this particular field seems to be attributed mainly to the complexity of the method and its requirements concerning the data quantity. Besides, the factor analysis technique has great potential and can be used as an efficient tool to reduce the complexity of observed phenomenon or verify the accuracy of theoretical models. Therefore, the purpose of this paper is to present a vast potential of factor analysis (both exploratory and confirmatory) applied to solve various problems in company management, especially related to competitiveness and market success. Two case studies covering the subject of business management are presented to illustrate the benefits of factor analysis application. The exploratory factor analysis is exemplified by the search of factors related to the commercial success of the company, while the confirmatory technique is illustrated by a case study of the intellectual capital of the company and its factors related to competitiveness. The paper also presents the essence of the factor analysis, types of analysis, subsequent procedures, purposes, and its specific features. Finally, the applicability of the factor analysis to solve management issues and possible gain in management are discussed.
EN
Universities play central roles in the creation of knowledge economy and the fourth industrial revolution (Industry 4.0). They build critical human capital, generate new knowledge and strive to promote innovation through academic entrepreneurship. Despite the potential benefits of academic entrepreneurship (AE), the argument that AE fuels or impedes faculties’ commitment to traditional activities in both developed and developing countries is still open. Therefore, this paper empirically examines the influence of academic entrepreneurship on teaching and publishing potential of faculties with a view to suggesting appropriate policy guide for promoting innovations and enhancing traditional activities among the academia in Nigeria. Data for this paper were collected from 229 faculty members within science and technology-related fields in 13 selected universities across Nigeria, through a cross-sectional survey design approach. Data collected were analysed using factor and regression analyses. The results showed that participation of faculty members in start-up formation and industry collaboration (SUFIC) (β =2.8, p˂0.05) and faculty externship (FE) (β =2.3, p˂0.1) have statistically significant and positive effects on the potential for publishing among the faculty members. Faculty externship (FE) also shows a positive and significant relationship to the teaching performance of faculty members. However, university-related entrepreneurial engagements (UREE) show a negative and significant relationship to both publication and teaching performance, suggesting caution when selections are made regarding such activities by the university administrators. The study concludes with managerial implications for the university managers and policymakers.
PL
Uniwersytety odgrywają kluczową rolę w tworzeniu gospodarki opartej na wiedzy i czwartej rewolucji przemysłowej (Przemysł 4.0). Budują krytyczny kapitał ludzki, generują nową wiedzę i dążą do promowania innowacji poprzez przedsiębiorczość akademicką. Pomimo potencjalnych korzyści płynących z przedsiębiorczości akademickiej (AE), argument, że AE napędza lub utrudnia zaangażowanie wydziałów w tradycyjne działania zarówno w krajach rozwiniętych, jak i rozwijających się, pozostaje otwarty. Dlatego niniejszy artykuł empirycznie bada wpływ przedsiębiorczości akademickiej na potencjał dydaktyczny i publikacyjny wydziałów w celu zaproponowania odpowiedniego przewodnika politycznego dotyczącego promowania innowacji i wzmacniania tradycyjnych działań wśród środowisk akademickich w Nigerii. Dane do tego artykułu zostały zebrane od 229 wykładowców z dziedzin związanych z nauką i technologią na 13 wybranych uniwersytetach w Nigerii, poprzez podejście do projektowania badań przekrojowych. Zebrane dane analizowano za pomocą analiz czynnikowych i regresji. Wyniki pokazały, że udział pracowników wydziału w tworzeniu nowych przedsiębiorstw i współpracy branżowej (SUFIC) (β = 2,8, p˂0,05) oraz wydziałowych praktykach (FE) (β = 2,3, p˂0,1) ma statystycznie istotny i pozytywny wpływ na potencjał publikacyjny wśród pracowników wydziału. Staż wydziałowy (FE) również wykazuje pozytywny i znaczący związek z wynikami dydaktycznymi członków wydziału. Jednak związane z uniwersytetami zaangażowanie w przedsiębiorczość (UREE) wykazuje negatywny i znaczący związek zarówno z publikacjami, jak i wynikami nauczania, co sugeruje ostrożność przy dokonywaniu wyborów dotyczących takich działań przez administratorów uczelni. Badanie kończy się implikacjami menedżerskimi dla kierowników uniwersytetów i decydentów.
