Полу-Фредхолмови оператори на Хилбертовим C∗-модулима

In the first part of the thesis, we establish the semi-Fredholm theory on Hilbert C∗- modules as a continuation of the Fredholm theory on Hilbert C∗-modules which was introduced by Mishchenko and Fomenko. Starting from their definition of C∗-Fredholm operator, we give definition of semi-C∗-Fredholm operator and prove that these operators correspond to one-sided invertible elements in the Calkin algebra. Also, we give definition of semi-C∗-Weyl operators and semi-C∗-B-Fredholm operators and obtain in this connection several results generalizing the counterparts from the classical semi-Fredholm theory on Hilbert spaces. Finally, we consider closed range operators on Hilbert C∗-modules and give necessary and sufficient conditions for a composition of two closed range C∗-operators to have closed image. The second part of the thesis is devoted to the generalized spectral theory of operators on Hilbert C∗-modules. We introduce generalized spectra in C∗-algebras of C∗-operators and give description of such spectra of shift operators, unitary, self-adjoint and normal operators on the standard Hilbert C∗- module. Then we proceed further by studying generalized Fredholm spectra (in C∗-algebras) of operators on Hilbert C∗-modules induced by various subclasses of semi-C∗-Fredholm operators. In this setting we obtain generalizations of some of the results from the classical spectral semi-Fredholm theory such as the results by Zemanek regarding the relationship between the spectra of an operator and the spectra of its compressions. Also, we study 2×2 upper triangular operator matrices acting on the direct sum of two standard Hilbert C∗-modules and describe the relationship between semi-C∗-Fredholmness of these matrices and of their diagonal entries.У првом делу тезе успостављамо полу-Фредхолмову теориjу на Хилбертовим C∗- модулима као наставак Фредхолмове теориjе на Хилбертовим C∗-модулима коjу су увели Мишченко и Фоменко. Полазећи од њихове дефинициjе C∗-Фредхолмових оператора, даjе- мо дефинициjу полу-C∗-Фредхолмовог оператора и доказуjемо да ти оператори одговараjу jеднострано инвертибилним елементима у Калкиновоj алгебри. Такође, даjемо дефиници- jу полу-C∗-Ваjлових оператора и полу-C∗-Б-Фредхолмових оператора и добиjамо с тим у вези више резултата коjи генерализуjу пандане из класичне полу-Фредхолмове теориjе на Хилбертовим просторима. На краjу, разматрамо операторе са затвореном сликом на Хилбертовим C∗-модулима и даjемо потребне и довољне услове да композициjа два C∗- оператора са затвореном сликом има затворену слику. Други део тезе посвећен jе генера- лизованоj спектралноj теориjи оператора на Хилбертовим C∗-модулима. За C∗-операторе дефинишемо генерализоване спектре у C∗-алгебри и даjемо опис таквих спектара у кон- кретном случаjу оператора помака, унитарних, самоадjонгованих и нормалних оператора на стандардном Хилбертовом C∗-модулу. Затим настављамо даље проучаваjући генера- лизоване Фредхолмове спектре (у C∗-алгебрама) оператора на Хилбертовим C∗-модулима индукованим различитим подкласама полу-C∗-Фредхолмових оператора. У овом контек- сту добиjамо уопштење неких резултата из класичне спектралне полу-Фредхолмове теори- jе, као што су Земанекови резултати у вези релациjа између спектара оператора и спектара њихових компресиjа. Такође, проучавамо 2 × 2 горње триjангуларне операторске матрице коjе делуjу на директноj суми два стандардна Хилбертова C∗-модула и описуjемо однос између полу-C∗-Фредхолмности ових матрица и њихових диjагоналних елемената

Powder bed fusion–laser beam (PBF-LB) three-dimensional (3D) printing: Influence of laser hatching distance on the properties of zolpidem tartrate tablets

Laser sintering, known as powder bed fusion–laser beam (PBF-LB), offers promising potential for the fabrication of patient-specific drugs. The aim of this study was to provide an insight into the PBF-LB process with regard to the process parameters, in particular the laser hatching distance, and its influence on the properties of zolpidem tartrate (ZT) tablets. PHARMACOAT® 603 was used as the polymer, while Candurin® Gold Sheen and AEROSIL® 200 were added to facilitate 3D printing. The particle size distribution of the powder blend showed that the layer height should be set to 100 µm, while the laser hatching distance was varied in five different steps (50, 100, 150, 200 and 250 µm), keeping the temperature and laser scanning speed constant. Increasing the laser hatching distance and decreasing the laser energy input led to a decrease in the colour intensity, mass, density and hardness of the ZT tablets, while the disintegration and dissolution rate were faster due to the more fragile bonds between the particles. The laser hatching distance also influenced the ZT dosage, indicating the importance of this process parameter in the production of presonalized drugs. The absence of drug-polymer interactions and the amorphization of the ZT were confirmed

Антибактеријска својства талусних јетрењача marchantia polymorpha l., conocephalum conicum (l.) dum. И pellia endiviifolia (dicks.) dumort.

