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# Glasnik matematički : 55,1(2020) / glavni urednik Dražen Adamović.

NaslovGlasnik matematički : 55,1(2020) / glavni urednik Dražen Adamović.
ImpresumZagreb : Hrvatsko matematičko društvo : 2020.
ZbirkaDigitalna zbirka Croatica - obvezni primjerak
ID000659858
Vrsta publikaciječasopis; neomeđena građa

12 (1-10)
NaslovOn Y-coordinates of Pell equations which are base 2 rep-digits / Bernadette Faye-Fall, Florian Luca.
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OpisIn this paper, we show that if (Xk,Yk) is the kth solution of the Pell equation X2-dY2=1 for some non-square integer d>1, then the equation Yk=2n-1 has at most two positive integer solutions (k,n).
1
NaslovDiophantine equations connected to the Komornik polynomials / András Bazsó, Attila Bérczes, Ondřej Kolouch, István Pink, Jan Šustek.
Materijalni opisGraf. prikazi.
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OpisWe investigate the power and polynomial values of the polynomials Pn(X) = ∏nk=0 (X2 · 3k - X3k - 1 ) for n ∈ ℕ. We prove various ineffective and effective finiteness results. In the case 0≤ n ≤ 3, we determine all pairs x,y of integers such that Pn(x)=y2 or Pn(x)=y3.
2
NaslovMarkoff-Rosenberger triples with Fibonacci components / Szabolcs Tengely.
Materijalni opisGraf. prikazi.
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OpisWe characterize the solutions of the Markoff-Rosenberger equation a x 2 + b y 2 + c z 2 = d x y z with a,b,c,d ∈ ℤ, gcd(a,b)=gcd(a,c)=gcd(b,c)=1 and a,b,c | d, for which (x,y,z)=(Fi,Fj,Fk), where Fn denotes the n-th Fibonacci number for any integer n≥ 0.
3
NaslovPerfect powers in an alternating sum of consecutive cubes / Pranabesh Das, Pallab Kanti Dey, Bibekananda Maji, Sudhansu Sekhar Rout.
Materijalni opisGraf. prikazi.
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OpisIn this paper, we consider the problem about finding out perfect powers in an alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation (x+1) 3 - (x+2) 3 + ∙∙∙ - (x + 2d) 3 + (x + 2d + 1) 3 = z p, where p is prime and x,d,z are integers with 1 ≤ d ≤ 50.
4
NaslovExtension of the functional independence of the Riemann zeta-function / Antanas Laurinčikas.
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OpisIn 1972, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i. e., if the functions φj are continuous in ℂN and φ0(ζ(s), …, ζ(N-1)(s))+ ∙∙∙ + sn φn(ζ(s), …, ζ(N-1)(s)) ≡ 0, then φj≡ 0 for j=0,…, n. The problem goes back to Hilbert who obtained the algebraic-differential independence of ζ(s). In the paper, the functional independence of compositions F(ζ(s)) for some classes of operators F in the space of analytic functions is proved. For example, as a particular case, the functional independence of the function cosζ(s) follows.
5
NaslovOn the faithfulness of 1-dimensional topological quantum field theories / Sonja Telebaković Onić.
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OpisThis paper explores 1-dimensional topological quantum field theories. We separately deal with strict and strong 1-dimensional topological quantum field theories. The strict one is regarded as a symmetric monoidal functor between the category of 1-cobordisms and the category of matrices, and the strong one is a symmetric monoidal functor between the category of 1-cobordisms and the category of finite dimensional vector spaces. It has been proved that both strict and strong 1-dimensional topological quantum field theories are faithful.
6
NaslovCenters of subgroups of big mapping class groups and the Tits alternative / Justin Lanier, Marissa Loving.
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OpisIn this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a big mapping class group contains a nonabelian free group. In contrast, we show that no big mapping class group satisfies the strong Tits alternative enjoyed by finite-type mapping class groups. We also give examples of big mapping class groups that fail to satisfy even the classical Tits alternative; consequently, these examples are not linear.
7
NaslovUniqueness of solution of a heterogeneous evolution dam problem associated with a compressible fluid flow through a rectangular porous medium / Elmehdi Zaouche.
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OpisThis paper is concerned with the uniqueness of a weak solution of an evolution dam problem arising in a compressible fluid flow through a two-dimensional, rectangular, and heterogeneous porous medium. Our problem is associated with the equation a(x1)(ux2+χ)x2-(u+χ)t=0. The technique we use is based on a transformation of the weak form of this equation into a similar one that enables us to argue as in .
8
NaslovScalar conservation laws with Charatheodory flux revisited / Nikola Konatar.
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OpisWe introduce a new approach for dealing with scalar conservation laws with the flux discontinuous with respect to the space variable and merely continuous with respect to the state variable which employs a variant of the kinetic formulation. We use it to improve results about the existence of solutions for non-degenerate scalar conservation laws with Caratheodory flux under a variant of non-degeneracy conditions.
9
NaslovThe hyperspace of totally disconnected sets / Raúl Escobedo, Patricia Pellicer-Covarrubias, Vicente Sánchez-Gutiérrez.