scholarly journals Geometric invariance of determining and resonating centers: Odd- and any-number limitations of Pyragas control

2021 ◽  
Vol 31 (6) ◽  
pp. 063125
Author(s):  
B. de Wolff ◽  
I. Schneider
Keyword(s):  
Geometric Invariance

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

The theory of conditional invariance. I

1968 ◽  
Vol 305 (1482) ◽  
pp. 405-427 ◽  
Keyword(s):  
Bound States ◽  
General Relation ◽  
Variable Parameter ◽  
Geometric Invariance ◽  
Hermitian Conjugate ◽  
New Type ◽  
Definition Of ◽  
Conditional Invariance ◽  
Conditional Constant ◽  
The Continuum

In order to extend the use of group theoretical arguments to the problem of accidental degeneracy in quantum mechanics, a new type of constant of the motion, known as a conditional constant of the motion, is introduced. Such a quantity, instead of commuting with the Hamiltonian H for the system, satisfies the more general relation H A = A † H , where A † denotes the hermitian conjugate (adjoint) of the conditional constant of the motion A . This expression reduces, if A is hermitian, to the usual definition of a constant of the motion. Otherwise it defines a new type of invariance, and it is this which will be referred to as conditional invariance. A discussion of the difficulties arising from the lack of hermiticity of A , which is of course essential to its definition, is given. In particular it is shown, under fairly general conditions, that the process of introducing a variable parameter in the Hamiltonian enabling it to have simultaneous eigenfunctions with A , gives rise to an eigenvalue equation in this parameter with respect to which A may be chosen to be hermitian. Conditional invariance is contrasted with both dynamical and geometric invariance. It is found to be sometimes replaceable by either of the latter forms of invariance and for such, explicit conditions are given. Some applications of conditional invariance are discussed. These include a study of the crossing of potential energy curves, a new model of symmetry breaking, a possible means of calculating the exact number of bound states for certain potentials and conditions for the existence of bound states near to the continuum.

Geometric invariance

2002 ◽  
Vol 29 (2) ◽  
pp. 163-169 ◽  
Author(s):  
C. L. Bottasso ◽  
M. Borri ◽  
L. Trainelli
Keyword(s):  
Geometric Invariance

Geometric Invariance in Image Watermarking

2004 ◽  
Vol 13 (2) ◽  
pp. 145-153 ◽  
Author(s):  
M. Alghoniemy ◽  
A.H. Tewfik
Keyword(s):  
Image Watermarking ◽  
Geometric Invariance

Implementation of the PN-Approximation for Radiative Heat Transfer on OpenFOAM

2013 ◽  
Author(s):  
Ricardo Marquez ◽  
Michael Modest
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Variable Properties ◽  
3 Dimensional ◽  
Coupled Partial Differential Equations ◽  
Invariance Properties ◽  
Geometric Invariance ◽  
Benchmark Solutions

This work presents an OpenFOAM implementation of the PN approximation for radiative heat transfer, including higher orders P3, P5, and P7. Also described is a procedure which enables the sequential numerical computations of the coupled partial differential equations (PDEs) by re-expressing the boundary conditions in matrix form so that individual boundary conditions can be associated with each PDE. The implementation of the software programs are verified with derived analytical solutions for 1-D slabs with constant and variable properties, and are also tested with various orientations in order to demonstrate the geometric invariance properties of the 3-dimensional PN formulation. A few examples taken from the literature are also considered in this work and could be taken as benchmark solutions for the PN approximations.

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