Boundary maps and maximal representations on infinite-dimensional Hermitian symmetric spaces

We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite-dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type, we show that there cannot be Zariski-dense maximal representations, and whenever the existence of a boundary map can be guaranteed, the representation preserves a finite-dimensional totally geodesic subspace on which the action is maximal. In the opposite direction, we construct examples of geometrically dense maximal representation in the infinite-dimensional Hermitian symmetric space of tube type and finite rank. Our approach is based on the study of boundary maps, which we are able to construct in low ranks or under some suitable Zariski density assumption, circumventing the lack of local compactness in the infinite-dimensional setting.

Neural labeled LDA: a topic model for semi-supervised document classification

Recently, some statistical topic modeling approaches based on LDA have been applied in the field of supervised document classification, where the model generation procedure incorporates prior knowledge to improve the classification performance. However, these customizations of topic modeling are limited by the cumbersome derivation of a specific inference algorithm for each modification. In this paper, we propose a new supervised topic modeling approach for document classification problems, Neural Labeled LDA (NL-LDA), which builds on the VAE framework, and designs a special generative network to incorporate prior information. The proposed model can support semi-supervised learning based on the manifold assumption and low-density assumption. Meanwhile, NL-LDA has a consistent and concise inference method while semi-supervised learning and predicting. Quantitative experimental results demonstrate our model has outstanding performance on supervised document classification relative to the compared approaches, including traditional statistical and neural topic models. Specially, the proposed model can support both single-label and multi-label document classification. The proposed NL-LDA performs significantly well on semi-supervised classification, especially under a small amount of labeled data. Further comparisons with related works also indicate our model is competitive with state-of-the-art topic modeling approaches on semi-supervised classification.

Enhanced algorithms to ensure the success of rendezvous maneuvers using aerodynamic forces

A common practice in the field of differential lift and drag controlled satellite formation flight is to analytically design maneuver trajectories using linearized relative motion models and the constant density assumption. However, the state-of-the-art algorithms inevitably fail if the initial condition of the final control phase exceeds an orbit and spacecraft-dependent range, the so-called feasibility range. This article presents enhanced maneuver algorithms for the third (and final) control phase which ensure the overall maneuver success independent of the initial conditions. Thereby, all maneuvers which have previously been categorized as infeasible due to algorithm limitations are rendered feasible. An individual algorithm is presented for both possible control options of the final phase, namely differential lift or drag. In addition, a methodology to precisely determine the feasibility range without the need of computational expensive Monte Carlo simulations is presented. This allows fast and precise assessments of possible influences of boundary conditions, such as the orbital inclination or the maneuver altitude, on the feasibility range.

The Bouguer-Rudzki-Hotine scheme for geoid computations

<p>The Rudzki inversion gravimetric reduction maps the Earth’s topographic masses inside the geoid in such a way that the inverted masses produce exactly the same potential as the topographic masses on the geoid. In other words, the indirect effect to the geoid is zero so that its computation is not needed. This paper proposes a geoid computation scheme that combines the Bouguer reduction and Rudzki inversion reduction under the spherical approximation and constant density assumption. The proposed computation scheme works with the Bouguer gravity field that is smooth and theoretically legitimate for the harmonic downward continuation. Then the Bouguer potential is compensated by the potential of the inverted masses, ensuring zero indirect effect to the geoid. The direct effect of the Rudzki inversion gravimetric reduction is added to the Bouguer gravity disturbance, resulting in the reduced gravity disturbance for geoid computation. A spherical harmonic reference gravity model is also developed so that the kernel modification/truncation can be applied to the Hotine integral. If the density of the topographic masses becomes available, the effect of density anomalies can be computed separately and added to the geoid computed under the constant density assumption. The combined ellipsoidal effect of the Bouguer and Rudzki inversion reduction should be insignificant because of the canceling effect between them.</p>

The second-degree gravity coefficients of Phobos from two Mars Express flybys

ABSTRACT Several close spacecraft flybys of Phobos have been performed over the past 40 yr in order to determine the gravity field of this tiny Martian moon. In this work, the second-degree coefficients of the gravity field of Phobos were derived from the radio tracking data of two combined Mars Express flybys (2010 and 2013), by applying a least squares regularized inverse technique, that introduces as an a priori the gravity field retrieved from a shape model based on constant density hypothesis. A gravitational mass estimate of $(7.0765\pm 0.0075)\times 10^5 \, \mathrm{m^3\, s}^{-2}$ and second-degree gravity coefficients C20 = −0.1378 ± 0.0348 and C22 = 0.0166 ± 0.0153(3σ) were derived. The estimated C20 value, in contrast to the value of C20 computed from the shape model under the constant density assumption, supports an inhomogeneous distribution inside Phobos at a confidence interval of 95 per cent (1.96σ). This result indicates a denser mass in the equatorial region or lighter mass in polar areas.