The antimicrobial activity of methanol extracts of three thalloid liver­worts, Marchantia polymorpha, Conocephalum conicum and Pellia endiviifolia and bis-bibenzyl marchantin A, the most dominant compound in the methanol extract of M. polymorpha, have been investigated in this research. 1H-NMR spec­troscopy revealed that the M. polymorpha and P. endiviifolia extracts of liverwort contain terpenes, oils, sugars and bis-bibenzyls, while these specific macrocyclic compounds were absent in the C. conicum extract. The anti­mic­robial potential was tested on eight bacterial strains. Antimicrobial effects of extracts and mar­chantin A were observed against Gram-positive bacteria, while they showed no effect against Gram-negative bacteria in both methods used – well diffusion and broth microdilution.У овом раду испитиван је хемијски састав и антибактеријска активност метанолних екстраката три јетрењачe, Marchantia polymorpha, Conocephalum conicum и Pellia endiveifolia и бис-бибензила маршанцина A, доминантне компоненте у метанолном екстракту M. polymorpha. 1H-NMR спектроскопија је показала присуство терпена, уља, шећера и бис-бибензила у екстрактима M. polymorpha и P. endiviifolia, док екстракт C. conicum не садржи специфична макроциклична једињења – бис-бибензиле. Антимикробни потен- цијал је тестиран на осам бактеријских сојева. Антимикробни ефекат маршанцина А уочен је на све грам позитивне сојеве, док је ефекат изостао код грам негативних сојева у обе тестиране методе – дифузионе методе у бунарима и микродилуционе методе у хранљивом бујону

Understanding the Effect of Energy Density and Formulation Factors on the Printability and Characteristics of SLS Irbesartan Tablets-Application of the Decision Tree Model

Selective laser sintering (SLS) is a rapid prototyping technique for the production of three-dimensional objects through selectively sintering powder-based layer materials. The aim of the study was to investigate the effect of energy density (ED) and formulation factors on the printability and characteristics of SLS irbesartan tablets. The correlation between formulation factors, ED, and printability was obtained using a decision tree model with an accuracy of 80%. FT-IR results revealed that there was no interaction between irbesartan and the applied excipients. DSC results indicated that irbesartan was present in an amorphous form in printed tablets. ED had a significant influence on tablets' physical, mechanical, and morphological characteristics. Adding lactose mon-ohydrate enabled faster drug release while reducing the possibility for printing with different laser speeds. However, formulations with crospovidone were printable with a wider range of laser speeds. The adjustment of formulation and process parameters enabled the production of SLS tablets with hydroxypropyl methylcellulose with complete release in less than 30 min. The results suggest that a decision tree could be a useful tool for predicting the printability of pharmaceutical formulations. Tailoring the characteristics of SLS irbesartan tablets by ED is possible; however, it needs to be governed by the composition of the whole formulation

Uloga krvno-moždane barijere u psihijatrijskim oboljenjima

The blood-brain barrier (BBB) is formed by continuous, closely connected endothelial cells, enveloped in the basal lamina, pericytes, and foot extensions of astrocytes. BBB has a vital role in brain metabolism and protects the brain parenchyma from harmful agents present in the systemic circulation. Damage to the BBB and an increase in its permeability have an important role in many neurodegenerative diseases. This paper aims to review the literature on the impact of the BBB damage on psychiatric illness, a largely neglected and under researched area. Links between BBB impairment and specific neuropsychiatric disorders are described including schizophrenia, affective disorders, dementias with behavioral disorders, and alcohol use disorder, with comparison to typical hereditary small vessel diseases affecting the BBB such as cerebral autosomal dominant arteriopathy with subcortical infarction and leukoencephalopathy (CADASIL) and mitochondrial encephalomyopathy, lactic acidosis, and stroke-like episodes (MELAS). The authors critically summarize possible pathogenic mechanisms linking BBB damage and these common disorders.Крвно-мождана баријера (КМБ) се састоји од континураних, тесно спојених ендотелних ћелија омотаних базалном ламином, перицитима и сто-паластим продужецима астроцита. КМБ има виталну функцију и можданом метаболизму и штити мождани паренхим од штетних фактора присутних у системској циркулацији. Показано је да оштећење КМБ и повећање њене пропустљи-вости има значајну улогу у многим неуродегене-ративним обољењима. Циљ овога рада је преглед литературе о значају оштећења КМБ код психијатријских обољења, до сада занемареној и недовољно истраженој облас-ти. Повезаност измедју поремећаја КМБ и неуро-психијатријских поремећаја је посебно анализи-рана за схизофренију, афективне поремећаје, де-менције са бихевиоралним изменама, поремећај употребе алкохола, са посебним освртом на на-следне болести малих крвних судова мозга са оштећењем КМБ као што су церебрална аутозо-мално доминантна артериопатија са супкортика-ним инфарктима и леукоенцефалопатијом (CADASIL) и митохондријска енцефаломиопатија са лактатном ацидозом и епизодама налик можда-ном удару (MELAS). Аутори критички сумирају могуће патогенетске механизме који повезују оштећења КМБ са овим честим обољењима

