1. On certain functional equation in prime ringsMaja Fošner, Benjamin Marcen, Joso Vukman, 2022, original scientific article Abstract: The purpose of this paper is to prove the following result. Let R be prime ring of characteristic different from two and three, and let F:R→R be an additive mapping satisfying the relation F(x3)=F(x2)x−xF(x)x+xF(x2) for all x∈R. In this case, F is of the form 4F(x)=D(x)+qx+xq for all x∈R, where D:R→R is a derivation, and q is some fixed element from the symmetric Martindale ring of quotients of R.
Keywords: prime ring, derivation, Jordan derivation, functional equation, algebra
Published in DKUM: 12.06.2024; Views: 131; Downloads: 14
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2. Functionalized copolymers from macrolactones by enzymatic ring-opening polymerizationMaja Ivanovski, 2018, master's thesis Abstract: The work reported in the present thesis is focused predominantly to investigate how to synthesize random copolymers from ω-pentadecalatone (ω-PDL) and globalide (Gl) by enzymatic ring-opening polymerization (eROP). The reason for choosing this specific theme, i.e. "Functionalized copolymers from macrolactones by enzymatic ring-opening polymerization", was to explore a relatively new concept, in which two cyclic esters (macrolactones) – ω-PDL and Gl were synthesized by a combination of eROP and thiol-ene click reaction using biocatalyst Novozym 435 (lipase B from Candida antarctica). The aim was to position the newborn copolymer from ω-pentadecalactone and globalide among other biomaterials, identify possible applications and prepare nanoparticles that can be used in drug delivery systems.
Random copolymers PPDLx-r-PGly with different feed ratios were successfully synthesized and later modified via thiol-ene click reaction when using BAET as a suitable compound for this polymeric functionalization, due to its thiol functionality. Boc-amino deprotection lasted and at the end, graft-copolymers were obtained (PPDLx-r-(PGly-g-PBLGz).
Characterization methods were performed on GPC and NMR. The yield for all obtained random copolymers ranged between 67% and 88% and Mn between 14 000 g/mol and 45 000 g/mol depending on feed ratio of random copolymers. Meanwhile, the calculated yield for obtained grafted-copolymers ranged between 63% and 95%. Mn detected by GPC was around 7 000 g/mol for both grafted-copolymers (PPDL90(PGl10-PBLGz) and PPDL50(PGl50-PBLGz)) and Mw between 14 000 g/mol and 21 000 g/mol. Thermal analyses were performed on TGA and DSC. TGA showed that obtained PPDLx-r-PGly copolymers start to decompose at around 400 °C and grafted PPDLx-r-(PGly-g-PBLGz) copolymers at around 250 °C. DSC showed that PPDL and PGl are semicrystalline polymers with Tm ranging between (95 and 96 °C) for PPDL and (41 and 42 °C) for PGl.
AFM technique was used for nanoparticles characterization. The resulting surface and deep resolution of PPDL50(PGl50-PBLGz) nanoparticles was between (2 to 88.8 nm) and PPDL10(PGl90-PBLGz) between (2 nm to 94.4 nm).
Keywords: ring-opening polymerization, macrolactones, ω-pentadecalatone, globalide, nanoparticles, Novozym 435
Published in DKUM: 04.10.2018; Views: 1287; Downloads: 279
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3. Nanocomposite foams from iron oxide stabilized dicyclopentadiene high internal phase emulsions : preparation and brominationSebastijan Kovačič, Christian Slugovc, Gregor Ferk, Nadejda B. Matsko, 2014, professional article Abstract: Nanocomposite polyHIPE foams with open-cellular morphology were obtained using nanoparticles ($γFe_2O_3/Fe_3O_4$), surfactant (Pluronic L121) or nanoparticle/surfactant stabilized dicyclopentadiene high internal phase emulsions (DCPD HIPEs). Upon curing, cavity sizes were found to vary drastically between 950 ± 360 µm down to 7 ±3 µm de- pending on the HIPE formulations. As-obtained nanocomposite polyHIPE foams were functionalized using elemental bromine in THF. Upon bromination the nanoparticles are moved from the cavities surfaces into the bulk phase of the polymer scaffold, which affects the inductive-heating capability of the magnetic nanocomposite foams decreasing it by the factor of 2.