A new mean ergodic theorem for tori and recurrences

Let $X$ be a finite-dimensional connected compact abelian group equipped with the normalized Haar measure $\unicode[STIX]{x1D707}$. We obtain the following mean ergodic theorem over ‘thin’ phase sets. Fix $k\geq 1$ and, for every $n\geq 1$, let $A_{n}$ be a subset of $\mathbb{Z}^{k}\cap [-n,n]^{k}$. Assume that $(A_{n})_{n\geq 1}$ has $\unicode[STIX]{x1D714}(1/n)$ density in the sense that $\lim _{n\rightarrow \infty }(|A_{n}|/n^{k-1})=\infty$. Let $T_{1},\ldots ,T_{k}$ be ergodic automorphisms of $X$. We have $$\begin{eqnarray}\frac{1}{|A_{n}|}\mathop{\sum }_{(n_{1},\ldots ,n_{k})\in A_{n}}f_{1}(T_{1}^{n_{1}}(x))\cdots f_{k}(T_{k}^{n_{k}}(x))\stackrel{L_{\unicode[STIX]{x1D707}}^{2}}{\longrightarrow }\int f_{1}\,d\unicode[STIX]{x1D707}\cdots \int f_{k}\,d\unicode[STIX]{x1D707},\end{eqnarray}$$ for any $f_{1},\ldots ,f_{k}\in L_{\unicode[STIX]{x1D707}}^{\infty }$. When the $T_{i}$ are ergodic epimorphisms, the same conclusion holds under the further assumption that $A_{n}$ is a subset of $[0,n]^{k}$ for every $n$. The density assumption on the $A_{i}$ is necessary. Immediate applications include certain Poincaré style recurrence results.

Bouguer Density Analysis using Nettleton Method at Banten NPP Site

BOUGUER DENSITY ANALYSIS USING NETTLETON METHOD AT BANTEN NPP SITE. Sub-surface information become crucial in determining a feasible NPP site that safe from external hazards. Gravity survey which result as density information, is essential to understand the sub-surface structure. Nevertheless, overcorrected or under corrected will lead to a false interpretation. Therefore, density correction in term of near-surface average density or Bouguer density is necessary to be calculated. The objective of this paper is to estimate and analyze Bouguer density using Nettleton method at Banten NPP Site. Methodology used in this paper is Nettleton method that applied in three different slices (A-B, A-C and A-D) with density assumption range between 1700 and 3300 kg/m3. Nettleton method is based on minimum correlation between gravity anomaly and topography to determine density correction. The result shows that slice A-B which covers rough topography difference, Nettleton method failed. While using the other two slices, Nettleton method yield with a different density value, 2700 kg/m3 for A-C and 2300 kg/m3 for A-D. A-C provides the lowest correlation value which represents the Upper Banten tuff and Gede Mt. volcanic rocks in accordance with Quartenary rocks exist in the studied area.

A New Snow Density Parameterization for Land Data Initialization

Snow initialization is crucial for weather and seasonal prediction, but the National Centers for Environmental Prediction (NCEP) operational models have been found to produce too little snow water equivalent, partly because they assume a constant and unrealistically low snow density for the snowpack. One possible solution is to use the snow density formulation from the Noah land model used in NCEP operational forecast models. While this solution is better than the constant density assumption, the seasonal evolution of snow density in Noah is still found to be unrealistic, through the evaluation of both the offline Noah model output and the Noah snow density formulation itself. A physically based snow density parameterization is then developed, which performs considerably better than the Noah parameterization based on the measurements from the SNOTEL network over the western United States and Alaska. It also performs better than the snow density schemes used in three other models. This parameterization could be easily implemented in NCEP operational snow initialization. With the consideration of up to 10 snow layers, this parameterization can also be applied to multilayer snowpack initiation or to estimate snow water equivalent from in situ and airborne snow depth measurements.

Least-squares reverse time migration in the presence of density variations

Least-squares migration (LSM) is commonly regarded as an amplitude-preserving or true amplitude migration algorithm that, compared with conventional migration, can provide migrated images with reduced migration artifacts, balanced amplitudes, and enhanced spatial resolution. Most applications of LSM are based on the constant-density assumption, which is not the case in the real earth. Consequently, the amplitude performance of LSM is not appropriate. To partially remedy this problem, we have developed a least-squares reverse time migration (LSRTM) scheme suitable for density variations in the acoustic approximation. An improved scattering-integral approach is adopted for implementation of LSRTM in the frequency domain. LSRTM images associated with velocity and density perturbations are simultaneously used to generate the simulated data, which better matches the recorded data in amplitudes. Summation of these two images provides a reflectivity model related to impedance perturbation that is in better accordance with the true one, than are the velocity and density images separately. Numerical examples based on a two-layer model and a small part of the Sigsbee2A model verify the effectiveness of our method.

Validation of URANS Simulation of Truck Cooling Fan Performance

The performance of an axial heavy duty truck cooling fan was investigated by measurements in a test rig and by CFD simulations. In order to account for the unsteadiness of the flow, URANS simulations were employed. Good agreement was achieved between the simulation and test data, in particular in the axial regime, despite the constant density assumption. To improve the simulation accuracy in the radial and transitional regime it is most likely insufficient to assume constant density. New simulations with ideal gas assumptions for these regimes are believed to give better agreement with the test data. The simulations show that URANS CFD can produce results very close to the ones obtained in the test facilities and thereby can be used for the industrial applications when flow unsteadiness has to be taken into account. The fact that it requires long computational time and is CPU-demanding can no longer be regarded as a major preventing factor for its application in the industry. In addition, it provides valuable information about the details of the flow which can contribute to the optimization of the geometry for improved efficiency and higher performance.