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1
Content available remote Pewien sposób badania rozwiązalności równań z parametrem
100%
Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
tom Vol. 7
84--96
2
Content available remote About definition of a periodic function
63%
Rygał G. , Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom 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.
3
Content available remote On mistakes connected with differentiating
63%
Sochacki R. , Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom Vol. 12
399-405
EN
Many students have problems with solving tasks concerning the existence of the derivative of a function at a point. In this paper we discuss some of them.
4
Content available remote About Two Different Ways of Characterization of Łuksiewicz's Three-valued Modal Propositional Calculus
63%
Bryll G. , Kaptur M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2005
|
tom Vol. 10
25-31
EN
In this article we consider two systems of Lukasiewicz's three- valued modal propositional calculus. One of them is the system based on such primary terms as the disjunction (A), negation (N) and necessity (L), whereas the second is based on such primary terms as the implication (C), negation (N) and definitively improved by modal necessity terms. The both systems are definitively equivalent.
5
Content available remote Certain Classes of Elimination Operators
63%
Bryll G. , Sochacki R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2000/2001
|
tom Vol. 8
13--18
6
Content available remote Construction of trigonometry using the scalar product
63%
Bryll G. , Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2008
|
tom 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.
7
Content available remote Some Propositional Calculus Oppositional with Respect to the Intuitionistic Propositional Calculus
63%
Bryll G. , Kaptur M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2005
|
tom Vol. 10
17--23
EN
A fragmentary system of the classical propositional calculus, in which the law C N N αα is valid instead of the law CαN N α, is presented.
8
Content available remote Remarks about the Replacement of School Induction Definitions by Normal Definitions
63%
Bryll G. , Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2003
|
tom 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).
9
Content available remote Rachunek refutacyjny a rachunek dualny
63%
Bryll G. , Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
tom Vol. 7
23--29
10
Content available remote Several Remarks about Three-valued Kleene's Propositional Logic, without Tautologies
63%
Bryll G. , Jaworski L.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2003
|
tom Vol. 9
11--15
EN
In this article we give, in the syntetic way, diferent formal aproachings to Kleene's propositional logic. In the work [5] S. C. Kleene gives a three-valued sentential calculus characterized by the following matrix:[formula]. The operators of the matrix are given by the formulas:[formula]. The operators have the tables: [tables]. It is easy to see that the set of tautologies is an empty set.
11
Content available remote Dwie formalizacje rachunku dualnego względem systemu W.
63%
Bryll G. , Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
tom Vol. 7
9--22
12
Content available remote On Usability of Ordering and Equivalence Relations to Define and to Ground Some Mathematical Notions in Secondary Schools
63%
Bryll G. , Sochacki R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2003
|
tom Vol. 9
131--136
EN
Many important mathematical notions can be introduced by means of the notions of supremum, infimum and equivalence class. Our considerations refer to mainly pupils of mathematical sections.
13
Content available remote About Various Methods of Calculating the Sum [formula]
63%
Bryll G. , Rygał G.
|
2006
|
tom 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.
14
Content available remote A Method of Axiomatic Rejection of Formulas in Propositional Logics
63%
Borowik P. , Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1999
|
tom Vol. 7
5--8
15
Content available remote About definition of a periodic function
63%
Rygał G. , Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom 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.
16
Content available Arithmetic sequences of higher degrees characterizing figurate numbers
51%
Rygał G. , Bryll A. , Bryll G.
|
|
tom 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.
17
Content available remote A Formalization of a Logic Without Tautologies
51%
Bryll G. , Chotomska A. , Jaworski L.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2000/2001
|
tom Vol. 8
11--12
18
Content available remote The use of finite expansion of functions for evaluation of limits
51%
Bryll A. , Bryll G. , Rygał G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom Vol. 12
143-154
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