An Elementary Method on a Minimization Problem

一、ＴｈｅＰｒｏｂｌｅｍ .Ｌｅｔｆ(ｘ) =ａｘ2 ｂｘ ｃ ａｘ2 ｐｘ ｑ,ｗｈｅｒｅａ >0 ,ｂ2 - 4ａｃ≤ 0ａｎｄｐ2 - 4ａｑ≤ 0 .ＯｕｒＰｒｏｂｌｅｍｉｓ“Ｗｈｅｔｈｅｒｄｏｅｓｍｉｎｘ∈Ｒｆ(ｘ)ｅｘｉｓ?Ｍｏｒｅｏｖｅｒ ,,ｉｆｍｉｎｘ∈Ｒｆ(ｘ)ｅｘｉｓｔｓ,ｔｈｅｎｍｉｎｘ∈Ｒｆ(ｘ)=?ａｎｄｉｎｔｈｉｓｃａｓｅｘ =?” .Ｎａｔｕｒａｌｌｙ ,ｗｅｋｎｏｗｔｈａｔｍｉｎｘ∈Ｒｆ(ｘ)ｅｘｉｓｔｓｆｒｏｍｔｈｅｋｎｏｗｌｅｄｇｅｏｆｍａｔｈｅｍａｔｉｃａｌａｎａｌｙｓｉｓ.Ａｌｓｏ,ｗｅｃａｎｇｉｖｅｔｈｅ…     

The Synthesis and Properties of New Metal-free and Metallophthalocyanines Containing Four Diloop Macrocyclic Moieties

The synthesis and characterization of new metal-free (9) and metal-containing (Zn, Ni or Cu 10, 11, 12) derivatives of a symmetrically octasubstituted phthalocyanine derived from 21,22-dicyano-2,3,5,6,8,9,11,12,15,17,18,25,26,28-tetradecahydro[1,4,7,12] benzodioxadithiacyclotetradeceno[6,7-b][1,4,7,10,13]benzopentaoxacyclopentadecene (7), which was synthesized in a multi-step reaction sequence, have been described. The novel compouds have been characterized by a combination of elemental analysis, ¹H and ¹³C NMR, IR, UV–vis and MS spectral data.