(L,M)-fuzzy topological-convex spaces

Abstract

In this paper, the notion of (L, M)-fuzzy topological-convex spaces is introduced and some of its characterizations are obtained. Then the notion of (L, M)-fuzzy convex enclosed relation spaces is introduced and its one-to-one correspondence with (L, M)-fuzzy convex space is studied. Based on this, the notion of (L, M)-fuzzy topological-convex enclosed relation spaces is introduced and its categorical isomorphism to (L, M)-fuzzy topological-convex spaces is discussed.

Iodobismuthate(III) and Iodobismuthate(III)/Iodocuprate(I) Complexes with Organic Ligands

“…Efforts to understand and even predict the sizes of these anions have led to renewed attention on this long-known system. [1][2][3][4] Secondly, these systems represent precursors, or even alternatives to, BiOX photocatalysts. [5] Finally, some of these compounds have shown interesting luminescent, thermochromic, and/or solventochromic behavior.…”

“…[10] The [(Phen)BiI 4 ]ion has been crystallized with other cations, including [Cu(Phen) 2 ] + and [(Phen)BiI 2 -(dmso)] + . [8,12] Finally, the ions [(tpy)IBi(μ 2 -I) 3 BiI 3 ] -, [(tpy) 2 BiI 2 ] + , and [(tpy)BiI 4 ] -(tpy = 2,2′:6′2′′-terpyridine) are known. [13] muthate(III) centers are distorted octahedra and all cuprate(I) centers are tetrahedral, with organic ligands bonded to Cu I .…”

“…Mixed metal complexes of Bi III , especially those with photophysically active metals such as Cu I , are of increasing interest with regard to their optical and photocatalytic properties. [3] The polarizable organosulfide and iodide ions are particularly promising ligands for producing photoactive clusters. Known sulfidecontaining species include [BiCu 2 (SPh) 3 4 ], the latter two of which feature mixed Bi oxidation states.…”

“…[3] The polarizable organosulfide and iodide ions are particularly promising ligands for producing photoactive clusters. Known sulfidecontaining species include [BiCu 2 (SPh) 3 4 ], the latter two of which feature mixed Bi oxidation states. [14] A few mixed BiI 3 /CuI metal-organic complexes have been reported.…”

“…[14] A few mixed BiI 3 /CuI metal-organic complexes have been reported. One species is [(Hdeg) 3 (H 2 deg)Bi 2 ][Bi 5 CuI 19 ] (H 2 deg = diethylene glycol). [15] In the [Bi 5 CuI 19 ] 3anion Bi 5 I 19 4clusters are assembled from facesharing BiI 6 octahedra.…”