Duško Bogdanić

Chemical Papers

Moving towards sustainable tribology: Waste silica fumes as a novel lubricant base

S. Zeljkovic; V. D’Urso; T. Ivas; D. Bogdanic; A. Senatore

https://link.springer.com/article/10.1007/s11696-025-04062-z

We conducted ball-on-disk tests to explore the tribological properties of a carbon sodium silicate lubricant (CSS). This lubricant consists of a water-based sodium silicate (SS) suspension and amorphous carbon particles. Its solidification occurs as water gradually evaporates from the mixture. The CSS samples were derived from waste silica fume (SF), which is a mixture of SiO2 and carbon. We analyzed the SF by using X-ray fluorescence and optical microscopy. In order to investigate the impact of lubrication on hot metalworking we used various proportions of SF and NaOH, creating samples S2, S3, and S4 with modulus 1, 1.5, and 2. Additionally, a comparative SS lubricant sample (Sample S5 with modulus 1.5) was made from pure SiO2. We conducted two types of tests: a steady-state test at a constant sliding speed of 50 mm s−1 and a fretting test involving oscillations at a 75° angle and a frequency of 2 Hz, both at 100 °C. Distilled water served as the benchmark tribological fluid (Sample S1) for comparing coefficients of friction (CoF) values. The average CoF (fretting test) values for S1, S2, S3, S4 and S5 are 0.43 ± 0.026, 0.29 ± 0.048, 0.22 ± 0.042, 0.34 ± 0.041, and 0.25 ± 0.041, respectively. In steady-state CoF test, average values for S1, S2, S3, S4, and S5 are 0.27 ± 0.076, 0.28 ± 0.034, 0.40 ± 0.027, 0.42 ± 0.077, and 0.35 ± 0.051, respectively. Statistical analysis, including one-way ANOVA and post-hoc comparisons, revealed significant differences in friction means between sample types in both test types (p-values < 10–15). These results highlight the potential of repurposing SF waste material as a novel lubricant base.

Sustainability; Solid lubricants; Recycling; Carbon sodium silicate; Green tribology

M23

Linear Algebra and its Applications

Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size

D. Bogdanic; A. Đurić; S. Koljančić; P. Oblak; K. Šivic

https://www.sciencedirect.com/science/article/pii/S0024379524000910?via%3Dihub

In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix B consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the nilpotent matrices that commute with B by characterizing the corresponding partitions.

Nilpotent matrix

M21

Kragujevac Journal of Mathematics

Indecomposable Modules in the Grassmannian Cluster Category CM(B_(5,10))

D. Bogdanic and I.-V. Boroja

https://imi.pmf.kg.ac.rs/kjm/en/index.php?page=10.46793/KgJMat2406.907B

In this paper, we study indecomposable rank 2 modules in the Grassmannian cluster category CM(B5,10). This is the smallest wild case containing modules whose profile layers are 5-interlacing. We construct all rank 2 indecomposable modules with a specific natural filtration, classify them up to isomorphism, and parameterize all infinite families of non-isomorphic rank 2 modules.

Cohen-Macaulay modules; Grassmannian cluster categories; Indecomposable modules

M24

Advanced Studies in Pure Mathematics

Construction of Rank 2 Indecomposable Modules in Grassmannian Cluster Categories

K. Baur; D. Bogdanic; J.-R. Li

https://projecteuclid.org/.../10.2969/aspm/08810001

The category CM(Bk,n) of Cohen-Macaulay modules over a quotient Bk,n of a preprojective algebra provides a categorification of the cluster algebra structure on the coordinate ring of the Grassmannian variety of k-dimensional subspaces in Cn, [13]. Among the indecomposable modules in this category are the rank 1 modules which are in bijection with k-subsets of {1,2,…,n}, and their explicit construction has been given by Jensen, King and Su. These are the building blocks of the category as any module in CM(Bk,n) can be filtered by them. In this paper we give an explicit construction of rank 2 modules. With this, we give all indecomposable rank 2 modules in the cases when k=3 and k=4. In particular, we cover the tame cases and go beyond them. We also characterise the modules among them which are uniquely determined by their filtrations. For k≥4, we exhibit infinite families of non-isomorphic rank 2 modules having the same filtration.

Cohen-Macaulay modules; Grassmannian cluster categories; rank 2 modules

M34

Sarajevo Journal of Mathematics

Decomposable extensions between rank 1 modules in Grassmannian cluster category

D. Bogdanic and I.-V. Boroja

https://sjm.anubih.ba/index.php/sjm/article/view/119

Rank modules are the building blocks of the category CM(Bk,n) of Cohen-Macaulay modules over a quotient Bk,n of a preprojective algebra of affine type A. Jensen, King and Su showed in \cite{JKS16} that the category CM(Bk,n) provides an additive categorification of the cluster algebra structure on the coordinate ring C[CM(Bk,n)] of the Grassmannian variety of k-dimensional subspaces in C^n. Rank modules are indecomposable, they are known to be in bijection with k-subsets of {1,2,…,n}, and their explicit construction has been given in [8]. In this paper, we give necessary and sufficient conditions for indecomposability of an arbitrary rank 2 module in CM(Bk,n) whose filtration layers are tightly interlacing. We give an explicit construction of all rank 2 decomposable modules that appear as extensions between rank 1 modules corresponding to tightly interlacing k-subsets I and J.

Cohen-Macaulay modules; Grassmannian cluster categories; decomposable extensions

M51