Novel versions of Hölder's-Like and related inequalities with newly defined space, and their applications over fuzzy domain.

It is widely recognized that fuzzy number theory relies on the characteristic function. However, within the fuzzy realm, the characteristic function transforms into a membership function contingent upon the interval [0,1]. This implies that real numbers and intervals represent exceptional cases of fuzzy numbers.

Lentivirus-mediated SMO RNA interference inhibits SMO expression and cell proliferation, and affects the cell cycle in LNCaP and PC3 cancer cell lines.

Smoothened (SMO) is an important member of the Hedgehog signaling pathway. We constructed a specific recombinant lentiviral vector for RNA interference, targeting the SMO gene (NM_005631) to observe its effect on SMO expression, cell proliferation and the cell cycle in the human androgen-sensitive prostate cancer cell line, LNCaP, and in the androgen-independent prostate cancer cell line, PC3. Four siRNA sequences were designed and inserted into a lentiviral vector pGCSIL-GFP to construct four recombinant vectors.