Keywords: chemical technology, nanocomposites, bromination, microstructure, pickering HIPEs, $γFe_2O_3/Fe_3O_4$ nanoparticles, Ring Opening Metathesis Polymerization (ROMP), dicyclopentadiene, inductive heating
Published in DKUM: 24.08.2017; Views: 1237; Downloads: 143
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4. Particle identification performance of the prototype aerogel RICH counter for the Belle II experimentS. Iwata, Samo Korpar, Peter Križan, Rok Pestotnik, Luka Šantelj, Andrej Seljak, Elvedin Tahirović, 2016, original scientific article Abstract: We have developed a new type of particle identification device, called an aerogel ring imaging Cherenkov (ARICH) counter, for the Belle II experiment. It uses silica aerogel tiles as Cherenkov radiators. For detection of Cherenkov photons, hybrid avalanche photo-detectors (HAPDs) are used. The designed HAPD has a high sensitivity to single photons under a strong magnetic field. We have confirmed that the HAPD provides high efficiency for single-photon detection even after exposure to neutron and $\gamma$-ray radiation that exceeds the levels expected in the 10-year Belle II operation. In order to confirm the basic performance of the ARICH counter system, we carried out a beam test at the using a prototype of the ARICH counter with six HAPD modules. The results are in agreement with our expectations and confirm the suitability of the ARICH counter for the Belle II experiment. Based on the in-beam performance of the device, we expect that the identification efficiency at $3.5\,{\rm GeV}/c$ is 97.4% and 4.9% for pions and kaons, respectively. This paper summarizes the development of the HAPD for the ARICH and the evaluation of the performance of the prototype ARICH counter built with the final design components.
Keywords: H14, elementary particle physics, particle detectors, Belle II detector, ring imaging Cherenkov counters, RICH counters
Published in DKUM: 21.07.2017; Views: 1365; Downloads: 487
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5. Integrations on ringsIztok Banič, 2017, original scientific article Abstract: In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to f. The main goal of the paper is to generalize this notion of the indefinite integral from the ring of real functions to any ring. We also investigate basic properties of such generalized integrals and compare them to the well-known properties of indefinite integrals of real functions.
Keywords: ring, integration, Jordan integration, derivation, Jordan derivation
Published in DKUM: 10.05.2017; Views: 1151; Downloads: 202
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6. Ring opening metathesis polymerisation (ROMP) as a tool for polyhipes with extraordinary mechanical propertiesSebastijan Kovačič, 2013, professional article Abstract: PolyHIPE materials have been prepared by Ring Opening Metathesis Polymerisation (ROMP) of dicyclopentadiene. Two characteristic features for successful stabilization of high internal phase emulsions (HIPEs) were tuned in order to achieve improvements regarding mechanical properties of polyHIPEs.Mechanical properties of the new materials were related to variations of the surfactant concentration and the volume ratio of the internal phase in HIPEs. Values for Youngʼs moduli were about a hundred times higher than in standard polyHIPE materials with the same level of porosity, which represents a major improvement for highly porous cellular polymeric materials. Moreover, fully interconnected macroporous morphology was found forpolyHIPEs, where respective HIPEs were stabilized with only 0.25 v% of surfactant.
Keywords: emulsion templating, ring opening metathesis polymerization, dicyclopentadiene, ROMP, mechanical characteristics, polyHIPEs
Published in DKUM: 21.12.2015; Views: 2518; Downloads: 104
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7. On functional equations related to derivations in semiprime rings and standard operator algebrasNejc Širovnik, 2012, original scientific article Abstract: In this paper functional equations related to derivations on semiprime rings and standard operator algebras are investigated. We prove, for example, the following result, which is related to a classical result of Chernoff. Let ▫$X$▫ be a real or complex Banach space, let ▫$L(X)$▫ be the algebra of all bounded linear operators of ▫$X$▫ into itself and let ▫$A(X) subset L(X)$▫ be a standard operator algebra. Suppose there exist linear mappings ▫$D,G colon A(X) to L(X)$▫ satisfying the relations ▫$D(A^3)=D(A^2)A + A^2G(A)$▫, ▫$G(A^3) = G(A^2)A + A^2D(A)$▫ for all ▫$A in A(X)$▫. In this case there exists ▫$B in L(X)$▫ such that ▫$D(A) = G(A) = [A,B]$▫ holds for all ▫$A in A(X)$▫.
