Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

2000 Mathematics Subject Classification: 12D10.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Nanoengineering heterogeneous catalysts for the selective hydrogenation of key agrochemical derivatives

Rapidly rising world populations have sparked growing concerns over global food production to meet this increasing demand. Figures released by The World Bank suggest that a 50 % increase in worldwide cereal production is required by 2030. Primary amines are important intermediates in the synthesis of a wide variety of fine chemicals utilised within the agrochemical industry, and hence new 'greener' routes to their low cost manufacture from sustainable resources would permit significantly enhanced crop yields. Early synthetic pathways to primary amines employed stoichiometric (and often toxic) reagents via multi-step protocols, resulting in a large number of by-products and correspondingly high Environmental factors of 50-100 (compared with 1-5 for typical bulk chemicals syntheses). Alternative catalytic routes to primary amines have proven fruitful, however new issues relating to selectivity and deactivation have slowed commercialisation. The potential of heterogeneous catalysts for nitrile hydrogenation to amines has been demonstrated in a simplified reaction framework under benign conditions, but further work is required to improve the atom economy and energy efficiency through developing fundamental insight into nature of the active species and origin of on-stream deactivation. Supported palladium nanoparticles have been investigated for the hydrogenation of crotononitrile to butylamine (Figure 1) under favourable conditions, and the impact of reaction temperature, hydrogen pressure, support and loading upon activity and selectivity to C=C versus CºN activation assessed.

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.

A kockázat megjelenése a származtatott pénzügyi termékekben (The risk appearing in financial derivatives)

A pénzügyi kockázatok szerepe, modellezése, kezelése az utóbbi évtizedekben vált egyre hangsúlyosabbá az elméletben és a gyakorlatban egyaránt. A 2007-ben kezdődő pénzügyi válság egyik kiváltó oka a kockázatok nem megfelelő felmérése volt. A válság egyik tanulsága, hogy bár a matematika és a fizika hozzájárulása rendkívül mély módszertani apparátust biztosított a kockázatok számszerűsítésére, ezen eredmények pénzügyi alkalmazása csak akkor sikeres, ha pontosan értjük a modellek feltételeit és korlátait. Jelen cikk a pénzügyi derivatívák értékelésének alapelveit, valamint a származtatott ügyletekben megjelenő kockázatokat tekinti át, illetve bemutatja azokat a bizonytalansági tényezőket, amelyek megkérdőjelezik az értékelés objektivitását. / === / The modeling and management of financial risks became one of the most important topics of the last decade both in theory and fi nancial practice. The mismanagement of fi nancial risks can be mentioned among the reasons contributing to the eruption of the recent crisis. In order to use successfully the methodology of mathematics and physics in pricing of derivatives, we have to consider the assumptions and limits of the models. This paper introduces the main concepts – no arbitrage pricing and risk neutral valuation – in derivatives’ pricing, then presents and quantifies the risk of some derivative products. I am arguing that the assumptions of the Black–Scholes and Merton model are injured at several points, so the pricing can not be perfectly cleared from all the risk preferences. All those risks, deriving from the difference of the reality and the model are priced in the volatility parameter in the practice.

Derivatív pénzügyi termékek árdinamikája és az új típusú kamatlábmodellek (Interest rate models and the price processes of financial derivatives)

Ennek a cikknek az a célja, hogy áttekintést adjon annak a folyamatnak néhány főbb állomásáról, amit Black, Scholes és Merton opcióárazásról írt cikkei indítottak el a 70-es évek elején, és ami egyszerre forradalmasította a fejlett nyugati pénzügyi piacokat és a pénzügyi elméletet. / === / This review article compares the development of financial theory within and outside Hungary in the last three decades starting with the Black-Scholes revolution. Problems like the term structure of interest rate volatilities which is in the focus of many research internationally has not received the proper attention among the Hungarian economists. The article gives an overview of no-arbitrage pricing, the partial differential equation approach and the related numerical techniques, like the lattice methods in pricing financial derivatives. The relevant concepts of the martingal approach are overviewed. There is a special focus on the HJM framework of the interest rate development. The idea that the volatility and the correlation can be traded is a new horizon to the Hungarian capital market.

