Universal equations for Pythagorean and Sauter-type formulas of mean value calculation and classification of the Extended Pythagorean Means

• Autorzy: Drzymała J.

Identyfikatory

DOI

10.5277/msc172416

• Języki publikacji: EN

Abstrakty

EN

A general equation, combining the Pythagorean and Sauter-type formulas, which can be used for calculation of a mean of a set of values is given and discussed in the paper. A classification of means, forming the Extended Pythagorean Means family, including power (arithmetic, geometric, quadratic, cubic, etc.), inverted power (harmonic, inverted quadratic, inverted cubic, etc.), and Sauter-type (volumesurface, volume-length, etc.) is presented. The calculated means, depending on their type, are different. Formulas for calculating mean values for a set of values treated individually, in groups and as a fraction (weighted mean) are also given.

Słowa kluczowe

EN

average value; mean size; mean diameter; weighted mean

• Wydawca: Wydział Geoinżynierii, Górnictwa i Geologii, Instytut Górnictwa Politechniki Wrocławskiej
• Czasopismo: Mining Science
• Rocznik: 2017
• Tom: Vol. 24
• Strony: 227--235
• Opis fizyczny: Bibliogr. 13 poz., tab.

Twórcy

autor

Drzymała J.

• Wroclaw University of Science and Technology, Laboratory of Mineral Processing, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw

Bibliografia

• ACZEL J., DHOMBRES J.G., 1989, Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences, Encyclopedia of Mathematics and its Applications, 31, Cambridge
• ANONIMUS, 2017, Generalized f-mean, Project Gutenberg Self-Publishing eBooks, World Heritage, self.gutenberg.org/articles/generalized_f-mean
• BULLEN P.S., 1990, Averages still on the move, Mathematics Magazine, 63 (4), 250–255.
• BULLEN S., 2003, Handbook of means and their inequalities, Second Edition, Kluwer Academic Publishers, Dordrecht, Mathematics and its Applications, Vol. 560.
• KOLMOGOROV A., 1930, On the notion of mean. In: Mathematics and Mechanics, Kluwer, 1991, 144–146.
• KOWALCZUK P.B., DRZYMALA J., 2016, Physical meaning of the Sauter mean diameter of spherical particulate matter, Part. Sci. Technol., 34(6), 645–647.
• NEUMANN E., PALES A.S., 2003, On comparison of Stolarsky and Gini means, J. Math. Anal. Appl. 278, 274–284.
• PACEK A.W., MAN C.C., NIENOW A.W., 1998, On the Sauter mean diameter and size distribution in turbulent liquid/liquid dispersion in a stirred vessel, Chemical Eng. Sci., 53, 2005–2011.
• SAUTER J., 1926, Die Grössenbestimmung der im Gemischnebel von Verbrennungskraft-maschinen Vorhandenen Brennstoffteilchen, Forschungsarbeiten auf dem Gebiete des Ingenieurwesens, Hefte 279, 1–34, VDI-Verlag, GMBH, Berlin SW19.
• SOKOLOWSKI M., 1995, Energia rozdrabniania, IMBiGS, Warszawa.
• SOKOLOWSKI M., 1996, Energy consumed in comminution. A new of a general law of comminution. New test stands and testing results, Réc. progrés en génie des procédés, 10, Ed. Tec & Doc, Lavoisier, Paris.
• STOLARSKY K.B., 1996, Hölder means, Lehmer means, and x-1 log cosh x, J. Math. Anal. Appl., 202, 810–818.
• WIKIPEDIA, 2017, Mean, https://en.wikipedia.org/wiki/Mean