Abstract We determine the 6-dimensional nilpotent metric Lie algebras such that algebra $${\mathfrak {n}}$$ n has a descending series of ideals invariant under all automorphisms and dimension consecutive members decreases by one. call them having framing determined ideals. classify isometry equivalence classe...

A pseudo-Euclidean space (R, μ) is such a Euclidean space R associated with a mapping μ : − → V x → x − → V for x ∈ R, and a linear isometry T : (R, μ) → (R, μ) is such a linear isometry T : R → R that Tμ = μT . In this paper, we characterize curvature of s-line, particularly, Smarandachely embedded graphs and determine linear isometries on (R, μ).

This is part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in part I, a compactification of these isometry groups, and called “bipolarized” those Lorentz manifolds having a “trivial ” compactification. Here we show a geometric rigidity of non-bipolarized Lorentz manifolds; that is, they are (at least locally) warped products of constant curvature Lorentz ...

Isometry classes of linear codes can be expressed as orbits under the group action of a wreath product. Some combinatorial and algebraic methods are discussed which can be applied for generating linear codes distributed uniformly at random over all isometry classes.

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL(2,R) × U(1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

| In the cryptanalysis of stream ciphers and pseudorandom sequences, the notions of linear, jump, and 2{adic complexity arise naturally to measure the (non)randomness of a given string. We de ne an isometry K on Fq that is the precise equivalent to Euclid’s algorithm over the reals to calculate the continued fraction expansion of a formal power series. The continued fraction expansion allows to...

In this paper we look at isometry properties of random matrices. During the last decade these properties gained a lot attention in a field called compressed sensing in first place due to their initial use in [7, 8]. Namely, in [7, 8] these quantities were used as a critical tool in providing a rigorous analysis of l1 optimization’s ability to solve an under-determined system of linear equations...

Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitive algorithm for sparse recovery. Recent developments have shown that OMP guarantees exact recovery of K-sparse signals in K iterations if the observation matrix Φ satisfies the Restricted Isometry Property (RIP) with Restricted Isometry Constant (RIC) δK+1 < 1

We prove: For all n and all n-cylic isometriesφ : ΛQ → ΛQ of the rational K3 lattice there exists an algebraic realization of φ, i.e. marked algebraic K3 surfaces (S,ηS) and (M,ηM), whereM is a moduli space of sheaves on S, and a Hodge isometry ψ : H2(S,Q)→ H2(M,Q) such that φ = ηM ◦ψ ◦ η−1 S . 1 Facts about cyclic isometries We need the existence of a triple ((S,ηS), (M,ηM),ψ) to have a point ...