G-Strong Chain Recurrent Point and G-Chain Equivalent Point of Topological G-Conjugacy on Metric G-Space

Author(s):  
Zhan-Jiang Ji ◽  
Jing-Xian Tu
2003 ◽  
Vol 78 (1) ◽  
pp. 79-83 ◽  
Author(s):  
Keiko Nagaizumi ◽  
Hiroshi Inaba ◽  
Kagehiro Amano ◽  
Midori Suzuki ◽  
Morio Arai ◽  
...  

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 610-622 ◽  
Author(s):  
Chao C. Ku

A computational method, which combines the Gaussian quadrature formula for numerical integration and a cubic spline for interpolation in evaluating the limits of integration, is employed to compute directly the gravity and magnetic anomalies caused by 2-dimensional and 3-dimensional bodies of arbitrary shape and arbitrary magnetic polarization. The mathematics involved in this method is indeed old and well known. Furthermore, the physical concept of the Gaussian quadrature integration leads us back to the old concept of equivalent point masses or equivalent magnetic point dipoles: namely, the gravity or magnetic anomaly due to a body can be evaluated simply by a number of equivalent points which are distributed in the “Gaussian way” within the body. As an illustration, explicit formulas are given for dikes and prisms using 2 × 2 and 2 × 2 × 2 point Gaussian quadrature formulas. The basic limitation in the equivalent‐point method is that the distance between the point of observation and the equivalent points must be larger than the distance between the equivalent points within the body. By using a reasonable number of equivalent points or dividing the body into a number of smaller subbodies, the method might provide a useful alternative for computing in gravity and magnetic methods. The use of a simplified cubic spline enables us to compute the gravity and magnetic anomalies due to bodies of arbitrary shape and arbitrary magnetic polarization with ease and a certain degree of accuracy. This method also appears to be quite attractive for terrain corrections in gravity and possibly in magnetic surveys.


2022 ◽  
Vol 2022 ◽  
pp. 1-6
Author(s):  
Zhan jiang Ji

According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their dynamical properties. The following results are obtained: (1) Regularly recurrent point sets of the double shift map σ f ∘ σ g are equal to the double inverse limit space of the double self-map f ∘ g in the regularly recurrent point sets. (2) The double self-map f ∘ g has sequence shadowing property if and only if the double shift map σ f ∘ σ g has sequence shadowing property. Thus, the conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space.


1966 ◽  
Vol 56 (6) ◽  
pp. 1363-1371 ◽  
Author(s):  
William Stauder ◽  
G. A. Bollinger

Abstract P- and S-wave data for thirty-five earthquakes selected from among the larger earthquakes of 1963 have been investigated. Focal mechanism determinations for twenty-six of these shocks are here presented. The solutions are based upon a combination of a graphical and a computer method for determining the poles of the nodal planes. In all cases it has been found that the mechanism may be adequately represented by a double couple as an equivalent point source of the focus, although in some few instances a single couple cannot be excluded as a possible alternate interpretation. The solution of a mid-Atlantic earthquake of November 17, 1963 is presented as an example of a focus which clearly conforms to the double couple model. Special attention is called to the solutions for a series of earthquakes in the Kurile Islands, and to three earthquakes of the mid-Atlantic.


Author(s):  
Kostadin Cvejoski ◽  
Ramses J. Sanchez ◽  
Bogdan Georgiev ◽  
Christian Bauckhage ◽  
Cesar Ojeda
Keyword(s):  

1970 ◽  
Vol 7 (02) ◽  
pp. 476-482 ◽  
Author(s):  
S. K. Srinivasan ◽  
G. Rajamannar

In an earlier contribution to this Journal, Ten Hoopen and Reuver [5] have studied selective interaction of two independent recurrent processes in connection with the unitary discharges of neuronal spikes. They have assumed that the primary process called excitatory is a stationary renewal point process characterised by the interval distribution ϕ(t). The secondary process called the inhibitory process also consists of a series of events governed by a stationary renewal point process characterised by the interval distribution Ψ(t). Each secondary event annihilates the next primary event. If there are two or more secondary events without a primary event, only one subsequent primary event is deleted. Every undeleted event gives rise to a response. For this reason, undeleted events may be called registered events. Ten Hoopen and Reuver have studied the interval distribution between two successive registered events. As is well-known, the interval distribution does not fully characterise a point process in general and in this case it would be interesting to obtain other statistical features like the moments of the number of undeleted events in a given interval as well as correlations of these events. The object of this short note is to point out that the point process consisting of the undeleted events can be studied directly by the recent techniques of renewal point processes ([1], [3]).


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