This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article propos...

The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinatesˆx i , ˆ x j = ω ij (ˆ x), and construct the complete algebra of commutation relations, including the operators of mo-menta. The constructed algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi identity. T...

The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

In this Brief Communication we present a new mathematical tool, which we call local spectrum analysis, that can be used to obtain information about local spectral content of the commutation error in large eddy simulations and its dependence on the filter shape and the non-uniformity of the filter width. To illustrate these theoretical findings, the local commutation spectrum analysis is applied...

US conscription in the Civil War is analyzed. Conscription was designed to gain federal control of enlistments, leaving state and local governments much of the fiscal and administrative responsibility for raising troops. Due to the hiring of substitutes, the payment of a fee to avoid service (commutation), and community-provided funds, only 2% of those who served were conscripted. Theory sugges...

An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are re...

The commutation relation $$KL = LK$$ between finite convolution integral operator K and differential L has implications for spectral properties of K. We characterize all operators admitting this relation. Our analysis places no symmetry constraints on the kernel extending well-known results Morrison real self-adjoint operators.

Given q1, q2 ∈ C \ {0}, we construct a unital Banach algebra Bq1,q2 which contains a universal normalized solution to the (q1, q2)-deformed Heisenberg–Lie commutation relations in the following specific sense: (i) Bq1,q2 contains elements b1, b2, and b3 which satisfy the (q1, q2)-deformed Heisenberg–Lie commutation relations (that is, b1b2 − q1b2b1 = b3, q2b1b3 − b3b1 = 0, and b2b3 − q2b3b2 = 0...

We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian interpolation.