On a Class of Fractional Type Integral Equations in Variable Exponent Spaces

2000 Mathematics Subject Classification: 45A05, 45B05, 45E05,45P05, 46E30

On the Operational Solution of a System of Fractional Differential Equations

MSC 2010: 26A33, 44A45, 44A40, 65J10

Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

New genre of antioxidants from renewable natural resources:synthesis and characterisation of rosemary plant-derived antioxidants and their performance in polyolefins

Several ester derivatives of rosmarinic acid (rosmarinates) were synthesised, characterised (1D and 2D NMR, UV and FTIR spectroscopy) and tested for their potential use as antioxidants derived from a renewable natural resource. The intrinsic free radical scavenging activity of the rosmarinates was assessed, initially using a modified DPPH (2, 2-diphenyl-1-picrylhydrazyl radical) method, and found to be higher than that of commercial synthetic hindered phenol antioxidants Irganox 1076 and Irganox 1010. The thermal stabilising performance of the rosmarinates in polyethylene (PE) and polypropylene (PP) was subsequently examined and compared to that of samples prepared similarly but in the presence of Irganox 1076 (in PE) and Irganox 1010 (in PP) which are typically used for polyolefin stabilisation in industrial practice. The melt stability and the long-term thermo-oxidative stability (LTTS) of processed polymers containing the antioxidants were assessed by measuring the melt flow index (MFI), melt viscosity, oxidation induction time (OIT) and long-term (accelerated) thermal ageing performance. The results show that both the melt and the thermo-oxidative stabilisation afforded by the rosmarinates, and in particular the stearyl derivative, in both PE and PP, are superior to those of Irganox 1076 and Irganox 1010, hence their potential as effective sustainable bio-based antioxidants for polymers. The rosmarinic acid used for the synthesis of the rosmarinates esters in this study was obtained from commercial rosemary extracts (AquaROX80). Furthermore, a large number of different strains of UK-grown rosemary plants (Rosmarinum officinalis) were also extracted and analysed in order to examine their antioxidant content. It was found that the carnosic and the rosmarinic acids, and to a much lesser extent the carnosol, constituted the main antioxidant components of the UK-plants, with the two acids being present at a ratio of 3:1, respectively.

Válság és hitelderivatívák. A szintetikus fedezett adósságkötelezettségek (CDO-k) árazása és kockázataik (Crisis and loan derivatives. The pricing and risks of synthetic collateralized debt obligations)

A dolgozat első részében röviden áttekintjük a 2007-ben kezdődött pénzügyi válság lefolyását és a válsághoz vezető okokat. A bemutatás során igyekszünk végig a mögöttes folyamatokra és azok mozgatórugóira koncentrálni, ezzel megragadva a válság egyfajta "elméletét". A bemutatásból láthatóvá válik a hitelderivatívák kiemelt szerepe a válság során. A dolgozat második részében az egyik legnépszerűbb hitelderivatív termék, a szintetikus fedezett adósságkötelezettségek (CDO-k) matematikai modellezését és annak problémáit mutatjuk be. Sokak szerint ezek a matematikai modellek okozták - vagy legalábbis felerősítették - a válságot. Az elemzés során megmutatjuk, hogy nemcsak a modellezési eszközök nem voltak megfelelők, hanem az árazás elve sem állta meg a helyét a kockázatsemleges árazási keretben. Ez az eredmény élesen rámutat a mögöttes elméletek válságára. / === / The first part of the paper examines briefly the financial crisis of 2007 and its causes, focusing on its driving processes and key motifs. This shows clearly the importance and centrality of credit derivatives in the crisis. The second part presents a mathematical modelling of one of the most popular credit derivative products: synthetic collateralized debt obligations, along with the drawbacks and problems of the modelling process. It is widely claimed that these products caused or at least precipitated the crises. The authors show not only that the modelling tools were inappropriate, but that the principle for pricing did not match adequately the risk-neutral valuation framework.

Obama és az új világrend a gazdasági válság tükrében (Obama and the new world order in light of the economic crisis)

Napjainkban a nemzetközi kapcsolatok meghatározó jelensége a gazdasági világválság, amelynek kezelése kapcsán egyre gyakrabban merül fel a politikusok és az elemzők szóhasználatában az „új világrend” fogalma. ____ In treating the current global economic crisis, politicians and analysts increasingly refer to a "new world order". The paper examines this concept, its different meanings and historical evolution, as well as the role it plays in the rhetoric of the Obamaadministration.

Spontaneous order and social norms. Hayek’s theory of socio-cultural evolution

Hayek’s theory of socio-cultural evolution is a generalization of his theory on spontaneous market order. Hayek explains both the emergence of market and social institutions serving as a social basis for that order within the framework of a unified evolutionary logic. This logic interprets the emergence and survival of spontaneous order and group-level rules of conduct as an unintended consequence of human action. In order to explain the emergence of social norms exclusively on the basis of methodological individualism, one would have to give up an exclusively evolutionary explanation of these norms. Since Hayek applies the invisible-hand explanation to the investigation of social norms, he combines the position of methodological individualism with functionalist-evolutionary arguments in his analysis. Hayek’s theory of socio-cultural evolution represents a theory in the framework of which methodological individualism and functionalism do not crowd out but complement each other.

