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In this paper, we deal with numerical approximations for solving the Black-Scholes Partial Differential Equation (PDE). This PDE is well known to be degenerated. The space discretization is performed using the classical finite volume method with Two-Point Flux Approximation (TPFA) and a novel scheme called fitted Two-Point Flux Approximation (TPFA).The fitted Two-Point Flux Approximation (TPFA) combines the fitted finite volume method and the standard TPFA method. More precisely the fitted finite volume method is used when the stock price approaches zero in order to handle the degeneracy of the PDE and the TPFA method is used on the rest of space domain. This combination yields our novel fitted TPFA scheme. The Euler method is used for the time discretization. We provide the rigorous convergence proofs of the two fully discretized schemes. Numerical experiments to support our theoretical results are provided.

Structure functions, as measured in lepton-nucleon scattering, have proven to be very useful in studying the quark dynamics within the nucleon. However, it is experimentally difficult to separately determine the longitudinal and transverse structure functions, and consequently there are substantially less data available for the longitudinal structure function in particular. Here we present separated structure functions for hydrogen and deuterium at low four--momentum transfer squared, Q^2< 1 GeV^2, and compare these with parton distribution parameterizations and a k_T factorization approach. While differences are found, the parameterizations generally agree with the data even at the very low Q^2 scale of the data. The deuterium data show a smaller longitudinal structure function, and smaller ratio of longitudinal to transverse cross section R, than the proton. This suggests either an unexpected difference in R for the proton and neutron or a suppression of the gluonic distribution in nuclei., Comment: 11 pages, 7 figures, 2 data tables

A large set of cross sections for semi-inclusive electroproduction of charged pions ($\pi^\pm$) from both proton and deuteron targets was measured. The data are in the deep-inelastic scattering region with invariant mass squared $W^2$ > 4 GeV$^2$ and range in four-momentum transfer squared $2 < Q^2 < 4$ (GeV/c)$^2$, and cover a range in the Bjorken scaling variable 0.2 < x < 0.6. The fractional energy of the pions spans a range 0.3 < z < 1, with small transverse momenta with respect to the virtual-photon direction, $P_t^2 < 0.2$ (GeV/c)$^2$. The invariant mass that goes undetected, $M_x$ or W', is in the nucleon resonance region, W' < 2 GeV. The new data conclusively show the onset of quark-hadron duality in this process, and the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark --> pion production mechanisms. The x, z and $P_t^2$ dependences of several ratios (the ratios of favored-unfavored fragmentation functions, charged pion ratios, deuteron-hydrogen and aluminum-deuteron ratios for $\pi^+$ and $\pi^-$) have been studied. The ratios are found to be in good agreement with expectations based upon a high-energy quark-parton model description. We find the azimuthal dependences to be small, as compared to exclusive pion electroproduction, and consistent with theoretical expectations based on tree-level factorization in terms of transverse-momentum-dependent parton distribution and fragmentation functions. In the context of a simple model, the initial transverse momenta of $d$ quarks are found to be slightly smaller than for $u$ quarks, while the transverse momentum width of the favored fragmentation function is about the same as for the unfavored one, and both fragmentation widths are larger than the quark widths.

The process $ep \to e^{\prime}p^{\prime}\pi^0$ has been measured at $Q^2$ = 6.4 and 7.7 GeV/c$^2$)$^2$ in Jefferson Lab's Hall C. Unpolarized differential cross sections are reported in the virtual photon-proton center of mass frame considering the process $\gamma^{\ast}p \to p^{\prime}\pi^0$. Various details relating to the background subtractions, radiative corrections and systematic errors are discussed. The usefulness of the data with regard to the measurement of the electromagnetic properties of the well known $\Delta(1232)$ resonance is covered in detail. Specifically considered are the electromagnetic and scalar-magnetic ratios $R_{EM}$ and $R_{SM}$ along with the magnetic transition form factor $G_M^{\ast}$. It is found that the rapid fall off of the $\Delta(1232)$ contribution continues into this region of momentum transfer and that other resonances, Comment: 41 pages including numerical cross section tables, updates include new phenomenological fit for multipole extraction in addition to simplified previous method, These fits are seen in figures 24,26 and 27 and the values are reported in Table VIII

The differential cross-section for the process p(e,e'p)eta has been measured at Q2 ~ 5.7 and 7.0 (GeV/c)2 for centre-of-mass energies from threshold to 1.8 GeV, encompassing the S11(1535) resonance, which dominates the channel. This is the highest momentum transfer measurement of this exclusive process to date. The helicity-conserving transition amplitude A_1/2, for the production of the S11(1535) resonance, is extracted from the data. Within the limited Q2 now measured, this quantity appears to begin scaling as 1/Q3 - a predicted, but not definitive, signal of the dominance of perturbative QCD, at Q2 ~ 5 (GeV/c)2., Comment: LaTeX, 30 pages, 29 figures, uses longtable.sty, slashbox.sty, ifthen.sty; (v2) corrected figure inclusions; (v3) changes in filenames for prc and added Report-no; (v4) correction based on comments from referee {small changes to abstract and conclusion, inserted figure 9, other small changes to the text} (v5) very minor additions to improve clarity

Cross sections for semi-inclusive electroproduction of charged pions ($\pi^{\pm}$) from both proton and deuteron targets were measured for $0.2

