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1
Content available The model of temporary temperature field during multi-pass arc weld surfacing. Pt. 1, Analitycal description
Winczek J., Rygał G., Skrzypczak T.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 2
123--130
EN
This work presents a model of a temperature field in a steel element during multi-pass Gas Metal Arc Weld surfacing taking into account heat of the melted electrode material. An analytical solution for a half-infinite body model is obtained by aggregating temperature increments caused by applying liquid metal and heat radiation of a moving electrode. The assumptions are Gaussian distributed heat sources of applied melted electrode material and of an electric arc.
2
Content available The model of a temporary temperature field during multi-pass arc weld surfacing. Pt. 2, Example of computations
Winczek J., Rygał G., Skrzypczak T.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 3
141--148
EN
In this work computations of a temperature field are carried out during multipass Gas Metal Arc Weld surfacing of a cuboidal steel element taking into account heat of the melted electrode material. The results are presented in the form of temporary and maximum temperature distribution in the element’s cross-section and thermal cycles at selected points.
3
Content available Modelling of a temporary temperature field during arc weld surfacing of steel elements taking into account heat of the weld
Winczek J., Rygał G.
Journal of Applied Mathematics and Computational Mechanics
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2015
|
Vol. 14, nr 1
111-120
EN
In this work, a model of a temperature field in a steel element during a singlepass arc weld surfacing is presented. Analytical solution for half-infinite body model is obtained by aggregating temperature increments caused by applying liquid metal and heat radiation of a moving electrode. The assumptions are Gaussian distributed heat sources of applied metal and the weld and of an electric arc heat source. Computations of the temperature field were carried out during arc weld surfacing of cuboidal steel element. The results are presented as temporary and maximum temperature distribution in the element’s crosssection and thermal cycles at selected points. The accuracy of the solution is verified comparing a calculated fusion line to that obtained experimentally.
4
Content available Didactic remarks on the power set
Rygał G., Bryll A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
331--334
EN
The paper is devoted to correct understanding of the notation for the power set. Often this notation is mistaken with a power of the number 2. The correct definition of the power set is presented as well as several task which an serve for strengthening the understanding of this notion.
5
Content available Arithmetic sequences of higher degrees characterizing figurate numbers
Rygał G., Bryll A., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
335--344
EN
Figurate numbers have simple geometric illustration: polygonal numbers can be represented by polygons, pyramidal numbers by pyramids, prismatic numbers by prisms, and trapezoidal numbers by trapezoids. The numbers mentioned above can be defined by formulae 1 or can be characterized by some arithmetic sequences of higher degrees which allow to obtain the corresponding formulae [3]. Figurate numbers due to their geometrical illustration and interesting properties can be of interest for school pupils.
6
Content available remote Uwagi o przeszkodach semantycznych i syntaktycznych
Jędrzejewski J., Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2008
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Vol. 13
127-140
EN
In this paper we discuss several obstacles which, in our opinion, can cause pupils' problems in understanding both of mathematical texts and of mathematics. These obstacles are of a epistemological nature as well as of essential and semantic nature. All the examples of incorrect formulations are taken from Polish school and academic text-books. The goal of this article is to call the attention of authors which write mathematical texts to these problems in an attempt to avoid such mistakes.
7
Content available remote Construction of trigonometry using the scalar product
Bryll G., Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2008
|
Vol. 13
114-126
EN
At school, trigonometry is constructed traditionally starting from the definition of trigonometric functions in right triangle and generalizing those definitions for arbitrary angles in rectangular coordinates without using vector tools. The method of construction of trigonometry using the scalar product was presented in the article [1] published in 1961 in Gottingen. This work is difficult of access. We intend to popularize this method, because it is general, brief and clear.
8
Content available remote Development of pupil's mathematical thinking
Rygał G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 2
71-76
EN
In this paper three types of exercises which develop mathematical reasoning and allow intuitive understanding of mathematical problems are presented. These exercises can be used during the lessons of mathematics.
9
Content available remote The use of finite expansion of functions for evaluation of limits
Bryll A., Bryll G., Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
143-154
10
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
375-380
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
11
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
375-380
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
12
Content available remote About Various Methods of Calculating the Sum [formula]
Bryll G., Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2006
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Vol. 11
7--16
EN
Pupils of secondary school as well as students often have problems with calculating the sums of the mth powers of successive natural numbers. In this paper we present certain methods of finding such sums.
13
Content available remote Remarks about the Replacement of School Induction Definitions by Normal Definitions
Bryll G., Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2003
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Vol. 9
123--129
EN
Pupils and teachers often ask themselves a question: can induction definitions be replaced in an equivalent way by normal definitions? In this paper we present a method of replacement of induction definitions by normal definitions illustrating the given theorems by a few examples. From the viewpoint of the set theory operations and relations can be treated as certain sets. We discuss a method of replacement of an induction definition of the given set by a normal definition of this set. An induction definition of a set A has in general the following form (compare with [2]): D1. A set A is the least one from among the sets X satisfying the conditions: W1 (X) : a1,...,an ∈ X (the starting conditions), W 2 (X) : x1,...,xn ∈ X ⤇f (x1,...,xn) ∈ X (the induction conduction).
14
Content available remote Using a Graphic Calculator in Teaching and Learning Mathematics
Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2000/2001
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Vol. 8
159--160
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