On multiple precision based Montgomery multiplication without precomputation of N'/sub 0/=-N/sub 0//sup -1/ mod W

2002 ◽  
Author(s):  
H. Ploog ◽  
D. Timmermann
Keyword(s):  
Montgomery Multiplication ◽  
Multiple Precision

Synthesis of Single-Input and Multiple-Output Port Mechanisms with Springs for Specified Energy Absorption

1994 ◽  
Vol 116 (3) ◽  
pp. 937-943 ◽  
Author(s):  
J. G. Jenuwine ◽  
A. Midha
Keyword(s):  
Energy Absorption ◽  
Output Port ◽  
Constant Force ◽  
Plane Symmetry ◽  
Multiple Precision ◽  
Linear Spring ◽  
Single Input ◽  
Force Mechanism ◽  
Closure Method ◽  
Constant Force Mechanism

A means of synthesis of single-input and multiple-output port mechanisms for specified energy absorption is formulated for multiple precision points. The synthesis presented makes use of an extension of the loop closure method which includes expressions for energy absorption by linear spring elements. The configuration considered locates spring elements at two output ports of a multi-loop, planar mechanism. Economies realized for the symmetric mechanism are discussed for both one- and two-plane symmetry. Synthesis examples are included for both the general and symmetric mechanism. Special applications presented include synthesis of a constant force mechanism and synthesis of a mechanism suited to the energy absorption requirements of an automotive crashworthiness system.

scholarly journals Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon

2018 ◽  
Vol 10 (8) ◽  
pp. 2749
Author(s):  
Qi Wang ◽  
Fenzhen Su ◽  
Yu Zhang ◽  
Huiping Jiang ◽  
Fei Cheng
Keyword(s):  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Effective Means ◽  
Slope Aspect ◽  
Change Rate ◽  
Local Slope ◽  
Evaluation Approach ◽  
Multiple Precision ◽  
Surface Models ◽  
Reconstructed Surface

In addition to remote-sensing monitoring, reconstructing morphologic surface models through interpolation is an effective means to reflect the geomorphological evolution, especially for the lagoons of coral atolls, which are underwater. However, which interpolation method is optimal for lagoon geomorphological reconstruction and how to assess the morphological precision have been unclear. To address the aforementioned problems, this study proposed a morphological precision index system including the root mean square error (RMSE) of the elevation, the change rate of the local slope shape (CRLSS), and the change rate of the local slope aspect (CRLSA), and introduced the spatial appraisal and valuation approach of environment and ecosystems (SAVEE). In detail, ordinary kriging (OK), inverse distance weighting (IDW), radial basis function (RBF), and local polynomial interpolation (LPI) were used to reconstruct the lagoon surface models of a typical coral atoll in South China Sea and the morphological precision of them were assessed, respectively. The results are as follows: (i) OK, IDW, and RBF exhibit the best performance in terms of RMSE (0.3584 m), CRLSS (51.43%), and CRLSA (43.29%), respectively, while with insufficiently robust when considering all three aspects; (ii) IDW, LPI, and RBF are suitable for lagoon slopes, lagoon bottoms, and patch reefs, respectively; (iii) The geomorphic decomposition scale is an important factor that affects the precision of geomorphologic reconstructions; and, (iv) This system and evaluation approach can more comprehensively consider the differences in multiple precision indices.

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