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Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections.
      
The aqueous and solvent extracts when tested against 11 gram-negative and 2 gram-positive bacteria and 3 fungi expressed activity to most of the organisms.
      
Activity was not recorded for hexane extract, against A.
      
Methanol extract showed more activity amongst all the solvent extracts, particularly remarkable activity recorded against gram-positive bacteria.
      
Activity against diarrhea and dysentery causing organisms such as A.
      
Aqueous and organic solvent extracts tested by agar-well diffusion method against 12 human pathogenic bacteria and 3 fungal strains showed activity to most of the organisms.
      
Fermentation broth and cell extracts were tested against typed test organisms.
      
The cell extract showed activity against Candida albicans, Aspergillus niger, Trichoderma viridae, Fusarium moniliforme and Alternaria brassicicola.
      
In vitro enzyme inhibition studies have identified three inhibitors (14, 16, 23) of the falcipains with one (14) showing dual activity against both falcipain-2 and falcipain-3 and IC50 values of 6.6 and 29.4 μM, respectively.
      
While compound 8a showed distinct antifungal activity against C.
      
The library has been tested against Leishmania donovani and Plasmodium falciparum, with activity at the micromolar level.
      
Among the nine compounds tested, 5h showed the best selective antiproliferative properties in vitro, being especially active against the human metastatic melanoma cells - inhibition by 93% after 96 h treatment at 10-4 M concentration.
      
Compounds 4-21 were evaluated for cytotoxic activity against a panel NCI-H460 (lung), MCF7 (breast) and SF-268 (CNS) cancer cell lines.
      
Compounds 26 and 30 exhibited potent in vitro antibacterial activity against Salmonella typhi, Escherichia coli and Klebsiella pneumoniae.
      
While compound 28 proved to be potent against Salmonella typhi and Klebsiella pneumoniae.
      
Like wise, compounds 26 and 28 exerted potent in vitro antifungal activity against Cryptococcus neoformans, Aspergillus niger and Aspergillus flavus whereas 30 showed very good activity than the standard drug against all the tested organisms.
      
Caffeoyl naphthalene sulfonamide derivatives act against HIV integrase and thus have the potential to become a part of an anti-HIV drug regimen.
      
Compound 6 exerted potent in vitro antibacterial activity against B.
      
subtilis while compound 6 exhibited in vitro antifungal activity against Candida-6.
      
All newly synthesized compounds were evaluated for their antimycobacterial activities against isoniazid-resistant Mycobacterium tuberculosis using agar dilution.
      
 

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