Jordan triple product homomorphisms on Hermitian matrices of dimension two

We characterise all Jordan triple product homomorphisms, that is, mappings $\Phi$ satisfying $$\Phi(ABA) = \Phi(A)\Phi(B)\Phi(A)$$ on the set of all Hermitian $2 \times 2$ complex matrices.Comment: 34 page

Jordan triple product homomorphisms on Hermitian matrices to and from dimension one

We characterise all Jordan triple product homomorphisms, that is, mappings $\Phi$ satisfying $$\Phi(ABA) = \Phi(A)\Phi(B)\Phi(A)$$ from the set of all Hermitian $n \times n$ complex matrices to the field of complex numbers. Further we characterise all Jordan triple product homomorphisms from the field of complex or real numbers or the set of all nonnegative real numbers to the set of all Hermitian $n \times n$ complex matrices.Comment: 10 page

Software Development with Scrum: A Bibliometric Analysis and Profile

Introduction of the Scrum approach into software engineering has changed the way software is being developed. The Scrum approach emphasizes the active end-user involvement, embracing of change, and /iterative delivery of products. Our study showed that Scrum has different variants or is used in combination with different methods. Some tools not normally used in the conventional software approaches, like gamification, content analysis and grounded theory are also employed. However, Scrum like other software development approach focuses on improvement of software process, software quality, business value, performance, usability and efficiency and at the same time to reduce cost, risk and uncertainty. Contrary to some conventional approaches it also strives to boost soft factors like agility, trust, motivation, responsibility and transparency. The bibliometric synthetic scoping study revealed seven main research themes concerned with the Scrum research

Diameters of commuting graphs of matrices over semirings

We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the lower bound for the diameter of the commuting graph of the semiring of matrices over an arbitrary commutative entire antinegative semiring.Comment: 8 page

MODELI FINANCIRANJA BIBLIOMETRIJSKIH ISTRAŽIVANJA

To identify research funding patterns behind bibliometrics as a rapidly expanding science was the aim of the study presented in this paper. We analyzed funding information of 8,622 bibliometric papers harvested from Web of Science, among which 1,786 (20.7%) were Papers with Reported Funding (PRFs). The trend in a number of PRFs funding in the last five years was positive. The most productive countries in PRFs` production were China, the USA and the UK. The same countries were also the most prolific regarding how many times they were mentioned in funding acknowledgments. The number of PRFs published per country was related to OECD reported Gross Domestic Spending on R&D for 2015. There was a significant correlation between number of PRFs per country and the number of all bibliometric papers per country. Far the most prolific funding agency was National Natural Science Foundation of China, followed by the European Commission and the USAs National Science Foundation. The Research trend and direction prediction is the most prolific research theme regarding the percent of PRF and thus most likely to get funded.Cilj istraživanja predstavljenog u ovom radu bio je identificirati obrasce financiranja istraživanja iz područja bibliometrije kao znanosti koja se brzo širi. Analizirane su informacije o financiranju 8.622 bibliometrijskih radova prikupljenih iz Web of Science, od kojih je 1.786 (20,7%) bilo radova s prijavljenim financiranjem (PRF). Trend u broju PRF-ova u posljednjih pet godina bio je pozitivan. Najproduktivnije zemlje u proizvodnji PRF-a bile su Kina, SAD i Velika Britanija. Iste su zemlje bile i najplodnije u pogledu koliko su puta spomenute u priznanjima za financiranje. Broj PRF-ova objavljenih po zemlji povezan je s OECD-ovim izvješćem o bruto domaćoj potrošnji na istraživanje i razvoj za 2015. Postoji značajna korelacija između broja PRF-ova po zemlji i broja svih bibliometrijskih radova po zemlji. Daleko najplodnija agencija za financiranje bila je Nacionalna zaklada za prirodne znanosti u Kini, a slijede je Europska komisija i Nacionalna zaklada za znanost SAD-a. Predviđanje trenda i smjera istraživanja je najplodnija tema istraživanja u odnosu na postotak PRF-a i stoga najvjerojatnije da će se financirati

Stability of Ranked Gene Lists in Large Microarray Analysis Studies

This paper presents an empirical study that aims to explain the relationship between the number of samples and stability of different gene selection techniques for microarray datasets. Unlike other similar studies where number of genes in a ranked gene list is variable, this study uses an alternative approach where stability is observed at different number of samples that are used for gene selection. Three different metrics of stability, including a novel metric in bioinformatics, were used to estimate the stability of the ranked gene lists. Results of this study demonstrate that the univariate selection methods produce significantly more stable ranked gene lists than the multivariate selection methods used in this study. More specifically, thousands of samples are needed for these multivariate selection methods to achieve the same level of stability any given univariate selection method can achieve with only hundreds