EN
The separation of coal material of three types of coals originating from three various Polish hard coal mines (types 31, 34.2 and 35, according to Polish nomenclature, which were steam coal, semi-coking coal and coking coal) into particle size fractions and then into particle density fractions was done and then the following parameters were measured for each particle size-density fraction: combustion heat, ash contents, sulfur contents, volatile parts contents, analytic moisture. In this way a 7-dimensional vector of data was created. Using methods of factor analysis the important features of coal were selected, which decide about their membership to individual types. To evaluate the appropriateness of the applied method the Bartlett’s sphericity test as well coefficient of Kaiser-Mayer-Olkin (KMO) were used. To select important factors the Kaiser criterion and Cattell’s scree test were used. The obtained results were compared with the results obtained in previous works by means of observation tunnels method. The results showed which particular features are crucial to define the type of coal what is also important to select appropriate method of its enrichment. Furthermore, the construction of a mathematical model presenting the relations between these properties and particle size and density is presented. Because of the fact that particles of certain size or density may occur in neighboring fractions three sorts of relations were examined basing on regression analysis.The analysis was conducted for all three coal types. Because of the fact that the models contain various amounts of independent variables R2 coefficient, mean squared error (MSE) and Mallow’s statistics Cp were applied to evaluate and compare obtained results.
PL
Wykonano rozdział trzech typów węgla o różnych charakterystykach, pochodzących z trzech różnych kopalni węgla kamiennego w Polsce (typy 31, 34.2 oraz 35, według Polskich norm, którymi były węgiel energetycznym, pół-koksujący oraz koksujący) na klasy ziarnowe a następnie na frakcje gęstościowe. Dla każdej otrzymanej w ten sposób frakcji wielkościowo-gęstościowej zmierzono następujące parametry: ciepło spalania, zawartość popiołu, zawartość siarki, zawartość części lotnych, wilgotność analityczna. W ten sposób otrzymano siedmiowymiarowy wektor danych. Za pomocą analizy czynnikowej wybrano istotne cechy węgla, które decydują o jego przynależności do określonego typu węgla. Aby ocenić prawidłowość zastosowanej metody wykorzystano test sferyczności Bartletta oraz współczynnik Kaisera-Mayera-Olkina (KMO). Otrzymane wyniki porównano z wynikami otrzymanymi w poprzednich pracach, które uzyskano metodą tuneli obserwacyjnych. Wyniki pokazały, które cechy węgla są niezbędne do określenia typu węgla, co wpływa na dobór odpowiedniej metody jego wzbogacania. Ponadto, zaprezentowano model prezentujący relacje pomiędzy tymi cechami a wielkością i gęstością ziaren. Ponieważ ziarna określonej wielkości lub gęstości mogą występować w sąsiednich klasach lub frakcjach, wykonano trzy typy modeli, bazując na analizie regresji. Analiza została wykonana dla trzech typów węgli. Ponieważ modele zawierają różne ilości zmiennych niezależnych do oceny i porównania otrzymanych wyników zastosowano współczynnik determinacji R2, błąd średniokwadratowy (MSE) oraz statystykę Mallowa Cp.
EN
The selection of the formwork system for high rise building affects the entire construction project duration and cost. The study reports the factors influencing the selection of different formwork system in the construction of high rise buildings through structural questionnaire survey from the client, contractor, consultant, and interviews with expert members. Total of 40 technical factors was identified from the literature and 220 filled questionnaires were received from the respondent. Relative Importance Index method is used to find the topmost factors affecting the selection of formwork system. Additionally, from factor analysis 22 factors were identified to have a correlation with one another. Regression analysis reveals that duration of the project, maintenance cost, adaptability, and safety have impact on formwork selection across time, cost and quality. These findings could potentially increase the construction company’s existing knowledge in relation to formwork selection.
