• Title/Summary/Keyword: Mild conditions

Search Result 599, Processing Time 0.029 seconds

Solid-Phase Synthesis of 2-Arylbenzothiazole Using Silica Sulfuric Acid under Microwave Irradiation

  • Niralwad, Kirti S.;Shingate, Bapurao B.;Shingare, Murlidhar S.
    • Bulletin of the Korean Chemical Society
    • /
    • v.31 no.4
    • /
    • pp.981-983
    • /
    • 2010
  • The condensation of several aromatic/heteroaromatic aldehydes with 2-aminothiophenol catalyzed by silica sulfuric acid under microwave irradiation afforded 2-arylbenzothiazoles in high yields and short reaction times under solvent-free conditions. The major advantages of the present method are good yields, ecofriendly, reusable catalyst, mild and solvent-free reaction conditions.

COMPLEX SYMMETRIC WEIGHTED COMPOSITION-DIFFERENTIATION OPERATORS ON H2

  • Lian Hu;Songxiao Li;Rong Yang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.5
    • /
    • pp.1141-1154
    • /
    • 2023
  • In this paper, we study the complex symmetric weighted composition-differentiation operator D𝜓,𝜙 with respect to the conjugation JW𝜉,𝜏 on the Hardy space H2. As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of D𝜓,𝜙 is also investigated.

HEMIVARIATIONAL INEQUALITIES

  • ASLAM NOOR MUHAMMAD
    • Journal of applied mathematics & informatics
    • /
    • v.17 no.1_2_3
    • /
    • pp.59-72
    • /
    • 2005
  • The auxiliary principle is used to suggest and analyze some iterative methods for solving solving hemivariational inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. Since hemivariational in­equalities include variational inequalities and nonlinear optimization problems as special cases, our results continue to hold for these problems.