In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

In this paper, we represent the generating function of w-torsion Fubini polynomials by fermionic p-adic integral on Z_p. Then we consider a quotient of such fermionic p-adic integrals on Z_p, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

Rice is an important cereal crop worldwide, the growth of which is affected by rice blast disease, caused by the fungal pathogen Magnaporthe oryzae. As climate change increases the diversity of pathogens, the disease-resistance genes (R genes) in plants must be identified. The major blast-resistance genes have been identified in indica rice varieties; therefore, japonica rice varieties with R genes now need to be identified. Because leucine-rich repeat (LRR) domain proteins possess R-gene properties, we used bioinformatics analysis to identify the rice candidate LRR domain receptor-like proteins (OsLRR-RLPs). OsLRR-RLP2, which contains six LRR domains, showed differences in the DNA sequence, containing 43 single-nucleotide polymorphisms (SNPs) in indica and japonica subpopulations. The results of M. oryzae inoculation analysis indicated that indica varieties with partial deletion of OsLRR-RLP2 showed susceptibility, whereas japonica varieties with intact OsLRR-RLP2 showed resistance. oslrr-rlp2 mutant generated using clustered regularly interspaced palindromic repeats (CRISPR)/CRISPR-associated protein 9 (Cas9) showed increased pathogen susceptibility, whereas plants overexpressing this gene showed pathogen resistance. These results indicate that OsLRR-RLP2 confers resistance to rice, and OsLRR-RLP2 may be useful for breeding resistant cultivars.