A simple device, based on the factorization of invertible matrix polynomials, enabling to identify the possibility of fast implementation of linear transforms is presented. Its applicability is demonstrated in the case of Hadamard matrices and their generalization, Hadamard matrix polynomials.
An improved version of the Integrative Optical Imaging (IOI) method for diffusion measurements in a geometrically complex environment of the brain extracellular space has been developed. We present a theory for this Fast Optical Tracking Of Diffusion (FOTOD) which incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media with time-dependent nonspecific linear clearance. FOTOD can be used to measure rapid changes in extracellular diffusion permeability that occur,...
In this paper, we investigate the a priori and the a posteriori error analysis for the finite element approximation to a regularization version of the variational inequality of the second kind. We prove the abstract optimal error estimates in the - and -norms, respectively, and also derive the optimal order error estimate in the -norm under the strongly regular triangulation condition. Moreover, some residual–based a posteriori error estimators are established, which can provide the global upper...
This work is focused on a weak solution of a coupled physical task of the microwave wood drying process with stress-strain effects and moisture/temperature dependency. Due to the well known weak solutions for the individual physical fields, the author concerns with the coupled stress-strain relation coupled with the moisture and temperature distributions. For the scale dependency the subgrid upscaling method was used. The solved region is assumed to be divided into discontinuous subregions according...
A two-dimensional depth-averaged flow and temperature model was applied to study the circulation patterns in the Oder (Szczecin) Lagoon located on the border between Germany and Poland. The system of shallow water and temperature evolution equations is discretized with the modified Utnes scheme [4], which is characterized by a semi-decoupling algorithm. The continuity equation is rearranged to Helmholtz equation form. The upwinding Tabata method [3] is used to approximate convective terms. Averaged...
We deal with modelling of flows in channels or tubes with abrupt changes of the diameter. The goal of this work is to construct the FEM solution in the vicinity of these corners as precise as desired. We present two ways. The first approach makes use of a posteriori error estimates and the adaptive strategy. The second approach is based on the asymptotic behaviour of the exact solution in the vicinity of the corner and on the a priori error estimate of the FEM solution. Then we obtain the solution...
Let be a cell complex obtained by attaching a 2-cell to a finite bouquet of circles (for example, a closed surface). In terms of the combinatorial type of the attaching map, the paper gives conditions for the existence of a fixed point free (topological) homeomorphism of the complex . Also, quotients of finite group actions on such complexes are considered as well as a condition under which the induced actions on cohomology are trivial.
[For the entire collection see Zbl 0699.00032.] The author defines a general notion of a foliated groupoid over a foliation with singularities, within the framework of a (known) general notion of a differentiable structure. Then, he generalizes the classical correspondence between the subalgebras of Lie algebras and the subgroups of the corresponding Lie groups for this type of pseudogroups.