Schwartz - Zippelov teorem i neke njegove primjene

U ovom radu izložen je rezultat poznat pod nazivom Schwartz - Zippelova lema ili Schwartz - Zippelov teorem. Tema rada pripada pretežno algebri, ali ima značajne primjene u drugim matematičkim područjima kao što je na primjer teorija algoritama, te kombinatorika. Rad se sastoji od tri poglavlja. U uvodu je ukratko opisana tema i cilj rada. Prvo poglavlje sadrži kratku povijest nastanka teorema, različite oblike rezultata pojedinih autora, te kratki opis pojmova korištenih u samom radu. Drugo poglavlje sastoji se od iskaza i dokaza Schwartz - Zippelovog teorema, a u trećem poglavlju izložene su neke primjene tog teorema na probleme koji se mogu svesti na testiranje jednakosti polinoma. Takvi su, primjerice, problem postojanja savršenog sparivanja u grafu i ispitivanje svojstva asocijativnosti u grupoidu. Uz svaku primjenu navedeni su i prikladni primjeri.In this diploma thesis we present the result usually called the Schwartz-Zippel lemma or the Schwartz-Zippel theorem. The nature of this theorem is basically algebraic, but it has significant applications in other areas of mathematics, such as the theory of algorithms and combinatorial theory. The thesis consists of three chapters. The main theme and objective are briefly described in the introduction. The first chapter contains a short history of the theorem’s origins, various forms of the main results by different authors and some comments of basic concepts related to this topic. The statement and a proof of the Schwartz-Zippel theorem are given in the second chapter, together with the general outline of its applications. The third and final chapter consists of some applications to problems which can be reduced to polynomial identity testing, including the existence of a perfect matching in a graph and testing of the associativity property in a groupoi

Scaling-up batch conditions for efficient sucrose hydrolysis catalyzed by an immobilized recombinant Pichia pastoris cells in a stirrer tank reactor

Background: Invert sugar is used greatly in food and pharmaceutical industries. This paper describes scaling-up batch conditions for sucrose inversion catalyzed by the recombinant Pichia pastoris BfrA4X whole cells expressing Thermotoga maritima invertase entrapped in calcium alginate beads. For the first time, we describe the application of a kinetic model to predict the fractional conversion expected during sucrose hydrolysis reaction in both, a model and a prototype bioreactor with 0.5- and 5-L working volume, respectively. Results: Different scaled-up criteria used to operate the 0.5-L bioreactor were analyzed to explore the invert sugar large scale production. After model inversion studies, a 5-L scaled-up reaction system was performed in a 7-L stirred reactor. Both scaled-up criteria, immobilized biocatalyst dosage and stirring speed, were analyzed in each type of bioreactors and the collected data were used to ensure an efficient scale-up of this biocatalyst. Conclusions: To date, there is not enough information to describe the large-scale production of invert sugar using different scaled-up criteria such as dose of immobilized biocatalyst and stirring speed effect on mass transfer. The present study results constitute a valuable tool to successfully carry out this type of high-scale operation for industrial purposes

VALES VI: ISM enrichment in star-forming galaxies up to z∼\sim0.2 using 12^{12}CO(1-0), 13^{13}CO(1-0) and C18^{18}O(1-0) line luminosity ratios

