On a problem of Lang for matrix polynomials

In this paper, we consider a problem of Lang about finiteness of torsion points on plane rational curves, and prove some results towards a matrix analogue of this problem, including a full analogue for $2\times 2$ matrices defined over $\mathbb{C}$

Fractional jumps: complete characterisation and an explicit infinite family

In this paper we provide a complete characterisation of transitive fractional jumps by showing that they can only arise from transitive projective automorphisms. Furthermore, we prove that such construction is feasible for arbitrarily large dimension by exhibiting an infinite class of projectively primitive polynomials whose companion matrix can be used to define a full orbit sequence over an affine space

On sets of irreducible polynomials closed by composition

Let $\mathcal S$ be a set of monic degree $2$ polynomials over a finite field and let $C$ be the compositional semigroup generated by $\mathcal S$. In this paper we establish a necessary and sufficient condition for $C$ to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set $\mathcal S$. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree $2$ polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions

Supplementary data for the article: Ostafe, R.; Prodanovic, R.; Ung, W. L.; Weitz, D. A.; Fischer, R. A High-Throughput Cellulase Screening System Based on Droplet Microfluidics. Biomicrofluidics 2014, 8 (4). https://doi.org/10.1063/1.4886771

Supplementary material for: [https://doi.org/10.1063/1.4886771]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1873

Supplementary data for article: Utech, S.; Prodanovic, R.; Mao, A. S.; Ostafe, R.; Mooney, D. J.; Weitz, D. A. Microfluidic Generation of Monodisperse, Structurally Homogeneous Alginate Microgels for Cell Encapsulation and 3D Cell Culture. Advanced Healthcare Materials 2015, 4 (11), 1628–1633. https://doi.org/10.1002/adhm.201500021

Supporting information for: [https://doi.org/10.1002/adhm.201500021]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1751]Related to accepted version: [http://cherry.chem.bg.ac.rs/handle/123456789/2785

A high.throughput screening system based on droplet microfluidics for glucose oxidase gene libraries

Glucose oxidase (GOx) is an important industrial enzyme that can be optimized for specific applications by mutagenesis and activity.based screening. To increase the efficiency of this approach, we have developed a new ultrahigh.throughput screening platform based on a microfluidic lab.on.chip device that allows the sorting of GOx mutants from a saturation mutagenesis library expressed on the surface of yeast cells. GOx activity was measured by monitoring the fluorescence of water microdroplets dispersed in perfluorinated oil. The signal was generated via a series of coupled enzyme reactions leading to the formation of fluorescein. Using this new method, we were able to enrich the yeast cell population by more than 35.fold for GOx mutants with higher than wild.type activity after two rounds of sorting, almost double the efficiency of our previously described flow cytometry platform. We identified and characterized novel GOx mutants, the most promising of which (M6) contained a combination of six point mutations that increased the catalytic constant kcat by 2.1.fold compared to wild.type GOx and by 1.4.fold compared to a parental GOx variant. The new microfluidic platform for GOx was therefore more sensitive than flow cytometry and supports comprehensive screens of gene libraries containing multiple mutations per gene. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)

Supplementary data for article: Utech, S.; Prodanovic, R.; Mao, A. S.; Ostafe, R.; Mooney, D. J.; Weitz, D. A. Microfluidic Generation of Monodisperse, Structurally Homogeneous Alginate Microgels for Cell Encapsulation and 3D Cell Culture. Advanced Healthcare Materials 2015, 4 (11), 1628–1633. https://doi.org/10.1002/adhm.201500021

Supporting information for: [https://doi.org/10.1002/adhm.201500021]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1751]Related to accepted version: [http://cherry.chem.bg.ac.rs/handle/123456789/2785

Polynomial values in affine subspaces of finite fields

In this paper we introduce a new approach and obtain new results for theproblem of studying polynomial images of affine subspaces of finite fields. Weimprove and generalise several previous known results, and also extend therange of such results to polynomials of degrees higher than the characteristicof the field. Such results have a wide scope of applications similar to thoseassociated with their counterparts studying consecutive intervals over primefields instead of affine subspaces. Here we give only two immediateconsequences: to a bound on the size of the intersection of orbits ofpolynomial dynamical systems with affine subspaces and to the Waring problem inaffine subspaces. These results are based on estimates for a certain new typeof exponential sums