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.

Glutathione adducts induced by ischemia and deletion of glutaredoxin-1 stabilize HIF-1α and improve limb revascularization

Reactive oxygen species (ROS) are increased in ischemic tissues and necessary for revascularization; however, the mechanism remains unclear. Exposure of cysteine residues to ROS in the presence of glutathione (GSH) generates GSH-protein adducts that are specifically reversed by the cytosolic thioltransferase, glutaredoxin-1 (Glrx). Here, we show that a key angiogenic transcriptional factor hypoxia-inducible factor (HIF)-1α is stabilized by GSH adducts, and the genetic deletion of Glrx improves ischemic revascularization. In mouse muscle C2C12 cells, HIF-1α protein levels are increased by increasing GSH adducts with cell-permeable oxidized GSH (GSSG-ethyl ester) or 2-acetylamino-3-[4-(2-acetylamino-2-carboxyethylsulfanyl thiocarbonylamino) phenylthiocarbamoylsulfanyl] propionic acid (2-AAPA), an inhibitor of glutathione reductase. A biotin switch assay shows that GSSG-ester-induced HIF-1α contains reversibly modified thiols, and MS confirms GSH adducts on Cys520 (mouse Cys533). In addition, an HIF-1α Cys520 serine mutant is resistant to 2-AAPA–induced HIF-1α stabilization. Furthermore, Glrx overexpression prevents HIF-1α stabilization, whereas Glrx ablation by siRNA increases HIF-1α protein and expression of downstream angiogenic genes. Blood flow recovery after femoral artery ligation is significantly improved in Glrx KO mice, associated with increased levels of GSH-protein adducts, capillary density, vascular endothelial growth factor (VEGF)-A, and HIF-1α in the ischemic muscles. Therefore, Glrx ablation stabilizes HIF-1α by increasing GSH adducts on Cys520 promoting in vivo HIF-1α stabilization, VEGF-A production, and revascularization in the ischemic muscles

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.

Synthetic studies of azulenyl and pseudoazulenyl nitrones

Free radicals have been implicated in various pathological conditions such as, stroke, aging and ischemic heart disease (IHD), as well as neurodegenerative diseases like Alzheimer’s, Parkinson’s, and Huntington’s disease. The role of antioxidants in protection from the harmful effects of free radicals has long been recognized. Trapping extremely reactive free radicals and eliminating them from circulation has been shown to be effective in animal models. Nitrone-based free radical traps have been extensively explored in biological systems. Examples include nitrones such as PBN, NXY-059, MDL-101,002, DMPO and EMPO. However, these nitrones have extremely high oxidation potentials as compared to natural antioxidants such as Vitamin E (α-tocopherol), and glutathione. Becker et al. (1995) synthesized novel azulenyl nitrones, which were shown to have oxidation potentials much lower than that of any of the previously reported nitrone based spin traps. Another azulenyl nitrone derivative, stilbazulenyl nitrone (STAZN), was shown to have an even lower oxidation potential within the range of natural antioxidants. STAZN, a second generation free radical trap, was found to be markedly superior than the two most studied nitrones, PBN and NXY-059, in animal models of cerebral ischemia and in an in vitro assay of lipid peroxidation. In this study, a third generation azulenyl nitrone was synthesized with an electron donating group on the previously synthesized STAZN derivative with the aim to lower the oxidation potential even more. Pseudoazulenes, because of the presence of an annular heteroatom, have been reported to possess even lower oxidation potential than that of the azulenyl counterpart. Therefore, pseudoazulenyl nitrones were synthesized for the first time by extracting and elaborating valtrate from the roots of Centranthus ruber (Red valerian or Jupiter’s beard). Several pseudoazulenyl nitrones were synthesized by using a facile experimental protocol. The physical and biological properties of these pseudoazulenyl nitrones can be easily modified by simply changing the substituent on the heteroatom. Cyclic voltammetry experiments have shown that these pseudoazulenyl nitrones do indeed have low oxidation potentials. The oxidation potential of these nitrones was lowered even more by preparing derivatives bearing an electron donating group at the 3-position of the five membered ring of the pseudoazulenyl nitrone.