We present Atacama Large Millimeter/sub-millimeter Array (ALMA) observations towards 27 low-redshift ($0.02< z<0.2$) star-forming galaxies taken from the Valpara\'iso ALMA/APEX Line Emission Survey (VALES). We perform stacking analyses of the $^{12}$CO($1-0$), $^{13}$CO($1-0$) and C$^{18}$O($1-0$) emission lines to explore the $L'$ ($^{12}$CO($1-0$))/$L'$($^{13}$CO($1-0$))) (hereafter $L'$($^{12}$CO)/$L'$($^{13}$CO)) and $L'$($^{13}$CO($1-0$))/$L'$(C$^{18}$O($1-0$)) (hereafter $L'$($^{13}$CO)/$L'$(C$^{18}$O) line luminosity ratio dependence as a function of different global galaxy parameters related to the star formation activity. The sample has far-IR luminosities $10^{10.1-11.9}$L$_{\odot}$ and stellar masses of $10^{9.8-10.9}$M$_{\odot}$ corresponding to typical star-forming and starburst galaxies at these redshifts. On average we find a $L'$($^{12}$CO)/$L'$($^{13}$CO) line luminosity ratio value of 16.1$\pm$2.5. Galaxies with evidences of possible merging activity tend to show higher $L'$($^{12}$CO)/$L'$($^{13}$CO) ratios by a factor of two, while variations of this order are also found in galaxy samples with higher star formation rates or star formation efficiencies. We also find an average $L'$($^{13}$CO)/$L'$(C$^{18}$O) line luminosity ratio of 2.5$\pm$0.6, which is in good agreement with those previously reported for starburst galaxies. We find that galaxy samples with high $L_{\text{IR}}$, SFR and SFE show low $L'$($^{13}$CO)/$L'$(C$^{18}$O) line luminosity ratios with high $L'$($^{12}$CO)/$L'$($^{13}$CO) line luminosity ratios, suggesting that these trends are produced by selective enrichment of massive stars in young starbursts.Comment: 16 pages, 10 figures to be published in MNRA

Optimization of worm-bed leachate for culturing of tomato ( Lycopersicon esculentum Mill) inoculated with Glomus fasciculatum and Pseudomonas fluorescens

A response surface technique was used to analyze the effect of Glomus fasciculatum , Pseudomonas fluorescens and worm-bed leachate (WBL) on growth, yield and characteristics of tomato ( Lycopersicon esculentum Mill). The treatments combined inoculation with or without P. fluorescens or G. fasciculatum and the application of WBL at 20% (v/v) each day or every three days. Plant height, number of leaves and yield of tomato fruits was not affected by the factors studied. However, plants with foliar application of WBL each day developed wider stems than those with an application every three days. The pH of the fruits was lower when WBL was applied every three days compared to a daily application. The soluble solids content of the fruits was higher when WBL was applied daily compared to those sprayed every three days. Plant development was not affected by addition of P. fluorescens, G. fasciculatum or WBL, but WBL changed fruit characteristics

Ethanol induction of laccase depends on nitrogen conditions of Pycnoporus sanguineus

Background: Ethanol has been pointed out as a laccase inducer. However, there are controversial reports about its efficiencywith some fungi. In this study,we hypothesized that ethanol laccase induced in Pycnoporus sanguineus depends on nitrogen nutriment conditions. To prove this,we assessed laccase production in submerged cultures of P. sanguineus,with different nitrogen concentrations andwith, orwithout ethanol added in a factorial designed experiment. Results: In order to analyze the effects of factors on the response variables, a factorial ANOVA, and response-surface models were performed. It was found that the nitrogen source was the main factor that affected laccase production in P. sanguineus. The treatments with yeast extract (2 g/L) and ethanol (3 g/L) induced the highest laccase activity (31.01 \ub1 4.9 U/L), while the treatments with urea reached the lowest activity (less than 1.6 U/L). Ethanol had positive and synergic effects on laccase production, in accordance with the surface response model, as long as simple nitrogen sources (urea) were not available. Conclusions: We suggest that laccase in P. sanguineus is regulated by a catabolic nitrogen repressionmechanism; laccase activity is strongly inhibited by urea used as nitrogen source and it decreases when the amount of urea increases; contrarily, a synergic positive effect was observed between yeast extract and ethanol on laccase production

Synthesis of Densely Packaged, Ultrasmall Pt02Clusters within a Thioether-Functionalized MOF: Catalytic Activity in Industrial Reactions at Low Temperature

