谈微积分基本定理

凡是学过微积分的人,大概都不会忘记一个公式(或者说是一个定理):     

Design and synthesis of new bicyclic diketopiperazines as scaffolds for receptor probes of structurally diverse functionality

Diketopiperazines (DKPs) are a common motif in various biologically active natural products, and hence they may be useful scaffolds for the rational design of receptor probes and therapeutic agents. We constructed a new bicyclic scaffold that combines a DKP bridged with a 10-membered ring. In this way we obtained a three-dimensional molecular skeleton, with several amendable sites that provide a starting point to design a new combinatorial library having diverse substituent groups. Structural variation is based upon the flexibility of alkylation of the nitrogen atoms of the DKP and on the side-chain olefin. We obtained a 10-membered secondary ring through a ring-closure metathesis reaction using the second generation Grubbs catalyst. Rings containing both O-ethers and S-ethers were compared. N-Alkyl or arylalkyl groups were introduced optionally at the two Nalpha-atoms. This is a general scheme that will allow us to test rings of varying sizes, linkages, and stereochemical parameters. The DKP derivatives were tested for activity in astrocytoma cells expressing receptors coupled to phospholipase C. Inhibitory effects were observed for signaling elicited by activation of human nucleotide P2Y receptors but not m3 muscarinic receptors. Compound 20 selectively inhibited calcium mobilization (IC50 value of 486 +/- 16 nM) and phosphoinositide turnover elicited by a selective P2Y1 receptor agonist, but this compound did not compete for binding of a radiolabeled nucleotide-competitive receptor antagonist. Therefore, the new class of DKP derivatives shows utility as pharmacological tools for P2Y receptors.     

TDDFT study of one- and two-photon absorption properties: donor-pi-acceptor chromophores

We report a comprehensive time-dependent density functional theory (TDDFT) study of one-photon and two-photon absorption (OPA and TPA, respectively) spectra for donor-pi-acceptor molecules. The calculated excitation energies were generally shown to be in good agreement with experiment, particularly when compared to results from measurements carried out in a nonpolar solvent, although the oscillator strengths were overestimated in some cases. Calculated TPA cross sections applying the two-state approximation were shown to be highly dependent on the form of the line-shape function used. Although a good agreement with experimental TPA spectra was generally observed, the wide range in the experimentally measured values and lack of systematic experimental data on solvent effects limited a detailed comparison as yet.     

A versatile catalyst for asymmetric reactions of carbonyl groups working purely by activation through hydrogen bonding: Mukaiyama-aldol, hetero Diels-Alder and Friedel-Crafts reactions

Bis-sulfonamides are demonstrated to be promising candidates for the efficient activation of carbonyl compounds through hydrogen bonding. Exemplified by three carbonyl addition reactions: Mukaiyama-aldol, hetero Diels-Alder and Friedel-Crafts reactions we show that bis-triflamides or bis-nonaflamides of commercially available chiral diamines act as chiral Br?nsted-acid catalysts, leading to the optically active products in moderate to excellent yields and with enantioselectivities up to 73% ee.     

Novel imidazolidine-tetrazole organocatalyst for asymmetric conjugate addition of nitroalkanes

The Michael addition of nitroalkanes to alpha,beta-unsaturated enones catalyzed by a novel chiral imidazolidine-2-yltetrazole organocatalyst has been investigated. The new more soluble organocatalyst decreases reaction times and improves enantioselectivities compared to other catalysts. The Michael addition adducts were obtained with up to 92% ee. [reaction: see text]     

Electronic and steric effects in fragmentation reactions of Os3(CO)9(mu-C4Ph4)

P-Donor nucleophiles of cone angle >or=145 degrees are known to react with Os3(CO)9(mu-C4Ph4) quite differently from those with cone angles 相似文献   

Investigations into the role of ion pairing in reactions of heteroatom-substituted cyclic oxocarbenium ions

[reaction: see text] The O-to-C rearrangement of vinyl acetals is used to demonstrate that tight ion pairing is not involved in the stereoselective nucleophilic addition reactions of alkoxy-substituted cyclic oxocarbenium ions.     

The complement: a solution to liquid drop finite size effects in phase transitions

The effects of the finite size of a liquid drop undergoing a phase transition are described in terms of the complement, the largest (but mesoscopic) drop representing the liquid in equilibrium with the vapor. Vapor cluster concentrations, pressure, and density from fixed mean density lattice gas (Ising) calculations are explained in terms of the complement generalization of Fisher's model. Accounting for this finite size effect is important for extracting the infinite nuclear matter phase diagram from experimental data.     

Intrinsic ferromagnetism in insulating cobalt doped anatase TiO2

Using complementary experiments we show that the room temperature ferromagnetism observed in anatase Co:TiO(2) films is not carrier mediated, but coexists with the dielectric state. TEM and x-ray absorption spectroscopy reveal a solid solution of Co in anatase, where Co is not metallic but in the +2 state substituting for Ti. Measurements at 300 K yield a M(S) of 1.1 mu(B)/Co atom, while all films are highly insulating. The evidence of intrinsic ferromagnetism in the dielectric ground state of Co:TiO(2) leads to new considerations for the origin of ferromagnetism in transition metal doped oxides.     

Comparison of measurements of phase velocity in human calcaneus to Biot theory

Biot's theory for elastic propagation in porous media has previously been shown to be useful for modeling the dependence of phase velocity on porosity in bovine cancellous bone in vitro. In the present study, Biot's theory is applied to measurements of porosity-dependent phase velocity in 53 human calcanea in vitro. Porosity was measured using microcomputed tomography for some samples (n = 23) and estimated based on bone mineral densitometry for the remaining samples (n = 30). The phase velocity at 500 kHz was measured in a water tank using a through-transmission technique. Biot's theory performed well for the prediction of the dependence of sound speed on porosity. The trend was quasilinear, but both the theory and experiment show similar slight curvature. The root mean square error (RMSE) of predicted versus measured sound speed was 15.8 m/s.