EN
There is no set of constructs or measurement tools in the subject literature that would be widely accepted. In this paper three dimensions of the organisation’s environment namely dynamism, hostility, and complexity, were reviewed. These dimensions are common to most environment research but, especially on the native background, only a few researchers have attempted to synthesize these dimensions in the one research approach. The aim of the paper is synthesis of three dimensions of the organisation’s environment and an empirical verification of whether the existing business practice dimensions of the organisation’s environment correspond to the dimensions laid down and proposed on the theoretical level. In the paper, three dimensions of the organisation’s environment - dynamism, hostility, and complexity were characterised, a research tool developed for measuring them was presented. The approach uses data from a sample of fifty-three new technology-based firms in Poland. Factor analysis was used to explore the viability of these environmental dimensions. The results of the conducted research indicate that the organisation’s environment is a multidimensional construct and could be described by dynamism, hostility and complexity.
EN
The most important factor in small and medium-sized enterprises is undoubtedly the training; intellectual capital directly impacts the growth and productivity of the organization, so the preparation given to employees is vital. The study carried out a factorial analysis to identify the components to be considered in the training of the SMEs in the industrial sector of Ciudad Obregon, Sonora, México. The considered variables were: training, legal aspects of training, training budget, training course instructors, training culture and seniority in the company. As a result, the analysis of communalities allows us to observe that of these variables, the one that produces the lowest percentage of the variance is the age of the company, so it could be dispensed as a component of the training.
EN
The aim of this study was to analyse the factors affecting agricultural water management in Iran based on irrigation experts' point of view using factor analysis approach. The results indicated that conservation of modern irrigation equipment, promoting farmers’ knowledge, creating a watercourse (surface water collection), imposing a ban on digging new wells and educating the effectiveness of pressurized irrigation system were all known as the most important factors affecting agricultural water management. Moreover, factor analysis results showed that five factors influencing agricultural water management (institutional and legislative, educational and promotional, economic, technical and farming system) explained 64.29% of the total variance. At the end, some policy suggestions were provided in order to improve agricultural water management in Iran.
PL
Celem badań była analiza czynników wpływających na gospodarkę wodną w rolnictwie w oparciu o poglądy ekspertów, z wykorzystaniem metody analizy czynnikowej. Wyniki wskazują, że zachowanie nowoczesnych urządzeń irygacyjnych, promocja wiedzy rolniczej, tworzenie cieków (gromadzenie wód powierzchniowych), wprowadzenie zakazu wiercenia nowych studni i edukacja w zakresie wydajności ciśnieniowych systemów irygacyjnych, to znane i najważniejsze czynniki wpływające na gospodarkę wodną. Ponadto, analiza czynnikowa wykazała, że pięć czynników wpływających na gospodarkę wodną w rolnictwie (systemy instytucjonalne i prawne, edukacja i promocja, system ekonomiczny i techniczny oraz gospodarka rolna) wyjaśniały 64,29% całkowitej zmienności. W podsumowaniu sformułowano kilka sugestii co do polityki wodnej w celu usprawnienia gospodarki wodnej w rolnictwie w Iranie.
EN
Purpose: The current study aimed to quantify the main influences and the interactions (joint effects) of gender, leg and type of target on the biomechanics of front kick quality. Through the quantification, we tried to identify the relevant factors related to the kick accuracy and maximum velocity for coaching practice. Methods: A ten-camera NIR VICON MX40 motion capture system (250 Hz) was used to determine the kicking foot maximum velocity from two well-trained subject groups (8 males and 6 females). Each subject performed both left and right front kicks in a lateral standing position into the air (without a physical target), to a board, to a table tennis ball and to a training shield. The target were set on a height corresponding to a height of solar plexus of each participant. Results: The results showed that all the three factors (gender, leg and type of target) have significant influences on kicking speed ( p < 0.001) and significant interaction (joint effect) was only found between gender and target ( p < 0.001). Further analysis revealed that the males’ kicking maximum velocity was affected more by board, while females’ one was affected by the size of the target. Conclusions: The results would seem to suggest that, for males, kick-to-a-board may be the more effective method for increasing kick quality, compared to other type of target. For females, kick-to-a-small-ball appears to be effective method for increasing kick maximum velocity.
