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Classe des sciences mathematiques et naturelles
ISSN 0561-7332
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Graph energies and their applications
(Beograd : Académie Serbe des sciences et des arts, 2019)
The energy E(G) of a graph G is the sum of absolute values of the
eigenvalues of the adjacency matrix of G. This spectral quantity was introduced in 1978 by
Ivan Gutman, but its extensive research started only twenty ...
Special cases of orthogonal polynomials on the semicircle and applications in numerical analysis
(Beograd : Académie Serbe des sciences et des arts, 2019)
Orthogonal polynomials on the semicircle was introduced by Gautschi and
Milovanovic in ´ [Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (July 1985), 179−185]
and [J. Approx. Theory 46 (1986), 230 − 250]. In this ...
In Memorium: Bogoljub Stanković (November 1, 1924 –May 16, 2018)
(Beograd : Académie Serbe des sciences et des arts, 2018)
The eminent scientist Bogoljub Stanković, Full member of the Serbian Academy
of Sciences and Arts (SASA) and a longtime Editor-in-Chief of the SASA Bulletin
of Mathematical Sciences, died on 16 May 2018.
A front row seat to the work of Aleksandar Ivić
(Beograd : Académie Serbe des sciences et des arts, 2021)
We provide a survey of the vast contribution of Aleksandar Ivic´ to analytic
number theory. Emphasis is put on Ivic´’s work on arithmetical functions. Highlights of his
contribution to the study of the Riemann zeta-function ...
Summation of slowly convergent series by Gaussian type of quadratures and application to calculation of values of the Riemann zeta function
(Beograd : Académie Serbe des sciences et des arts, 2021)
Beside a short account on the summation/integration methods for slowly
convergent series (Laplace transform method for numerical and trigonometric series and the
method of contour integration over a rectangle), a method ...
Incomplete Kloosterman sums to prime power modules
(Beograd : Académie Serbe des sciences et des arts, 2021)
We prove that for prime p, p → +∞, integer r ! 4 and q = pr an
incomplete Kloosterman sum of length N to modulus q can be estimated non-trivially (with
power-saving factor) for very small N, namely, for N ≫ (q log q)1/(r−1)
.
Fifty years of Kurepa’s !n hypothesis
(Beograd : Académie Serbe des sciences et des arts, 2021)
Djuro Kurepa formulated in 1971 the so called left factorial hypothesis.
This hypothesis is still open, despite much efforts to solve it. Here we give some historical
notes and review the current status of the hypothesis. ...
Gutman index – a critical personal account
(Beograd : Académie Serbe des sciences et des arts, 2021)
In the recent literature there are numerous publications concerned with a
graph invariant named “Gutman index” (ZZ). In this paper, some details about the discovery
of ZZ are explained. In particular, it is pointed out ...
On some integrals involving ∆2(x) and ∆3(x)
(Beograd : Académie Serbe des sciences et des arts, 2021)
Let k ≥ 2 be a fixed natural number and dk(n) denote the number of
ways n can be written as a product of k positive integers. Let ∆k(x) denote the error term
in the asymptotic formula of the summatory function of dk(n). ...