Полу-Фредхолмови оператори на Хилбертовим C∗-модулима

In the first part of the thesis, we establish the semi-Fredholm theory on Hilbert C∗- modules as a continuation of the Fredholm theory on Hilbert C∗-modules which was introduced by Mishchenko and Fomenko. Starting from their definition of C∗-Fredholm operator, we give definition of semi-C∗-Fredholm operator and prove that these operators correspond to one-sided invertible elements in the Calkin algebra. Also, we give definition of semi-C∗-Weyl operators and semi-C∗-B-Fredholm operators and obtain in this connection several results generalizing the counterparts from the classical semi-Fredholm theory on Hilbert spaces. Finally, we consider closed range operators on Hilbert C∗-modules and give necessary and sufficient conditions for a composition of two closed range C∗-operators to have closed image. The second part of the thesis is devoted to the generalized spectral theory of operators on Hilbert C∗-modules. We introduce generalized spectra in C∗-algebras of C∗-operators and give description of such spectra of shift operators, unitary, self-adjoint and normal operators on the standard Hilbert C∗- module. Then we proceed further by studying generalized Fredholm spectra (in C∗-algebras) of operators on Hilbert C∗-modules induced by various subclasses of semi-C∗-Fredholm operators. In this setting we obtain generalizations of some of the results from the classical spectral semi-Fredholm theory such as the results by Zemanek regarding the relationship between the spectra of an operator and the spectra of its compressions. Also, we study 2×2 upper triangular operator matrices acting on the direct sum of two standard Hilbert C∗-modules and describe the relationship between semi-C∗-Fredholmness of these matrices and of their diagonal entries.У првом делу тезе успостављамо полу-Фредхолмову теориjу на Хилбертовим C∗- модулима као наставак Фредхолмове теориjе на Хилбертовим C∗-модулима коjу су увели Мишченко и Фоменко. Полазећи од њихове дефинициjе C∗-Фредхолмових оператора, даjе- мо дефинициjу полу-C∗-Фредхолмовог оператора и доказуjемо да ти оператори одговараjу jеднострано инвертибилним елементима у Калкиновоj алгебри. Такође, даjемо дефиници- jу полу-C∗-Ваjлових оператора и полу-C∗-Б-Фредхолмових оператора и добиjамо с тим у вези више резултата коjи генерализуjу пандане из класичне полу-Фредхолмове теориjе на Хилбертовим просторима. На краjу, разматрамо операторе са затвореном сликом на Хилбертовим C∗-модулима и даjемо потребне и довољне услове да композициjа два C∗- оператора са затвореном сликом има затворену слику. Други део тезе посвећен jе генера- лизованоj спектралноj теориjи оператора на Хилбертовим C∗-модулима. За C∗-операторе дефинишемо генерализоване спектре у C∗-алгебри и даjемо опис таквих спектара у кон- кретном случаjу оператора помака, унитарних, самоадjонгованих и нормалних оператора на стандардном Хилбертовом C∗-модулу. Затим настављамо даље проучаваjући генера- лизоване Фредхолмове спектре (у C∗-алгебрама) оператора на Хилбертовим C∗-модулима индукованим различитим подкласама полу-C∗-Фредхолмових оператора. У овом контек- сту добиjамо уопштење неких резултата из класичне спектралне полу-Фредхолмове теори- jе, као што су Земанекови резултати у вези релациjа између спектара оператора и спектара њихових компресиjа. Такође, проучавамо 2 × 2 горње триjангуларне операторске матрице коjе делуjу на директноj суми два стандардна Хилбертова C∗-модула и описуjемо однос између полу-C∗-Фредхолмности ових матрица и њихових диjагоналних елемената

Age and weather effects on between and within ring variations of number, width and coarseness of tracheids and radial growth of young Norway spruce

Annual growth, fibre and wood properties of Norway spruce are all under strong influence from genetics, age and weather. They change dynamically, particularly at young ages. Most genetic research and tree improvement programs are based on data from this most dynamic phase of the life of trees, affected by differences in weather among sites and years. In the work presented, influences of age and weather were investigated and modelled at the detail of annual rings and at the sub-tree ring level of earlywood, transitionwood and latewood. The data used were analysed from increment cores sampled at age 21 years from almost 6000 Norway spruce trees of known genetic origin, grown on two sites in southern Sweden. The traits under investigation were radial growth, cell widths, cell numbers, cell wall thickness and coarseness as a measure of biomass allocation at cell level. General additive mixed models (GAMMs) were fitted to model the influences of age, local temperature and precipitation. The best models were obtained for number of tracheids formed per year, ring width, average radial tracheid width in earlywood, and ring averages for tangential tracheid width and coarseness. Considering the many sources behind the huge variation, the explained part of the variability was high. For all traits, models were developed using both total tree age and cambial age (ring number) to express age. Comparisons indicate that the number of cell divisions and ring width are under stronger control of tree age, but the other traits under stronger control of cambial age. The models provide a basis to refine data prior to genetic evaluations by compensating for estimated differences between sites and years related to age and weather rather than genetics. Other expected applications are to predict performance of genotypes in relation to site or climate and simulation of climate change scenarios.Bio4Energ