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The micellar solubilization of naphthalene from its saturated aqueous solutions using the biosurfactant rhamnolipid was studied. Using the NMR diffusion method, selective measurements of the self-diffusion coefficients of molecules of all components of the solution—naphthalene, rhamnolipid, and water—were carried out at various rhamnolipid concentrations from 0.06 to 100 g/L. Based on the results of diffusometry, the distribution of naphthalene molecules between the states free in solution and states bound by micelles was found. With an increase in the concentration of rhamnolipids, the proportion of bound naphthalene molecules increases from 50% at CRL = 2 g/L to 100% at CRL ≥ 50 g/L. The micelle-water partition coefficient Km and the molar solubilization ratio MSR were calculated., Validerad;2024;Nivå 2;2024-09-11 (joosat);Full text license: CC BY;Funder: Kazan Federal University (FZSM-2023-0016)

The micellar solubilization of naphthalene from its saturated aqueous solutions using the biosurfactant rhamnolipid was studied. Using the NMR diffusion method, selective measurements of the self-diffusion coefficients of molecules of all components of the solution—naphthalene, rhamnolipid, and water—were carried out at various rhamnolipid concentrations from 0.06 to 100 g/L. Based on the results of diffusometry, the distribution of naphthalene molecules between the states free in solution and states bound by micelles was found. With an increase in the concentration of rhamnolipids, the proportion of bound naphthalene molecules increases from 50% at CRL = 2 g/L to 100% at CRL ≥ 50 g/L. The micelle-water partition coefficient Km and the molar solubilization ratio MSR were calculated., Validerad;2024;Nivå 2;2024-09-11 (joosat);Full text license: CC BY;Funder: Kazan Federal University (FZSM-2023-0016)

We studied the micellar and solubilizing properties of aqueous solutions of unfractionated rhamnolipids produced by Pseudomonas aeruginosa. We used nuclear magnetic resonance (NMR) diffusometry, dynamic light scattering, and conductometry to measure the critical micelle concentration (CMC) of rhamnolipid solutions and determined the effective hydrodynamic radii of rhamnolipid monomers and micelles. Based on selective measurements of the self-diffusion coefficients of molecules, performed by NMR diffusometry, the solubilizing properties of rhamnolipids were studied depending on their concentration in solution; aromatic hydrocarbons, benzene, toluene, ethylbenzene, and para-xylene were taken as solubilizates. On the basis of the measurement results, we estimated the distribution coefficient of the solubilizate between the micellar (solubilized) and free (in the aqueous phase) states and the solubilizing capacity of rhamnolipid micelles., Validerad;2023;Nivå 2;2023-07-21 (sofila);Funder; Ministry of Science and Higher educationof the Russian Federation (grant no. 075-15-2021-699); Kazan Federal University (ProgramPriority-2030);Licens fulltext: CC BY-NC-ND License

The dynamic and aggregation properties of Triton X-100 in a mixture of ordinary and heavy water in a wide temperature range from room temperature to the cloud point and above were studied. The ratio of ordinary and heavy water was calculated in such a way as to ensure equal densities of Triton X-100 and the water mixture. This made it possible to exclude the effects of sedimentation and study the evolution of Triton X-100 micelles and aggregates, without complication by the effects of spatial phase separation above the cloud point. Self-diffusion coefficients of Triton X-100 molecules were measured by NMR, and the effective hydrodynamic radii of micelles and aggregates were calculated using the Stokes-Einstein relation. The anomalous temperature behavior of the diffusion coefficient of Triton X-100 molecules is explained by changes in the sizes of diffusing objects during their evolution from micelles to dehydrated aggregates below the cloud point and by changes in the sizes of aggregates above the cloud point. The results of the NMR studies are confirmed by data obtained by dynamic light scattering., Validerad;2023;Nivå 2;2023-03-15 (hanlid);Funder: Ministry of Science and Higher Education of the Russian Federation (075-10-2021-115); Program Priority-2030 for Kazan Federal University

