Theorems of Tauberian type for matrix transformations of double series

1991 ◽  
Vol 43 (5) ◽  
pp. 662-667
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Matrix Transformations ◽  
Tauberian Type

Tauberian type theorems for double series summable by Cesaro methods

1972 ◽  
Vol 23 (6) ◽  
pp. 597-606 ◽  
Author(s):  
M. A. Kalatalova
Keyword(s):  
Double Series ◽  
Tauberian Type

The (C?)-property of abel summability of double series and theorems of tauberian type

1972 ◽  
Vol 24 (5) ◽  
pp. 465-475
Author(s):  
M. F. Burlyai
Keyword(s):  
Double Series ◽  
Abel Summability ◽  
Tauberian Type

Jacobians of Matrix Transformations and Functions of Matrix Argument

1999 ◽  
Vol 94 (446) ◽  
pp. 652
Author(s):  
Ingram Olkin ◽  
A. M. Mathai
Keyword(s):  
Matrix Transformations ◽  
Matrix Argument

scholarly journals The Reconstruction of Magnetic Particle Imaging: Current Approaches Based on the System Matrix

Diagnostics ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 773
Author(s):  
Xiaojun Chen ◽  
Zhenqi Jiang ◽  
Xiao Han ◽  
Xiaolin Wang ◽  
Xiaoying Tang
Keyword(s):  
Magnetic Particle ◽  
Clinical Medicine ◽  
Practical Importance ◽  
Superparamagnetic Iron Oxide ◽  
Matrix Transformations ◽  
System Matrix ◽  
Magnetic Particle Imaging ◽  
Reconstruction Methods ◽  
Spatial Coverage ◽  
Particle Imaging

Magnetic particle imaging (MPI) is a novel non-invasive molecular imaging technology that images the distribution of superparamagnetic iron oxide nanoparticles (SPIONs). It is not affected by imaging depth, with high sensitivity, high resolution, and no radiation. The MPI reconstruction with high precision and high quality is of enormous practical importance, and many studies have been conducted to improve the reconstruction accuracy and quality. MPI reconstruction based on the system matrix (SM) is an important part of MPI reconstruction. In this review, the principle of MPI, current construction methods of SM and the theory of SM-based MPI are discussed. For SM-based approaches, MPI reconstruction mainly has the following problems: the reconstruction problem is an inverse and ill-posed problem, the complex background signals seriously affect the reconstruction results, the field of view cannot cover the entire object, and the available 3D datasets are of relatively large volume. In this review, we compared and grouped different studies on the above issues, including SM-based MPI reconstruction based on the state-of-the-art Tikhonov regularization, SM-based MPI reconstruction based on the improved methods, SM-based MPI reconstruction methods to subtract the background signal, SM-based MPI reconstruction approaches to expand the spatial coverage, and matrix transformations to accelerate SM-based MPI reconstruction. In addition, the current phantoms and performance indicators used for SM-based reconstruction are listed. Finally, certain research suggestions for MPI reconstruction are proposed, expecting that this review will provide a certain reference for researchers in MPI reconstruction and will promote the future applications of MPI in clinical medicine.

scholarly journals Fabrication of a Three-dimensional Force Measurement System Using Double Series Magnetic Suspension

2016 ◽  
Vol 49 (21) ◽  
pp. 536-540 ◽  
Author(s):  
Takeshi Mizuno ◽  
Yuji Ishino ◽  
Masaya Takasaki
Keyword(s):  
Measurement System ◽  
Force Measurement ◽  
Three Dimensional ◽  
Double Series ◽  
Magnetic Suspension ◽  
Force Measurement System

SETS OF SEQUENCES THAT ARE STRONGLY r-BOUNDED AND MATRIX TRANSFORMATIONS BETWEEN THESE SETS

2003 ◽  
Vol 36 (1) ◽  
Author(s):  
Bruno de Malafosse
Keyword(s):  
Matrix Transformations

On Relationships Between Norlund Means for Double Series

1954 ◽  
Vol 5 (6) ◽  
pp. 957
Author(s):  
Charles N. Moore
Keyword(s):  
Double Series ◽  
Nörlund Means
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