Self-cleaning treatment on historical stone surface via titanium dioxide nanocoatings

Purpose The purpose of this study is to evaluate the possibility of using titanium dioxide coating in the field of architectural heritage. Design/methodology/approach In this research, a titanium dioxide coating was prepared and then applied to the travertine stone surfaces. The nature of the coating was determined through various observations and analyses. Moreover, the effect of photocatalytic self-cleaning was evaluated using an organic dye (Rhodamine B). Findings The results of XRD, DLS and SEM confirmed the formation of small anatase crystals. The hydrophilic behavior on the surface was observed by coatings based on titanium dioxide. Research limitations/implications The self-cleaning ability of titanium dioxide is due to the synergistic effect of its optical inductive property, which is activated with sunlight. Practical implications The self-cleaning coatings are interested for many industries. The reported data can be used by the formulators working in the research and development departments. Social implications Self-cleaning systems are considered as smart coatings. Therefore, the developing of its knowledge can help to extend its usage to different applications. Originality/value The application of titanium dioxide coating in the field of architectural heritage is a great challenge. Therefore, in this research, a titanium dioxide coating was prepared by sol-gel method and then applied on travertine surfaces and its properties were studied.

Nearest Prototype and Nearest Neighbor Clustering with Twofold Memberships Based on Inductive Property

The aim of this paper is to study methods of twofold membership clustering using the nearest prototype and nearest neighbor. The former uses theK-means, whereas the latter extends the single linkage in agglomerative hierarchical clustering. The concept of inductive clustering is moreover used for the both methods, which means that natural classification rules are derived as the results of clustering, a typical example of which is the Voronoi regions inK-means clustering. When the rule of nearest prototype allocation inK-means is replaced by nearest neighbor classification, we have inductive clustering related to the single linkage in agglomerative hierarchical clustering. The former method usesK-means or fuzzyc-means with noise clusters, whereby twofold memberships are derived; the latter method also derives two memberships in a different manner. Theoretical properties of the both methods are studied. Illustrative examples show implications and significances of this concept.

Tychonoff's theorem in the framework of formal topologies

In this paper we give a constructive proof of the pointfree version of Tychonoff's theorem within formal topology, using ideas from Coquand's proof in [7]. To deal with pointfree topology Coquand uses Johnstone's coverages. Because of the representation theorem in [3], from a mathematical viewpoint these structures are equivalent to formal topologies but there is an essential difference also. Namely, formal topologies have been developed within Martin Löf's constructive type theory (cf. [16]), which thus gives a direct way of formalizing them (cf. [4]).The most important aspect of our proof is that it is based on an inductive definition of the topological product of formal topologies. This fact allows us to transform Coquand's proof into a proof by structural induction on the last rule applied in a derivation of a cover. The inductive generation of a cover, together with a modification of the inductive property proposed by Coquand, makes it possible to formulate our proof of Tychonoff s theorem in constructive type theory. There is thus a clear difference to earlier localic proofs of Tychonoff's theorem known in the literature (cf. [9, 10, 12, 14, 27]). Indeed we not only avoid to use the axiom of choice, but reach constructiveness in a very strong sense. Namely, our proof of Tychonoff's theorem supplies an algorithm which, given a cover of the product space, computes a finite subcover, provided that there exists a similar algorithm for each component space.