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Devices for water consumption measurement provide data from periodical readings in a non-simultaneous and cumulative manner. This may result in inaccuracies within the process of inference about the short-term habitual patterns of water supply network users. Maintaining systems at the interface between periodic and continuous processes requires the continuous improvement of research methodology. To obtain reliable results regarding the variability of water consumption, the first step should be to estimate it for each observation day by periodic averaging and a possible water balancing approach, but the analysis of the value of estimators obtained in this way usually does not allow for studying autocorrelation. However, other methods indicate the existence of multiplicative parameters characterizing short- and long-term variations in water demand. The purpose of this study is to create a new and deterministic method for tackling the problem associated with a lack of short-term detailed data with fuzzy time series using a multiplicative model for water consumption. Satisfactory results have been obtained, demonstrating that the dispersed data, received in a cumulative manner for random periods of measurement, can be analyzed by the methodology of proposed statistical inference. The observed variability in water consumption may be used in the planning and modernization of water supply systems, development of water demand patterns, hydraulic models, and in the creation of forecasting models of water consumption.
Jacek Wawrzosek; Syzmon Ignaciuk; Justyna Stańczyk; Joanna Kajewska-Szkudlarek. Water Consumption Variability Based on Cumulative Data From Non-simultaneous and Long-term Measurements. Water Resources Management 2021, 1 -14.
AMA StyleJacek Wawrzosek, Syzmon Ignaciuk, Justyna Stańczyk, Joanna Kajewska-Szkudlarek. Water Consumption Variability Based on Cumulative Data From Non-simultaneous and Long-term Measurements. Water Resources Management. 2021; ():1-14.
Chicago/Turabian StyleJacek Wawrzosek; Syzmon Ignaciuk; Justyna Stańczyk; Joanna Kajewska-Szkudlarek. 2021. "Water Consumption Variability Based on Cumulative Data From Non-simultaneous and Long-term Measurements." Water Resources Management , no. : 1-14.
The European Standard ISO 16122-2:2015 requires that the coefficient of variation for sprayed liquid fall should not exceed 10%. Field sprayers generate a stream of liquid sprayed at an angle that depends on the design of the nozzles. Among field boom sprayers, previous methods for selecting the shape of the opening of a single-slotted spray nozzle have been based on the following rectangular, triangular, normal, beta, and truncated normal distributions; distribution obtained from a nozzle with a stream in the form of an empty cone; and glued square functions. These methods, however, have provided a limited range of uniformity. Consequently, the initial assumption that the monotonicity of the function corresponds to the shape of a quarter of the symmetrical oval nozzle opening allows for a full computerized optimization of nozzle shape with a spray angle of α = 110° (or α = 120°). In this case, the spray uniformity parameter is controlled and freely declines almost to zero. In this study, based on the nonlinear shape obtained, we developed the shape of the nozzle outlet opening with a coefficient of variation of 0.388% using spline linear functions. Further applications of the symmetry of the developed model would allow for multiple modifications of the shape of this opening, and therefore, without changing the spray uniformity parameter, nozzles with slightly different characteristics could be obtained.
Jacek Wawrzosek; Stanisław Parafiniuk. Optimization of the Opening Shape in Slot Spray Nozzles in a Field Boom Sprayer. Sustainability 2021, 13, 3291 .
AMA StyleJacek Wawrzosek, Stanisław Parafiniuk. Optimization of the Opening Shape in Slot Spray Nozzles in a Field Boom Sprayer. Sustainability. 2021; 13 (6):3291.
Chicago/Turabian StyleJacek Wawrzosek; Stanisław Parafiniuk. 2021. "Optimization of the Opening Shape in Slot Spray Nozzles in a Field Boom Sprayer." Sustainability 13, no. 6: 3291.
Jacek Wawrzosek; Szymon Ignaciuk; Andrzej Bochniak. Selected problems of ambiguity of the dual price of water in the post-optimization analysis of the water supply system. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2019, 21, 329 -340.
AMA StyleJacek Wawrzosek, Szymon Ignaciuk, Andrzej Bochniak. Selected problems of ambiguity of the dual price of water in the post-optimization analysis of the water supply system. Eksploatacja i Niezawodnosc - Maintenance and Reliability. 2019; 21 (2):329-340.
Chicago/Turabian StyleJacek Wawrzosek; Szymon Ignaciuk; Andrzej Bochniak. 2019. "Selected problems of ambiguity of the dual price of water in the post-optimization analysis of the water supply system." Eksploatacja i Niezawodnosc - Maintenance and Reliability 21, no. 2: 329-340.
