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1
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Some norm inequalities for special Gram matrices

100%
Türkmen R., Kan O., Gökbas H.
Special Matrices
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2016
|
tom 4
|
nr 1
262-269
EN
In this paper we firstly give majorization relations between the vectors Fn = {f0, f1, . . . , fn−1},Ln = {l0, l1, . . . , ln−1} and Pn = {p0, p1, . . . , pn−1} which constructed with fibonacci, lucas and pell numbers. Then we give upper and lower bounds for determinants, Euclidean norms and Spectral norms of Gram matrices GF=〈Fn,Fni〉, GL=〈Ln,Lni〉, GP=〈Pn,Pni〉, GFL=〈Fn,Lni〉, GFP=〈Fn,Pni〉.
2
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Unbounded stability of two-term recurrence sequences modulo $2^k$

100%
Carlip W., Jacobson E.
Acta Arithmetica
|
1996
|
tom 74
|
nr 4
329-346
3
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Counting Maximal Distance-Independent Sets in Grid Graphs

88%
Euler R., Oleksik P., Skupień Z.
Discussiones Mathematicae Graph Theory
|
2013
|
tom 33
|
nr 3
531-557
EN
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
4
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Leonardo Pisano called Fibonacci, between advanced mathematics, history of mathematics and mathematics education: three examples drawn from Liber Quadratorum

63%
Bussotti P.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2015
|
tom 7
5-25
PL
In this research, three problems faced by Leonardo Pisano, called Fibonacci,are dealt with. The main purpose is to show that history of mathematics can offerinteresting material for mathematics education. The approach to the use of history ofmathematics in mathematics education cannot be merely historical, but adapted to theneeds of the explanations in a classroom. In the course of this paper, the meaning ofsuch assertion will be clarified. A further purpose is a trying to explore the relationshistory of mathematics-mathematics education-advanced mathematics. Last, but notthe least, a further aim is to offer a specific series of interesting material to the teacherin order to develop stimulating lessons. The material here expounded is conceived forpupils frequenting the third and the fourth years of the high school, but, with minormodifications, it can be adapted to the fifth year of the high school and to the initialyears of the scientific faculties at the university.
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