Within the framework of theories where both scalars and fermions are present, we develop a systematic prescription for the construction of CP-violating quantities that are invariant under basis transformations of those matter fields. In theories with Spontaneous Symmetry Breaking, the analysis involves the vevs’ transformation properties under a scalar basis change, with a considerable simplifi...

A simple, label-free cytometry technique is introduced. It is based on the analysis of the fluctuation of image Gray Level Information Entropy (GLIE) which is shown to reflect intracellular biophysical properties like generalized entropy. In this study, the analytical relations between cellular thermodynamic generalized entropy and diffusivity and GLIE fluctuation measures are explored for the ...

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function, the entropy potential. The validity and the consequences of this hypothesis are explored in detail. The numerical investigation of a continuous-time model provides a further confirmation to the existence of the entropy potential. Furthe...

Common program specification and verification build on concepts like method preand postconditions and loop invariants. These lectures notes teach those concepts in the context of the language and verifier Dafny.

An axiomatization of the concept of entropy of a discrete Choquet capacity is given. It is based on three axioms: the symmetry property, a boundary condition for which the entropy reduces to the classical Shannon entropy, and a generalized version of the well-known recursivity property. This entropy, recently introduced to extend the Shannon entropy to nonadditive measures, fulfills several pro...

Software engineering comprises some processes such as designing, implementing and modifying of code. These processes are done to generate software fast and have a high quality, efficient and maintainable software. In order to perform these processes, invariants can useful and help programmers and testers. Arrays and pointers are frequent data types and are used in program code repeatedly. Becau...

We show that the Vassiliev invariants of a knot K, are obstructions to finding a regular Seifert surface, S, whose complement looks “simple” (e.g. like the complement of a disc) to the lower central series of its fundamental group.

Abstract In this article, the gas dynamics equations with an equation of state special form are considered.The is pressure which equal to sum two functions, one being a function density, and other entropy. The system invariant under action 12-parameter transformations group. For three-dimensional subalgebra 3.32 12-dimensional Lie algebra invariants calculated, submodel rank 1 constructed, fami...

We analyze the formation of maximally entangled Rydberg atom pairs subjected to Landau-Zener sweeps atom-light detuning. Though populations reach a steady value at longer times, phases evolve continuously, leading periodic oscillations in entanglement entropy. The local unitary equivalence between obtained states and Bell is verified by computing polynomial invariants. Finally, we study effect ...

Abstract Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete used to reason about correctness systems without having unroll their loops, differential equations solve them. Automatic generation remains one the biggest practical challenges automation formal proofs safety for There at present many disparate methods availab...