Konformalna preslikavanja

Najvažniji rezultat ovog diplomskog rada je Riemannov teorem o preslikavanju. Prije njegovog dokaza, u početnom poglavlju definirali smo sama konformalna preslikavanja. Nakon toga smo proučili razlomljene linearne transformacije i njihovu povezanost sa tim preslikavanjima. Važnu ulogu u dokazu Riemannovog teorema o preslikavanju imale su normalne familije koje smo definirali u trećem poglavlju i dokazali sljedeće: ako je $F \subset H(\Omega)$ i $F$ je uniformno ograničena na svakom kompaktnom podskupu područja $\Omega$, onda je $F$ normalna familija. Nakon sto smo definirali i konformalno ekvivalentna područja, mogli smo dokazati Riemannov teorem o preslikavanju. U petom poglavlju definirali smo klasu $S$ koju čine sve $f \in H(U)$ koje su injekcije na $U$ i za koje vrijedi $f(0)=0, f'(0)=1$, te smo pokazali neka svojstva te klase. U poglavlju "Neprekidnost na rubovima" definirali smo jednostavne rubne točke i dokazali sljedeću tvrdnju: ako je $\Omega$ ograničeno jednostavno povezano područje u kompleksnoj ravnini i ako je svaka rubna točka od $\Omega$ jednostavna, tada se svako konformalno preslikavanje iz $\Omega$ na $U$ može proširiti na homeomorfizam iz $\overline{\Omega}$ na $\overline{U}$. U posljednjem poglavlju bavili smo se konformalnim preslikavanjima kružnih vijenaca i dokazali zanimljivo svojstvo: kružni vijenci $A(r_1, R_1)$ i $A(r_2, R_2)$ su konformalno ekvivalentni ako i samo ako je $R_1/r_1=R_2/r_2$.The most important result of this diploma thesis is the Riemann mapping theorem. Before we could prove it, we defined the conformal mappings in the first chapter. After that we studied linear fractional transformations and their connection with those mappings. The important part of proving the Riemann mapping theorem are normal families which we defined in the third chapter. We also proved that if $F \subset H(\Omega)$ and $F$ is uniformly bounded on every compact subset of the region $\Omega$; then $F$ is a normal family. After we defined conformally equivalent regions, we could prove the Riemann mapping theorem. In the fifth chapter we defined the class $S$ ; which is the class of all $f \in H(U)$ which are one-to-one in $U$ and satisfy \8f(0)=0, f'(0)=1\), and proved some of its properties. In the chapter "Continuity at the boundary" we defined simple boundary points and proved the next statement: if \8\Omega\) is a bounded simply connected region in the plane and if every boundary point of $\Omega$ is simple, then every conformal mapping of $\Omega$ onto $U$ extends to a homeomorphism off $\Omega$ onto $U$. In the last chapter we studied the conformal mapping of an annulus and proved this interesting property: $A(r_1, R_1)$ and $A(r_2, R_2)$ are conformally equivalent if and only if $R_1/r_1=R_2/r_2$

Influence of transplantation of neural stem cells on the expression of genes involved in the programmed cell death following ischemic brain stroke

