The Experts below are selected from a list of 153324 Experts worldwide ranked by ideXlab platform
Richard H. Rapp - One of the best experts on this subject based on the ideXlab platform.
-
use of Potential Coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly geoid undulation difference
Journal of Geodesy, 1997Co-Authors: Richard H. RappAbstract:This paper suggests that Potential Coefficient models of the Earth's gravitational Potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a Potential Coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A Potential Coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions.
-
use of Potential Coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly geoid undulation difference
Journal of Geodesy, 1997Co-Authors: Richard H. RappAbstract:This paper suggests that Potential Coefficient models of the Earth's gravitational Potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a Potential Coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A Potential Coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions.
H. Nahavandchi - One of the best experts on this subject based on the ideXlab platform.
-
two different methods of geoidal height determinations using a spherical harmonic representation of the geoPotential topographic corrections and the height anomaly geoidal height difference
Journal of Geodesy, 2002Co-Authors: H. NahavandchiAbstract:It is suggested that a spherical harmonic representation of the geoidal heights using global Earth gravity models (EGM) might be accurate enough for many applications, although we know that some short-wavelength signals are missing in a Potential Coefficient model. A `direct' method of geoidal height determination from a global Earth gravity model Coefficient alone and an `indirect' approach of geoidal height determination through height anomaly computed from a global gravity model are investigated. In both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction terms used for the indirect determination of geoidal heights from height anomalies.
S Aihara - One of the best experts on this subject based on the ideXlab platform.
-
on adaptive boundary control for stochastic parabolic systems with unknown Potential Coefficient
IEEE Transactions on Automatic Control, 1997Co-Authors: S AiharaAbstract:An adaptive boundary control problem for a stochastic heat diffusion equation is studied. The considered system contains an unknown Potential Coefficient which is a function of the spatial variables. The estimation algorithm for the unknown Potential Coefficient is proposed by using the stochastic approximation technique. After showing the strong consistency of the estimated parameter, the cost for the adaptive control scheme presented here is shown to converge to the optimal ergodic cost. Finally some numerical examples are shown.
-
adaptive boundary control for stochastic parabolic systems with unknown Potential Coefficient
Conference on Decision and Control, 1994Co-Authors: S AiharaAbstract:An adaptive boundary control problem for a stochastic heat diffusion equation is studied. The system considered contains the unknown Potential Coefficient which is a function of the spatial variables. The estimation algorithm for the unknown Potential Coefficient is proposed by using the stochastic approximation technique. After showing the strong consistency of the estimated parameter, the cost for the adaptive control scheme presented here is shown to converge to the optimal ergodic cost. Finally some numerical examples are shown. >
Gerald Teschl - One of the best experts on this subject based on the ideXlab platform.
-
weyl titchmarsh theory for sturm liouville operators with distributional Potentials
Opuscula Mathematica, 2013Co-Authors: Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols, Gerald TeschlAbstract:We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals \((a,b) \subseteq \mathbb{R}\) associated with rather general differential expressions of the type \begin{equation*}\tau f = \frac{1}{\tau} (-(p[f'+sf])'+sp[f'+sf]+qf),\end{equation*} where the Coefficients \(p, q, r, s\) are real-valued and Lebesgue measurable on \((a,b)\), with \(p \neq 0\), \(r \gt 0\) a.e. on \((a,b)\), and \(p^{-1}, q, r, s \in L_{loc}^1((a,b),dx)\), and \(f\) is supposed to satisfy \begin{equation*} f \in AC_{loc}((a,b)), p[f'+sf] \in AC_{loc}((a,b)). \end{equation*} In particular, this setup implies that \(\tau\) permits a distributional Potential Coefficient, including Potentials in \(H_{loc}^{-1}((a,b))\). We study maximal and minimal Sturm-Liouville operators, all self-adjoint restrictions of the maximal operator \(T_{max}\), or equivalently, all self-adjoint extensions of the minimal operator \(T_{min}\), all self-adjoint boundary conditions (separated and coupled ones), and describe the resolvent of any self-adjoint extension of \(T_{min}\). In addition, we characterize the principal object of this paper, the singular Weyl-Titchmarsh-Kodaira m-function corresponding to any self-adjoint extension with separated boundary conditions and derive the corresponding spectral transformation, including a characterization of spectral multiplicities and minimal supports of standard subsets of the spectrum. We also deal with principal solutions and characterize the Friedrichs extension of \(T_{min}\). Finally, in the special case where \(\tau\) is regular, we characterize the Krein-von Neumann extension of \(T_{min}\) and also characterize all boundary conditions that lead to positivity preserving, equivalently, improving, resolvents (and hence semigroups).