A case study of the tools used by an analyst of the economic aspects of the operation of the water supply network has been undertaken in this paper. All issues discussed here are formulated by using degenerated linear programming models ( PL ). Below, it is noted that the linear dependence of binding constraints ( CO ) distorts standard postoptimization procedures in PL. This observed fact makes postoptimization analysis mostly unhelpful for an average analyst due to problems with the int erpretation of ambiguous sensitivity reports which are obtained from popular computer packages. In standard postoptimization methods, changes to single parameters of the right-hand vector CO are analyzed or referred to parametric linear programming that unfortunately requires prior knowledge of mathematically and economically justified vectors of changes of right-hand sides CO. Therefore, it is suggested that modifications are introduced to some of the postoptimization procedures in this work. For issues in the field of hydrology, the following were presented: interpretation and methods of generating justified vectors of changes of right-hand sides of limiting conditions. And so, the procedure of generating infinitely many solutions of the dual issue based on certain vectors orthogonal to the vector of right-hand sides of constraint conditions was demonstrated. Furthermore, the same orthogonal vectors were used to obtain nodal solutions of the dua0l model and the corresponding vectors of changes of the entire right-hand sides of the constraint conditions. Then, managerial interpretation was applied to this way of proceeding. The methods presented in the work serve to improve the functioning of the system of water supply.
Jacek Wawrzosek; Szymon Ignaciuk. Postoptimization of the model of water supply for urban and industrial agglomeration. ITM Web of Conferences 2018, 23, 00035 .
AMA StyleJacek Wawrzosek, Szymon Ignaciuk. Postoptimization of the model of water supply for urban and industrial agglomeration. ITM Web of Conferences. 2018; 23 ():00035.
Chicago/Turabian StyleJacek Wawrzosek; Szymon Ignaciuk. 2018. "Postoptimization of the model of water supply for urban and industrial agglomeration." ITM Web of Conferences 23, no. : 00035.
Andrzej Kornacki; Jacek Wawrzosek; Andrzej Bochniak; Andrzej Szymanek; Halina Pawlak. Critical values of driver response time and its impact on reducing reliability and safety in road traffic. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2016, 19, 142 -148.
AMA StyleAndrzej Kornacki, Jacek Wawrzosek, Andrzej Bochniak, Andrzej Szymanek, Halina Pawlak. Critical values of driver response time and its impact on reducing reliability and safety in road traffic. Eksploatacja i Niezawodnosc - Maintenance and Reliability. 2016; 19 (1):142-148.
Chicago/Turabian StyleAndrzej Kornacki; Jacek Wawrzosek; Andrzej Bochniak; Andrzej Szymanek; Halina Pawlak. 2016. "Critical values of driver response time and its impact on reducing reliability and safety in road traffic." Eksploatacja i Niezawodnosc - Maintenance and Reliability 19, no. 1: 142-148.
Artykuł Wykorzystanie programu AutoCAD w projektowaniu wyrobów ceramiki artystycznej | Mechanik Miesięcznik Naukowo-Techniczny
Zbigniew Krzysiak; Grzegorz Bartnik; Waldemar Samociuk; Janusz Zarajczyk; Jacek Wawrzosek; Marek Szmigielski; Jarosław Tatarczak; Józef Kowalczuk; Leszek Krzywonos. Application of AutoCAD software for ceramic pottery design. Mechanik 2015, 147/48 .
AMA StyleZbigniew Krzysiak, Grzegorz Bartnik, Waldemar Samociuk, Janusz Zarajczyk, Jacek Wawrzosek, Marek Szmigielski, Jarosław Tatarczak, Józef Kowalczuk, Leszek Krzywonos. Application of AutoCAD software for ceramic pottery design. Mechanik. 2015; (2):147/48.
Chicago/Turabian StyleZbigniew Krzysiak; Grzegorz Bartnik; Waldemar Samociuk; Janusz Zarajczyk; Jacek Wawrzosek; Marek Szmigielski; Jarosław Tatarczak; Józef Kowalczuk; Leszek Krzywonos. 2015. "Application of AutoCAD software for ceramic pottery design." Mechanik , no. 2: 147/48.
