It is shown that a collapsible, compact, connected, simplicial polyhedron admits a cubical subdivision and a median convexity, such that all cubes are convex subspaces with a convexity of subcubes. Conversely, a compact, connected, cubical polyhedron with a convexity as described admits a collapsible simplicial subdivision. Such a convexity, when it exists, is uniquely determined by the corresp...

a new metal-organic compound, [fe(pydc)(dmso)(h2o)cl], (where pydc is pyridine-2, 6-dicarboxylate and dmso is dimethyl sulfoxide), has been synthesized and characterized by singlecrystal x-ray diffraction, tga/dta, ir and raman spectroscopy. green-yellow crystals,crystallized in the monoclinic system, space group p21/n, a = 7.2461(4) å, b = 10.3018(4) å, c =17.7667(10) å, α = 90°, β = 90.014°(5...

The SDS, PEG and CTAB roofed MgO nano powders were synthesized by co-precipitation method.  The sintered nano powders was shown Fm-3m space group with cubic phase obtained by the XRD pattern. The lattice strain was calculated to be used Williamson-Hall equations (W-H). The formation of Mg-O bond and hydroxyl radicals on the surface were confirmed by the FTIR analyses. The TEM revealed that the ...

zinc oxide (zno) nanopowders were synthesized by the sol–gel method from an ethanol solution of zinc sulfate heptahydrate in the presence of diethylene glycol surfactant. detailed structural and microstructural investigations were carried out using x-ray diffraction (xrd), high-resolution transmission electron microscopy (hrtem), field emission scanning electron microscopy (fe-sem), fourier tra...

the purpose of this paper is the generalization of structure factor for rods by polygon section in two dimensional phononic crystals. if we use the plane wave expansion method (pwe) for the propagation of acoustic waves in 2d phononic crystals, structure factor will be an important quantity. in order to confirm the obtained relations, we have calculated the band structure for xy and z vibration...

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...

There is an on-going connection between type theory and homotopy theory, based on the similarity between types and the notion of homotopy types for topological spaces. This idea has been made precise by exhibiting the category cSet of cubical sets as a model of homotopy type theory. It is natural to wonder, conversely, to what extend this model can be reflected in a type theory. The homotopy st...

We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories. We prove that all our sites are test categories in the sense of Grothendieck, meaning that the corresponding presheaf categories of cubical sets model classical homotopy theory. We delineate exactly which ones are even strict test categories, me...

Cubical sets and their homology have been used in dynamical systems as well as in digital imaging. We take a refreshing view on this topic, following Zariski ideas from algebraic geometry. The cubical topology is defined to be a topology in R in which a set is closed if and only if it is cubical. This concept is a convenient frame for describing a variety of important features of cubical sets. ...

A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical ω-category. This also has the structure of connections in the sense of Brown and Higgins, but cancellation of connections does not hold.