The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

A nonclassical multi-valued logic based on Post algebra is presented. Besides the conventional Post's cyclic negation, this nonclassical logic algebra defines new operators that simplify the truth-table minimization techniques. An electronic implementation of this algebra for a 3-level logic is proposed. Electronics gates of Post negation and the new operators were designed and simulated using ...

We experimentally demonstrate sum-frequency generation with entangled photon pairs, generating as many as 40,000 photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonc...

What is modularity? Which kind of modularity should developers strive for? Despite decades of research on modularity, these basic questions have no definite answer. We submit that the common understanding of modularity, and in particular its notion of information hiding, is deeply rooted in classical logic. We analyze how classical modularity, based on classical logic, fails to address the need...

Large size effects are experimentally measured in lattices of triangular unit cells: about a factor of 36 in torsion rigidity and 29 in bending rigidity. This nonclassical phenomenon is consistent with Cosserat elasticity, which allows for the rotation of points and distributed moments in addition to the translation of points and force stress of classical elasticity. The Cosserat characteristic...

We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant ...

Existing measures of bipartite nonclassical correlations that are typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in the computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completelyeigenvalue-preserving (EnCE) maps. The class is in analogy to the cla...

Tableau–Based theorem provers can be extended to cover many of the nonclassical logics currently used in AI research. For both, classical and nonclassical first–order logic, equality is a crucial feature to increase expressivity of the object language. Unfortunately, all so far existing attempts of adding equality to semantic tableaux have been more or less experimental and turn out to be usele...

This article discusses the meaning and scope of biological hypercomputation (BH) that is to be considered as new research problem within the sciences of complexity. The framework here is computational, setting out that life is not a standard Turing Machine. Living systems, we claim, hypercompute, and we aim at understanding life not by what it is, but rather by what it does. The distinction is ...