The dynamic and aggregation properties of Triton X-100 in a mixture of ordinary and heavy water in a wide temperature range from room temperature to the cloud point and above were studied. The ratio of ordinary and heavy water was calculated in such a way as to ensure equal densities of Triton X-100 and the water mixture. This made it possible to exclude the effects of sedimentation and study the evolution of Triton X-100 micelles and aggregates, without complication by the effects of spatial phase separation above the cloud point. Self-diffusion coefficients of Triton X-100 molecules were measured by NMR, and the effective hydrodynamic radii of micelles and aggregates were calculated using the Stokes-Einstein relation. The anomalous temperature behavior of the diffusion coefficient of Triton X-100 molecules is explained by changes in the sizes of diffusing objects during their evolution from micelles to dehydrated aggregates below the cloud point and by changes in the sizes of aggregates above the cloud point. The results of the NMR studies are confirmed by data obtained by dynamic light scattering., Validerad;2023;Nivå 2;2023-03-15 (hanlid);Funder: Ministry of Science and Higher Education of the Russian Federation (075-10-2021-115); Program Priority-2030 for Kazan Federal University

We studied the micellar and solubilizing properties of aqueous solutions of unfractionated rhamnolipids produced by Pseudomonas aeruginosa. We used nuclear magnetic resonance (NMR) diffusometry, dynamic light scattering, and conductometry to measure the critical micelle concentration (CMC) of rhamnolipid solutions and determined the effective hydrodynamic radii of rhamnolipid monomers and micelles. Based on selective measurements of the self-diffusion coefficients of molecules, performed by NMR diffusometry, the solubilizing properties of rhamnolipids were studied depending on their concentration in solution; aromatic hydrocarbons, benzene, toluene, ethylbenzene, and para-xylene were taken as solubilizates. On the basis of the measurement results, we estimated the distribution coefficient of the solubilizate between the micellar (solubilized) and free (in the aqueous phase) states and the solubilizing capacity of rhamnolipid micelles., Validerad;2023;Nivå 2;2023-07-21 (sofila);Funder; Ministry of Science and Higher educationof the Russian Federation (grant no. 075-15-2021-699); Kazan Federal University (ProgramPriority-2030);Licens fulltext: CC BY-NC-ND License

Aim. To study the characteristics of heart rate variability (HRV) in episodes of paroxysmal atrial fibrillation (AF) and sinus rhythm (SR) during the 24-hour Holter electrocardiographic (ECG) monitoring and to assess the presence and nature of their relationships. Material and methods. We analyzed 37 records of 24-hour Holter ECG monitoring obtained from patients with paroxysmal AF. For analysis, records were selected from the Long Term Atrial Fibrillation database (LTAFDB) (n=26), as well as from the long-term storage database “Myocard-holter” of the Sverdlovsk Regional Clinical Hospital № 1 (n=11). Each record contained at least 120 min of SR and at least 120 min of paroxysmal AF episodes. In addition, 48 HRV indices were calculated independently for SR and for AF episodes, after which the 96 HRV parameters obtained for each record were subjected to exploratory data analysis. Results. Analysis of HRV in AF paroxysm showed a significant increase in the RMSSD, SD1, pNN50 indices, which confirmed the great importance of para-sympathetic influence in the regulation of AF. Despite the fact that single HRV parameters in AF are not directly related to any single parameters in SR, we have shown that the AF is not completely chaotic and independent of the characteristics of baseline HR variability. We found that for some of the HRV indices determined during AF paroxysm (PAF_CVI, PAF_pNN20, PAF_pNN50, PAF_ApEn, PAF_SDNN, PAF_SD2), up to 74% of the variance of these indices can be explained using multivariate linear models, including 4 HRV indices for SR and taken as predictors. It was shown that among all the indices analyzed, only the PAF_HTI, calculated in paroxysmal AF, had a moderate negative correlation with the duration of AF episodes (r=0,60, p<0,01). Conclusion. It is shown that the study of HRV indices on AF paroxysm has a wide clinical and electrophysiological potential. The paper proposes statistical models that demonstrate the relationship between HRV in SR and

Collective processes in a quasi-classical electron gas are investigated within the framework of the interpolational self-consistent method of moments, which makes it possible to express the dispersion and decrement of plasma waves, and the dynamic structural factor of the system exclusively in terms of its static structural factor so that five sum rules are satisfied automatically. Different models are used of the static structure factor; the stability and robustness of the results of the moment approach taking into account the accuracy of these models is confirmed and tested by comparison to the alternative molecular dynamics simulation data.

