scholarly journals The Dirac matrix group and Fierz transformations

1970 ◽  
Vol 17 (4) ◽  
pp. 322-342 ◽  
Author(s):  
E. de Vries ◽  
A. J. van Zanten
Keyword(s):  
Matrix Group ◽  
Dirac Matrix

scholarly journals Computing Matrix Group Decompositions with Respect to a Normal Subgroup

1996 ◽  
Vol 184 (3) ◽  
pp. 818-838 ◽  
Author(s):  
Derek F. Holt ◽  
C.R. Leedham-Green ◽  
E.A. O'Brien ◽  
Sarah Rees
Keyword(s):  
Normal Subgroup ◽  
Matrix Group

scholarly journals An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Zhongli Zhou ◽  
Guangxin Huang
Keyword(s):  
Iterative Algorithm ◽  
Matrix Group ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Matrix Solution ◽  
Initial Matrix ◽  
Special Cases ◽  
Reflexive Matrix ◽  
General Coupled Matrix Equations ◽  
Sylvester Matrix Equations

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflexive solution can be determined automatically by the iterative algorithm within finite iterative steps in the absence of round-off errors. The least Frobenius norm reflexive solution of the general coupled matrix equations can be derived when an appropriate initial matrix is chosen. Furthermore, the unique optimal approximation reflexive solution to a given matrix group in Frobenius norm can be derived by finding the least-norm reflexive solution of the corresponding general coupled matrix equations. A numerical example is given to illustrate the effectiveness of the proposed iterative algorithm.

scholarly journals Asthmatic Bronchial Matrices Determine the Gene Expression and Behavior of Smooth Muscle Cells in a 3D Culture Model

2021 ◽  
Vol 2 ◽  
Author(s):  
Selma Ben Hamouda ◽  
Maria Angélica Miglino ◽  
Gustavo de Sá Schiavo Matias ◽  
Guy Beauchamp ◽  
Jean-Pierre Lavoie
Keyword(s):  
Gene Expression ◽  
Smooth Muscle ◽  
Control Cell ◽  
3D Culture ◽  
Matrix Group ◽  
Cell Phenotype ◽  
Cell Control ◽  
Control Matrix ◽  
And Control

Asthma is associated with increased deposition and altered phenotype of airway smooth muscle (ASM) cells. However, little is known about the processes responsible for these changes. It has been suggested that alterations of the extracellular matrix (ECM) contribute to the remodeling of ASM cells in asthma. Three-dimensional matrices allow the in vitro study of complex cellular responses to different stimuli in a close-to-natural environment. Thus, we investigated the ultrastructural and genic variations of ASM cells cultured on acellular asthmatic and control bronchial matrices. We studied horses, as they spontaneously develop a human asthma-like condition (heaves) with similarities to chronic pulmonary changes observed in human asthma. Primary bronchial ASM cells from asthmatic (n = 3) and control (n = 3) horses were cultured on decellularized bronchi from control (n = 3) and asthmatic (n = 3) horses. Each cell lineage was used to recellularize six different bronchi for 41 days. Histomorphometry on HEPS-stained-recellularized matrices revealed an increased ASM cell number in the control cell/control matrix (p = 0.02) and asthmatic cell/control matrix group (p = 0.04) compared with the asthmatic cell/asthmatic matrix group. Scan electron microscopy revealed a cell invasion of the ECM. While ASM cells showed high adhesion and proliferation processes on the control ECM, the presence of senescent cells and cellular debris in the asthmatic ECM with control or asthmatic ASM cells suggested cell death. When comparing asthmatic with control cell/matrix combinations by targeted next generation sequencing, only AGC1 (p = 0.04), MYO10 (p = 0.009), JAM3 (p = 0.02), and TAGLN (p = 0.001) were differentially expressed out of a 70-gene pool previously associated with smooth muscle remodeling. To our knowledge, this is the first attempt to evaluate the effects of asthmatic ECM on an ASM cell phenotype using a biological bronchial matrix. Our results indicate that bronchial ECM health status contributes to ASM cell gene expression and, possibly, its survival.

New Routines for Algebraic Programming of the Dirac Equation

1997 ◽  
Vol 08 (02) ◽  
pp. 273-286 ◽  
Author(s):  
Ion I. Cotăescu ◽  
Dumitru N. Vulcanov
Keyword(s):  
Dirac Equation ◽  
Main Part ◽  
Space Time ◽  
Curved Space ◽  
Algebraic Programming ◽  
Matrix Algebras ◽  
Dirac Matrix ◽  
New Procedures

We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.

Matrix Group Actions Transforming Patterns

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Coordinate System ◽  
Spatial Patterns ◽  
Group Actions ◽  
Temporal Patterns ◽  
Matrix Group ◽  
Matrix Groups ◽  
Pattern Theory ◽  
Complex Patterns

Thus far Pattern theory has been combinatore constructing complex patterns by connecting simpler ones via graphs. Patterns typically occurring in nature may be extremely complex and exhibit invariances. For example, spatial patterns may live in a space where the choice of coordinate system is irrelevant; temporal patterns may exist independently of where time is counted from, and so on. For this matrix groups as transformations are introduced, these transformations often forming groups which act on the generators.

scholarly journals The Weighted Fractional Fourier Transform and Its Application in Image Encryption

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Tieyu Zhao ◽  
Qiwen Ran
Keyword(s):  
Fourier Transform ◽  
Theoretical Analysis ◽  
Image Encryption ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Rapid Development ◽  
Matrix Group ◽  
Future Developments ◽  
Security And Reliability ◽  
Fractional Fourier Transforms

With the rapid development of information, the requirements for the security and reliability of cryptosystems have become increasingly difficult to meet, which promotes the development of the theory of a class of fractional Fourier transforms. In this paper, we present a review of the development and applications of the weighted fractional Fourier transform (WFRFT) in image encryption. Relationships between the algorithms are established using the generalized permutation matrix group in theoretical analysis. In addition, the advantages and potential weaknesses of each algorithm in image encryption are analyzed and discussed. It is expected that this review will provide a clear picture of the current developments of the WFRFT in image encryption and may shed some light on future developments.

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