• Journal for History of Mathematics
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• v.30 no.3
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.10
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• pp.1365-1371
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• 2011

The intensity and duration of sexual behavior in Bos indicus was assessed through the continuous observation of sexual receptivity. Two groups of cows were formed: only synchronized (n = 50) and other group further superovulated (n = 20). An intravaginal implant that released progesterone over 9 d was used. After removing the implant, 25 mg of $PGF_{2{\alpha}}$ was administered. In the superovulated group, the administration of 280 mg (Follicle stimulant hormone) FSH-P1 per cow with a decreasing dosage over 4 d was utilized. In both groups, behavioral observations began at the moment of implant removal. Sexual behavior was analyzed using a Kruskal-Wallis test to compare the mean of hours in estrus, effective mountings and number of mounts/hour during estrus. A nonparametric survival analysis was performed using the time in two ways: i) when an event happened it was placed in a 24 h timeframe and, ii) the time of observation in continuous form (96 h) assessing the difference between curves by the log rank test Chi-square. The only significant difference was the number of mounts/h during receptivity (p<0.05). In the superovulated group three periods of sexual activity during the day were identified, with these events being of greater frequency and duration than the synchronized group (p = 0.02); besides, the superovulated group began estrus before the synchronized group (p = 0.0035) when using the total period. In a simulation study, when the number of observations went from two (06:00-18:00) to three periods (06:00, 12:00 and 18:00) cows detected accurately (<6 h after the onset) increased more than 20%. The results show that superovulated cows presented greater intensity and duration of sexual activity in contrast with only synchronized animals.

• Parasites, Hosts and Diseases
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• v.23 no.1
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• pp.139-150
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• 1985

In order to determine the seasonal prevalence and population density of vector mosquitoes in Kyungpook Province, a survey based on average numbers of female mosquito per trap-night, were carried out during the period from May to November in 1984. Among the 34, 571 mosquitoes collected in Kyungsan county in animal shelters and human dwellings by light traps, approximately 45.0 per cent were Culex tritaeniorhynchus, 34.0 per cent Culex pipiens pallens, and 19.0 per cent Anopheles sinensis. By comparison, distribution of mosquito species in Ankang town, in which Japanese encephalitis had been reported in the past, were quite different and A. sinensis was the most abundant species, being constituted in 75.8 per cent, followed by C. tritaeniorhynchus(23.2 per cent), and C. pipiens pallens(O.6 per cent). In the general pattern of seasonal prevalence, C. tritaeniorhynchus first appeared in mid-June, and trapped in large numbers during the periods from mid-August to early September, showing a simple sharply pointed one-peaked curve, while C. pipiens pallens was found to be active through almost the entire season showing irregular curves with several peaks. The trend of seasonal distribution of A. sinensis was similar to that of C. tritaeniorhynchus, but the earliest dates of appearance and disappearance differed from that of C. tritaeniorhynchus. The results of hourly catches of mosquitoes by human baited traps have clearly shown the differences in the biting rhythm among the vector mosquitoes of this Province, such as the facts that C. tritaeniorhynchus and A. sinensis are rather constantly active all through a night with more or less inconspicuous peaks twice a night, while C. pipiens pallens exhibits an irregular curve, and the numbers of A. vexans nipponii, C. vagans and Armigeres subalbatus are very small and are not sufficient for estimating the biting rhythm. Four genera and fourteen species of larval mosquitoes collected from eighteen kinds of habitats which classified according to the categories followed by Bates (1949). The main breeding sites contributing to peak C. tritaeniorhynchus adult densities in this surveyed areas were evidently ricefields, ground pools, puddles and swamps and marshes, etc. Summarizing the results, this study indicated that the highest population density of C. tritaeniorhynchus was encountered in late August and early September, showing a simple sharply pointed one-peaked curve.