Gd flake samples were prepared by conventional ball milling technique starting from rapidly quenched Gd ribbons and followed by vacuum annealing in different conditions. Heat treatments were conducted in a vacuum at selected temperatures up to 600 K. The structural features, magnetic and magnetocaloric properties were comparatively analyzed. The change in magnetic entropy was calculated using an experimental set of magnetic isotherms measured in a wide range of temperatures. The variations in the refrigeration capacity and the exponent of the magnetic entropy change in the external magnetic field were carefully calculated and analyzed.

The magnetocaloric properties of Gd ribbons processed by different kinds of mechanical treatments such as plastic deformation and ball milling were comparatively analyzed and discussed. The maximum of the temperature dependence of the magnetic entropy change for the ribbon in the initial state was as high as 11.8 J/kg•K in magnetic fields up to 7 T, i.e. it was very close to the corresponding value for the bulk gadolinium. The maximum values of the magnetic entropy change for the powder sample and the deformed sample in the same fields were as high as 3.2 and 1.9 J/kg•K respectively. © 2020 American Institute of Physics Inc.. All rights reserved.

[EN] Grounded on the premise that dust particles are charged hard balls, the analysis in Davletov et al. (Contrib. Plasma Phys., vol. 56, 2016, 308) provides an original pseudopotential model of intergrain interaction in complex (dusty) plasmas. This accurate model is engaged herein to consistently treat the finite-size effects from the process of dust particle charging to determination of the thermodynamic quantities and the dust-acoustic wave dispersion in the strongly coupled regime. The orbital motion limited approximation is adopted to evaluate an electric charge of dust grains immersed in a neutralizing background of the buffer plasma. To account for finite dimensions of dust particles, the radial distribution function is calculated within the reference hypernetted-chain (RHNC) approximation to demonstrate a well-pronounced short-range order formation at rather large values of the coupling parameter and the packing fraction. The evaluated excess pressure of the dust component is compared to the available theoretical approaches and the simulation data and is then used to predict the dust-acoustic wave (DAW) dispersion in the strongly coupled regime under the assumption that the dust particles charge varies in the course of propagation. In contrast to many previous investigations, it is demonstrated for the first time ever that for DAWs the charge variation of dust particles should necessarily be taken into account while evaluating the dust isothermal compressibility.

[EN] Grounded on the premise that dust particles are charged hard balls, the analysis in Davletov et al. (Contrib. Plasma Phys., vol. 56, 2016, 308) provides an original pseudopotential model of intergrain interaction in complex (dusty) plasmas. This accurate model is engaged herein to consistently treat the finite-size effects from the process of dust particle charging to determination of the thermodynamic quantities and the dust-acoustic wave dispersion in the strongly coupled regime. The orbital motion limited approximation is adopted to evaluate an electric charge of dust grains immersed in a neutralizing background of the buffer plasma. To account for finite dimensions of dust particles, the radial distribution function is calculated within the reference hypernetted-chain (RHNC) approximation to demonstrate a well-pronounced short-range order formation at rather large values of the coupling parameter and the packing fraction. The evaluated excess pressure of the dust component is compared to the available theoretical approaches and the simulation data and is then used to predict the dust-acoustic wave (DAW) dispersion in the strongly coupled regime under the assumption that the dust particles charge varies in the course of propagation. In contrast to many previous investigations, it is demonstrated for the first time ever that for DAWs the charge variation of dust particles should necessarily be taken into account while evaluating the dust isothermal compressibility.