The gram\u2010scale synthesis, stabilization, and characterization of well\u2010defined ultrasmall subnanometric catalytic clusters on solids is a challenge. The chemical synthesis and X\u2010ray snapshots of Pt02 clusters, homogenously distributed and densely packaged within the channels of a metal\u2013organic framework, is presented. This hybrid material catalyzes efficiently, and even more importantly from an economic and environmental viewpoint, at low temperature (25 to 140\u2009\ub0C), energetically costly industrial reactions in the gas phase such as HCN production, CO2 methanation, and alkene hydrogenations. These results open the way for the design of precisely defined catalytically active ultrasmall metal clusters in solids for technically easier, cheaper, and dramatically less\u2010dangerous industrial reactions

Analysis of a suppressive subtractive hybridization library of Alternaria alternata resistant to 2-propenyl isothiocyanate

Background: Isothiocyanates (ITCs) are natural products obtained from plants of the Brassicas family. They represent an environmentally friendly alternative for the control of phytopathogenic fungi. However, as it has been observed with synthetic fungicides, the possibility of inducing ITC-resistant strains is a major concern. It is, therefore, essential to understanding the molecular mechanisms of fungal resistance to ITCs. We analyzed a subtractive library containing 180 clones of an Alternaria alternata strain resistant to 2-propenyl ITC (2-pITC). After their sequencing, 141 expressed sequence tags (ESTs) were identified using the BlastX algorithm. The sequence assembly was carried out using CAP3 software; the functional annotation and metabolic pathways identification were performed using the Blast2GO program. Results: The bioinformatics analysis revealed 124 reads with similarities to proteins involved in transcriptional control, defense and stress pathways, cell wall integrity maintenance, detoxification, organization and cytoskeleton destabilization; exocytosis, transport, DNA damage control, ribosome maintenance, and RNA processing. In addition, transcripts corresponding to enzymes as oxidoreductases, transferases, hydrolases, lyases, and ligases, were detected. Degradation pathways for styrene, aminobenzoate, and toluene were induced, as well as the biosynthesis of phenylpropanoid and several types of N-glycan. Conclusions: The fungal response showed that natural compounds could induce tolerance/resistancemechanisms in organisms in the same manner as synthetic chemical products. The response of A. alternata to the toxicity of 2-pITC is a sophisticated phenomenon including the induction of signaling cascades targeting a broad set of cellular processes. Whole-transcriptome approaches are needed to elucidate completely the fungal response to 2-pITC

Corrigendum: Analysis of the common genetic component of large-vessel vasculitides through a meta-Immunochip strategy.

Giant cell arteritis (GCA) and Takayasu's arteritis (TAK) are major forms of large-vessel vasculitis (LVV) that share clinical features. To evaluate their genetic similarities, we analysed Immunochip genotyping data from 1,434 LVV patients and 3,814 unaffected controls. Genetic pleiotropy was also estimated. The HLA region harboured the main disease-specific associations. GCA was mostly associated with class II genes (HLA-DRB1/HLA-DQA1) whereas TAK was mostly associated with class I genes (HLA-B/MICA). Both the statistical significance and effect size of the HLA signals were considerably reduced in the cross-disease meta-analysis in comparison with the analysis of GCA and TAK separately. Consequently, no significant genetic correlation between these two diseases was observed when HLA variants were tested. Outside the HLA region, only one polymorphism located nearby the IL12B gene surpassed the study-wide significance threshold in the meta-analysis of the discovery datasets (rs755374, P\u2009=\u20097.54E-07; ORGCA\u2009=\u20091.19, ORTAK\u2009=\u20091.50). This marker was confirmed as novel GCA risk factor using four additional cohorts (PGCA\u2009=\u20095.52E-04, ORGCA\u2009=\u20091.16). Taken together, our results provide evidence of strong genetic differences between GCA and TAK in the HLA. Outside this region, common susceptibility factors were suggested, especially within the IL12B locus