Ishemijski moždani udar, te posljedične tkivna hipoksija i ishemija, uzrokuju značajno oštećenje moždanog tkiva. Jedan od pristupa u potrazi za pronalaskom uspješne obnove oštećenog tkiva uključuje primjenu matičnih stanica. U ovom istraživanju osnovni cilj bio je istražiti kako transplantacija živčanih matičnih stanica u mozak miša zahvaćen ishemijskim moždanim udarom utječe na ekspresiju gena uključenih u programiranu staničnu smrt. Istražili smo staničnu smrt posredovanu proteinom AIF (Aifm1), nekroptozu (Ripk1, Ripk3, Mlkl) te apoptozu (Casp3). Nakon što je moždani udar induciran privremenom okluzijom lijeve srednje moždane arterije, živčane matične stanice su transplantirane u striatum zahvaćene polutke (lijeve, ipsilateralne) mozga 24 h nakon moždanog udara. Miševi su žrtvovani 15 dana nakon induciranja moždanog udara te su za analizu ekspresije navedenih gena korištene obje polutke mozga. Transplantacija živčanih matičnih stanica u mozak miševa zahvaćenih moždanim udarom značajno je smanjila ekspresiju gena Aifm1 i Casp3 koji potiču staničnu smrt. Istovremeno, ekspresija gena uključenih u nekroptozu (Ripk1, Ripk3, Mlkl) značajno je povišena nakon moždanog udara, dok injiciranje medija nakon moždanog udara smanjuje njihovu ekspresiju. Nalaz da transplantacija živčanih matičnih stanica održava visoku ekspresiju gena Ripk3 te Mlkl može se objasniti njihovom novootkrivenom ulogom u prometu staničnih vezikula.Ischemic brain stroke is followed by significant tissue damage caused by hypoxia and ischemia. One of the most utilized experimental approaches for treatment of tissue hypoxia includes application of stem cells. In this study, we have analysed the effects of neural stem cell (NSC) transplantation in the mouse brain affected by stroke, on the expression of genes involved in programmed cell death: AIF-mediated cell death (Aifm1), necroptosis (Ripk1, Ripk3, Mlkl) and apoptosis (Casp3). Stroke had been induced by transient left middle cerebral artery occlusion (tMCAO) and NSC in proliferation supporting medium or the medium alone were transplanted in the striatum of affected (ipsilatheral) hemisphere 24 h following stroke. Mice had been sacrificed 14 days following stroke and both hemispheres were used for gene expression analysis. Transplantation of NSC in the mouse brain affected by stroke significantly downregulated damage-supportive genes Aifm1 and Casp3. Moreover, expression of genes involved in necroptosis (Ripk1, Ripk3, Mlkl) was increased following stroke, injection of proliferation supporting medium managed to reduce their level but transplantation of NSC supported high expression levels of Ripk3 and Mlkl for which was recently shown that play important roles in endosomal trafficking and extracellular vesicle generation

Preschoolers' fears

Strah je stanje koje je nelagodno i u sebi sadrži prijetnju, a posljedica je unutrašnjeg ili vanjskog podražaja. No, strah u evaluacijskom smislu može biti i koristan jer pomaže samozaštiti i preživljavanju pojedinca. Strah se pojavljuje u dobi od šest mjeseci. Većina djece u toj dobi ima izraženi strah od odvajanja od primarnog skrbnika. Kako djeca odrastaju, pojavljuju se i mnogi drugi strahovi npr. od: životinja, liječnika, otmičara, lopova, vremenskih nepogoda, imaginarnih bića, mraka, škole, bolesti, smrti, itd. Strah od liječnika jedan je od mnogih strahova karakterističnih za predškolsku dob. Cilj ovog istraživanja je bila utvrditi intenzitet straha, iskustva i doživljaje djece predškolske dobi pri odlascima liječniku/ci. Ispitivanje je provedeno na ukupno 61 djece, od toga 31 djevojčice i 30 dječaka. Sva djeca tijekom istraživanja pohađala su Dječje vrtiće Osijek.Fear is a condition that is uncomfortable and contains threat. It is a result of internal or external stimulation. However, in terms of evaluation, fear can be useful – it helps self-protection and survival of the individual . Fear appears at the age of six months. Most children at this age have expressed fear of separation from their primary guardian. As children grow older, there are many other fears such as fear of animals, doctors, being kidnapped, thieves, weather, imaginary creatures, the dark, school, illness, death, etc. Fear of doctors is one of many fears that are characteristic of preschool age. The aim of this study was to determine intensity of fear and experiences of preschool children when they go to the doctor's. Testing was conducted on a total of 61 children , of whom 31 are girls and 30 boys. All children during the research attended kindergartens in Osijek

Matrice nad nekomutativnim prstenima

Tema ovog radu su matrice nad nekomutativnim prstenom. U prvom i drugom poglavlju pod nazivom Prsteni i Moduli uvodimo osnovne pojmove koji su nam potrebni u daljnjem dijelu rada. Pojam poluprostota, kojim se bavimo u trećem poglavlju, je najosnovniji termin koji se proteze kroz čitav diplomski rad. Prezentiramo tri definicije poluprostog modula i dokazujemo da su one ekvivalentne. Pomoću navedenih uvjeta možemo dokazati Jacobsonov teorem o gustoći te definirati pojmove poluprostog i prostog prstena. Uz Jacobsonov teorem u radu dokazujemo i druge važne teoreme, kao primjer Wedderburnov teorem koji nam daje prikaz prstena R kao D-endomorfizam nad modulom E, gdje sa D označavamo konačnodimenzionalnu algebru sa dijeljenjem nad poljem k.The theme of this paper are matrices over noncommutative ring. In the first and second chapter titled Rings and Modules we introduce the basic concepts that are required in the far part of the work. The concept semisimplicity, the main theme of the third chapter, is the most basic term that runs through this entire graduate paper. We present three definitions of semisimple modules and prove that they are equivalent. Besides Jacobson’s theorem we also prove some others very important theorems, for example Wedderbun’s theorem which gives us a representation of a ring R as the ring of D-endomorphisms of module E, where D is a finite-dimensional division algebra over a field k. Using the above conditions we can prove Jacobson’s density theorem and define the terms of semisimple and simple ring