[EN] In this paper, various methods for calculating static characteristics of plasma, such as HNC, MHNC, VMHNC, Percus-Yevik and analytical models were analyzed to satisfy a mathematical condition. Structural characteristics of a one-component plasma were reconstructed in a wide range of coupling parameters within the most requested various modern methods (HNC, MHNC, VMHNC, Percus-Yevik, and analytical models). All these methods were analyzed to fulfill the fundamental Cauchy ¿ Schwartz mathematical inequality. As a result a HNC method with the empirical expression of the bridge function and one of the recent methods for obtaining a structural factor based on a parameterized formula does not satisfy the inequality. The other methods for calculating static characteristics listed above beside the stated ones satisfy the condition. For the general analysis of a method, functional dependence was obtained expressing the Cauchy-Schwartz inequality. This dependence includes the frequency moments, which are defined within the framework of the method of moments. To satisfy the inequality, this relationship must be strictly positive. For each considered method of obtaining static structural characteristics, this relationship was calculated and analyzed. As a result, it was found that a number of methods do not satisfy the Cauchy-Schwartz inequality.

[EN] In this paper, various methods for calculating static characteristics of plasma, such as HNC, MHNC, VMHNC, Percus-Yevik and analytical models were analyzed to satisfy a mathematical condition. Structural characteristics of a one-component plasma were reconstructed in a wide range of coupling parameters within the most requested various modern methods (HNC, MHNC, VMHNC, Percus-Yevik, and analytical models). All these methods were analyzed to fulfill the fundamental Cauchy ¿ Schwartz mathematical inequality. As a result a HNC method with the empirical expression of the bridge function and one of the recent methods for obtaining a structural factor based on a parameterized formula does not satisfy the inequality. The other methods for calculating static characteristics listed above beside the stated ones satisfy the condition. For the general analysis of a method, functional dependence was obtained expressing the Cauchy-Schwartz inequality. This dependence includes the frequency moments, which are defined within the framework of the method of moments. To satisfy the inequality, this relationship must be strictly positive. For each considered method of obtaining static structural characteristics, this relationship was calculated and analyzed. As a result, it was found that a number of methods do not satisfy the Cauchy-Schwartz inequality.

[EN] Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed, and other characteristics of the collective modes are determined using exclusively the static structure factor calculated from various theoretical approaches including the hypernetted chain approximation. A good quantitative agreement with molecular dynamics simulation data is achieved.

[EN] Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed, and other characteristics of the collective modes are determined using exclusively the static structure factor calculated from various theoretical approaches including the hypernetted chain approximation. A good quantitative agreement with molecular dynamics simulation data is achieved.

The linear density response formalism is used to analytically obtain an effective pairwise interaction potential of charged particles that simultaneously takes into account quantum mechanical and quantum statistical effects in weakly and moderately non-ideal plasmas at thermal equilibrium. The static dielectric function is obtained by interpolating long - and short wavelength asymptotic forms of the dielectric function in the random-phase approximation. The exchange effects are neglected in the micropotential, while the quantum-statistical effects are accounted for in the screening. The effective potential constructed in such a way takes a finite value at the origin and proves to be screened at large distances. The thermodynamic properties of two-component plasmas are then calculated and comparison is made with some data available in the literature. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The problem of calculation of the electric charge of dust particles in a plasma is considered from different points of view. At first the charging of polarizable dust particles is studied within the orbital motion limited approach. Secondly, the plasma electrodynamics is applied to show that the electric charge of a dust particle is determined by the normal component of the dielectric displacement vector near the grain surface rather than the normal component of the electric field strength. And, finally, the chemical model, initially proposed for determination of partially ionized plasma composition, is demonstrated to be very productive in evaluating the electric charge of the dust component. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The problem of calculation of the electric charge of dust particles in a plasma is considered from different points of view. At first the charging of polarizable dust particles is studied within the orbital motion limited approach. Secondly, the plasma electrodynamics is applied to show that the electric charge of a dust particle is determined by the normal component of the dielectric displacement vector near the grain surface rather than the normal component of the electric field strength. And, finally, the chemical model, initially proposed for determination of partially ionized plasma composition, is demonstrated to be very productive in evaluating the electric charge of the dust component. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The linear density response formalism is used to analytically obtain an effective pairwise interaction potential of charged particles that simultaneously takes into account quantum mechanical and quantum statistical effects in weakly and moderately non-ideal plasmas at thermal equilibrium. The static dielectric function is obtained by interpolating long - and short wavelength asymptotic forms of the dielectric function in the random-phase approximation. The exchange effects are neglected in the micropotential, while the quantum-statistical effects are accounted for in the screening. The effective potential constructed in such a way takes a finite value at the origin and proves to be screened at large distances. The thermodynamic properties of two-component plasmas are then calculated and comparison is made with some data available in the literature. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The dense plasma dynamic collision frequency is modeled by the first two terms of its asymptotic expansion at high frequencies and its values at a few interpolation points on the real axis. This makes the dynamic collision frequency a non-rational function whose extension onto the upper half-plane of the complex frequency is holomorphic with a non-negative imaginary part and with a continuous extension to the real axis. The validity of the suggested analytic form of the latter is tested against the simulation data, where the Kelbg effective potential was used.

