Dynamics Analysis of a Filippov Pest Control Model with Time Delay
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This paper aims at providing a framework to combine fuzzy
sets and rough sets together via multifunction, which gives rise to several
interesting new concepts such as rough sets, rough fuzzy sets via multi-
function and some properties of them. Although many results reported
here are only concerned with basic properties about these new notions,
one could see that this study presents a very preliminary, but potentially
interesting research direction.
The notion of rough set was originally proposed by Pawlak (1982) [6].Carmel Richard et al.[3] introduce a new topology
called rough topology in terms of the lower and upper approximations of Pawlak approximation space.In this paper, we have introduced
a new topology called rough topology in terms of lower and upper approximations of a rough set via multifunction.In addition we study
and investigate some properties of rough generalized closed sets in rough topological spaces via multifunction (multi rough topological
space).
Our goal of this work is to show the deviations between
some properties of soft approximation spaces and the same properties of
Pawlak approximation space. We also introduce and study the concepts of
soft rough topology and a new class of function called soft rough continuous
functions. Finally some basic properties of these concepts are explored.
The present paper, some well-known theorems have been improved, such as a proof of one theorem and the inverse direction of another theorem in the fuzzifying topological space and the fuzzifying bitopological space. We prove one theorem by use less conditions in the fuzzifying topological space and the fuzzifying bitopological space. Also, we prove the equivalent definition of semi open sets in the fuzzifying topological space and the fuzzifying bitopological space. Additionally, the equivalent definition of the closure operator in the fuzzifying topological space and the fuzzifying bitopological space has been also proved. Finally, some supporting examples are provided.
Four genera of entomopathogenic fungi and two hyphomycetes were identified from the cadavers of the aphid infesting wheat plants in the two growing seasons of 2013-2014. Entomophthorales was represented by four species belonging to three families; Ancylistaceae represented by Conidiobolus, Entomophthoraceae by Entomophthora planchoniana and Pandora neoaphidis and Neozygitaceae by Neozygites fresenii. The hyphomycetes fungi were represented by two species Beauveria bassiana and Verticillium lecanii which belong to the family Moniliaceae, order Moniliales. Data show that the aphid began to infest wheat plants early during the middle of January when wheat plants were in the stem-elongation stage. Thereafter, numbers of aphids increased gradually to reach a peak, when the plants were at the flowering stage during the third week of February; during the next three weeks the number of the oat aphid declined sharply. Mortality rate with the fungal pathogens was observed from the end of January up to the end of March. The number of cadavers increased gradually to reach the maximum level during the end of March.