Matrix Transformations and Generalized Almost Convergence II

1978 ◽  
pp. 041-051
Author(s):  
MURSALEEN MURSALEEN
Keyword(s):  
Matrix Transformations ◽  
Almost Convergence

scholarly journals Almost convergence and some matrix transformations

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 261-266 ◽  
Author(s):  
Q Qamaruddin ◽  
S.A. Mohiuddine
Keyword(s):  
Matrix Transformations ◽  
Almost Convergence ◽  
Matrix Classes ◽  
The Matrix

In this paper we characterize the matrix classes (l(p, u),??) and (l(p, u), ?) which generalize the matrix classes given by Mursaleen [6]. .

scholarly journals ALMOST CONVERGENCE AND ALMOST SUMMABILITY

1990 ◽  
Vol 21 (4) ◽  
pp. 327-332
Author(s):  
EKREM SAVAS
Keyword(s):  
Matrix Transformations ◽  
Almost Convergence

The purpose of this paper is to introduce and discuss the spaces of almost summable sequences. Also some matrix transformations have been charac- terized.

scholarly journals Some matrix transformations and almost convergence

2013 ◽  
Vol 8 (2) ◽  
pp. 89-92 ◽  
Author(s):  
Neyaz Ahmad Sheikh ◽  
Ab. Hamid Ganie
Keyword(s):  
Sequence Space ◽  
Matrix Transformations ◽  
Almost Convergence ◽  
Infinite Matrices ◽  
Engineering And Technology ◽  
Bounded Sequences ◽  
Convergent Sequences

The sequence space bv(u,p) has been defined and the classes (bv(u,p):l?), (bv(u,p):c),and (bv(u,p):c0) of infinite matrices have been characterized by Ba?ar, Altay and Mursaleen ( see, [2] ). The main purposes of the present paper is to characterize the classes (bv(u,p):ƒ?),(bv(u, p):ƒ), and (bv(u,p):ƒ0), where ƒ?, ƒ, and ƒ0 denotes the spaces of almost bounded sequences, almost convergent sequences and almost convergent null sequences, respectively, with real or complex terms. Kathmandu University Journal of Science, Engineering and Technology Vol. 8, No. II, December, 2012, 89-92 DOI: http://dx.doi.org/10.3126/kuset.v8i2.7330

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.

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