On an isolation and a generalization of Hölder's inequality

We generalize the well-known Hölder inequality and give a condition at which the equality holds

Oscillation and nonoscillation criteria for quasilinear differential equations

AbstractSome oscillation and nonoscillation criteria for quasilinear differential equations of second order are obtained. These results are extensions of earlier results of Huang (J. Math. Anal. Appl. 210 (1997) 712–723) and Elbert (J. Math. Anal. Appl. 226 (1998) 207–219)

Insights into specificity of cleavage and mechanism of cell entry from the crystal structure of the highly specific Aspergillus ribotoxin, restrictocin

AbstractBackground: Restrictocin, a highly specific ribotoxin made by the fungus Aspergillus restrictus, cleaves a single phosphodiester bond in the 28S RNA of eukaryotic ribosomes, inhibiting protein synthesis. The sequence around this cleavage site is a binding site for elongation factors, and is conserved in all cytoplasmic ribosomes. The catalytic mechanism of restrictocin and the reasons for its high substrate specificity are unknown. No structure has been determined for any other member of the Aspergillus ribotoxin family.Results The crystal structure of restrictocin was determined at 2.1 å resolution by single isomorphous replacement and anomalous scattering techniques, and refined to 1.7 å resolution using synchrotron Laue data. The structural core of the protein, in which a three-turn α helix is packed against a five-stranded antiparallel β sheet, can be well aligned with that of ribonuclease T1. Large positively charged peripheral loops near the active site construct a platform with a concave surface for RNA binding.Conclusion Restrictocin appears to combine the catalytic components of T1 ribonucleases with the base recognition components of Sa ribonucleases. Modeling studies using an NMR structure of an RNA substrate analog suggest that the tertiary structure of the substrate RNA is important in protein–RNA recognition, fitting closely into the concavity of the presumed binding site. We speculate that the large 39-residue loop L3, which has similarities to loops found in lectin sugar-binding domains, may be responsible for restrictocin's ability to cross cell membranes

Intelligent Modeling and Verification

System modeling tends to have many complex features, and uncertainties often lead to numerous complications and influence many important aspects related to its applications. Intelligent modeling merges mathematical and computer based approaches, and it utilizes pioneering new scientific methods and cutting-edge technologies