Is it possible to formulate least action principle for dissipative systems?

A longstanding open question in classical mechanics is to formulate the least action principle for dissipative systems. In this work, we give a general formulation of this principle by considering a whole conservative system including the damped moving body and its environment receiving the dissipated energy. This composite system has the conservative Hamiltonian $H=K_1+V_1+H_2$ where $K_1$ is the kinetic energy of the moving body, $V_1$ its potential energy and $H_2$ the energy of the environment. The Lagrangian can be derived by using the usual Legendre transformation $L=2K_1+2K_2-H$ where $K_2$ is the total kinetic energy of the environment. An equivalent expression of this Lagrangian is $L=K_1-V_1-E_d$ where $E_d$ is the energy dissipated by the friction from the moving body into the environment from the beginning of the motion. The usual variation calculus of least action leads to the correct equation of the damped motion. We also show that this general formulation is a natural consequence of the virtual work principle.Comment: 11 pages, no figur

Lipids constituents from Gardenia aqualla Stapf & Hutch

peer reviewe

Vitellaroside, A New Cerebroside from Vitellaria paradoxa (Sapotaceae) and its Bioactivities

peer reviewe

DPPH antiradical scavenging, anthelmintic and phytochemical studies of Cissus poulnea rhizomes

peer reviewe

Jean Baptist le Rond d´Alembert (1717-1783), französischer Mathematiker und Physiker

Publikationen: Traite Dynamique, 1743. Traite de l´Equilibre et du mouvement des Fluides, 1744. Reflexions sur la cause generale des vents, 1747. Recherches sur la precession des equinoxes et sur la nutation, de l´axe de la terre, 1749. Essai d´une nouvelle theorie sur la resistance des fluides, 1752. Recherches sur differens points importans du systeme de monde, 1754-1756. Nouvelles tables de la lune et Nova tabularum lunarium emendatio. Opusculus mathematiques, 1761-1780. Elements de musique theorique et practique suivant les principes de M.Rameau, e´claircis, de´veloppis et […], Lyon 1779. Melanges de litterature et de philosophie. Eloges lu dans les seances de l´Academi francais, 1779-1787. Sur la destruction des Jesuites, 1765. Ouevres posthumes publices par M. Ponges, 1799. Eloge de Milord Marechal, 1779. Dissertation sur le gout, 1776. Apologie de l´abbe de Prades, 1752. Alle Werke D´Alembert´s sind gesammelt in: Ouevres philosophique, historiques et litteraries de d´Alembert par M. Bastien, 18 Bände, Paris 1805 (inklusive Briefwechsel D´Alembert mit Friedrich II.). Quelle: Michaud, Biographie universelle ancienne et moderne. Teilnachlass: Kurzbiographie Umfang: 12 S. Datum: undatiert Archiv-Signatur: Astr.-NL-4.28

Antioxidant Activity of Compounds Isolated from the Root Woods of Erythrina droogmansiana

peer reviewedThe aim of this study was to isolate, to characterize secondary metabolites from methanolic extract of the root woods of Erythrina droogmansiana and to assess the antioxidant activity of the crude extract and isolated compounds. The phytochemical study led to the isolation of 3-(3’,4’-methelenedioxyphenyl)-2,3-epoxypropanol (1), asperphenamate (2) and three flavonoids namely genistein, diadzein and 4’,5,7-trihydroxy-8-prenylisoflavone. These compounds were characterized using their 1H NMR, 13C NMR, HMBC, HSQC, COSY, mass spectral and the literature. To evaluate antioxidant activity of crude extract and isolated compounds, the radical scavenging (DPPH) and Ferric Reducing Ability Power (FRAP) were performed using ascorbic acid as standard. Compounds 1 and 2 showed moderate radical scavenging potential with IC50 value of 3.14 and 3.31 mg/ml respectively, and moderate reducing power ability with value of 0.14±0.01 mgAAE/mg and 0.21±0.01 mgAAE/mg respectively. The more active compound was genistein (3) with IC50 value of 1.96 mg/ml for the DPPH radical scavenging potential and 0.24±0.02 mgAAE/mg for its ability to reduce iron

[Obras]

Marca tip. en port.Antep.Texto a dos col.Grab. calc.: "Retrato de Montesquieu"Contiene: Lettres persanes -- Considerations sur les causes de la grandeur des romains et leur décadence -- De l'esprit des lois -- Défense de l'esprit des lois -- Discours - Pensées diverse

ANTIPROLIFERATIVE ACTIVITY OF FLAVONOIDS ISOLATED FROM ECHINOPS GRACILIS O. HOFFM

Apigenin-7-O-(4′′-feruloyl)-β-D-glucopyranoside (1) were isolated from the methanol extract of aerial part of Echinops gracilis, together with apigenin-7-O-(4′′-trans-p-hydroxycinnamoyl)-β-D-glucopyranoside (2) and apigenin-7-O-β-D-glucopyranoside (3). Compound (1) previously displayed antioxidant and antibacterial activity. The present study aims at evaluating the antiproliferative potential of flavonoids, isolated from the aerial part of E. gracilis O. Hoffm. The effect of compounds (1), (2) and (3) on the viability of HeLa cells was determined by the method of 3-(4,5-dimethythiazol-2-yl)-2,5-diphenyl tetrazolium bromide (MTT) assay at different concentrations. The ability of compounds to induce the cell death was evaluated by using acridine orange/ethidium bromide (AO/EtBr) staining. Compound (1) induced an effective change in the cell viability of HeLa cells with IC50 concentration value of 27.36 µgmL-1. Induction of cell death alteration in cell morphology and cancer cell population was observed in cells treated with compound (1), which makes it behave as a potent synergistic antiproliferative agent against HeLa cells

Supplément à l\u27Encyclopédie, ou, Dictionnaire raisonné des sciences, des arts et des métiers

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