Temat: numbers - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On Pell and Pell−Lucas Hybrid Numbers
Autorzy:: Szynal-Liana, Anetta
Włoch, Iwona
Powiązania:: https://bibliotekanauki.pl/articles/962854.pdf
Data publikacji:: 2018
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Pell numbers
recurrence relations
complex numbers
hyperbolic numbers
dual numbers
Opis:: In this paper we introduce the Pell and Pell−Lucas hybrid numbers as special kinds of hybrid numbers. We describe some properties of Pell hybrid numbers and Pell−Lucas hybrid numbers among other we give the Binet formula, the character and the generating function for these numbers.
Źródło:: Commentationes Mathematicae; 2018, 58, 1-2; 11-17
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Composition of Arithmetical functions with generalization of perfect and related numbers
Autorzy:: Shukla, D.P.
Yadav, Shikha
Powiązania:: https://bibliotekanauki.pl/articles/746376.pdf
Data publikacji:: 2012
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Arithmetic Functions
Abundent numbers
Deficient numbers
Inequalities
Geometric Numbers
Harmonic Numbers
Opis:: In this paper we have studied the deficient and abundent numbers connected with the composition of \(\varphi\), \(\varphi^*\), \(\sigma\), \(\sigma^*\) and \(\psi\) arithmetical functions, where \(\varphi\) is Euler totient, \(\varphi^*\) is unitary totient, \(\sigma\) is sum of divisor, \(\sigma^*\) is unitary sum of divisor and \(\psi\) is Dedekind's function. In 1988, J. Sandor conjectured that \(\psi(\varphi(m)) \geq m\), for all \(m\), all odd \(m\) and proved that this conjecture is equivalent to \(\psi(\varphi(m)) \geq \frac{m}{2}\), we have studied this equivalent conjecture. Further, a necessary and sufficient conditions of primitivity for unitary r-deficient numbers and unitary totient r-deficient numbers have been obtained. We have discussed the generalization of perfect numbers for an arithmetical function \(E_\alpha\).
Źródło:: Commentationes Mathematicae; 2012, 52, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Generalized Perfect Numbers
Autorzy:: Shukla, D.P.
Yadav, Shikha
Powiązania:: https://bibliotekanauki.pl/articles/746659.pdf
Data publikacji:: 2013
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Prime numbers, perfect numbers, super perfect numbers, arithmetical Functions
Opis:: In this paper a modified form of perfect numbers called \((p,q)\)+ perfect numbers and their properties with examples have been discussed. Further properties of \(\sigma _{+}\) arithmetical function have been discussed and on its basis a modified form of perfect number called \((p,q)\)+ super perfect numbers have been discussed. A modified form of perfect number called \((p,0)\)-perfect and their characterization has been studied. In the end of this paper almost super perfect numbers have been introduced.
Źródło:: Commentationes Mathematicae; 2013, 53, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: On Unitary Analogue of \(f_g\)-perfect numbers and \(\Psi_s\)-perfect numbers
Autorzy:: Shukla, D.P.
Pandey, Shikha
Powiązania:: https://bibliotekanauki.pl/articles/744875.pdf
Data publikacji:: 2011
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: \(f_g\)-Perfect Numbers
unitary divisors
arithmetic functions
Dedekind’s function
g-perfect numbers
\(\Psi_s\)-perfect numbers
Opis:: In this paper unitary analogue of \(f_g\)-Perfect numbers and some properties of Dedekind’s function and all the \(\Psi_s\)-perfect numbers have been discussed.
Źródło:: Commentationes Mathematicae; 2011, 51, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Distance Fibonacci numbers, their interpretations and matrix generators
Autorzy:: Bednarz, Urszula
Wołowiec-Musiał, Małgorzata
Powiązania:: https://bibliotekanauki.pl/articles/746716.pdf
Data publikacji:: 2013
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Fibonacci numbers, matching, covering, matrix generators
Opis:: In this paper we define a distance Fibonacci numbers, also for negative integers, which generalize the classical Fibonacci numbers and Padovan numbers, simultaneously. We give different interpretations of these numbers with respect to special partitions and compositions, also in graphs. We show a construction of the sequence of distance Fibonacci numbers using the Pascal's triangle. Moreover, we give matrix generators of these numbers, for negative integers, too.
Źródło:: Commentationes Mathematicae; 2013, 53, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Tytuł:: On a new generalization of Jacobsthal quaternions and several identities involving these numbers
Autorzy:: Bród, Dorota
Szynal-Liana, Anetta
Powiązania:: https://bibliotekanauki.pl/articles/1912840.pdf
Data publikacji:: 2019
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Jacobsthal numbers
Jacobsthal quaternions
recurrence relations
generating functions
Opis:: In this paper we generalize Jacobsthal quaternions to \((s,p)\)\dywiz Jacobsthal quaternions. We give some of their properties, among others the Binet formula, the generating function and the matrix representation of these quaternions. We will show how a~graph interpretation can be used in proving some identities for quaternions.
Źródło:: Commentationes Mathematicae; 2019, 59, 1-2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 7.

Tytuł:: Series representation of compact linear operators in Banach spaces
Autorzy:: Edmunds, David E.
Lang, Jan
Powiązania:: https://bibliotekanauki.pl/articles/745232.pdf
Data publikacji:: 2016
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Eigenvalues
Banach spaces
compact operators
nuclear maps
Gelfand numbers
Opis:: Let \(p\in(1,\infty)\) and \(I=(0,1)\); suppose that \(T\colon L_{p}(I)\rightarrow L_{p}(I)\) is a~compact linear map with trivial kernel and range dense in \(L_{p}(I)\). It is shown that if the Gelfand numbers of \(T\) decay sufficiently quickly, then the action of \(T\) is given by a series with calculable coefficients. The special properties of \(L_{p}(I)\) enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
Źródło:: Commentationes Mathematicae; 2016, 56, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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