Cubical sets have a directed homology, studied in a previous paper and consisting of preordered abelian groups, with a positive cone generated by the structural cubes. By this additional information, cubical sets can provide a sort of ‘noncommutative topology’, agreeing with some results of noncommutative geometry but lacking the metric aspects of C∗-algebras. Here, we make such similarity stri...

We provide a number of new construction techniques for cubical complexes and cubical polytopes, and thus for cubifications (hexahedral mesh generation). Thus we obtain the first instance of a cubical 4-polytope that has a non-orientable dual manifold (a Klein bottle). This confirms the existence conjecture of Hetyei [17, Conj. 2, p. 325]. More systematically, we prove that every normal crossing...

This paper proposes a new cubical space model for the representation of continuous objects and surfaces in the n-dimensional Euclidean space by discrete sets of points. The cubical space model concerns the process of converting a continuous object in its digital counterpart, which is a graph, enabling us to apply notions and operations used in digital imaging to cubical spaces. We formulate a d...

It is shown that the cubical nerve of a strict omega-category is a sequence of sets with cubical face operations and distinguished subclasses of thin elements satisfying certain thin filler conditions. It is also shown that a sequence of this type is the cubical nerve of a strict omega-category unique up to isomorphism; the cubical nerve functor is therefore an equivalence of categories. The se...

single-walled carbon nanotubes (swcnt) and multi-walled carbon nanotubes(mwcnt) were melt-blended with polyvinylidene fluoride (pvdf).ft-ir technique revealed that swcnt has insignificant effect on the crystalline structure of pvdf and at 3wt% modification only 14% beta crystal isformed. this observation was accounted for by the chair structure of swcnt. in mwcnt nancomposites it was found that...

the zinc(ii) complex [zn2(dmdtc)2(μ-dmdtc)2] has been synthesized directly from thiram ligand, containing a disulfide bond {dmdtc = n,n-dimethyldithiocarbamate; thiram = n,n-tetramethylthiuram disulfide}, and characterized by elemental analysis and spectroscopic methods. surprisingly thiram, undergoes a reductive disulfide bond scission upon reaction with zn2+ in methanolic media to give the [z...

an octahedral cobalt(iii) complex, trans-[(me2bpb)co(bzlan)2]clo4 (1), with h2me2bpb = n,n’-(4,5-dimethyl-1,2-phenylene)dipicolinamide and bzlan = benzylamine, has been synthesized and characterized by elemental analyses, ir, uv-vis, and 1h nmr spectroscopy. the structure of this complex has been determined by x-ray crystallography. the me2bpb2– is a di-anionic tetradentate ligand furnishing a ...

calcium dichloride tetra urea was prepared by the reaction of calcium chloride with urea in aqueous solution. the crystals are monoclinic, a= 7.633, b= 12.45 1, c= 8.118 ?,? = 113.17, z = 4, space group p 2,/a. the crystal structure was determined by single crystal x-ray methods and refined to r= 0.041. the calcium atoms are coordinated to four oxygen atoms of urea and to two chloride ions. the...

Having addressed the issue ofgenerating octrees from raster scan efficiently using parallel computation, it is worthwhile to ensure that the encoding is accomplished without much loss of information. Knowing that each cube usually stores an average ofthe intensity value in the cubical subspace, the encoding could lead to a "blocky" (as against ''patchy'') solid during regeneration. Retaining th...

designing a power splitter with five ports has been shown in this article. in order to prevent the direct coupling between waveguides, a t-shaped structure with an appropriate distance has been used. the coupling between the parallel photonic crystal waveguides is based on multimode interference, while selecting the output efficiency is performed by setting the refractive coefficients and radiu...