17
Content available Zdolność sieciowa. Konstrukt i jego wymiary
PL
W artykule podjęto próbę uchwycenia istoty zdolności sieciowej organizacji oraz jej składników i wymiarów. Celem artykułu jest empiryczne sprawdzenie, czy istniejące w praktyce gospodarczej wymiary zdolności sieciowej pokrywają się z wymiarami przedstawionymi i zaproponowanymi w warstwie teoretycznej. Wyniki przeprowadzonych badań wskazują na istnienie czterech wymiarów zdolności sieciowej: koordynacja, zdolność relacyjna, wiedza o partnerach oraz komunikacja wewnętrzna.
EN
The paper attempts to capture the essence of the network capability of the organizations and its constituents and dimensions. The aim of the paper is an empirical verification of whether the existing business practice dimensions of the network capability correspond to the dimensions laid down and proposed in the theoretical level. Results of this study indicate the existence of four dimensions of network capability: coordination, relational ability, knowledge of partners and internal communication.
PL
Celem artykułu jest empiryczne sprawdzenie, czy istniejące w praktyce gospodarczej wymiary orientacji przedsiębiorczej pokrywają się z wymiarami przedstawionymi i zaproponowanymi w warstwie teoretycznej. Wyniki przeprowadzonych badań wskazują na istnienie pięciu wymiarów orientacji przedsiębiorczej: autonomii, innowacyjności, proaktywności, podejmowania ryzyka i konkurencyjnej agresywności.
EN
The aim of the paper is empirical verification of whether the existing business practice of entrepreneurial orientation dimensions correspond to the dimensions laid down and proposed theoretical layer. Findings indicate the existence of five dimensions of entrepreneurial orientation: autonomy, innovation, proactive, risk-taking and competitive aggressiveness.
EN
The Ścinawka River catchment is located in the middle part of the Sudetes, in the Polish-Czech border area. This multiaquifer system, forming a fissured-porous medium for groundwater, is mostly drained through its hypergenic zone. The most common hydrochemical types are Ca-Mg-HCO3 and Ca-HCO3, some addition of sulphates may occur. No substantial depth-related differences in the concentrations of most of the analyzed ions have been found. The multi-aquifer system is relatively homogenous with respect to groundwater chemistry, which indicates occurrence of strong hydraulic contacts between the individual aquifers. The observed increased concentrations of some ions (U, Th, Li) may be an effect of groundwater intrusions from the deeper parts of the multi-aquifer system. Chemical composition of the groundwater is locally modified by ion exchange processes.
20
Content available remote On graduation of enrolment size in a multi-echelon educational system
EN
This paper focuses on an educational system wherein demotion and double promotion are not allowed. The total enrolment in such a system is modelled as a linear model within the context of factor analysis. The goal is to represent the total enrolment in terms of latent factors which generate the flows in the system. The notion of the matrix spectrum and the spectral radius are used to benchmark the specific variances and to approximate the factor loading vector, respectively. Two main theorems are propounded alongside with their proofs. A numerical illustration is given.
PL
Artykuł koncentruje się na systemie edukacyjnym, w którym nie jest możliwe powtarzanie i podwójna promocja są niedozwolone. Całkowita liczba uczestników w takim systemie może być badana w ramach modelu liniowego z zastosowaniem analizy czynnikowej. Celem jest przedstawienie całkowitej liczby rekrutowanych w zależności od ukrytych czynników, które generują przepływy w systemie. Pojęcie spektrum macierzy i promienia spektralnego są używane dla porównania wariancji i do przybliżenia odpowiednio wektora wag czynników. Sformułowano dwa twierdzenia wraz z dowodami. Podano numeryczną ilustrację.
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