Comparing a Matrix to its Off-Diagonal Part

1989 ◽  
pp. 151-164 ◽  
Author(s):  
Rajendra Bhatia ◽  
Man-Duen Choi ◽  
Chandler Davis
Keyword(s):  
Diagonal Part

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

scholarly journals An Image Denoising Method with Enhancement of the Directional Features Based on Wavelet and SVD Transforms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Min Wang ◽  
Zhen Li ◽  
Xiangjun Duan ◽  
Wei Li
Keyword(s):  
Wavelet Transform ◽  
Singular Value Decomposition ◽  
Image Denoising ◽  
High Frequency ◽  
Low Frequency ◽  
Singular Value ◽  
Denoising Method ◽  
Diagonal Part ◽  
Value Decomposition ◽  
Image Part

This paper proposes an image denoising method, using the wavelet transform and the singular value decomposition (SVD), with the enhancement of the directional features. First, use the single-level discrete 2D wavelet transform to decompose the noised image into the low-frequency image part and the high-frequency parts (the horizontal, vertical, and diagonal parts), with the edge extracted and retained to avoid edge loss. Then, use the SVD to filter the noise of the high-frequency parts with image rotations and the enhancement of the directional features: to filter the diagonal part, one needs first to rotate it 45 degrees and rotate it back after filtering. Finally, reconstruct the image from the low-frequency part and the filtered high-frequency parts by the inverse wavelet transform to get the final denoising image. Experiments show the effectiveness of this method, compared with relevant methods.

scholarly journals Modified Jacobi-Gradient Iterative Method for Generalized Sylvester Matrix Equation

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1831
Author(s):  
Nopparut Sasaki ◽  
Pattrawut Chansangiam
Keyword(s):  
Iterative Method ◽  
Matrix Equation ◽  
Recursive Formula ◽  
Sylvester Matrix Equation ◽  
Hierarchical Identification ◽  
Sylvester Matrix ◽  
Generalized Sylvester Matrix Equation ◽  
Iteration Matrix ◽  
Diagonal Part ◽  
Gradient Based

We propose a new iterative method for solving a generalized Sylvester matrix equation A1XA2+A3XA4=E with given square matrices A1,A2,A3,A4 and an unknown rectangular matrix X. The method aims to construct a sequence of approximated solutions converging to the exact solution, no matter the initial value is. We decompose the coefficient matrices to be the sum of its diagonal part and others. The recursive formula for the iteration is derived from the gradients of quadratic norm-error functions, together with the hierarchical identification principle. We find equivalent conditions on a convergent factor, relied on eigenvalues of the associated iteration matrix, so that the method is applicable as desired. The convergence rate and error estimation of the method are governed by the spectral norm of the related iteration matrix. Furthermore, we illustrate numerical examples of the proposed method to show its capability and efficacy, compared to recent gradient-based iterative methods.

Is the Gravitational Force Elementary?

1993 ◽  
Vol 48 (12) ◽  
pp. 1151-1165
Author(s):  
H. Stumpf ◽  
Th. Borne ◽  
H. J. Kaus
Keyword(s):  
Functional Equation ◽  
Gravitational Force ◽  
Effective Interaction ◽  
Canonical Quantization ◽  
Low Energy ◽  
Quantum Level ◽  
Energy Limit ◽  
Diagonal Part ◽  
Functional States ◽  
Villars Regularization

Abstract The gravitational force is assumed to be mediated by spin 2 gravitons which are composed of four spin 1/2 (sub-) fermions. The dynamics is governed by a nonlinear spinorfield equation with nonperturbative Pauli-Villars regularization and canonical quantization. On the quantum level the fermion dynamics is expressed by a functional equation for algebraic state functionals, and the "graviton" (functional) states are defined to be solutions of the diagonal part of this equation. The effective interaction between such graviton states and fermions is studied by means of a weak mapping between the original functional equation and an effective functional equation for gravitons and fermions. In the low energy limit this mapping produces for the effective fermion dynamics (apart from selfinteractions) a Dirac equation in anholonomic coordinates coupled to the anholonomic connections of a gravitational field, i.e. the usual phenomenological expression for a gravitational force acting on spin 1 /2 fermions.

scholarly journals Image Denoising Using Singular Value Difference in the Wavelet Domain

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Min Wang ◽  
Wei Yan ◽  
Shudao Zhou
Keyword(s):  
Wavelet Transform ◽  
Image Denoising ◽  
High Frequency ◽  
Low Frequency ◽  
Singular Values ◽  
Singular Value ◽  
Wavelet Domain ◽  
Noisy Image ◽  
Denoising Method ◽  
Diagonal Part

