ROMBERG方法的改进

本文研究了全部根构成一个等比数列的多项式的性质，并将所得的结果用到数值积分的Ｒｏｍｂｅｒｇ方法＾「１」，得到了相应遥改进。     

A simplified proof of the representation of functionals of diffusions

A simple proof is given for the stochastic integral representation of a Fréchet differentiable functional of the paths of a given diffusion process. The proof begins when the functional depends on one coordinate, then passes to (by appropriate conditioning) a perhaps more difficult case—when the functional depends on a finite number of coordinates—and finally, by approximation, to the general case.     

Phenyliodine(III) Diacetate/I2-Mediated Domino Approach for Pyrrolo[1,4]Thiazines and 1,4-Thiazines by a One-Pot Morin Rearrangement of N,S-Acetals

An efficient domino transformation using a phenyliodine(III) diacetate (PIDA)/I₂ combination towards Morin 1,4-thiazine compounds has been developed starting from N,S-acetals. The latter leads to “one-step” regioselective methylene insertion without the need for traditional sulfoxide intermediates in good yields. The reaction involves easily accessible N,S-acetals obtained from cost-effective basic ketones and cysteamine as starting materials. This process ultimately leads to 1,4-thiazines related to natural product and fused derivatives necessary for further QSAR study.     

A Common Conformation of Stabilized Triphenyl Phosphonium Ylidic Diesters with Bulky Alkoxy Groups

The phosphonium ylidic diesters, methyl and ethyl isopropyl and, methyl and ethyl t-butyl triphenylphosphoranylidene malonates, 1a,b and 2a,b , respectively, have the syn-anti conformation in solution, as in the crystal, and the bulkier alkoxy group is oriented towards phosphorus. The ¹ H NMR spectra show that in 1a,b , the isopropyl group is oriented towards the face of a phenyl group, consistent with π shielding in the ¹ H signals, and examination of the ¹ H coupled ¹³ C NMR spectra allows assignment of the acyl carbon signals. Computed bond lengths and angles for isolated molecules are similar to those in the crystal, and the geometry and the NMR spectra indicate extensive ylidic resonance. Estimated partial atomic charges on the ester oxygens are more negative when they are oriented towards, rather than away from, phosphorus.     

Protease Inhibitors Purified from the Canola Meal Extracts of Two Genetically Diverse Genotypes Exhibit Antidiabetic and Antihypertension Properties

Valorization of vegetable oil waste residues is gaining importance due to their high protein and polyphenol contents. Protease inhibitors (PIs), proteins from these abundantly available waste residues, have recently gained importance in treating chronic diseases. This research aimed to use canola meal of genetically diverse Brassica napus genotypes, BLN-3347 and Rivette, to identify PIs with diverse functionalities in therapeutic and pharmacological applications. The canola meal PI purification steps involved: native PAGE and trypsin inhibition activity, followed by ammonium sulfate fractionation, anion exchange, gel filtration, and reverse-phase chromatography. The purified PI preparations were characterized using SDS-PAGE, isoelectric focusing (IEF), and N terminal sequencing. SDS-PAGE analysis of PI preparations under native reducing and nonreducing conditions revealed three polymorphic PIs in each genotype. The corresponding IEF of the genotype BLN-3347, exhibited three acidic isoforms with isoelectric points (pI) of 4.6, 4.0, and 3.9, while Rivette possessed three isoforms, exhibiting two basic forms of pI 8.65 and 9.9, and one acidic of pI 6.55. Purified PI preparations from both the genotypes displayed dipeptidyl peptidase-IV (DPP-IV) and angiotensin-converting enzyme (ACE) inhibition activities; the BLN-3347 PI preparation exhibited a strong inhibitory effect with lower IC₅₀ values (DPP-IV 37.42 µg/mL; ACE 129 µg/mL) than that from Rivette (DPP-IV 67.97 µg/mL; ACE 376.2 µg/mL). In addition to potential human therapy, these highly polymorphic PIs, which can inhibit damaging serine proteases secreted by canola plant pathogens, have the potential to be used by canola plant breeders to seek qualitative trait locus (QTLs) linked to genes conferring resistance to canola diseases.     

Focal Point Evaluation of Energies for Tautomers and Isomers for 3-hydroxy-2-butenamide: Evaluation of Competing Internal Hydrogen Bonds of Types -OH…O=, -OH…N, -NH…O=, and CH…X (X=O and N)

The title compound is a small molecule with many structural variations; it can illustrate a variety of internal hydrogen bonds, among other noncovalent interactions. Here we examine structures displaying hydrogen bonding between carbonyl oxygen and hydroxyl H; between carbonyl oxygen and amino H; hydroxyl H and amino N; hydroxyl O and amino H. We also consider H-bonding in its tautomer 2-oxopropanamide. By extrapolation algorithms applied to Hartree-Fock and correlation energies as estimated in HF, MP2, and CCSD calculations using the cc-pVNZ correlation-consistent basis sets (N = 2, 3, and 4) we obtain reliable relative energies of the isomeric forms. Assuming that such energy differences may be attributed to the presence of the various types of hydrogen bonding, we attempt to infer relative strengths of types of H-bonding. The Atoms in Molecules theory of Bader and the Local Vibrational Modes analysis of Cremer and Kraka are applied to this task. Hydrogen bonds are ranked by relative strength as measured by local stretching force constants, with the stronger =O…HO- > NH…O= > -OH…N well separated from a cluster > NH…O= ≈ >NH…OH ≈ CH…O= of comparable and intermediate strength. Weaker but still significant interactions are of type CH…N which is stronger than CH…OH.