A bipartition of n is an ordered pair of partitions (λ, μ) such that the sum of all of the parts equals n. In this article, we concentrate on the function c5(n), which counts the number of bipartitions (λ, μ) of n subject to the restriction that each part of μ is divisible by 5. We explicitly establish four Ramanujan type congruences and several infinite families of congruences for c5(n) modulo 3.

Introduction The beginning chapter in the UCSMP Geometry book introduces students to four definitions of a point dot as a point, location as a point, ordered pair as a point, and a network node as a point. A lot of information is presented to students but not necessarily a lot of physical experience with each idea. The Artistic Expression Institute in the Educator's Science and Mathematics Inst...

This paper analyses the determinants of happiness in seven Eastern European transition countries during the early phase of economic transition. The analysis of representative survey data in an ordered logit model shows that those core socio-demographic and economic variables known to be relevant from studies on the US and Western European countries have a similar impact on happiness in Eastern ...

Dickson On a problem concerning separating systems of a nite set, Journal of Combinatorial Theory, 7 (1969), 191{196.] introduced the notion of a completely separating set system. We study such systems with the additional constraint that each set in the system has the same size. Let T denote an n-set. We say that a subset S of T separates i from j if i 2 S and j 6 2 S. A collection of k-sets C ...

— Itis proved that thefamily of finite index matrix languages coincides with the families of finite index random context languages generated withforbidding sets and with or without X-rules and is included in thefamily of finite index conditional languages. Finally, the Szilard languages associated to finite index matrix grammars are briefly investigated. Résumé. — On montre que lafamille de lan...

‎A common approach to determine efficient solutions of a multiple objective optimization problem‎ ‎is reformulating it to a parameter dependent scalar optimization problem‎. ‎This reformulation is called scalarization approach‎. Here, a well-known scalarization approach named Pascoletti-Serafini scalarization is considered‎. First, some difficulties of this scalarization are discussed and then ...

an efficient flood alarm system may significantly improve public safety and mitigate damages caused by inundation. flood forecasting is undoubtedly a challenging field of operational hydrology and a huge literature has been developed over the years. in this paper, we first define ordered ideal intuitionistic fuzzy sets and establish some results on them. then, we define similarity measures betw...

Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...

1 ECS University of Westminster, London, HA1 3TP, UK e-mail: [email protected] 2 Warrane College, University of New South Wales, Kensington, 1465, Australia e-mail: [email protected] 3 Department of Mathematics, Vellalar College for Women, Erode 638 009, Tamilnadu, India e-mail: [email protected] 4 Centre of Biomedical Engineering, Bulgarian Academy of Sciences P.O.Box 12, ...

Suppose that all groups of order n are defined on the same set G of cardinality n, and let the distance of two groups of order n be the number of pairs (a, b) ∈ G×G where the two group operations differ. Given a group G(◦) of order n, we find all groups of order n, up to isomorphism, that are closest to G(◦).