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”...

Based on a geometrically linearized theory, we describe the partition into twins observed in microstructures of shape memory alloys undergoing cubic-to-tetragonal transformations an ansatz-free ...

Acyclic cubical complexes have first been introduced by Bandelt and Chepoi in analogy to acyclic simplicial complexes. They characterized them by cube contraction and elimination schemes and showed that the graphs of acyclic cubical complexes are retracts of cubes characterized by certain forbidden convex subgraphs. In this paper we present an algorithm of time complexity O(m log n) which recog...

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that G is a group for which there is a bound on the orders of its finite subgroups. We prove that if G acts properly on a finitedimensional CAT(0) cubical complex, then either G contains a free subgroup of rank 2 or G is finitely generated and virtually abelian. In particular the above conclusion ...

This is the third in a series of papers extending Martin-Löf’s meaning explanations of dependent type theory to a Cartesian cubical realizability framework that accounts for higherdimensional types. We extend this framework to include a cumulative hierarchy of univalent Kan universes of Kan types; exact equality and other pretypes lacking Kan structure; and a cumulative hierarchy of pretype uni...

Persistent homology is a powerful tool in topological data analysis (TDA) to compute, study, and encode efficiently multi-scale features being increasingly used digital image classification. The represent number of connected components, cycles, voids that describe the shape data. extracts birth death these through filtration process. lifespan can be represented using persistent diagrams (topolo...

The size and shape of a surfactant aggregate could be altered by using supersaturation like in crystal growth, rather than applying common laws that drive surfactant aggregate formation.

Functionally graded NiTi structures benefit from the combination of the smart properties of NiTi and those of functionally graded structures. This article provides experimental data for thermomechanical deformation behaviour of microstructurally graded, compositionally graded and geometrically graded NiTi alloy components, related to the research article entitled "Functionally graded shape memo...

Characteristics of produced concrete become changedthrough changingthe characteristics of materials constituting the concrete. These changes include: The quality of cement, the real ration of water to cement: with neglecting the further water within the aggregates or lack of that, the consideredratio fluctuates and the characteristics of the aggregate which are related to the following dimensio...