In this paper, the notion of closure operators of matroids  is generalized to fuzzy setting  which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...

Several species in the rodent genus Mus are used as model research organisms, but comparative studies of these mice have been hampered by the lack of a well-supported phylogeny. We used DNA sequences from six genes representing paternally, maternally, and biparentally inherited regions of the genome to infer phylogenetic relationships among 10 species of Mus commonly used in laboratory research...

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

Hybrids between species are often sterile or inviable. This form of reproductive isolation is thought to evolve via the accumulation of mutations that interact to reduce fitness when combined in hybrids. Mathematical formulations of this "Dobzhansky-Muller model" predict an accelerating buildup of hybrid incompatibilities with divergence time (the "snowball effect"). Although the Dobzhansky-Mul...

The phylogenetic relationships between gobies of the genus Gymnogobius were analyzed using mitochondrial cytochrome b gene sequences, focusing on the species currently classified as G. taranetzi and G. castaneus that occur in Japan, South Korea, and Russia. Gobies of the two species collected at 12 localities in Japan, South Korea, and Russia formed a monophyletic clade (called the "castaneus s...