Fast calculation of Laplace-Beltrami eigenproblems via subdivision linear subspace

2021 ◽  
Author(s):  
Chenkai Xu ◽  
Hongwei Lin ◽  
Hui Hu ◽  
Yaqi He
Keyword(s):  
Linear Subspace ◽  
Fast Calculation

scholarly journals Tensors with eigenvectors in a given subspace

2021 ◽  
Author(s):  
Giorgio Ottaviani ◽  
Zahra Shahidi
Keyword(s):  
Algebraic Geometry ◽  
Linear Subspace ◽  
Chern Classes ◽  
Symmetric Tensors

AbstractThe first author with B. Sturmfels studied in [16] the variety of matrices with eigenvectors in a given linear subspace, called the Kalman variety. We extend that study from matrices to symmetric tensors, proving in the tensor setting the irreducibility of the Kalman variety and computing its codimension and degree. Furthermore, we consider the Kalman variety of tensors having singular t-tuples with the first component in a given linear subspace and we prove analogous results, which are new even in the case of matrices. Main techniques come from Algebraic Geometry, using Chern classes for enumerative computations.

scholarly journals A Novel High Performance Discrete Flux Integrator for Control Algorithms of Fast Rotating AC Machines

2021 ◽  
Vol 11 (5) ◽  
pp. 2150
Author(s):  
Claudio Rossi ◽  
Alessio Pilati ◽  
Marco Bertoldi
Keyword(s):  
High Performance ◽  
Permanent Magnets ◽  
Machine Model ◽  
Ac Machines ◽  
Fast Calculation ◽  
Calculation Time ◽  
Digital Implementation ◽  
Rotating Speed ◽  
Interior Permanent Magnets ◽  
Accuracy Performance

This paper deals with the digital implementation of a motor control algorithm based on a unified machine model, thus usable with every traditional electric machine type (induction, brushless with interior permanent magnets, surface permanent magnets or pure reluctance). Starting from the machine equations in matrix form in continuous time, the paper exposes their discrete time transformation, suitable for digital implementation. Since the solution of these equations requires integration, the virtual division of the calculation time in sub-intervals is proposed to make the calculations more accurate. Optimization of this solver enables faster runs and higher precision especially when high rotating speed requires fast calculation time. The proposed solver is presented at different implementation levels, and its speed and accuracy performance are compared with standard solvers.

To the fast calculation of the solvation free energy. Combining expanded ensembles with L2MC

2021 ◽  
Vol 42 (11) ◽  
pp. 787-792
Author(s):  
Alexei Nikitin ◽  
Vladislava Milchevskaya ◽  
Alexander Lyubartsev
Keyword(s):  
Free Energy ◽  
Solvation Free Energy ◽  
Fast Calculation

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

Fast calculation of digitally reconstructed radiographs using light fields

2003 ◽  
Author(s):  
Daniel B. Russakoff ◽  
Torsten Rohlfing ◽  
Daniel Rueckert ◽  
Ramin Shahidi ◽  
Daniel Kim ◽  
...  
Keyword(s):  
Light Fields ◽  
Fast Calculation ◽  
Digitally Reconstructed Radiographs

On projected thick sections of stationary point processes and Boolean models

1996 ◽  
Vol 28 (2) ◽  
pp. 335-335
Author(s):  
Markus Kiderlen
Keyword(s):  
Point Process ◽  
Stationary Point ◽  
Point Processes ◽  
Linear Subspace ◽  
Isotropic Case ◽  
Thick Section ◽  
Boolean Models ◽  
Dimensional Linear Subspace ◽  
Stationary Point Process ◽  
Stationary Point Processes

For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

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