Syntheses of aza analogs of kainoids

The kainoids are a class of non-proteinogenic pyrrolidine dicarboxylates that exhibit both excitatory and excitotoxic activities. These activities are a result of the ability of the kainoids to act as glutamate receptor agonists by activating ionotropic glutamate receptors. The parent of this group of compounds is α-kainic acid. Kainic acid is isolated from the seaweed Diginea simplex and has been used in Asian countries as a treatment for intestinal worms in children. In addition it is used extensively by neuropharmacologists for the study of glutamate receptors. Several years ago, the world's sole supplier of kainic acid discontinued this product. Since that time, other sources have appeared, however, the price of kainic acid remains significantly higher than it once was. We have thus been working on synthesizing aza analogs of kainoids which would be less costly but potentially potent alternatives to kainic acid via the dipolar cycloadditions of diazoalkanes with trans diethyl glutaconate. These 1, 3-dipolar cycloadditions yielded 2-pyrazolines or pyrazoles. The 2-pyrazolines may be precursors to aza analogs of kainoids. The regioselectivity of these 1, 3-dipolar cycloadditions and isomerization of the 1-pyrazolines to 2-pyrazolines was evaluated. Reductions of the 2-pyrazolines yielded aza analogs of kainoids.^ TMS diazomethane, due to the commercial availability, has been frequently used as a synthetic reagent in 1, 3-dipolar cycloadditions, particularly in the preparation of novel amino acid analogs. A survey of the recent literature indicates that the regioselectivity of the double bond isomerization of TMS substituted 1-pyrazolines is variable and at first glance, unpredictable. In an effort to develop a mechanistic rational for the isomerization which could account for the products obtained, a systematic survey of dipolar cycloadditions between TMS diazomethane and α, β-unsaturated dipolarophiles was undertaken. It was suggested that the steric demand of the dipolarophiles had a profound effect on both the relative stereochemistry of dipolar cycloaddition reactions of TMSCHN2 and the preferred direction of isomerization of the resulting 1-pyrazoline.^

Syntheses of aza analogues of kainic acid

The kainate receptors are one of the three major groups of ionotropic glutamate receptors in the mammalian central nervous system. They are so named after their most potent agonist, kainic acid (KA), a natural product isolated from the seaweed Diginea simplex. This compound shows both neuroexcitatory and excitotoxic activities, and is an important pharmacological tool for neurophysiological studies. We predict that the more synthetically accessible aza analogues of kainic acid, could act as functional mimics of KA. These could be produced by the 1,3-dipolar cycloaddition of diazoalkanes with trans glutaconate esters. ^ 1,3-Dipolar cycloadditions have been shown to produce 1-pyrazolines that isomerize into 2-pyrazolines. The 1- and 2-pyrazolines can be precursors to aza analogs of kainoids. The regioselectivity, relative stereochemistry and isomerization of the 1-pyrazolines into 2-pyrazolines have been evaluated. Reductions of the 1- and 2-pyrazolines produced aza analogs of kainoids. TMS diazomethane was used as the dipole in 1,3-dipolar cycloaddition reactions leading to aza KA analogs via 2-pyrazolines. A systematic study of cycloaddition-isomerization processes involving TMS-diazomethane and various α, β-unsaturated dipolarophiles has been undertaken. 1H-NMR monitoring of the reaction mixture compositions during the cycloaddition reaction revealed evidence of retro-dipolar cycloaddition processes. Faster formation of 4,5- trans-1-pyrazoline at the beginning of the reaction and subsequent isomerization of this product into 4,5-cis-1-pyrazoline via a retro-dipolar cycloaddition has been observed. Increased reaction time and/or reaction temperature preferentially caused the irreversible isomerization of 4,5-cis-1-pyrazoline into 4,5-cis-2-pyrazoline, which led to high yields of 4,5-cis-2-pyrazolines in the overall process. ^ Two syntheses of the 5-unsubstituted aza-kainic acid have been performed; first, via the reduction of the TMS-eliminated 2-pyrazoline from TMS diazomethane; second by the direct reduction of 1-pyrazoline with Hg/Al-amalgam. 5-Phenyl aza-kainic acid has been produced by direct reduction of 1-pyrazoline, obtained in the reaction of phenyldiazomethane and dibenzyl glutaconate, with Hg/Al-amalgam. ^ Current responses to aza kainate analogs in Aplysia whole cell buccal ganglia indicate potent neuroexcitatory activity. The repetitive exposure of neuronal cells to the 5-unsubstituted aza-kainic acid led to non-desensitizing current responses, showing both binding affinity and neuronal ion-channel activation by the synthesized agonist compound. ^