-
weyl titchmarsh theory for sturm liouville operators with distributional Potentials
arXiv: Spectral Theory, 2012Co-Authors: Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols, Gerald TeschlAbstract:We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type \[ \tau f = \frac{1}{r} (- \big(p[f' + s f]\big)' + s p[f' + s f] + qf),] where the Coefficients $p$, $q$, $r$, $s$ are real-valued and Lebesgue measurable on $(a,b)$, with $p\neq 0$, $r>0$ a.e.\ on $(a,b)$, and $p^{-1}$, $q$, $r$, $s \in L^1_{\text{loc}}((a,b); dx)$, and $f$ is supposed to satisfy [f \in AC_{\text{loc}}((a,b)), \; p[f' + s f] \in AC_{\text{loc}}((a,b)).] In particular, this setup implies that $\tau$ permits a distributional Potential Coefficient, including Potentials in $H^{-1}_{\text{loc}}((a,b))$. We study maximal and minimal Sturm-Liouville operators, all self-adjoint restrictions of the maximal operator $T_{\text{max}}$, or equivalently, all self-adjoint extensions of the minimal operator $T_{\text{min}}$, all self-adjoint boundary conditions (separated and coupled ones), and describe the resolvent of any self-adjoint extension of $T_{\text{min}}$. In addition, we characterize the principal object of this paper, the singular Weyl-Titchmarsh-Kodaira $m$-function corresponding to any self-adjoint extension with separated boundary conditions and derive the corresponding spectral transformation, including a characterization of spectral multiplicities and minimal supports of standard subsets of the spectrum. We also deal with principal solutions and characterize the Friedrichs extension of $T_{\text{min}}$. Finally, in the special case where $\tau$ is regular, we characterize the Krein-von Neumann extension of $T_{\text{min}}$ and also characterize all boundary conditions that lead to positivity preserving, equivalently, improving, resolvents (and hence semigroups).
-
weyl titchmarsh theory for sturm liouville operators with distributional Coefficients
2012Co-Authors: Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols, Gerald TeschlAbstract:We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type \[ \tau f = \frac{1}{r} (- \big(p[f' + s f]\big)' + s p[f' + s f] + qf),] where the Coefficients $p$, $q$, $r$, $s$ are real-valued and Lebesgue measurable on $(a,b)$, with $p\neq 0$, $r>0$ a.e.\ on $(a,b)$, and $p^{-1}$, $q$, $r$, $s \in L^1_{\text{loc}}((a,b); dx)$, and $f$ is supposed to satisfy [f \in AC_{\text{loc}}((a,b)), \; p[f' + s f] \in AC_{\text{loc}}((a,b)).] In particular, this setup implies that $\tau$ permits a distributional Potential Coefficient, including Potentials in $H^{-1}_{\text{loc}}((a,b))$. We study maximal and minimal Sturm-Liouville operators, all self-adjoint restrictions of the maximal operator $T_{\text{max}}$, or equivalently, all self-adjoint extensions of the minimal operator $T_{\text{min}}$, all self-adjoint boundary conditions (separated and coupled ones), and describe the resolvent of any self-adjoint extension of $T_{\text{min}}$. In addition, we characterize the principal object of this paper, the singular Weyl-Titchmarsh-Kodaira $m$-function corresponding to any self-adjoint extension with separated boundary conditions and derive the corresponding spectral transformation, including a characterization of spectral multiplicities and minimal supports of standard subsets of the spectrum. We also deal with principal solutions and characterize the Friedrichs extension of $T_{\text{min}}$. Finally, in the special case where $\tau$ is regular, we characterize the Krein-von Neumann extension of $T_{\text{min}}$ and also characterize all boundary conditions that lead to positivity preserving, equivalently, improving, resolvents (and hence semigroups).
Anthony Szymczyk - One of the best experts on this subject based on the ideXlab platform.
-
electrokinetic characterization of hollow fibers by streaming current streaming Potential and electric conductance
Journal of Membrane Science, 2012Co-Authors: Y Lanteri, Patrick Fievet, Sebastien Deon, P Sauvade, W Ballout, Anthony SzymczykAbstract:Abstract The electrokinetic properties of hollow fiber polymer membranes were investigated from tangential streaming current/streaming Potential and electric conductance measurements. The experiments were conducted with a number of fibers n between 1 and 10 and for three fiber lengths l . The quite good linearity of (i) streaming current/Potential data versus pressure difference and (ii) streaming current Coefficient and “ SP × G ” ( SP : streaming Potential Coefficient; G : cell electric conductance) data versus n / l shows that expressions of the streaming current and streaming Potential derived in laminar flow are also valid for turbulent flux conditions (provided the electrical double layer lies within the laminar sublayer near the surface). The high experimental conductance, the nonlinear dependence of electric conductance on the number of fibers and the variation of streaming Potential Coefficient with n and l suggest that the solution in which fibers are immersed makes contribution to the cell electric conductance. A non negligible part of the total streaming current is likely to flow through the macroporous body of fibers. Unlike flat membranes, the contributions of the skin surface and the porous body of the fibers to the streaming current cannot be separated for this type of material due to the impossibility of varying channel cross section. The conversion of tangential electrokinetic measurements into zeta-Potential of lumen surface is then no more possible. In such cases, it is advisable to carry out streaming current measurements (or to combine streaming Potential measurements with electric conductance measurements) because the streaming current (or the product SP × G ) is not affected by the cell electric conductance and can then be considered a property of membrane surface.