The Curse of Dimension and a Universal Method For Numerical Integration

Author(s):  
Erich Novak ◽  
Klaus Ritter
1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.


Author(s):  
E. Rau ◽  
N. Karelin ◽  
V. Dukov ◽  
M. Kolomeytsev ◽  
S. Gavrikov ◽  
...  

There are different methods and devices for the increase of the videosignal information in SEM. For example, with the help of special pure electronic [1] and opto-electronic [2] systems equipotential areas on the specimen surface in SEM were obtained. This report generalizes quantitative universal method for space distribution representation of research specimen parameter by contour equal signal lines. The method is based on principle of comparison of information signal value with the fixed levels.Transformation image system for obtaining equal signal lines maps was developed in two versions:1)In pure electronic system [3] it is necessary to compare signal U (see Fig.1-a), which gives potential distribution on specimen surface along each scanning line with fixed base level signals εifor obtaining quantitative equipotential information on solid state surface. The amplitude analyzer-comparator gives flare sport videopulses at any fixed coordinate and any instant time when initial signal U is equal to one of the base level signals ε.


2019 ◽  
Vol 51 (04) ◽  
pp. 745-750
Author(s):  
A.A BHATTI ◽  
M.S CHANDIO ◽  
R.A MEMON ◽  
M.M SHAIKH

Author(s):  
V. Lyandres

Introduction:Effective synthesis of а mobile communication network includes joint optimisation of two processes: placement of base stations and frequency assignment. In real environments, the well-known cellular concept fails due to some reasons, such as not homogeneous traffic and non-isotropic wave propagation in the service area.Purpose:Looking for the universal method of finding a network structure close to the optimal.Results:The proposed approach is based on the idea of adaptive vector quantization of the network service area. As a result, it is reduced to a 2D discrete map split into zones with approximately equal number of service requests. In each zone, the algorithm finds such coordinates of its base station that provide the shortest average distance to all subscribers. This method takes into account the shortage of the a priory information about the current traffic, ensures maximum coverage of the service area, and what is not less important, significantly simplifies the process of frequency assignment.


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