The dynamic structure factor of dense two-component plasmas is studied within the method of moments. A new model for the Nevanlinna parameter function is suggested. Our results on the dynamic structure factor satisfy the sum rules and other exact relations automatically, independently of the choice of a mathematically consistent model of the latter. A quantitative agreement is obtained with the molecular dynamics simulation data. Our approach permits to correct and complement the results of alternative approaches.

The dynamic structure factor of dense two-component plasmas is studied within the method of moments. A new model for the Nevanlinna parameter function is suggested. Our results on the dynamic structure factor satisfy the sum rules and other exact relations automatically, independently of the choice of a mathematically consistent model of the latter. A quantitative agreement is obtained with the molecular dynamics simulation data. Our approach permits to correct and complement the results of alternative approaches.

The dense plasma dynamic collision frequency is modeled by the first two terms of its asymptotic expansion at high frequencies and its values at a few interpolation points on the real axis. This makes the dynamic collision frequency a non-rational function whose extension onto the upper half-plane of the complex frequency is holomorphic with a non-negative imaginary part and with a continuous extension to the real axis. The validity of the suggested analytic form of the latter is tested against the simulation data, where the Kelbg effective potential was used.

We report on a development of an alternative method of HED plasma diagnostics using the ideas of the method of moments [I.M. Tkachenko, J. Ortner, and J. Alcober, J. de Physique IV 10, 195 (2000)].

Mathematical, particularly, asymptotic properties of the random-phase approximation, Mermin approximation, and extended Mermin-type approximation of the coupled plasma dielectric function are analyzed within the method of moments. These models are generalized for two-component plasmas. Some drawbacks and advantages of the above models are pointed out. The two-component plasma stopping power is shown to be enhanced with respect to that of the electron fluid.

We report on a development of an alternative method of HED plasma diagnostics using the ideas of the method of moments [I.M. Tkachenko, J. Ortner, and J. Alcober, J. de Physique IV 10, 195 (2000)].

[EN] In this article radial distribution functions and static structure factors of nonideal plasma are investigated in the framework of Ornstein-Zernike equation with Percus-Yevick bridge function and Deutch micropotential. It is shown that short range symmetries appear in ionic subsystem of dense plasma and bridge contributions of electrons promote creation of symmetries in ionic subsystem of nonideal plasma.

[EN] The energy loss of relativistic projectiles in collisional one-component plasmas is analyzed within the method of moments. Both the canonical and non-canonical solutions of the Hamburger moment problem corresponding to five convergent power frequency moments of the electron plasma loss function are employed with the static, purely imaginary, Nevanlinna parameter with the imaginary part iqual to the collision frequency calculated within the Green-Kubo formalism in terms of static structure factors evaluated in the HNC approximation using the Deutsch effective potential.Thus we take into account the dissipation processes in the plasma. It is pointed out that the correlations only slightly influence the deviation of the stopping power with the relativistic corrections taken into account from the classical Bethe-Bohr-Larkin asymptotic form.

[EN] In this article radial distribution functions and static structure factors of nonideal plasma are investigated in the framework of Ornstein-Zernike equation with Percus-Yevick bridge function and Deutch micropotential. It is shown that short range symmetries appear in ionic subsystem of dense plasma and bridge contributions of electrons promote creation of symmetries in ionic subsystem of nonideal plasma.

