Optimal Campaign Strategies in Fractional-Order Smoking Dynamics

Zeb, Anwar,Zaman, Gul,Jung, Il Hyo,Khan, Madad Verlag der Zeitschrift für Naturforschung 2014 Zeitschrift für Naturforschung. A, A journal Vol.69 No.5

<P>This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin’s maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.</P>

Karpman–Washimi Ponderomotive Magnetization and Radiated Power: Streaming and Resonant Effects

Ki, Dae-Han,Jung, Young-Dae Verlag der Zeitschrift für Naturforschung 2013 Zeitschrift für Naturforschung. A, A journal Vol.68 No.6

<P>The electron streaming and resonance effects on the non-stationary Karpman-Washimi nonlinear ponderomotive magnetization and radiated power are investigated in a quantum plasma. The ponderomotive Karpman-Washimi magnetization and radiation power due to the ponderomotive force are obtained as functions of the electron streaming velocity, Fermi velocity, wave frequency, and wave number. In small wave numbers, it is found that the electron streaming effect enhances the Karpman-Washimi ponderomotive magnetization. It is found that the electron streaming effect shifts the resonant wave number to the smaller wave number domain. It is also found that the quantum effect reduces the electron streaming velocity for the ponderomotive magnetization near the resonant wave number. In addition, the wave frequency for the resonant Karpman-Washimi radiated power is found to be increased with increasing wave number.</P>

The ‘Missing Mass Problem’ in Astronomy and the Need for a Modified Law of Gravity

Verlag der Zeitschrift für Naturforschung 2014 Zeitschrift für Naturforschung. A, A journal Vol.69 No.3

<P>Since the 1930s, astronomical observations have accumulated evidence that our understanding of the dynamics of galaxies and groups of galaxies is grossly incomplete: assuming the validity of Newton’s law of gravity on astronomical scales, the observed mass (stored in stars and interstellar gas) of stellar systems can account only for roughly 10% of the dynamical (gravitating) mass required to explain the high velocities of stars in those systems. The standard approach to this ‘missing mass problem’ has been the postulate of ‘dark matter’, meaning an additional, electromagnetically dark, matter component that provides the missing mass. However, direct observational evidence for dark matter has not been found to date. More importantly, astronomical observations obtained during the last decade indicate that dark matter cannot explain the kinematics of galaxies. Multiple observations show that the discrepancy between observed and dynamical mass is a function of gravitational acceleration (or field strength) but not of other parameters (size, rotation speed, etc.) of a galaxy; the mass discrepancy appears below a characteristic and universal acceleration aM = (1:1±0:1) · 10<SUP>-10</SUP>ms<SUP>-2</SUP>(Milgrom’s constant). Consequently, the idea of a modified law of gravity, specifically the ansatz of modified Newtonian dynamics (MOND), is becoming increasingly important in astrophysics. MOND has successfully predicted various important empirical relations of galaxy dynamics, including the famous Tully-Fisher and Faber-Jackson relations. MOND is found to be consistent with stellar dynamics from binary stars to clusters of galaxies, thus covering stellar systems spanning eight orders of magnitude in size and 14 orders of magnitude in mass. These developments have the potential to initiate a paradigm shift from dark matter to a modified law of gravity as the physical mechanism behind the missing mass problem.</P>

Influence of the Dynamic Quantum Shielding on the Transition Bremsstrahlung Spectrum and the Gaunt Factor in Strongly Coupled Semiclassical Plasmas

Jung, Young-Dae,Hong, Woo-Pyo Verlag der Zeitschrift für Naturforschung 2013 Zeitschrift für Naturforschung. A, A journal Vol.68 No.1

