The current research was focused on synthesizing potassium sodium niobate (KNN) piezoelectric ceramics for the system (K0.48Na0.52) NbO3   by high energy ball milling process for 15h at the speed of 300 rpm.  The blended nano-crystalline powder was calcined in conventional box furnace at 700oC, 800oC and 900oC for duration of 5h, 7h and 10h.  Diffraction result of calcine powder confirmed the f...

After two papers on weak cubical categories and collarable cospans, respectively, we put things together and construct a weak cubical category of cubical collared cospans of topological spaces. We also build a second structure, called a quasi cubical category, formed of arbitrary cubical cospans concatenated by homotopy pushouts. This structure, simpler but weaker, has lax identities. It contai...

We define a notion of weak cubical category, abstracted from the structure of n-cubical cospans x : ∧ → X in a category X, where ∧ is the ‘formal cospan’ category. These diagrams form a cubical set with compositions x +i y in all directions, which are computed using pushouts and behave ‘categorically’ in a weak sense, up to suitable comparisons. Actually, we work with a ‘symmetric cubical struc...

We define a notion of weak cubical category, abstracted from the structure of n-cubical cospans x : ∧ → X in a category X, where ∧ is the ‘formal cospan’ category. These diagrams form a cubical set with compositions x +i y in all directions, which are computed using pushouts and behave ‘categorically’ in a weak sense, up to suitable comparisons. Actually, we work with a ‘symmetric cubical struc...

This is a brief study of the homology of cubical sets, with two main purposes. First, this combinatorial structure is viewed as representing directed spaces, breaking the intrinsic symmetries of topological spaces. Cubical sets have a directed homology, consisting of preordered abelian groups where the positive cone comes from the structural cubes. But cubical sets can also express topological ...

We will present a brief study of the homology of cubical sets, with two main purposes. First, this combinatorial structure is viewed as representing directed spaces, breaking the intrinsic symmetries of topological spaces. Cubical sets have a directed homology, consisting of preordered abelian groups where the positive cone comes from the structural cubes. But cubical sets can also express topo...

This paper is an exposition of the ideas and methods of Cisinksi, in the context of A-presheaves on a small Grothendieck site, where A is an arbitrary test category in the sense of Grothendieck. The homotopy theory for the category of simplicial presheaves and each of its localizations can be modelled by A-presheaves in the sense that there is a corresponding model structure for A-presheaves wi...

In this thesis we construct a new model of intensional type theory in the category of cubical sets with connections. To facilitate this we introduce the notion of a nice path object category, a simplification of the path object category axioms of [vdBG12] that nonetheless yields the full path object category structure. By defining cubical n-paths and contraction operators upon them we exhibit t...

Topological spaces such as classifying spaces, configuration spaces and spacetimes often admit extra directionality. Qualitative invariants on such directed spaces often are more informative, yet more difficult, to calculate than classical homotopy invariants because directed spaces rarely decompose as homotopy colimits of simpler directed spaces. Directed spaces often arise as geometric realiz...

the crystal structure of the title schiff base complex is obtained by single-crystal x-ray diffraction data.the solid state structure determination reveals that the coordination geometry around the copper(ii) center istetrahedrally distorted square-planar. the crystal packing shows one dimensional infinite chains which arisesfrom the intermolecular interaction and stabilize the crystal packing.