Inthispaper,weobtaincompletecharacterizationsoftheboundednessand compactness of the products of the multiplication and the radial derivative operator Mu R from mixed norm spaces H ( p, q ,φ )to Zygmund-type spaces on the unit ball.
In this paper, we use the viewpoint of Gromov-Haustorff convergence to give some new comprehension of well known theorem,it is Huber's classification theorem\cite{Huber}\cite{MS}for complete Riemannian surfaces immersed in $\mathbb{R}^n$ with finite total curvature( $\int_Σ|A|^2
Grasping in dense clutter is a fundamental skill for autonomous robots. However, the crowdedness and oc-clusions in the cluttered scenario cause significant difficul-ties to generate valid grasp poses without collisions, which results in low efficiency and high failure rates. To address these, we present a generic framework called GE-Grasp for robotic motion planning in dense clutter, where we leverage diverse action primitives for occluded object removal and present the generator-evaluator architecture to avoid spatial collisions. Therefore, our GE-Grasp is capable of grasping objects in dense clutter efficiently with promising success rates. Specifically, we define three action primitives: target-oriented grasping for target capturing, pushing, and nontarget-oriented grasping to reduce the crowdedness and occlusions. The gen-erators effectively provide various action candidates referring to the spatial information. Meanwhile, the evaluators assess the selected action primitive candidates, where the optimal action is implemented by the robot. Extensive experiments in simulated and real-world environments show that our approach outperforms the state-of-the-art methods of grasping in clutter with respect to motion efficiency and success rates. Moreover, we achieve comparable performance in the real world as that in the simulation environment, which indicates the strong gen-eralization ability of our GE-Grasp. Supplementary material is available at: https://github.com/CaptainWuDaoKou/GE-Grasp.
Automatic evaluation of perceptual similarity is crucial for music retrieval. However, previous works mainly focused on the similarity of timbre and rhythm but not the musical pattern of a song, such as melody and chord. In this paper, we propose a new feature, chroma histogram, to summarize the musical pattern and use a transposition-invariant matching method to compare two chroma histograms. Experiment results demonstrate the efficiency of this method in measuring the similarity of musical pattern.
On complete noncompact Riemannian manifolds with non-negative Ricci curvature, Li-Schoen proved the uniform Poincare inequality for any ge odesic ball. In this note, we obtain the sharp lower bound of the first Dirichlet eigenvalue of such geodesic balls, which implies the sharp Poincare inequality for geodesic balls.
In this paper, we obtain some characterizations of the boundedness and compactness of the products of the radial derivative and multiplication operator RM u between mixed norm spaces H(p, q, φ ) and Zygmund-type spaces on the unit ball.
In this section, we describe the vanilla GNNs proposed in Scarselli et al. [2009]. We also list the limitations of the vanilla GNN in representation capability and training efficiency. After this chapter we will talk about several variants ofthe vanilla GNN model.
'/%3e%3cuse xlink:href='%23a' transform='rotate(23.036 .093 25.536)'/%3e%3cuse xlink:href='%23a' transform='rotate(45.87 1.273 16.18)'/%3e%3cuse xlink:href='%23a' transform='rotate(69.945 .996 12.078)'/%3e%3cuse xlink:href='%23a' transform='rotate(20.66 -19.689 31.932)'/%3e%3c/svg%3e)