Singular value (SV) difference is the difference in the singular values between a noisy image and the original image; it varies regularly with noise intensity. This paper proposes an image denoising method using the singular value difference in the wavelet domain. First, the SV difference model is generated for different noise variances in the three directions of the wavelet transform and the noise variance of a new image is used to make the calculation by the diagonal part. Next, the single-level discrete 2-D wavelet transform is used to decompose each noisy image into its low-frequency and high-frequency parts. Then, singular value decomposition (SVD) is used to obtain the SVs of the three high-frequency parts. Finally, the three denoised high-frequency parts are reconstructed by SVD from the SV difference, and the final denoised image is obtained using the inverse wavelet transform. Experiments show the effectiveness of this method compared with relevant existing methods.

Structure of generic quantum Markov semigroup

2017 ◽  
Vol 20 (02) ◽  
pp. 1750012 ◽  
Author(s):  
R. Carbone ◽  
E. Sasso ◽  
V. Umanità
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
Fixed Points ◽  
Free Algebra ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Diagonal Part ◽  
Invariant States ◽  
Quantum Markov Semigroup

In this paper, we study some relevant properties of generic quantum Markov semigroups, in particular related to their asymptotic behavior. We can describe the structure of the set of fixed points and of the invariant states in terms of the Hamiltonian’s spectrum and of the communication classes of the classical Markov process associated with the diagonal part of the semigroup. Moreover we study the decoherence-free algebra and we complete the characterization of environmental decoherence for a generic quantum Markov semigroup.

New Method for Obliterative Treatment of an Anterior Wall Aneurysm in the Internal Carotid Artery: Encircling Silicone Sheet Clip Procedure—Technical Case Report

Neurosurgery ◽  
2001 ◽  
Vol 49 (2) ◽  
pp. 469-472 ◽  
Author(s):  
Yasutaka Kurokawa ◽  
Masahiko Wanibuchi ◽  
Masanori Ishiguro ◽  
Ken-ichi Inaba
Keyword(s):  
Carotid Artery ◽  
Internal Carotid Artery ◽  
Arterial Wall ◽  
Internal Carotid ◽  
Anterior Wall ◽  
Middle Part ◽  
Arterial Stenosis ◽  
Anterior Surface ◽  
Diagonal Part ◽  
Silicone Sheet

Abstract OBJECTIVE AND IMPORTANCE Aneurysms on the anterior surface of the internal carotid artery (ICA) have been shown to be somewhat different from ordinary berry aneurysms because they are rather small, grow rapidly in a short time, and easily lead to rupture, especially during surgery. The most difficult problem is that this type of aneurysm cannot be eliminated easily by an ordinary clipping procedure without causing apparent arterial stenosis or occlusion. CLINICAL PRESENTATION A 52-year-old man experienced a subarachnoid hemorrhage because of a ruptured aneurysm located on the anterior surface of the ICA. The tiny aneurysmal body, which was covered with a layer of brain tissue, was successfully exposed. The ICA seemed to be atherosclerotic, and the aneurysmal portion was solitary and had a reddish color. TECHNIQUE A large silicone sheet encircling clip (Vascwrap; Mizuho Ikakogyo Co., Ltd., Tokyo, Japan) was selected for this patient. The proximal margin of the silicone sheet was incised with a V-shaped cut, and the middle part of the sheet, which covered the diagonal part of the ICA, was trimmed to make it shorter. The blade of the fenestrated clip was applied to obliterate the aneurysm and was attached to the normal arterial wall together with this modified Vascwrap sheet to create a small space between the normal arterial wall and the surrounding Vascwrap sheet. Then tiny pieces of Teflon fiber (E.I. duPont de Nemours and Co., Wilmington, DE) was inserted from both margins, and the whole Vascwrap sheet was sealed with fibrin glue to ensure good adhesion. CONCLUSION This method seemed adequate in treating this difficult aneurysm without causing postoperative regrowth or occlusion of the patient's ICA.

An Alternative Lattice Boltzmann Model for Incompressible Flows and its Stabilization

2017 ◽  
Vol 21 (2) ◽  
pp. 443-465
Author(s):  
Liangqi Zhang ◽  
Zhong Zeng ◽  
Haiqiong Xie ◽  
Zhouhua Qiu ◽  
Liping Yao ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Present Model ◽  
Incompressible Flows ◽  
Hermite Polynomials ◽  
Collision Operator ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Equilibrium Distribution Function ◽  
Hydrodynamic Mode ◽  
Diagonal Part

AbstractIn this paper, an alternative lattice Boltzmann (LB)model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretizedwith the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

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