<P>The influence of the dynamic quantum shielding on the transition bremsstrahlung spectrum is investigated in strongly coupled semiclassical plasmas. The effective pseudopotential and the impact parameter analysis are employed to obtain the bremsstrahlung radiation cross section as a function of the de Broglie wavelength, Debye length, impact parameter, radiation photon energy, projectile energy, and thermal energy. The result shows that the dynamic screening effect enhances the transition bremsstrahlung radiation cross section. It is found that the maximum position of the transition bremsstrahlung process approaches to the center of the shielding cloud with increasing thermal energy. It is also found that the dynamic screening effect on the bremsstrahlung radiation cross section decreases with an increase of the quantum character of the semiclassical plasma. In addition, it is found that the peak radiation energy increases with an increase of the thermal energy. It is also found that the dynamic quantum screening effect enhances the bremsstrahlung Gaunt factor, especially for the soft-photon case.</P>

Influence of the Dynamic Shielding on the Collisional Entanglement Fidelity in Strongly Coupled Semiclassical Plasmas

Ki, Dae-Han,Jung, Young-Dae Verlag der Zeitschrift für Naturforschung 2013 Zeitschrift für Naturforschung. A, A journal Vol.68 No.1

<P>The influence of the dynamic plasma shielding on the collisional entanglement fidelity is investigated in strongly coupled semiclassical plasmas. The partial wave analysis with the effective dynamic screening length is employed to obtain the dynamic entanglement fidelity as a function of collision energy, de Broglie wavelength, Debye length, and thermal energy. The results show that the collisional entanglement fidelity increases with increasing plasma temperature as well as de Broglie wavelength and, however, decreases with an increase of the Debye length. It is also found that the dynamic screening effect suppresses the collisional entanglement fidelity in strongly coupled semiclassical plasmas. In addition, it is found that the entanglement fidelity decreases with increasing de Broglie wavelength and, however, increases with increasing thermal energy. It is also found that the thermal effect on the entanglement fidelity would be more significant in the domain of low-collision energies.</P>

Influence of Electron Exchange and Quantum Shielding on the Elastic Collisions in Quantum Plasmas

Lee, Gyeong Won,Jung, Young-Dae Verlag der Zeitschrift für Naturforschung 2013 Zeitschrift für Naturforschung. A, A journal Vol.68 No.10

<P>The influence of electron exchange and quantum shielding on the elastic electron-ion collision is investigated in degenerate quantum plasmas. The second-order eikonal method and effective screened potential are employed to obtain the scattering phase shift and collision cross section as functions of the impact parameter, collision energy, electron-exchange parameter, Fermi energy, and plasmon energy. It is found that the electron-exchange effect enhances the eikonal scattering phase shift as well as the eikonal collision cross section in quantum plasmas. The maximum position of the differential eikonal collision cross section is found to be receded from the collision center with an increase of the electron-exchange effect. It is interesting to note that the influence of the electron exchange on the eikonal collision cross section decreases with increasing collision energy. It is also found that the eikonal collision cross section decreases with an increase of the plasmon energy and, however, increases with increasing Fermi energy.</P>

Robust Control for Fuzzy Nonlinear Uncertain Systems with Discrete and Distributed Time Delays

Sakthivel, Rathinasamy,Vadivel, Ponnusamy,Mathiyalagan, Kalidass,Park, Ju H. Verlag der Zeitschrift für Naturforschung 2014 Zeitschrift für Naturforschung. A, A journal Vol.69 No.10

<P><B>Abstract</B></P><P>This paper addresses the problem of stability and stabilization issue for a class of fuzzy nonlinear uncertain systems with discrete and distributed time delays. By utilizing a new Lyapunov-Krasovskii functional together with free weighting matrix approach, a new set of delay-dependent sufficient conditions are derived which makes the closed loop system robustly asymptotically stable. In particular, the parameter uncertainties are assumed to be norm bounded. Further, a state feedback controller is proposed to guarantee the robust stabilization for uncertain systems and subsequently the controller is constructed in terms of the solution to a set of linear matrix inequalities (LMI). The derived conditions are expressed in the form of linear matrix inequalities which can be efficiently solved via standard LMI toolbox. Further, two numerical examples are provided to demonstrate the effectiveness and less conservatism of the obtained results.</P>