We define labeling homomorphisms on the cubical homology of higher-dimensional automata and show that they are natural with respect to cubical dimaps and compatible with tensor products. We also indicate two possible applications of labeled homology in concurrency theory.

Nanostructured Ni2As2O7 semiconductor samples were synthesized by a solid state method among As2O3 and Ni(NO3)2.6H2O raw materials at 650 °C (S1) and 750 °C (S2) as reaction temperatures. The synthesized nanomaterials were characterized by powder X-ray diffraction (PXRD) technique and F...

This paper is the third paper of a series devoted to higherdimensional transition systems. The preceding paper proved the existence of a left determined model structure on the category of cubical transition systems. In this sequel, it is proved that there exists a model category of labelled symmetric precubical sets which is Quillen equivalent to the Bousfield localization of this left determin...

Following the cubical set model of type theory which validates the univalence axiom, cubical type theories have been developed that interpret the identity type using an interval pretype. These theories start from a geometric view of equality. A proof of equality is encoded as a term in a context extended by the interval pretype. Our goal is to develop a cubical theory where the identity type is...

the effect of alkyl substituents on the c-phenyl and/or the n-phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. the predominant configuration in chcl3 is determined by steric and electronic effects. substituents on the c-phenyl ring favor the cis configuration, while substituents in the n-phenyl ring favor a trans configuration. t...

A new reduction algorithm for the efficient computation of the homology of cubical sets and polotypes, particularly strong for low dimensional sets embedded in high dimensions, is presented. The algorithm runs in linear time. The paper presents the theoretical background of the algorithm, the algorithm itself, experimental results based on an implementation for cubical sets as well as some theo...

Tables, Boolean Laws and different traits of Karnaugh Maps are used generally to establish a solution of Boolean equations. Cubical representation is another option to help in getting a solution of equations. Largest possible k-cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical meth...

A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature” etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. A new, holonomy-type invariant for cubical complexes is introduced, leading to a combinatorial “Theorema Egregium”...