Keywords: matematika, algebra, prakolobar, polprakolobar, Banachov prostor, standardna operatorska algebra, odvajanje, jordansko odvajanje, jordansko trojno odvajanje, mathematics, algebra, prime ring, semiprime ring, Banach space, standard operator algebra, derivation, Jordan derivation, Jordan triple derivation
Published in DKUM: 10.07.2015; Views: 1479; Downloads: 68
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8. On some functional equations arising from (m, n)-Jordan derivations and commutativity of prime ringsMaja Fošner, Joso Vukman, 2012, original scientific article Abstract: The purpose of this paper is to prove the following result. Let ▫$m, n ge 1$▫ be some fixed integers with ▫$m ne n$▫, and let ▫$R$▫ be a prime ring with ▫$(m+n)^2 < text{char} (R)$▫. Suppose a nonzero additive mapping ▫$D : R to R$▫ exists satisfying the relation ▫$(m+n)^2 D(x^3) = m(3m+n) D(x)x^2 + 4mnxD(x)x + n(3n+m)x^2 D(x)$▫ for all ▫$x in R$▫. In this case ▫$D$▫ is a derivation and ▫$R$▫ is commutative.
Keywords: matematika, prakolobar, polprakolobar, odvajanje, jordansko odvajanje, levo odvajanje, mathematics, prime ring, semiprime ring, derivation, Jordan derivation, left dderivation, left Jordan derivation, (m, n)-Jordan drivation
Published in DKUM: 10.07.2015; Views: 1292; Downloads: 88
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9. On certain functional equation arising from (m, n)-Jordan centralizers in prime ringsNina Peršin, Joso Vukman, 2012, original scientific article Abstract: The purpose of this paper is to prove the following result. Let ▫$m ge 1$▫, ▫$n ge 1$▫ be some fixed integers and let ▫$R$▫ be a prime ring with ▫$text{char}(R)= 0$▫ or ▫$(m+n)^2 < text{char}(R)$▫. Suppose there exists an additive mapping ▫$T colon R to R$▫ satisfying the relation ▫$2(m+n)^2T(x^3) = m(2m+n)T(x)x^2 + 2mnxT(x)x + n(2n+m)x^2T(x)$▫ for all ▫$x in R$▫. In this case ▫$T$▫ is a two-sided centralizer.
Keywords: matematika, algebra, kolobar, prakolobar, polprakolobar, Banachov prostor, Hilbertov prostor, algebra vseh omejenih linearnih operatorjev, standardna operatorska algebra, odvajanje, jordansko odvajanje, centralizator, algebra, ring, prime ring, semiprime ring, Banach space, Hilbert space, algebra of all bounded linear operators, standard operator algebra, derivation, Jordan derivation, left (right) centralizer, two-sided centralizer, left (right) Jordan centralizer, (m, n)-Jordan centralizer
Published in DKUM: 10.07.2015; Views: 1422; Downloads: 139
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10. Identities with generalized derivations in prime ringsMaja Fošner, Joso Vukman, 2012, original scientific article Abstract: In this paper we investigate identities with two generalized derivations in prime rings. We prove, for example, the following result. Let ▫$R$▫ be a prime ring of characteristic different from two and let ▫$F_1, F_2 colon R to R$▫ be generalized derivations satisfying the relation ▫$F_1(x)F_2(x) + F_2(x)F_1(x) = 0$▫ for all ▫$x in R$▫. In this case either ▫$F_1 = 0$▫ or ▫$F_2 = 0$▫.
Keywords: matematika, prakolobar, polprakolobar, odvajanje, posplošeno odvajanje, mathematics, prime ring, semiprime ring, derivation, generalized derivation
Published in DKUM: 10.07.2015; Views: 1212; Downloads: 100
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