On Higher Order Approximation for Nonlinear Variational Problems in Nonsmooth Mechanics

2012 ◽  
Author(s):  
J. Gwinner
Keyword(s):  
Order Approximation ◽  
Variational Problems ◽  
Higher Order ◽  
Nonsmooth Mechanics

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

scholarly journals Learning Graph Convolutional Network for Skeleton-Based Human Action Recognition by Neural Searching

2020 ◽  
Vol 34 (03) ◽  
pp. 2669-2676 ◽  
Author(s):  
Wei Peng ◽  
Xiaopeng Hong ◽  
Haoyu Chen ◽  
Guoying Zhao
Keyword(s):  
Action Recognition ◽  
Large Scale ◽  
Order Approximation ◽  
Human Action Recognition ◽  
Search Space ◽  
Human Action ◽  
Higher Order ◽  
Dynamic Graph ◽  
Convolutional Network ◽  
Representational Capacity

Human action recognition from skeleton data, fuelled by the Graph Convolutional Network (GCN) with its powerful capability of modeling non-Euclidean data, has attracted lots of attention. However, many existing GCNs provide a pre-defined graph structure and share it through the entire network, which can loss implicit joint correlations especially for the higher-level features. Besides, the mainstream spectral GCN is approximated by one-order hop such that higher-order connections are not well involved. All of these require huge efforts to design a better GCN architecture. To address these problems, we turn to Neural Architecture Search (NAS) and propose the first automatically designed GCN for this task. Specifically, we explore the spatial-temporal correlations between nodes and build a search space with multiple dynamic graph modules. Besides, we introduce multiple-hop modules and expect to break the limitation of representational capacity caused by one-order approximation. Moreover, a corresponding sampling- and memory-efficient evolution strategy is proposed to search in this space. The resulted architecture proves the effectiveness of the higher-order approximation and the layer-wise dynamic graph modules. To evaluate the performance of the searched model, we conduct extensive experiments on two very large scale skeleton-based action recognition datasets. The results show that our model gets the state-of-the-art results in term of given metrics.

Modeling of Long-Range Reverberation Signal for Rough Bottom Consisting of Polygon Facets

2018 ◽  
Vol 26 (04) ◽  
pp. 1850041
Author(s):  
Youngmin Choo ◽  
Woojae Seong
Keyword(s):  
Long Range ◽  
Order Approximation ◽  
Higher Order ◽  
Ocean Bottom ◽  
Analytic Surface ◽  
Surface Integral ◽  
Computational Burden ◽  
Analytic Integration ◽  
The Cost ◽  
Delay Difference

To acquire a stable reverberation signal from an irregular ocean bottom, we derive the analytic surface integral of a scattered signal using Stokes’ theorem while approximating the bottom using a combination of polygon facets. In this approach, the delay difference in the elemental scattering area is considered, while the representative delay is used for the elemental scattering area in the standard reverberation model. Two different reverberation models are applied to a randomly generated rough bottom, which is composed of triangular facets. Their results are compared, and the scheme using analytic integration shows a converged reverberation signal, even with a large elemental scattering area, at the cost of an additional computational burden caused by a higher order approximation in the surface integral of the scattered signals.

scholarly journals On Moore-Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Numerical Modeling ◽  
Computational Methods ◽  
Order Approximation ◽  
Higher Order ◽  
Benchmark Test ◽  
Essential Component ◽  
Stiffness Matrices ◽  
Penrose Pseudoinverse

Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.

scholarly journals Solar Diameter(s)

1983 ◽  
Vol 66 ◽  
pp. 139-150
Author(s):  
J. Rösch ◽  
R. Yerle
Keyword(s):  
Physical Parameter ◽  
Inflection Point ◽  
Order Approximation ◽  
Higher Order ◽  
Solar Oscillations ◽  
Maximum Brightness ◽  
Brightness Gradient ◽  
Solar Diameter ◽  
Long Period ◽  
Blurring Effect

AbstractBecause of the renewed attention now paid to the solar diameter, its variations from equator to pole, or its secular or long-period changes, the question: what is a solar diameter? is not meaningless. Two kinds of definitions may be given: either astrophysical, each one relating to a specific physical parameter, or observational, relating to a given quantity to be measured. Only the second kind is directly accessible, and astrophysical definitions should be linked to these quantities, once they are determined with the highest possible accuracy. In practice, all the programs under way refer to the point of the limb where the brightness gradient is maximum, or to a higher order approximation of the shape of the profile. Two of them are compared: the Pic-du-Midi experiment, using fast scans of the limb to define the inflection point after a correction for the blurring effect of the atmosphere, and the SCLERA experiment, using the algorithm called FFTD to eliminate this correction. The advantage of a fast scan is emphasized, and the remark is formulated that, once the signal is digitized and stored, FFTD or any processing of it can be performed. In collecting day-long one-limb scans to calibrate the blurring correction, the authors have found fluctuations of the maximum brightness gradient which provide a new entry to the field of solar oscillations.

Higher Order Approximation of an Inelastic Fluid Flow

2003 ◽  
Vol 72 (4) ◽  
pp. 964-965
Author(s):  
Nirmal C. Sacheti ◽  
Pallath Chandran ◽  
Tayfour El-Bashir
Keyword(s):  
Fluid Flow ◽  
Order Approximation ◽  
Higher Order

scholarly journals Unified formalism for higher-order variational problems and its applications in optimal control

2014 ◽  
Vol 11 (04) ◽  
pp. 1450034 ◽  
Author(s):  
Leonardo Colombo ◽  
Pedro Daniel Prieto-Martínez
Keyword(s):  
Optimal Control ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Higher Order ◽  
Point Of View ◽  
Regular Case ◽  
Underactuated Mechanical Systems ◽  
Interesting Application ◽  
Principal Bundles ◽  
Order Constraints

In this paper, we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical Skinner–Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics. As an interesting application we deduce the equations of motion for optimal control of underactuated mechanical systems defined on principal bundles.

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