In the multivariate linear normal model, definitions and interpretations are presented for many various following types: In the multivariate linear normal with the restrictive condition O s (or without this condition), the definition of testability of the any null hypothesis and estimability of parametric function C l are given. Also, equivalent conditions and necessary conditions for testability and estimability in this model are presented. The results of this work are a generalization of the results achieved by Seely (1977 Seely , J. ( 1977 ). Estimability and linear hypothese . Amer. Statistican 31 ( 3 ): 121 – 123 .[Taylor & Francis Online] [Google Scholar]), Seely and Birkes (1980 Seely , J. , Birkes , D. ( 1980 ). Estimability in partitioned linear models . Ann. Statist. 8 : 399 – 406 . [Google Scholar]), Baksalary and Kala (1976a Baksalary , J. K. , Kala , R. (1976a). Criteria for estimability in multivariate linear models. Math. Operationsforsch. Statist. 7:5–9. [Google Scholar]), Wawrzosek (1996 Wawrzosek , J. ( 1996 ). The testability in the generalized multivariate linear model with restrictions for parameters . . Mierki, ART Publishers Olsztyn, pp. 106–115 (in Polish). [Google Scholar]), and Wawrzosek and Wesołowska-Janczarek (1998 Wawrzosek , J. , Wesołowska-Janczarek , M. ( 1998 ). Testability conditions in a growth curve model with restrictions . PBS Biometr. Colloq. 28 : 179 – 191 . [Google Scholar]).
Jacek Wawrzosek; Mirosława Wesołowska-Janczarek. Testability and Estimability in Multivariate Linear Normal Model with Various Restrictions. Communications in Statistics - Theory and Methods 2009, 38, 828 -841.
AMA StyleJacek Wawrzosek, Mirosława Wesołowska-Janczarek. Testability and Estimability in Multivariate Linear Normal Model with Various Restrictions. Communications in Statistics - Theory and Methods. 2009; 38 (6):828-841.
Chicago/Turabian StyleJacek Wawrzosek; Mirosława Wesołowska-Janczarek. 2009. "Testability and Estimability in Multivariate Linear Normal Model with Various Restrictions." Communications in Statistics - Theory and Methods 38, no. 6: 828-841.
The problem of estimating parameters in the case of missing values up today was connected with the standard linear models with covariance matrix ?2I (cf. DODGE, 1984) where ?2 is an unknown scalar and I-the unit matrix. In this paper the results of the standard model are generalized for the linear GAUSS-MARKOFF (GM) model and ZYSKIND-MABTIN model (particular case of GM) with missing values and with covariance matrix ?2Vt where V≧0. R. A. FISHEB (I960) and many authors used improper standard models because the covariance matrix introduced by tiiero. corresponded to the covariance matrix witli lull observations but not, as it should be, to the complete model in which the estimator of missing values is substituted in the place of missing observations, In this paper the model with the oroper covariance matrix is considered in the case of the GM model and also in the case of ZYSKIND-MARTIN model (cf. def. 4.1). The invariance of some matrix expressions is proved (cf. lemma 2.4). In the general GATJSS-MABKOFF model the estimator y1 of the vector of missing values y1 is obtained (cf. 3.3) in th. 3.1), This is the generalization of OKTABA and JAGIELLO result (1973, 1982). By using the symmetric c-inverse matrix T* the analogue estimator y1 is given (th. 3.2, formula (3.28)). Two models are considered: 1) with actual observations and 2) with substitution vector y1 in missing vector y1. If 1) is ZYSKIND-MABTIN (1969) model then 2) is the same one (th. 4.1). The quadratic forms (4.13) and (4.14) in models 1) and 2) are identical (generalization of R. A. FISHEB'S (1960) rule) and the solutions ? of the normal equations in 1) and 2) ZYSKIND-MABTIN models are identical. This paper is a preliminary report
Wiktor Oktaba; Andrzej Kornacki; Jacek Wawrzosek. Estimation of missing values in the general gauss-maekoff model. Statistics 1986, 17, 167 -177.
AMA StyleWiktor Oktaba, Andrzej Kornacki, Jacek Wawrzosek. Estimation of missing values in the general gauss-maekoff model. Statistics. 1986; 17 (2):167-177.
Chicago/Turabian StyleWiktor Oktaba; Andrzej Kornacki; Jacek Wawrzosek. 1986. "Estimation of missing values in the general gauss-maekoff model." Statistics 17, no. 2: 167-177.
Several theorems on estimation and verification of linear hypotheses in some Zyskind‐Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ2V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ2V, where σ2 is unknown scalar parameter, V is a known non‐negative definite matrix such that R(X) ⊂ R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind‐Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector yy1y2 involves a vector y1 of m missing values and a vector y2 with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind‐Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ2I) to ZM model. Estimation of vector y1 (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ2 (cf. th. 3.4) in actual ZMa model and in diagonal quasi‐ZM model (ZMqd) are presented. Relation between y̌ 1 and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.
W. Oktaba; A. Kornacki; J. Wawrzosek. Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values. Biometrical Journal 1985, 27, 733 -740.
AMA StyleW. Oktaba, A. Kornacki, J. Wawrzosek. Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values. Biometrical Journal. 1985; 27 (7):733-740.
Chicago/Turabian StyleW. Oktaba; A. Kornacki; J. Wawrzosek. 1985. "Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values." Biometrical Journal 27, no. 7: 733-740.