Separation coordinates in Hénon-Heiles systems

© 2019 Elsevier B.V. In this paper we apply the method of the Kowalewski\u27s Conditions to separate the seven Hénon-Heiles integrable systems. For each of them we provide explicitly the separation coordinates in the form of eigenvalues of a matrix M called Control Matrix. A couple of systems (HH3 KK and HH4 1:12:16) are presented and discussed in a more general form than usually in the literature. We show that the process of separation of coordinates can be reduced, at the end, to the choice of a single function and, eventually, a vector field transversal to the Lagrangian foliation in an extended phase space

Explicit integration of a generic Hénon-Heiles system with quartic potential

© 2017 the authors. There are seven time independent, integrable, Hénon-Heiles systems: three with cubic and four with quartic potential. The cubic and one of the quartic cases have been separated in the last decades. The other three cases 1:6:1, 1:6:8 and 1:12:16 have resisted several attempts in the last years. In this paper we focus our attention on the 1:12:16 case whose equations of motion have been separated only in the degenerate case ab = 0. We give here the separation coordinates for the generic case using a method introduced by Franco Magri in 2005 under the name of Kowalevski’s Conditions

Simple homoclinic cycles in low-dimensional spaces

AbstractThe problem of a classification of robust homoclinic cycles in low-dimensional spaces has been frequently asked in recent years. In this paper, we resume the results in R3 and R4 and we solve the problem in R5 in the case of orientation-preserving group actions

Experimental method to assess the absorbed dose in mammography

Lo scopo di questo lavoro di tesi è quello di sviluppare un metodo di calcolo della dose media assorbita dalla mammella durante le procedure mammografiche. La mammografia, tecnica di imaging di riferimento per esplorare in modo completo la mammella, viene effettuata nei programmi regionali di screening per la diagnosi precoce del carcinoma mammario che coinvolgono la popolazione femminile in età 50-69 anni e si tratta di una procedura non invasiva e con un’elevata sensibilità. Tuttavia la mammella è ritenuta un organo superficiale altamente radiosensibile e la cadenza raccomandata è biennale, perciò è necessario adottare misure di radioprotezione adeguate per ridurre il rischio che si presenti un tumore radio-indotto in seguito all’esposizione a radiazioni ionizzanti. Le norme fondamentali di sicurezza relative all’esposizione alle radiazioni ionizzanti sono state recentemente aggiornate con la pubblicazione della nuova Direttiva Europea 59/2013/EURATOM che dovrà essere recepita entro Febbraio 2018. La nuova Direttiva pone l’attenzione sul tema del controllo delle dosi erogate durante le procedure radiologiche sotto la diretta responsabilità del fisico che deve occuparsi della dosimetria per la valutazione della dose al paziente. La Direttiva dispone anche che all’interno del referto dell’esame venga inserito un dato dosimetrico riferito all’esposizione stessa. Al fine di adempiere a quest’ultima richiesta è fondamentale disporre di un indicatore dosimetrico direttamente correlato al rischio da radiazioni che possa fornire le informazioni opportune al paziente, al medico radiologo, al medico prescrivente, e che possa essere monitorato mediante software dedicati che permettano di avere a disposizione un gran numero di dati provenienti dalle diverse apparecchiature radiologiche. L’attuale indice dosimetrico di riferimento per stimare la dose in mammografia è la dose ghiandolare media (AGD, Average Glandular Dose), rappresentativa della dose assorbita in media dal tessuto ghiandolare (più radiosensibile rispetto a cute e tessuto adiposo), e che dipende dalla qualità del fascio X, dallo spessore e dalla composizione della mammella. Essa si calcola a partire dal kerma in aria incidente Ka,i e, utilizzando fattori di conversione ottenuti da simulazioni Monte Carlo, si ottiene la formula: D= Ka,i ·g·c·s. Tale metodo è stato sviluppato negli anni ’90 da Dance e collaboratori e i fattori g, c e s sono fattori empirici tabulati. La dose media assorbita (Mean Absorbed Dose, MAD) può essere definita come funzione dei parametri espositivi impostati (kVp, mAs, accoppiamento anodo/filtro) e dello spessore della mammella (d). Risolvendo l’integrale che tiene conto dei parametri sopra detti, le quantità necessarie che devono essere individuate per la corretta valutazione della MAD sono il kerma in aria incidente sulla superficie di ingresso del volume target e il coefficiente di assorbimento di energia µ relativo al materiale considerato. Per ottenere questi parametri si è proceduto a fare delle misure sperimentali utilizzando i mammografi situati presso la SDO Senologia Radiologica dell’Azienda Ospedaliero Universitaria Pisana. Per il calcolo del kerma in aria è stato utilizzato un rivelatore a stato solido (Barracuda) e con misure ripetute di esposizione al variare dei kVp, dei mAs e dell’accoppiamento anodo/filtro è stato possibile caratterizzare i fasci X in modo esaustivo. Successivamente è stato misurato il coefficiente di assorbimento di energia µ per ogni accoppiamento anodo/filtro e per diversi valori di kVp utilizzando dei fantocci acqua equivalenti e dei rivelatori a termoluminescenza (TLD). A conclusione del lavoro è possibile quindi calcolare la MAD per ciascuna proiezione mammografica una volta noti i parametri di esposizione e lo spessore della mammella, senza dover ricorrere a coefficienti di conversione tabulati. A termine del lavoro è stato eseguito un confronto tra il valore di MAD ottenuto con il metodo sperimentale e il metodo standard di riferimento che prevede il calcolo della MGD secondo il metodo di Dance. I valori ottenuti risultano in perfetto accordo entro l’errore sperimentale

