Some of the Unanswered Questions in Finance

A very dynamic development of finance in the last 50 years is inter alia probably due to experiments and innovations in this field. Previously, theoretical base could not explain and predict movements especially in volatile times. The new finance appeared 50 years ago (portfolio theory, CAPM, the efficient market theory, M&M theorem) and made substantial progress in understanding movements in globalised and internationalised financial markets. However, many questions remain open. The author tries to put emphasis on some of these questions, perfectly aware that these are not the only ones. Unresolved questions are related to company's aims, project's risks, degree of port-folio optimisation, importance of liquidity, dividend policy, as well as factors that deter-mine M&A. As the new finance is not able to predict and explain volatile movements, a question that should be posed is whether it is appropriate to add some non-economic factors as the behaviourist theory suggests. Although the behaviourist theory is an important part of new finance, it is unfortunately the only theory able to explain movements in volatile times. In conclusion, many questions still remain unanswered and wait for appropriate theoretical explanations.New Finance, Operational leverage, Risk, Portfolio optimisation, Rating agencies, Efficient market hypothesis, Quality of liquidity, Behaviorist theory

Compressed zero-divisor graphs of noncommutative rings

We extend the notion of the compressed zero-divisor graph $\varTheta(R)$ to noncommutative rings in a way that still induces a product preserving functor $\varTheta$ from the category of finite unital rings to the category of directed graphs. For a finite field $F$, we investigate the properties of $\varTheta(M_n(F))$, the graph of the matrix ring over $F$, and give a purely graph-theoretic characterization of this graph when $n \neq 3$. For $n \neq 2$ we prove that every graph automorphism of $\varTheta(M_n(F))$ is induced by a ring automorphism of $M_n(F)$. We also show that for finite unital rings $R$ and $S$, where $S$ is semisimple and has no homomorphic image isomorphic to a field, if $\varTheta(R) \cong \varTheta(S)$, then $R \cong S$. In particular, this holds if $S=M_n(F)$ with $n \neq 1$.Comment: 30 page

Categorial properties of compressed zero-divisor graphs of finite commutative rings

We define a compressed zero-divisor graph $\varTheta(K)$ of a finite commutative unital ring $K$, where the compression is performed by means of the associatedness relation. We prove that this is the best possible compression which induces a functor $\varTheta$, and that this functor preserves categorial products (in both directions). We use the structure of $\varTheta(K)$ to characterize important classes of finite commutative unital rings, such as local rings and principal ideal rings.Comment: 14 page

The total zero-divisor graph of commutative rings

In this paper we initiate the study of the total zero-divisor graphs over commutative rings with unity. These graphs are constructed by both relations that arise from the zero-divisor graph and from the total graph of a ring. We characterize Artinian rings with the connected total zero-divisor graphs and give their diameters. Moreover, we compute major characteristics of the total zero-divisor graphs of the ring ${\mathbb Z}_m$ of integers modulo $m$ and prove that the total zero-divisor graphs of ${\mathbb Z}_m$ and ${\mathbb Z}_n$ are isomorphic if and only if $m=n$

Vizualizacija matematičkih tema koristeći react i D3

U ovom diplomskom radu je prikazano korištenje JavaScript biblioteka React i D3. U prvom poglavlju je fokus bio na biblioteci React. U drugom poglavlju je fokus bio na biblioteci D3. U trećem poglavlju se prikazuju različiti pristupi integracije biblioteka React i D3. U zadnjem poglavlju je ukratko opisan kompleksniji primjer korištenja React-a s D3-em.In this diploma thesis, the use of JavaScript libraries React and D3 is shown. In the first chapter, the focus is on the React library. The second chapter is focused on the D3 library. In the third chapter, different approaches to integrating React and D3 libraries are shown. The last chapter briefly describes a more complex example of integrating React with D3

Diskursi feminizma i modernizma u esejima Julke Chlapec Đorđević i Jele Spiridonović-Savić

I start from the definition of Serbian Yugoslav bourgeois culture as a semi-peripheral and having this in mind, I tend to analyze the essays by Julka Chlapec Đorđević and Jela Spiridonović-Savić, from the perspective of the world systemic theories applied to literature.I start from the definition of Serbian Yugoslav bourgeois culture as a semi-peripheral and having this in mind, I tend to analyze the essays by Julka Chlapec Đorđević and Jela Spiridonović-Savić, from the perspective of the world systemic theories applied to literature