Cross sections were measured for the near-threshold electrodisintegration of ^3He at momentum transfer values of q=2.4, 4.4, and 4.7 fm^{-1}. From these and prior measurements the transverse and longitudinal response functions R_T and R_L were deduced. Comparisons are made against previously published and new non-relativistic A=3 calculations using the best available NN potentials. In general, for q<2 fm^{-1} these calculations accurately predict the threshold electrodisintegration of ^3He. Agreement at increasing q demands consideration of two-body terms, but discrepancies still appear at the highest momentum transfers probed, perhaps due to the neglect of relativistic dynamics, or to the underestimation of high-momentum wave-function components., Comment: 9 pages, 7 figures, 1 table, REVTEX4, submitted to Physical Review C

We analyze the possibility of measuring the single spin asymmetry (SSA) in open charm production by linearly polarized photons in the planned E160/E161 experiments at SLAC using the inclusive spectra of secondary (decay) leptons. In leading order pQCD, the SSA in the azimuthal distribution of the charged decay lepton is predicted to be about 0.2 for SLAC kinematics. Our calculations show that the SSA in the decay lepton distribution is well defined in pQCD: it is stable both perturbatively and parametrically, and practically insensitive to theoretical uncertainties in the charm semileptonic decays. Nonperturbative contributions to the leptonic SSA due to the gluon transverse motion in the target, heavy quark fragmentation and Fermi motion of the $c$-quark inside the $D$-meson are predicted to be about 10%. We conclude that measurements of the azimuthal asymmetry in the secondary lepton distribution would provide a good test of the applicability of pQCD to open charm production at energies of fixed target experiments. Our analysis of the SLAC experimental conditions shows that this SSA can be measured in E160/E161 with an accuracy of about ten percent., Comment: 18 pages, 10 figures, RevTeX, references corrected

The inclusive A(e,e') cross section for $x \simeq 1$ was measured on $^2$H, C, Fe, and Au for momentum transfers $Q^2$ from 1-7 (GeV/c)$^2$. The scaling behavior of the data was examined in the region of transition from y-scaling to x-scaling. Throughout this transitional region, the data exhibit $\xi$-scaling, reminiscent of the Bloom-Gilman duality seen in free nucleon scattering., Comment: 4 pages, RevTeX; 4 figures (postscript in .tar.Z file)

The feasibility of using forebody tangential blowing to control the roll-yaw motion of a wind tunnel model is experimentally demonstrated. An unsteady model of the aerodynamics is developed based on the fundamental physics of the flow. Data from dynamic experiments is used to validate the aerodynamic model. A unique apparatus is designed and built that allows the wind tunnel model two degrees of freedom, roll and yaw. Dynamic experiments conducted at 45 degrees angle of attack reveal the system to be unstable. The natural motion is divergent. The aerodynamic model is incorporated into the equations of motion of the system and used for the design of closed loop control laws that make the system stable. These laws are proven through dynamic experiments in the wind tunnel using blowing as the only actuator. It is shown that asymmetric blowing is a highly non-linear effector that can be linearized by superimposing symmetric blowing. The effects of forebody tangential blowing and roll and yaw angles on the flow structure are determined through flow visualization experiments. The transient response of roll and yaw moments to a step input blowing are determined. Differences on the roll and yaw moment dependence on blowing are explained based on the physics of the phenomena.

Expanding man's presence in space requires capable, dexterous robots capable of being controlled from the Earth. Traditional 'hand-in-glove' control paradigms require the human operator to directly control virtually every aspect of the robot's operation. While the human provides excellent judgment and perception, human interaction is limited by low bandwidth, delayed communications. These delays make 'hand-in-glove' operation from Earth impractical. In order to alleviate many of the problems inherent to remote operation, Stanford University's Aerospace Robotics Laboratory (ARL) has developed the Object-Based Task-Level Control architecture. Object-Based Task-Level Control (OBTLC) removes the burden of teleoperation from the human operator and enables execution of tasks not possible with current techniques. OBTLC is a hierarchical approach to control where the human operator is able to specify high-level, object-related tasks through an intuitive graphical user interface. Infrequent task-level command replace constant joystick operations, eliminating communications bandwidth and time delay problems. The details of robot control and task execution are handled entirely by the robot and computer control system. The ARL has implemented the OBTLC architecture on a set of Free-Flying Space Robots. The capability of the OBTLC architecture has been demonstrated by controlling the ARL Free-Flying Space Robots from NASA Ames Research Center.

Post-stall roll control utilizing tangential leading edge blowing is demonstrated in a wind tunnel on a delta wing model that exhibited wing rock. The dampening effect of symmetric blowing alone on wing rock is found to be effective up to a certain maximum amount of blowing. A moderate amount of symmetric blowing was shown to be effective in linearizing the asymmetric blowing static rolling moment responses.

A feasibility study to determine if the use of tangential leading edge blowing over the forebody could produce effective and practical control of the F-18 HARV aircraft at high angles of attack was conducted. A simplified model of the F-18 configuration using a vortex-lattice model was developed to obtain a better understanding of basic aerodynamic coupling effects and the influence of forebody circulation on lifting surface behavior. The effect of tangential blowing was estimated using existing wind tunnel data on normal forebody blowing and analytical studies of tangential blowing over conical forebodies. Incorporation of forebody blowing into the flight control system was investigated by adding this additional yaw control and sideforce generating actuator into the existing F-18 HARV simulation model. A control law was synthesized using LQG design methods that would schedule blowing rates as a function of vehicle sideslip, angle of attack, and roll and yaw rates.