Study of Ammonia Borane and its Derivatives: Influence of Nanoconfinements and Pressures

Recently, ammonia borane has increasingly attracted researchers’ attention because of its merging applications, such as organic synthesis, boron nitride compounds synthesis, and hydrogen storage. This dissertation presents the results from several studies related to ammonia borane. The pressure-induced tetragonal to orthorhombic phase transition in ammonia borane was studied in a diamond anvil cell using in situ Raman spectroscopy. We found a positive Clapeyron-slope for this phase transformation in the experiment, which implies that the phase transition from tetragonal to orthorhombic is exothermic. The result of this study indicates that the rehydrogenation of the high pressure orthorhombic phase is expected to be easier than that of the ambient pressure tetragonal phase due to its lower enthalpy. The high pressure behavior of ammonia borane after thermal decomposition was studied by in situ Raman spectroscopy at high pressures up to 10 GPa. The sample of ammonia borane was first decomposed at ~140 degree Celcius and ~0.7 GPa and then compessed step wise in an isolated sample chamber of a diamond anvil cell for Raman spectroscopy measurement. We did not observe the characteristic shift of Raman mode under high pressure due to dihydrogen bonding, indicating that the dihydrogen bonding disappears in the decomposed ammonia borane. Although no chemical rehydrogenation was detected in this study, the decomposed ammonia borane could store extra hydrogen by physical absorption. The effect of nanoconfinement on ammonia borane at high pressures and different temperatures was studied. Ammonia borane was mixed with a type of mesoporous silica, SBA-15, and restricted within a small space of nanometer scale. The nano-scale ammonia borane was decomposed at ~125 degree Celcius in a diamond anvil cell and rehydrogenated after applying high pressures up to ~13 GPa at room temperature. The successful rehydrogenation of decomposed nano-scale ammonia borane gives guidance to further investigations on hydrogen storage. In addition, the high pressure behavior of lithium amidoborane, one derivative of ammonia borane, was studied at different temperatures. Lithium amidoborane (LAB) was decomposed and recompressed in a diamond anvil cell. After applying high pressures on the decomposed lithium amidoborane, its recovery peaks were discovered by Raman spectroscopy. This result suggests that the decomposition of LAB is reversible at high pressures.

Computer assisted synthesis and in-vitro cytotoxic evaluation of new pyrazole-fused isoquinolinoquinones derivatives as PI3K receptor antagonist with promising antitumoral activity

The importance of pyrazole and isoquinoline-5,8-dione scaffolds in medical chemistry is underlined by the high number of drugs currently on trading that contains these active ingredients. Due to their cytotoxic capability, the interest of medicinal chemists in these heterocyclic rings has grown exponentially especially, for cancer therapy. In this project, the first synthesis of pyrazole-fused isoquinoline-5,8-diones has been developed. 1,3-Dipolar cycloaddition followed by oxidative aromatization, established by our research group, has been employed. Screening of reaction conditions and characterization studies about the regioselectivity have been successfully performed. A remote control of regioselectivity, to achieve the two possible regioisomers has been accomplished. Through Molecular Docking studies, Structure-Activity relationship of differently substituted scaffolds containing our central core proved that a family of PI3K inhibitors have been discovered. Finally, in order to verify the promising antitumor activity, a first test of cell viability in vitro on T98G cell line of a solid brain tumor, the Glioblastoma Multiforme, showed cytotoxic inhibition comparable to currently trade anticancer drugs.

Weak interactions in the crystal structures of two indole derivatives

Acknowledgements We thank the EPSRC National Crystallography Service (University of Southampton) for the data collections and the EPSRC National Mass Spectrometry Service (University of Swansea) for the HRMS data.

Reactions of nitrilium salts with indole and pyrrole and their derivatives in the synthesis of imines, ketones and secondary amines

I thank SERC for a CASE studentship (to RG. Giles) with the former Fisons Pharmaceuticals division (with Dr. S. C. Eyley) and Dr. B. R. Buckley, of this department, for provided helpful comments on an earlier version of the manuscript.