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On similarity between topologies

Artur Bartoszewicz, Małgorzata Filipczak, Andrzej Kowalski, Małgorzata Terepeta (2014)

Open Mathematics

Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.

On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions

Dorota Bród, Anetta Szynal-Liana, Iwona Włoch (2022)

Czechoslovak Mathematical Journal

We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions.

On some Diophantine equations involving balancing numbers

Euloge Tchammou, Alain Togbé (2021)

Archivum Mathematicum

In this paper, we find all the solutions of the Diophantine equation B 1 p + 2 B 2 p + + k B k p = B n q in positive integer variables ( k , n ) , where B i is the i t h balancing number if the exponents p , q are included in the set { 1 , 2 } .

On Some Partition Functions Related to Some Mock Theta Functions

Alexander E. Patkowski (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.

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