On the generalized quotient integrals on homogeneous spaces

Abstract

A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient integral formula. Finally our results are supported by some examples.

Design, synthesis, characterization and catalytic performance of a new cellulose‐based magnetic nanocomposite in the one‐pot three‐component synthesis of α‐aminonitriles

“…For the optimization of the reaction conditions, the condensation of 4-chlorobenzaldehyde (1 mmol [12][13][14][15]. Cellulose catalyses the reaction in the same time, but the yield of the reaction is low (Table 1, entry 12).…”

“…Nowadays this reaction is extensively used because it provides a robust, direct and economically viable access to various α-amino acids. [5] Over recent years, many catalysts for the Strecker reaction and synthesis of α-amino nitriles have been introduced and developed: sulfuric acidmodified PEG-6000, [6] tin exchanged zeolite, [7] γ-Al 2 O 3 -supported 12-tungstosilicic acid, [8] sulfamic acid-functionalized magnetic Fe 3 O 4 nanoparticles, [9] SO 3 H-functionalized ionic liquid, [10] xanthan sulfuric acid, [11] guanidine hydrochloride, [12] Zr-MCM-41 nanoreactors, [13] nano-powder TiO 2 P25, [14] cellulose sulfuric acid, [15] chitosan, [16] SBA-15-supported sulfonic acid, [17] N-heterocyclic carbene amidate palladium(II) complex, [18] B-MCM-41, [19] montmorillonite KSF clay. [20] magnesium oxide, [21] indium(III) iodide, [22] Al-MCM-41, [23] MCM-41-anchored sulfonic acid, [24] Fe(Cp) 2 PF 6 , [25] K 2 PdCl 4 , [26] sulfated tungstate, [27] iron, [28] Zr(HSO 4 ) 4 , [29] 2,4,6-trichloro-1,3,5-triazine (cyanuric acid) [30] and PVP-SO 2 complex.…”