Search

V diplomskem delu se bom ukvarjala predvsem z območjem konvergence kompleksnih potenčnih vrst. Za potenčne vrste obstaja maksimalen odprti disk, na katerem vrsta konvergira, bolj zapleteno pa je preveriti konvergenco vrste na robu tega diska in določiti točke z roba, v katerih ima vsota vrste lokalno holomorfno razširitev. Ogledali si bomo nekaj zanimivih primerov potenčnih vrst na kompleksnem disku in natančno obravnavali konvergenco na robu konvergenčnega diska. Pri razumevanju konvergence na robu si bomo pomagali z Abelovim izrekom, ki ga bomo v diplomski nalogi tudi dokazali. This diploma thesis will mostly focus on the problem of convergence of the complex power series. There is a maximum open disk for the power series, which the series converges, however, it is much more complicated to under- stand the convergence at boundary points of this disk and to determine at which points of the boundary has the series has a local holomorphic exten- sion. This thesis includes some interesting examples of the power series on a complex disk and some detailed description of a convergence at boundary points of the disk. For better understanding of the convergence at boundary points, we used and prove Abel’s theorem.

Ob izbruhu svetovne finančne in gospodarske krize leta 2008 so njene razsežnosti kmalu dosegle tudi Evropo in razkrile njene temne plati, ko je Grčija v začetku leta 2010 postala središče svetovne gospodarske krize. Ob razkritjih načinov prirejanja podatkov ne moremo mimo skrbi o resnosti težav v Grčiji. Izvedeni finančni instrumenti so običajen del vladnega financiranja, nesprejemljivi postanejo v primeru, ko se jih uporabi za namene prikrivanja. Največji del krivde za grške težave nosijo neodgovorni grški politiki, ki so prek obljub o višjem življenjskem standardu povečevali zadolženost. Hkrati so s prikrivanjem resnice glede proračunskega primanjkljaja in javnega dolga povsem izgubili zaupanje mednarodne finančne javnosti. Da bi Grčiji pustili, da sama poskrbi za svoje probleme, kar bi vodilo v neplačilo dolga, ni v nikogaršnjem interesu. Zato je pomoč Grčiji smiselna ob pogoju, da sprejmejo stroge varčevalne ukrepe oziroma reforme, katerih so se grški politiki v preteklosti izogibali. Komisija je izvedla program reform, katerih ključni element je bila povrnitev zaupanja potrošnikov v enotni trg in finančni sektor. Prvi cilj je bila vzpostavitev učinkovitega sistema kriznega upravljanja, ki ga do sedaj ni bilo. Zakonodajna reforma je stopila v veljavo leta 2014. Ta proces je dolgotrajen in bo potreboval ustrezno izvrševanje v praksi. Države članice še vedno ostajajo osnovni izvajalec nadzora na svojem finančnem trgu in z vodenjem javnofinančne politike pomembno vplivajo na stabilnost finančnega trga. Na raven EU pa je preneseno postavljanje pravil za zagotavljanje finančne stabilnosti. Da bi se izognile prihodnjim gospodarskim krizam, bodo morale države članice EU vztrajanje pri avtonomiji zamenjati za fiskalno in morebiti celo politično unijo, ki bi navzven predstavila EU kot enotno in močno gospodarsko velesilo ter zahtevala ustrezen vpliv na ureditev mednarodnega finančnega trga. Sankcije za izkrivljanje statističnih podatkov niso izpolnile svojega namena. Državi članici, ki se znajde v takšni situaciji, kot se je Grčija, je nesmiselno naložiti globo v višini 0,2 % BDP, katere sredstva se nato stečejo v evropski mehanizem za stabilnost, saj je zaprosila za finančno pomoč, ki se financira iz njega. Zato ne čudi dejstvo, da Grčija za svoje početje do danes ni bila kaznovana. Upon the outbreak of the global financial and economic crisis in 2008, its magnitude soon reached Europe and revealed its dark sides when, in 2010, Greece became the centre of the global economic crisis. As the data manipulation methods are disclosed, it is impossible to ignore the concern about the depth of problems in Greece. Derivative products are a usual part of government financing they become unacceptable in cases when they are used for the purpose of concealing. A major part of the fault for the problems of Greece is attributable to Greek politicians promising a higher standard of living and consequently increasing indebtedness. At the same time, they completely lost the trust of international financial institutions and experts by covering up the truth about budget deficit and public debt. It is in nobody’s interest to let Greece to take care of their problems by themselves since this would lead to non-payment of the debt. Providing aid to Greece is therefore reasonable on condition that they adopt strict austerity measures and/or reforms which Greek politicians avoided in the past. The Commission implemented a reform programme, the key element of which was to regain the trust of consumers in the single market and financial sector. The first objective was to establish an effective crisis management system which had not existed before. The legislative reform entered in force in 2014. This is a lengthy process which will need appropriate enforcement in practice. Member States still remain the basic control bodies in their financial markets, significantly influencing the financial market stability by conducting their public finance policies. However, setting the rules for ensuring the financial stability has been transferred to the EU level. In order to avoid future crises, the EU Member States will have to replace their insistence on autonomy with a fiscal and perhaps even political union which will present Europe to the rest of the world as a single and strong economic superpower and demand adequate influence on the regulation of international financial market. The sanctions for statistical data manipulation failed to fulfil its purpose. It is unreasonable to impose a fine of 0,2 % of GDP on a Member State which finds itself in a situation such as Greece, the funds of which are then routed to ESM, since this State has applied for financial aid financed from it. It is therefore not surprising that so far Greece has not been sanctioned for their conduct.

Že od leta 2001 je vse več državam Evropske in monetarne unije skupna denarna valuta evro. Za uvedbo slednje mora država kandidatka izpolnjevati konvergenčne kriterije, kar pomeni, da ne sme imeti previsoke inflacije, javnega dolga, javnofinančnega primanjkljaja in obrestne mere. Uvedba sama je prinesla tako pozitivne kot negativne posledice tako na gospodarstvo, kot na politiko in vsakodnevno življenje. Čeprav omogoča preprostejše trgovanje na evropskem trgu, pa članice evroobmočja izgubijo svojo monetarno avtonomijo in nosijo posledice slabega delovanja drugih držav. Dober primer tega je aktualna grška finančna kriza, ki pa bi se lahko razširila tudi na druge države EU. V podobnih težavah bi se lahko kmalu znašle tudi ostale države skupine PIGS, to so Portugalska, Irska in Španija, kar bi gotovo resno ogrozilo stabilnost evra. Since 2001 a growing number of the European countries have been using a common currency, the Euro. In order to introduce the latter each candidate country must meet the convergence criteria, meaning it shouldn't have high inflation rates, public debt, budget deficit and interest rates. Introduction of the Euro has positive as well as negative effects on the economy as well as on politics and everyday life. Even though it simplifies trade in the European market, member states of the Euro zone lose their monetary autonomy and carry the consequences of other countries’ mistakes. A fine example of this is the Greek financial crisis that could also spread to other European countries. Other members of the so called PIGS group, Portugal, Ireland and Spain, could also find themselves in similar difficulty which could seriously jeopardise the stability of the Euro.