scholarly journals STUDY AND APPLICATION OF A RECURRENCE RELATIONSHIP / ESTUDO E APLICAÇÃO DE UMA RELAÇÃO DE RECORRÊNCIA

2020 ◽  
Vol 6 (12) ◽  
pp. 100561-100571
Author(s):  
Hamilton Brito da Silva ◽  
Matheus de Albuquerque Coelho dos Santos ◽  
Fernando Cardoso de Matos ◽  
Edson Costa Cruz
1972 ◽  
Vol 62 (3) ◽  
pp. 851-864 ◽  
Author(s):  
G. A. Bollinger

Abstract The seismic history of South Carolina is dominated by the great Charleston earthquake of August 31, 1886. In addition to having several unusual aspects (region essentially free from shocks for preceding 200 years, large felt area, dual epicenter points, “low intensity zone” in West Virginia), that intensity X event seriously perturbed the seismic regime of the area for at least the following 30 years. Of 438 earthquakes reported to have occurred in the state between 1754 and 1971, 402 have been in the Charleston-Summerville area. The remaining 36 shocks form a southeasterly-trending zone of activity that is transverse to the structural grain of the Appalachians. For the 60 shocks assigned an intensity value (1886-1971), a recurrence relationship between the number of earthquakes “N” of maximum intensity “I0” was found to be log N = 0.52-0.31 I0 for IV ≦ I0 ≦ VIII. This corresponds to a “b” value of 0.5 ± 0.1 in log N versus M relationship assuming M = 1 + (2/3)I0. These data suggest a frequency of seismic activity comparable to that reported for the New Madrid seismic zone. Three months of microearthquake monitoring in the Charleston area during the summer of 1971 yielded 505 hr of low-noise data. Sixty-one earthquakes, primarily in swarm occurrence, were recorded. An h value of 1.8 ± 0.5 was determined for these microshock events. This value is similar to that previously observed for a swarm sequence in New Jersey. Four shocks occurred in the state during 1971. Three of these events (May 19, July 31, August 11) were in the central part of the state near Orangeburg, while the third event (July 13) was near Seneca in northwestern South Carolina. All three events had 3.0 < ML < 4.0. Similar episodes of three or four shocks in 1 year happened in 1956 and again in 1965. The Orangeburg area had, according to historical data, been previously free of earthquake epicenters.


Author(s):  
Shivamanth Angadi ◽  
Apurva Hiravennavar ◽  
Mayank K. Desai ◽  
Chandresh H. Solanki ◽  
Goudappa R. Dodagoudar

2014 ◽  
Vol 46 (2) ◽  
pp. 446-477 ◽  
Author(s):  
Camille Coron

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.


1970 ◽  
Vol 60 (2) ◽  
pp. 393-446 ◽  
Author(s):  
J. F. Evernden

abstract This paper constitutes a compilation of seismicity data available in the literature plus regional and worldwide data obtained from the USCGS Preliminary Determination of Epicenter (PDE) lists. Data are presented in the form of the recurrence relationship of log N versus magnitude, where N is either cumulative or incremental number of earthquakes, and magnitude is either mb or MS. Relative shapes of these recurrence curves as regards mb versus MS, large magnitude versus small magnitude, shallow focus versus deep focus, etc. are discussed. Conclusions on variability of seismicity with time and on worldwide level of seismic activity are included.


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