Wyniki wyszukiwania - BazTech

1

Is the Galilean law of free fall an a priori truth?

Bigaj Tomasz

Postępy Fizyki

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2022

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T. 73, z. 1

21--23

PL

W niniejszym artykule omawiam znany argument a priori Galileusza przeciwko Arystotelesowskiemu prawu spadku swobodnego, przedstawiając go w uwspółcześnionej matematycznej postaci. Pokazuję, że argument ten nie dowodzi, iż tempo spadku swobodnego jest stałe dla wszystkich ciał, chyba że założymy, że jest ono funkcją jednego addytywnego parametru. Jednakże jest całkowicie możliwe, że tempo spadku będzie dane w postaci stosunku dwóch addytywnych parametrów. W takim wypadku argument upada.

EN

In this short note I discuss Galileo’s well-known a priori argument against Aristotle’s law of free fall, presented In a modern mathematical version. I show that the argument does not prove that the rate of fall should be constant for All bodies, unless we presuppose that the rate of fall is a function of one additive parameter. However, it is perfectly possibile that the rate of fall will be given in the form of the ratio of two additive parameters, in which case the argument does not go through.

2

Note on the stability of the system of functional equations

Adam M.

Silesian Journal of Pure and Applied Mathematics

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2017

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Vol. 7, iss. 1

93--98

EN

We deal with the system of functional equations connected with additive and quadratic mappings. We correct some mistakes made in the paper [W. Fechner, On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774–786] and provide accurate statements of those results. Moreover, we get the improvement of the Hyers-Ulam stability result of the considered system of functional equations.

3

Properties of the intersection ideal M ∩ N revisited

Weiss T.

Bulletin of the Polish Academy of Sciences. Mathematics

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2017

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Vol. 65, no. 2

107--111

EN

We investigate various properties of the intersection ideal M∩N of subsets of the reals that are related to the translations of its members. We are also concerned with cardinal coefficients associated with the ideal M∩N.

4

Brownian dynamics for calculation of the single fiber deposition efficiency of submicron particles

Sztuk E., Przekop R., Gradoń L.

Chemical and Process Engineering

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2012

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Vol. 33, nr 2

279-290

EN

The motion of submicron particles involves the deterministic terms resulting from the aerodynamic convection and/or electrostatic attraction, and the stochastic term from the thermal displacement of particles. The Langevin equation describes such behavior. The Brownian dynamics algorithm was used for integration of the Langevin equation for the calculation of the single fiber deposition efficiency. Additionally the deterministic and stochastic of the particle motion were derived, using the Lagrangian and Eulerian approaches of particle movement and balance, for the calculation of the single fiber deposition efficiency due to both mechanisms separately. Combination of the obtained results allows us for calculation of the coupling effect of inertia and interception with the Brownian diffusion in a form of correlation. The results of calculation show that the omitting of the coupling effect of particular mechanism and using the simple additive rule for determination of the single fiber deposition efficiency introduces significant error, especially for particles with diameter below 300 nm.

5

Modes, modals, and barycentric algebras: a brief survey and an additivity theorem

Smith J. D. H.

Demonstratio Mathematica

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2011

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Vol. 44, nr 3

571-587

EN

Modes are idempotent and entropic algebras.Modals are both join semi lattices and modes,where the mode structure distributes over the join.Barycentric algebras are equipped with binary operations from the open unit interval,satisfying idempo tence,skew commutativity,and skew associativity.The article aims to give a brief survey of these structures and some of their applications.Special attention is devoted to hierar chical statistical mechanics and the modeling of complex systems.An additivity theorem for the entropy of independent combinations of systems is proved.

6

Wzrost kultury mikroorganizmów w warunkach inhibicji

Grabowski J., Węgrzyn G., Kotlarska E., Kwaterska M.

Inżynieria i Aparatura Chemiczna

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2009

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Nr 3

46-48

PL

Badano wpływ azydku sodu, alkoholu etylowego i ich mieszanin na wzrost bakterii Vibrio harveyi (szczep B39)). Uzyskane wyniki inhibicji wzrostu wykorzystano do wykreślania krzywych: dawka / koncentracja - efekt toksyczny"=. W celu uzyskania informacji o charakterze ww. mieszaniny (addytywność, synergizm, antagonizm) wykorzystano teorię Grabowskiego toksyczności mieszaniny chemikaliów.

EN

The effect of toxic chemicals (sodium azide, ethanol and their mixtures) on the growth of bacteria Vibrio harveyi (strain B392) have been studied. Experimental toxicity data were then analysed with the use of Grabowski's theory on toxicity of chemical mixtures.

7

Topologia w metrologii na przykładzie warunku addytywności

Olejnik R.

Zeszyty Naukowe. Elektryka / Politechnika Śląska

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2005

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z. 195

187-196

PL

Addytywność to podstawowa własność funkcji miary, określanej według skali ilorazowej. Jej sens wyrażamy werbalnie następująco: miara sumy jest równa sumie miar. Własność ta w odniesieniu do funkcji skali jest definiowana na bazie sumy fizycznej, określonej na zbiorze przejawów (zwanych inaczej stanami) w postaci sumy fizycznej. Analogicznie, w odniesieniu do funkcji miary addytywność jest tworzona na bazie połączenia przedmiotów, czyli konkatenacji. Różne są sposoby określenia relacji połączenia, stosowanego choćby w geometrii. Często proponowane koncepcje nie dająjednoznaczności wyniku działań, przez co funkcja skalowania i funkcja miary tracą swój atrybut bycia funkcją, gdyż są niejednoznaczne. W artykule, pragnę przeprowadzić analizę nadania jednoznaczności obydwu funkcjom przez nową koncepcję sumy fizycznej. Na jej bazie definiujemy dwie odmiany addytywności: skończoną addytywność i słabą addytywność. Godny poddania dyskusji jest fakt zastosowania tych pojęć w rachunkowości, finansach i zarządzaniu.

EN

Additivity is the basie property of measure function, described according to quotient range. Its sense is verbally expressed in a following way: the measure ofsum equals to the sums of measures. This property with reference to scale function is defined on basis of physical sum, described on the symptoms set (in other words called states in the form of physical sum. Similarly, with reference to measure function, additivity is created on basis of subjects joint that is concatendency. There are different ways of describing relation's connection, applied even in geometry. Suggested conceptions often don't give unambiguous operations score, because of this fact calibrating and measure function lose their attribute of being function, because they are ambiguous. In the article I would like to carry out analysis of giving unambiguous form to both functions, through a new conception of the physical sum. On its basis are formed two additivity rypes: limited additivity and weak additivity. Worth discussing is fact of these concepts' application in accountancy, finance and management.

8

Fischer-Muszély additivity on Abelian groups

Ger R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2004

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Vol. 44, nr spec.

83-96

EN

A description of a general solution f : X -> Y mapping a commutative group (X, +) into a real normed linear space (Y, || o ||) of the functional equation [formula] is given in terms of isometrics and additive mappings. Several results describing the solutions of this equation that were obtained earlier under some alternative assumptions regarding the domains, ranges and//or by imposing some regularity upon the map f become special cases of our main result. To gain a proper proof tool we have also established an improvement of E. Berz's [4] representation theorem for sublinear functionals on Abelian groups.