On a Family of Integrable Hamiltonian Systems

We consider a family of Hamiltonian systems with homogeneous potentials Vn of degree n. These systems are known to be Liouville integrable and their first integrals of motion are known. We examine first the easiest case where the potential function is a cubic polynomial and we find the separation coordinates. After we prove that all the systems in the family can be completely solved in quadratures using these new coordinate

A new case of separability in a quartic hénon-heiles system

There are four quartic integrable Hénon-Heiles systems. Only one of them has been separated in the generic form while the other three have been solved only for particular values of the constants. We consider two of them, related by a canonical transformation, and we give their separation coordinates in a new case

Direct construction of a bi-hamiltonian structure for cubic hÉnon-heiles systems

The problem of separating variables in integrable Hamiltonian systems has been extensively studied in the last decades. A recent approach is based on the so called Kowalewski\u27s Conditions used to characterized a Control Matrix M whose eigenvalues give the desired coordinates. In this paper we calculate directly a second compatible Hamiltonian structure for the cubic Hénon-Heiles systems and in this way we obtain the separation variables as the eigenvalues of a recursion operator N. Finally we re-obtain the Control Matrix M from N. © 2020 Bulgarian Academy of Sciences. All rights reserved

Expression levels of GM3 synthase is transcriptionally regulated in HL60 cells differentiated in monocytoid lineage by phorbol esters

INTRODUCTION: During bi-directional differentiation of human myelogenous leukemia cell line HL-60 into monocytoid and granulocytoid lineages, ganglioside GM3 and neolacto series gangliosides (NeuAc-nLCs) are expressed in differentiation direction-specific manner (1). That is, GM3 markedly increases during monocytic differentiation of HL-60 cells induced by 12-O-tetradecanoyilphorbol-13-acetate (TPA), whereas NeuAc-nLCs noticeably increase in granulocytic differentiation induced by all-trans retinoic acid (RA). These observations suggest that the accumulation of specific gangliosides on the cell membrane plays an important role as a trigger in differentiation induction and as determinant of the differentiation direction in human hematopoietic cell lines (1). It is known that two key upstream glycosyltransferases, Lc3Cer synthase and GM3 synthase, play a critical role regulating the glycosphingolipid biosynthesis in HL-60 cells during bi-directional differentiation (2), but the mechanisms controlling expression and activity levels of these enzymes have not yet been elucidated. In this study our attention is directed to investigate the regulation of GM3 synthase activity. MATERIALS AND METHODS: HL-60 cells were grown in RPMI 1640 complete medium at 37\ub0C in a humidified atmosphere enriched with 5% CO2. Granulocytoid differentiation of HL-60 cells was induced by treatment with 1 mM RA for 48 hours; macrophage-like cell differentiation was produced by 4 nM TPA addition to the culture medium for the same period of time. Acidic and neutral glycolipid profiles of control, RA- and TPA-treated cells were quali-quantitatively analysed by HP-TLC and digital scanning of the plates. GM3 synthase activities were determined in control, RA- and TPA-treated cells by an in vitro radioactive assay using 50 mg and 100 mg of the microsomal enriched protein fraction as enzyme source. mRNA expression levels of GM3 synthase gene was determined by RT-PCR. The house-keeping gene encoding for hypoxantine phospho-ribosyl transferase (HPRT) was used as internal standard for quantitative evaluation of the RT-PCR products. RESULTS: After 48 hours RA treatment, a 30% granulocytic differentiation degree of HL-60 cells was evaluated by conventional cytoplasmic/nuclear histochemical staining of the cells. On the contrary, quite 80% of TPA-treated cells showed evident macrophage-like adherent ability and prominent pseudopods, phenotipic markers of differentiation. Indeed, no modification in the glycosphingolipid profiles, in the enzyme activities and in mRNA expression levels of the crucial glycosyltransferases (Lc3Cer synthase and GM3 synthase) were observed in RA-treated cells. On the other hand, in TPA-treated cells there is a sensible increase in ganglioside GM3 content, accompanied by a consistent up-regulation of GM3 synthase activity with respect to undifferentiated and to RA-treated cells. Through quantitative RT-PCR experiments performed on total RNA from undifferentiated, RA- and TPA-treated HL-60 cells, we demonstrate the strict correlation between GM3 synthase activity and its mRNA level: the GM3 synthase transcript is present in equal amount in either undifferentiated and RA-treated cells, but it is dramatically increased (quite 3 times) in TPA-treated cells. These results first give support to a regulation mechanism at the transcriptional level for this enzyme. REFERENCES (1) H. Nojiri et al., Characteristic expression of glycosphingolipid profiles in the bipotential cell differentiation of human promyelocytic leukemia cell line HL-60. Blood 64, 2:534-541 (1984); (2) M. Nakamura et al., Total metabolic flow of glycosphingolipid biosynthesis is regulated by UDP-GlcNAc:Lactosylceramide beta-1,3-N-Acetylglucosaminyltransferase and CMP-NeuAc:Lactosylceramide alfa-2,3sialyltransferase in human hematopoietic cell line HL-60 during differentiation. J. Biol. Chem. 267, 33: 23507-23541 (1992)