Anti-VEGF in Treatment of Central Retinal Vein Occlusion

Macular edema along with macular ischemia is responsible for decreased visual acuity in central retinal vein occlusion. Bevacizumab (Avastin, Genentech) blocks vascular endothelial growth factor (VEGF) induced hyperpermeability of blood vessels. In this prospective case series we investigated the efficacy of anti-VEGF treatment in reduction of central retinal thickness (CRT) and improvement in visual acuity (VA). 25 patients were followed up for 12 months and treated monthly with intravitreal bevacizumab. VA and CRT were measured at each visit. Treatment was discontinued as the peak improvement of either parameter was reached and reinstituted in case of deterioration/recurrence of edema. Study endpoints included: VA using ETDRS charts, CRT and number of injections at 12 months. Mean VA from all 25 patients increased by 3.1logMAR lines (p<0.05 compared to baseline). The improvement of VA after bevacizumab injection was in correlation with a decrease in CRT. In subgroup analyses, patients receiving bevacizumab injection within the first 3 months after CRVO showed an average VA gain of 4.2 logMAR lines. Mean of 4.5 injections was needed to control the disease during the follow-up period. Bevacizumab treatment was effective in VA and reducing CRT. It appears from subgroup analysis that initiation of treatment early in the course of disease produced better functional outcome. Several injections were needed to control the disease. Regular OCT examinations and retreatment are advised in order to maintain initially reached VA

Sestrinska skrb kod bolesnika sa tromboflebitisom i trombozom vena

Bolesti vena su izrazito česte u odrasloj populaciji. Tromboza je proces stvaranja ugruška u krvnoj ţili, dok je tromboflebitis površinskih vena upalni trombotički proces koji nastaje spontano ili nakon odreĎene kirurške intervencije (nastaje kao posljedica tromboze ili moţe izazvati trombozu) dijagnoza se najčešće postavlja klinički. Prikazani su podaci o etiopatogenezi,dijagnostici, terapiji i sestrinska skrb kod bolesnika sa tromboflebitisom i trombozom vena. U anamnezi bolesnika karakteristične su lokalne traume, ponavljajuće epizode, varikozne vene, korištenje raznih hormonskih pripravaka ili pojava koagulopatije u obitelji. Mnogi bolesnici oboljeli od tromboflebitisa imaju prikrivenu duboku vensku trombozu kasnije i plućnu emboliju koja ima visoku stopu smrtnosti. Osnovni cilj je prevencija, dok se liječenje temelji na sprečavanju proširenja flebitisa s površinskih na duboke vene i sestrinska skrb oko brige za terapiju (heparin niske molekularne mase) i primjena kompresivnih zavoja.Venous diseases are extremely common in the adult population. Thrombosis is the process of creating a clot in a blood vessel, while thrombophlebitis superficial venous thrombotic inflammatory process that occurs spontaneously or after certain surgical interventions (resulting from a thrombotic or can cause thrombosis) diagnosis is usually made clinically. There are presented on the etiopathogenesis, diagnosis, treatment and nursing care in patients with thrombophlebitis and venous thrombosis. In the history of the patient is characterized by local trauma, recurring episodes, varicose veins, use a variety of hormonal preparations or the occurrence of coagulopathy in the family. Many patients suffering from thrombophlebitis have hidden deep vein thrombosis and pulmonary embolism later that has a high mortality rate. The main goal is prevention, and the treatment is based on prevention of expansion of phlebitis with the surface to the deep veins, and a nurses concern of caring for therapy (heparin low molecular weight) and the application of compression bandages

Juvenīla idiopātiska artrīta klīniskās vadlīnijas

A.Vētra, D.Bērtule, I.Tāse - consultantspublishersversionPeer reviewe

Exercise induced rhabdomyolysis

Introduction. Rhabdomyolysis is a potentially life threatening disease, characterized by the release of intracellular calcium from skeletal muscles and can result in acute renal failure. Case report. A nineteen year old boy was admitted to the Clinic for Infective Diseases of Clinical Center Novi Sad. The disease was developing gradually and the symptoms were dizziness, muscle pain and dark color of urine. Due to the pathological level of aminotransferase he was hospitalized on the fourth day of the disease beginning with a suspicious diagnosis of acute viral hepatitis. In the hospital course of the disease, a further elevation of serum aminotransferases, creatine kinase and lactate dehydrogenase were registered. Additional serological analyses were done to exclude other possible causes of acute liver lesion. In the neurological status prolonged decontraction of quadriceps muscle was detected and the electromyography was suspicious on neuromyositis. Conclusion. Excessive muscular activity with the strenuous exercise is the leading, but very frequently overlooked, cause of rhabdomyolysis in healthy people. Excessive physical exercise may lead to elevation of the serum activity of aminotransferases and to suspicion of hepatitis

