• Journal for History of Mathematics
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• v.29 no.5
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• pp.295-314
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• 2016

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. We learned that dynamic programming in tropical algebraic geometry can be used to find the shortest path in graphs. We have also learned about the Bezout's Theorem, which is a theorem concerning the intersections of tropical plane curves, and the stable intersection principle.

• 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.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.7-11
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• 2002

This study introduces the first method that determines tropospheric ozone column directly from a space-based instrument. This method is based on the physical differences in the Total Ozone Mapping Spectrometer (TOMS) measurement as a function of its scan-angle geometry. Tropospheric ozone in September-October exhibits a broad enhancement over South America, the southern Atlantic Ocean, and western South Africa and a minimum over the central Pacific Ocean. Tropical tropospheric ozone south of the equator is higher than north of the equator in September-October, the southern burning season. Conversely, ozone north of the equator is higher in March, the northern burning season. Overall, the ozone over the southern tropics during September-October is significantly higher than over the northern tropics. Abnormally high tropospheric ozone occurs over the western Pacific Ocean during the El Nino season when the ozone amounts are as high as the ozone over the Africa.

• Korean Journal of Remote Sensing
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• v.19 no.1
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• pp.11-19
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• 2003

This paper applies the Scan-Angle Method (SAM) to the Total Ozone Mapping Spectrometer (TOMS) aboard Earth Probe (EP) satellite for determining tropospheric ozone based on TOMS scan geometry. In the northern tropical Africa burning season, the distribution of the SAM-derived tropospheric ozone presents a tropospheric ozone enhancement related to biomass burning. This distribution is consistent with that of fire counts observed from Along Track Scanning Radiometer (ATSR) and that of carbon monoxide, the tropospheric ozone precursor, observed from Measurements of Pollution In The Troposphere (MOPITI). However, this feature is not shown in the distribution of tropospheric ozone derived from other TOMS-based algorithms for the northern burning season. In the high latitudes, the influence of pollution in the SAM results is seen over the northern continents in agreement with carbon monoxide for northern summer when the dynamical activity is weak in the northern hemisphere.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.93-113
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• 2011

Let $a{\oplus}b$ = max(a, b), $a{\otimes}b$=a+b, a, $b\in\mathbb{R}_{\varepsilon}\;:=\cup\{-\infty\}$. In max-plus algebra we work on the linear algebra structure for the pair of operations (${\oplus},{\otimes}$) extended to matrices and vectors over $\mathbb{R}_{\varepsilon}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $\mathbb{R}_{\varepsilon}$.

• Journal of Biosystems Engineering
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• v.39 no.3
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• pp.205-214
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• 2014

Purpose: Phytosanitary irradiation treatment can effectively control regulated pests while maintaining produce quality. The objective of this study was to establish the best irradiation treatment for mangosteen, a popular tropical fruit, using a Monte Carlo simulation. Methods: Magnetic resonance image (MRI) data were used to generate a 3-D geometry to simulate dose distributions in a mangosteen using a radiation transport code (MCNP5). Microsoft Excel with visual basic application (VBA) was used to divide the image data into seed, flesh, and rind. Radiation energies used for the simulation were 10 MeV (high-energy) and 1.35 MeV (low-energy) for the electron beam, 5 MeV for X-rays, and 1.25 MeV for gamma rays from Co-60. Results: At 5 MeV X-rays and 1.25 MeV gamma rays, all areas (seeds, flesh, and rind) were irradiated ranging from 0.3 ~ 0.7 kGy. The average doses decreased as the number of fruit increased. For a 10 MeV electron beam, the dose distribution was biased: the dose for the rind where the electrons entered was $0.45{\pm}0.03$ kGy and the other side was $0.24 {\pm}0.10$ kGy. Use of an electron kinetic energy absorber improved the dose distribution in mangosteens. For the 1.35 MeV electron beam, the dose was shown only in the rind on the irradiated side; no significant dose was found in the flesh or seeds. One rotation of the fruit while in front of the beam improved the dose distribution around the entire rind. Conclusion: These results are invaluable for determining the ideal irradiation conditions for phytosanitary irradiation treatment of tropical fruit.

• Journal of Biosystems Engineering
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• v.38 no.2
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• pp.87-94
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• 2013

Purpose: Pineapple is now the third most important tropical fruit in world production after banana and citrus. Phytosanitary irradiation is recognized as a promising alternative treatment to chemical fumigation. However, most of the phytosanitary irradiation studies have dealt with physiochemical properties and its efficacy. Accurate dose calculation is crucial for ensuring proper process control in phytosanitary irradiation. The objective of this study was to optimize phytosanitary irradiation treatment of pineapple in various radiation sources using Monte Carlo simulation. Methods: 3-D geometry and component densities of the pineapple, extracted from CT scan data, were entered into a radiation transport Monte Carlo code (MCNP5) to obtain simulated dose distribution. Radiation energy used for simulation were 2 MeV (low-energy) and 10 MeV (high-energy) for electron beams, 1.25 MeV for gamma-rays, and 5 MeV for X-rays. Results: For low-energy electron beam simulation, electrons penetrated up to 0.75 cm from the pineapple skin, which is good for controlling insect eggs laid just below the fruit surface. For high-energy electron beam simulation, electrons penetrated up to 4.5 cm and the irradiation area occupied 60.2% of the whole area at single-side irradiation and 90.6% at double-side irradiation. For a single-side only gamma- and X-ray source simulation, the entire pineapple was irradiated and dose uniformity ratios (Dmax/Dmin) were 2.23 and 2.19, respectively. Even though both sources had all greater penetrating capability, the X-ray treatment is safer and the gamma-ray treatment is more widely used due to their availability. Conclusions: These results are invaluable for optimizing phytosanitary irradiation treatment planning of pineapple.