The baker map is investigated by two different theories of irreversibility by Prigogine and his colleagues, namely, the Λ-transformation and complex spectral theories, and their structures are compared. In both theories, the evolution operatorU† of observables (the Koopman operator) is found to acquire dissipativity by restricting observables to an appropriate subspaceΦ of the Hilbert space L2 ...

We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schrödinger operators H = − d2 dx2 + V in L2(R). Our technique is connected to Dirichlet data, that is, the spectrum of the operator HD on L2((−∞, x0))⊕L2((x0 ,∞)) with a Dirichlet boundary condition at x0. The transformation moves a single eigenvalue of HD and ...

This paper reports on investigations concerning the convergence of fractal transforms for signal modelling. Convergence is essential for the functionality of fractal based coding schemes. The coding process is described as non-linear transformation in the finite-dimensional vector space. Using spectral theory, a necessary and sufficient condition for the contractivity is derived from the eigenv...

The study purpose was to evaluate the use of computer-automated algorithms as a replacement for subjective, visual determination of muscle contraction onset using M-mode ultrasonography. Biceps and quadriceps contraction images were analyzed visually and with three different classes of algorithms: pixel standard deviation (SD), high-pass filter and Teager Kaiser energy operator transformation. ...

The aim of this paper is to study the integration of multiplicative preference relation as a preference representation structure in fuzzy multipurpose decision-making problems. Assuming fuzzy multipurpose decision-making problems under di4erent preference representation structures (ordering, utilities and fuzzy preference relations) and using the fuzzy preference relations as uniform representa...

The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of twoand three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization...

We analyze the problem of decision making under ignorance with regrets. Recently, Yager has developed a new method for decision making where instead of using regrets he uses another type of transformation called negrets. Basically, the negret is considered as the dual of the regret. We study this problem in detail and we suggest the use of geometric aggregation operators in this method. For doi...

Let ν be a unit normal vector field along M . Notice that ν : M −→ S satisfies that 〈ν(m),m〉 = 0. For any tangent vector v ∈ TmM , m ∈ M , the shape operator A is given by A(v) = −∇̄vν, where ∇̄ denotes the Levi Civita connection in S. For every m ∈ M , A(m) defines a linear symmetric transformation from TmM to TmM ; the eigenvalues of this transformation are known as the principal curvatures of ...

A theory of non-unitary unbounded similarity transformation operators is developed. To this end the class of J-unitary operators U is introduced. These operators are similar to unitary operators in their algebraic aspects but differ in their topological properties. It is shown how J-unitary operators are related to so-called J-biorthonormal systems and J-selfadjoint projections. Families {Uα} o...

The behavior of a particle moving according to the laws quantum mechanics in field, which potential changes over time, is studied. method unitary transformations for solving temporal Schrödinger equation considered. reduced Hamiltonian system quantum­-mechanical time­-dependent obtained, as well total operator evolution such system. We find new version transformation, which, compared known ones...