By using the Lie’s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations whi...

The transitive closure of a reflexive, symmetric, analytic relation is an analytic equivalence relation. Does some smaller class contain the transitive closure of every reflexive, symmetric, closed relation? An essentially negative answer is provided here. Every analytic equivalence relation on an arbitrary Polish space is Borel embeddable in the transitive closure of the union of two smooth Bo...

In this paper we investigate nonlinear equivalence of stream ciphers over a finite field, exemplified by the pure LFSR-based filter generator over F2. We define a nonlinear equivalence class consisting of filter generators of length n that generate a binary keystream of period dividing 2−1, and investigate certain cryptographic properties of the ciphers in this class. We show that a number of i...

We prove an intrinsic equivalence between strong hypercontractivity (sHC) and a strong logarithmic Sobolev inequality (sLSI) for the cone of logarithmically subharmonic (LSH) functions. We introduce a new large class of measures, Euclidean regular and exponential type, in addition to all compactly-supported measures, for which this equivalence holds. We prove a Sobolev density theorem through L...

In previous work the authors introduced a notion of generic states and obtained criteria for local equivalence of them. Here they introduce the concept of CHG states maintaining the criteria of local equivalence. This fact allows the authors to halve the number of invariants necessary to characterize the equivalence classes under local unitary transformations for the set of tripartite states wh...

We address the closed pattern discovery problem in sequential databases for the class of flexible patterns. We propose two techniques of coarsening existing equivalence relations on the set of patterns to obtain new equivalence relations. Our new algorithm GenCloFlex is a generalization of MaxFlex proposed by Arimura and Uno (2007) that was designed for a particular equivalence relation. GenClo...

object which we can call the number, the direction etc., most logicians settle for a conventional stipulation of which particular abstract object is to be the value ofthe function for each argument. With this step, one leaves facts behind and opts for convenience. This was the step Frege took when he decided to make the number belonging to the concept Fthe extension of the concept concept equin...

We study local conservation laws of variable coefficient diffusion–convection equations of the form f(x)ut = (g(x)A(u)ux)x + h(x)B(u)ux. The main tool of our investigation is the notion of equivalence of conservation laws with respect to the equivalence groups. That is why, for the class under consideration we first construct the usual equivalence group G∼ and the extended one Ĝ∼ including tran...

We consider the equivalence relation ∼ on the symmetric group Sn generated by the interchange of two adjacent elements ai and ai+1 of w = a1 · · · an ∈ Sn such that |ai − ai+1| = 1. We count the number of equivalence classes and the sizes of the equivalence classes. The results are generalized to permutations of multisets. In the original problem, the equivalence class containing the identity p...

Although the equivalence of two Ordered Binary Decision Diagrams (OBDDs) can be decided in polynomial time, the equivalence of two Free Binary Decision Diagrams (FBDDs) is only known to be probabilistically decidable in polynomial time. FBDDs are a strict superset of OBDDs, and are more succinct than OBDDs, which explains the interest in testing their equivalence. We show that the probabilistic...