Neurobiological basis of sexual orientation

Iako je spolna orijentacija ljudske populacije varijabilna, većina ljudi prednost daje suprotnom spolu (heteroseksualna orijentacija). Postoji tek manjina koja pokazuje homoseksualnu orijentaciju. Dugo se godina glavno objašnjenje homoseksualnosti temeljilo na utjecaju psiholoških faktora. Danas postoji nešto drugačije shvaćanje homoseksualnosti. Jedna od teorija smatra da je homoseksualnost zapisana u genima. Istraživanja provedena na braći, uključujući i blizance, dokazala su da genetski čimbenik igra ulogu u muškoj, ali i ne ženskoj homoseksualnosti. Homoseksualnost vjerojatno ide ženskom linijom, pošto muškarci primaju svoj jedini X kromosom od majke, pa svako svojstvo koje je vezano uz X kromosom prenosi se sa majki na sinove u svakoj sljedećoj generaciji. Glavni ishod istraživanja je pronalazak povezanosti između homoseksualne orijentacije i markera u regiji Xq28 na X kromosomu. No, naknadno su neki znanstvenici otkrili određene nepravilnosti u toj teoriji. Osim te teorije, postoji i ona o povezanosti utjecaja hormona i spolne orijentacije. Najprije je na životinjskim modelima, a kasnije i na ljudima pokazano da androgeni steroidi koji djeluju prije rođenja mogu utjecati na spolnu orijentaciju odraslih ljudi. Postoje brojni nalazi koji pokazuju da je kod nekih vrsta aromatizacija (pretvorba testosterona u estradiol) kritični korak za maskulinizaciju mozga testosteronom. S obzirom da hormoni u perinatalnom razvoju utječu na razvoj mozga, oni također utječu i na razvoj ponašanja. Perinatalna kastracija mužjaka štakora i primjena testosterona na ženke uzrokovala je preferenciju istog spola. Iako je malo dokaza postoje neke naznake da perinatalni hormoni utječu i na seksualnu orijentaciju kod ljudi. Prema trećoj teoriji, mozgovi homoseksualaca i heteroseksualaca strukturno se razlikuju. Razlike se očituju u veličini treće intersticijske jezgre hipotalamusa, veličini suprahijazmatske jezgre te prednje komisure. Nakon različitih mišljenja o nastanku i uzrocima homoseksualnosti, znanstvenici su pokazali da je homoseksualnost orijentacija koja je nepromjenjiva. Ona nije izbor.Although sexual orientation of the human population is variable, most people give priority to the opposite sex (heterosexual orientation). There are only a minority of people who show homosexual orientation. For many years psychological factors were hold responsive for homosexuality. Understanding of homosexuality is today somewhat different. One of the theories believes that homosexuality is influenced by genes. Researches that were conducted on brothers, including twins, have proved that genetic factors play a role in male but not in female homosexuality. Homosexuality is probably transmitted across female line. Since males receive their single X chromosome exclusively from their mothers, any trait that is influenced by an X-linked gene will be preferentially passed through the mother’s side of the family. The main outcome of the research is finding of link between homosexual orientation and markers in the Xq28 region on the X chromosome. But later, some scientists have discovered certain irregularities in the theory. In addition to these theories, there is one suggested a connection between influence of hormones and sexual orientation. The influence of prenatal androgen steroids on the sexual orientation of adults was demonstrated first on animal models, and later in humans. Numerous findings indicate that in some species, aromatization (conversion of testosterone to estradiol) is a critical step for brain masculinization with testosterone. Since hormones dump the prenatal development affect brain development, they also affect the development of behavior. Perinatal castration of male rats and application of testosterone to females caused a preference for the same sex. There are some indications that perinatal hormones affect sexual orientation in humans, but there is still little evidence to support that. According to the third theory, brains of homosexuals and heterosexuals are structurally different. The differences are reflected in the size of the third interstitial nucleus of hypothalamus, size of suprachiasmatic nucleus and anterior commissure. After various opinions about the origin and causes of homosexuality, scientists have shown that homosexuality is not a choice, but an unchangeable orientation