Spontaneous order and social norms. Hayek’s theory of socio-cultural evolution

Hayek's theory of socio-cultural evolution is a generalization of his theory on spontaneous market order. Hayek explains both the emergence of market and social institutions serving as a social basis for that order within the framework of a unified evolutionary logic. This logic interprets the emergence and survival of spontaneous order and group-level rules of conduct as an unintended consequence of human action. In order to explain the emergence of social norms exclusively on the basis of methodological individualism, one would have to give up an exclusively evolutionary explanation of these norms. Since Hayek applies the invisiblehand explanation to the investigation of social norms, he combines the position of methodological individualism with functionalist-evolutionary arguments in his analysis. Hayek's theory of socio-cultural evolution represents a theory in the framework of which methodological individualism and functionalism do not crowd out but complement each other.

Piaci rend és társadalmi normák. Hayek elmélete a társadalmi evolúcióról (Market order and social norms Hayek's theory of social evolution)

A hayeki szociokulturális evolúció elmélete a piaci rend elemzésének általánosítása. Hayek mind a piaci rend, mind a piaci rend alapzatául szolgáló társadalmi intézmények kialakulását és működését azonos logika alapján magyarázza. Ez a logika az egyéni cselekvések nem szándékolt következményeként értelmezi a spontán rend és a csoportszintű magatartásszabályok kialakulását és fennmaradását. A társadalmi normák magyarázatában a módszertani individualizmus elveinek érvényesítéséért az evolucionista perspektíva feladásával kellene fizetni. Hayek azonban a társadalmi normák magyarázatára is az evolucionista megközelítést alkalmazza, ezért egészíti ki a módszertani individualista megközelítést funkcionalista-evolucionista érvekkel. A szociokulturális evolúció hayeki elmélete példa arra, hogy a módszertani individualizmusra épülő magyarázat és a funkcionalista érvelés nem kiszorítja, hanem kiegészíti egymást. _____ Hayek's theory of socio-cultural evolution is a generalization of his theory of market order. He explains in the same way the development and operation of market order and those of the social institutions on which market order is based. This logic interprets the development and persistence of spontaneous order and group-level behaviour rules as an unintentional consequence of individual actions. In his explanation of social norms, enforcement of the principles of methodological individualism has to be paid for by abandoning the evolutionist perspective. But Hayek also employs an evolutionist approach in his explanation of social norms, and so he augments his methodological individualist approach with some functionalist-cum-evolutionist arguments. Hayek's theory of sociocultural evolution, for instance, exemplifies how an explanation resting on methodological individualism and a functionalist argument can complement, not preclude each other.

The application of aryne chemistry and use of α-diazo carbonyl derivatives in indazole synthesis with biological evaluation

This thesis outlines the synthetic chemistry involved in the preparation of a range of novel indazole compounds and details the subsequent investigation into their potential as biologically active agents. The synthetic route utilised in this research to form the indazole structure was the [3+2] dipolar cycloaddition of diazo carbonyl compounds with reactive aryne intermediates generated in situ. The preparation of further novel indazole derivatives containing different functional groups and substituents was performed by synthesising alternative 1,3- dipole and dipolarophile analogues and provided additionally diverse compounds. Further derivatisation of the indazole product was made possible by deacylation and alkylation methods. Transformation reactions were performed on alkenecontaining ester side chains to provide novel epoxide, aldehyde and tertiary amine derivatives. The first chapter is a review of the literature beginning with a short overview on the structure, reactivity and common synthetic routes to diazo carbonyl derivatives. More attention is given to the use of diazo compounds as 1,3-dipoles in cycloaddition reactions or where the diazo group is incorporated into the final product. A review of the interesting background, structure and reactivity of aryne intermediates is also presented. In addition, some common syntheses of indazole compounds are presented as well as a brief discussion on the importance of indazole compounds as therapeutic agents. The second chapter discusses the synthetic routes employed towards the synthesis of the range of indazoles. Initially, the syntheses of the diazo carbonyl and aryne precursors are described. Next, the synthetic methods to prepare the indazole compounds are provided followed by discussion on derivatisation of the indazole compounds including N-deacylation, N-benzylation and ester side-chain transformation of some alkene-containing indazoles. A series of novel indazole derivatives were submitted for anti-cancer screening at the U.S National Cancer Institute (NCI). A number of these derivatives were identified as hit compounds, with excellent growth inhibition. The results obtained from biological evaluation from the NCI are provided with further results pending from the Community for Open Antimicrobial Drug Discovery. The third chapter details the full experimental procedures, including spectroscopic and analytical data for all the compounds prepared during this research.

Vegetative and reproductive development of shoots of different order of three maize hybrids at two contrasting population densities

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Second-order cyclostationarity-based detection and classification of LTE SC-FDMA signals for cognitive radio

Cognitive radio (CR) was developed for utilizing the spectrum bands efficiently. Spectrum sensing and awareness represent main tasks of a CR, providing the possibility of exploiting the unused bands. In this thesis, we investigate the detection and classification of Long Term Evolution (LTE) single carrier-frequency division multiple access (SC-FDMA) signals, which are used in uplink LTE, with applications to cognitive radio. We explore the second-order cyclostationarity of the LTE SC-FDMA signals, and apply results obtained for the cyclic autocorrelation function to signal detection and classification (in other words, to spectrum sensing and awareness). The proposed detection and classification algorithms provide a very good performance under various channel conditions, with a short observation time and at low signal-to-noise ratios, with reduced complexity. The validity of the proposed algorithms is verified using signals generated and acquired by laboratory instrumentation, and the experimental results show a good match with computer simulation results.