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2. The Waring problem for matrix algebras, IIMatej Brešar, Peter Šemrl, 2023, original scientific article Abstract: Let $f$ be a noncommutative polynomial of degree $m\ge 1$ over an algebraically closed field $F$ of characteristic $0$. If $n\ge m-1$ and $\alpha_1,\alpha_2,\alpha_3$ are nonzero elements from $F$ such that $\alpha_1+\alpha_2+\alpha_3=0$, then every trace zero $n\times n$ matrix over $F$ can be written as $\alpha_1 A_1+\alpha_2A_2+\alpha_3A_3$ for some $A_i$ in the image of $f$ in $M_n(F)$.
Keywords: Waring problem, noncommutatative polynomials, matrix algebras
Published in DiRROS: 10.04.2024; Views: 58; Downloads: 22
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3. Short term effect of plant hybridosomes on growth of phaeodactylum tricornutum cultureAnna Romolo, Matej Hočevar, Aleš Iglič, Tjaša Griessler Bulc, Veronika Kralj-Iglič, 2023, published scientific conference contribution Keywords: Phaeodactylum tricornutum, hybridosomes, liposomes, nanoalgosomes, extracellular vesicles, small cellular particles, microalgae
Published in DiRROS: 21.03.2024; Views: 83; Downloads: 42
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4. Microsatellite instability in colorectal cancerMatej Horvat, Borut Štabuc, 2011, review article Abstract: Background. Colorectal cancer (CRC) is the third most common cancer in the world. In 75% CRC develops sporadically, in 25% hereditary or as a consequenceof inflammatory bowel disease. CRC carcinogenesis develops over many years. The cause of CRC in 85% is chromosomal instability (CIN) and in 15% microsatellite instability (MSI-H), where hereditary nonpolyposis colorectal cancer (HNPCC) represents 10-20%. Microsatellite sequences (MS) arerepeated sequences of short stretches of DNA all over the genome. Microsatellite stability (MSS) means MS are the same in each cell of an individual, whereas microsatellite instability (MSI-H) means MS differ in normal and cancer cells of an individual. The cause of MSI-H is a damaged mismatch repair mechanism (MMR), with the most important MMR proteins being MSH2, MLH1 and MSH6. Conclusions. MSI-H seems to be an important prognostic factor in CRC and an important predictive factor of CRC chemotherapeutic treatment efficacy. Clinical trials conducted until now have shown contradictory findings in different chemotherapeutic settings, adjuvant and palliative; therefore MSI-H is going to be the object of the future research. The future of cancer treatment is in the individualized therapy based on molecular characteristics of the tumour, such as MSI-H in CRC.
Published in DiRROS: 19.03.2024; Views: 97; Downloads: 47
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7. Qualitative analysis of the minimal Higgins model of glycolysisBrigita Ferčec, Matej Mencinger, Tatjana Petek, Orhan Ozgur Aybar, Ilknur Kusbeyzi Aybar, 2023, original scientific article Abstract: Glycolysis, one of the leading metabolic pathways, involves many
different periodic oscillations emerging at positive steady states of
the biochemical models describing this essential process. One of
the models employing the molecular diffusion of intermediates is
the Higgins biochemical model to explain sustained oscillations. In
this paper, we investigate the center-focus problem for the minimal
Higgins model for general values of the model parameters with the
help of computational algebra. We demonstrate that the model
always has a stable focus point by finding a general form of the first
Lyapunov number. Then, varying two of the model parameters, we
obtain the first three coefficients of the period function for the stable focus point of the model and prove that the singular point is actually a bi-weak monodromic equilibrium point of type $[1, 2]$. Additionally, we prove that there are two (small) intervals for a chosen parameter $a > 0$ for which one critical period bifurcates from this singular point after small perturbations.
Keywords: biological processes, biochemical models, glycolysis
Published in DiRROS: 18.03.2024; Views: 68; Downloads: 35
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8. Characterisation of the microstructure and defects during the direct energy deposition of hybrid Ti6Al4V in a low-quality atmosphereSimon Malej, Črtomir Donik, Matej Balažic, Matija Bizjak, Marko Kač, Matjaž Godec, 2023, original scientific article Keywords: direct energy deposition, Ti6Al4V, protective atmosphere
Published in DiRROS: 08.03.2024; Views: 91; Downloads: 48
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