[EN] The energy loss of relativistic projectiles in collisional one-component plasmas is analyzed within the method of moments. Both the canonical and non-canonical solutions of the Hamburger moment problem corresponding to five convergent power frequency moments of the electron plasma loss function are employed with the static, purely imaginary, Nevanlinna parameter with the imaginary part iqual to the collision frequency calculated within the Green-Kubo formalism in terms of static structure factors evaluated in the HNC approximation using the Deutsch effective potential.Thus we take into account the dissipation processes in the plasma. It is pointed out that the correlations only slightly influence the deviation of the stopping power with the relativistic corrections taken into account from the classical Bethe-Bohr-Larkin asymptotic form.

Simulation data on hydrogen-like plasmas, modelled with the Kelbg pseudopotential, are treated within the classical theory of moments. The possibility is analyzed for the model inverse dielectric function to satisfy five convergent sum rules and other exact relations. The sum rules are the power frequency moments of the loss function and the latter are calculated using the hypernetted chain approximation with the Kelbg interaction potential. An approach to the reconstruction of the Nevanlinna parameter function is proposed and successfully tested against the simulation data. Conclusions on the applicability of the Kelbg potential are drawn and a model is put forward to define the Coulomb dielectric function with the space dispersion taken into account.

[EN] Asymptotic properties of the collisional one-component plasma dielectric function in the random-phase (RPA) and Mermin approximation, with a constant collision frequency, are analyzed from the point of view of the verification of sum rules. The latter are the power frequency moments of the loss function, a positive even function of frequency directly related to the imaginary part of the inverse dielectric function. The zero moment is shown to coincide with that of the RPA, the f-sum rule is satisfied, and the fourth moment sum rule is verified only partly, without taking the correlations into account. These drawbacks of the Mermin model expression for the dielectric function define the realm of applicability of this approximation.

[EN] Asymptotic properties of the collisional one-component plasma dielectric function in the random-phase (RPA) and Mermin approximation, with a constant collision frequency, are analyzed from the point of view of the verification of sum rules. The latter are the power frequency moments of the loss function, a positive even function of frequency directly related to the imaginary part of the inverse dielectric function. The zero moment is shown to coincide with that of the RPA, the f-sum rule is satisfied, and the fourth moment sum rule is verified only partly, without taking the correlations into account. These drawbacks of the Mermin model expression for the dielectric function define the realm of applicability of this approximation.

Simulation data on hydrogen-like plasmas, modelled with the Kelbg pseudopotential, are treated within the classical theory of moments. The possibility is analyzed for the model inverse dielectric function to satisfy five convergent sum rules and other exact relations. The sum rules are the power frequency moments of the loss function and the latter are calculated using the hypernetted chain approximation with the Kelbg interaction potential. An approach to the reconstruction of the Nevanlinna parameter function is proposed and successfully tested against the simulation data. Conclusions on the applicability of the Kelbg potential are drawn and a model is put forward to define the Coulomb dielectric function with the space dispersion taken into account.

Relativistic and correlation contributions to the polarizational energy losses of heavy projectiles moving in dense two-component plasmas are analyzed within the method of moments that allows one to reconstruct the Lindhard loss function from its three independently known power frequency moments. The techniques employed result in a thorough separation of the relativistic and correlation corrections to the classical asymptotic form for the polarizational losses obtained by Bethe and Larkin. The above corrections are studied numerically at different values of plasma parameters to show that the relativistic contribution enhances only slightly the corresponding value of the stopping power.

BRST formulation of cohomological Hamiltonian mechanics is presented. In the path integral approach, we use the BRST gauge fixing procedure for the partition function with trivial underlying Lagrangian to fix symplectic diffeomorphism invariance. Resulting Lagrangian is BRST and anti-BRST exact and the Liouvillian of classical mechanics is reproduced in the ghost-free sector. The theory can be thought of as a topological phase of Hamiltonian mechanics and is considered as one-dimensional cohomological field theory with the target space a symplectic manifold. Twisted (anti-)BRST symmetry is related to global N=2 supersymmetry, which is identified with an exterior algebra. Landau-Ginzburg formulation of the associated $d=1$, N=2 model is presented and Slavnov identity is analyzed. We study deformations and perturbations of the theory. Physical states of the theory and correlation functions of the BRST invariant observables are studied. This approach provides a powerful tool to investigate the properties of Hamiltonian systems., Comment: 40 pages, LaTeX2e