The 4-aza-S-ribosyl-L-homocysteine derivatives and the related gamma-lactam and azahemiacetal analogs: Synthesis, inhibition and quorum sensing activity

Quorum sensing (QS) is a population-dependent signaling process bacteria use to control multiple processes including virulence, critical for establishing infection. There are two major pathways of QS systems. Type 1 is species specific or intra-species communication in which N-acylhomoserine lactones (Gram-negative bacteria) or oligopeptides (Gram-positive bacteria) are employed as signaling molecules (autoinducer one). Type 2 is inter-species communication in which S-4,5-dihydroxy-2,3-pentanedione (DPD) or its borate esters are used as signaling molecules. The DPD is biosynthesized by LuxS enzyme from S-ribosylhomocysteine (SRH). Recent increase in prevalence of bacterial strains resistant to antibiotics emphasizes the need for the development of new generation of antibacterial agents. Interruption of QS by small molecules is one of the viable options as it does not affect bacterial growth but only virulence, leading to less incidence of microbial resistance. Thus, in this work, inhibitors of both N-acylhomoserine lactone (AHL) mediated intra-species and LuxS enzyme, involved in inter-species QS are targeted. The γ-lactam and their reduced cyclic azahemiacetal analogs, bearing the additional alkylthiomethyl substituent, were designed and synthesized targeting AHL mediated QS systems in P. aeruginosa and Vibrio harveyi. The γ-lactams with nonylthio or dodecylthio chains acted as inhibitors of las signaling in P. aeruginosa with moderate potency. The cyclic azahemiacetal with shorter propylthio or hexylthio substituent were found to strongly inhibit both las and rhl signaling in P. aeruginosa at higher concentrations. However, lactam and their azahemiacetal analogs were found to be inactive in V. harveyi QS systems. The 4-aza-S-ribosyl-L-homocysteine (4-aza-SRH) analogs and 2-deoxy-2-substituted-S-ribosyl-L-homocysteine analogs were designed and synthesized targeting Bacillus subtilis LuxS enzyme. The 4-aza-SRH analogs in which oxygen in ribose ring is replaced by nitrogen were further modified at anomeric position to produce pyrrolidine, lactam, nitrone, imine and hemiaminal analogs. Pyrrolidine and lactam analogs which lack anomeric hydroxyl, acted as competitive inhibitors of LuxS enzyme with KI value of 49 and 37 µM respectively. The 2,3-dideoxy lactam analogs were devoid of activity. Such findings attested the significance of hydroxyl groups for LuxS binding and activity. Hemiaminal analog of SRH was found to be a time-dependent inhibitor with IC50 value of 60 µM.

Alterations in Glutathione Levels and Apoptotic Regulators Are Associated with Acquisition of Arsenic Trioxide Resistance in Multiple Myeloma

Arsenic trioxide (ATO) has been tested in relapsed/refractory multiple myeloma with limited success. In order to better understand drug mechanism and resistance pathways in myeloma we generated an ATO-resistant cell line, 8226/S-ATOR05, with an IC50 that is 2–3-fold higher than control cell lines and significantly higher than clinically achievable concentrations. Interestingly we found two parallel pathways governing resistance to ATO in 8226/S-ATOR05, and the relevance of these pathways appears to be linked to the concentration of ATO used. We found changes in the expression of Bcl-2 family proteins Bfl-1 and Noxa as well as an increase in cellular glutathione (GSH) levels. At low, clinically achievable concentrations, resistance was primarily associated with an increase in expression of the anti-apoptotic protein Bfl-1 and a decrease in expression of the pro-apoptotic protein Noxa. However, as the concentration of ATO increased, elevated levels of intracellular GSH in 8226/S-ATOR05 became the primary mechanism of ATO resistance. Removal of arsenic selection resulted in a loss of the resistance phenotype, with cells becoming sensitive to high concentrations of ATO within 7 days following drug removal, indicating changes associated with high level resistance (elevated GSH) are dependent upon the presence of arsenic. Conversely, not until 50 days without arsenic did cells once again become sensitive to clinically relevant doses of ATO, coinciding with a decrease in the expression of Bfl-1. In addition we found cross-resistance to melphalan and doxorubicin in 8226/S-ATOR05, suggesting ATO-resistance pathways may also be involved in resistance to other chemotherapeutic agents used in the treatment of multiple myeloma.

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.

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.

A critical review of both the synthesis approach and the receptor profile of the 8-chloro-1-(2′,4′-dichlorophenyl)-N-piperidin-1-yl-1,4,5,6-tetrahydrobenzo[6,7]cyclohepta[1,2-c]pyrazole-3-carboxamide and analogue derivatives

We thank European Commission (project “PET BRAIN: Mapping the brain with PET radiolabeled cannabinoid CB1 ligands”; FP7-People-2009-IAPP; Grant Agreement N.25142).