Jianfeng He^1,2, Haowei Ye¹, Jie Ning¹, Hui Zhou^1,2,*, Bo She^3,*

CMC-Computers, Materials & Continua, Vol.79, No.2, pp. 3355-3372, 2024, DOI:10.32604/cmc.2024.048706

Abstract In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our study introduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learning-based framework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques, which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency and overemphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective feature extraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Lie group domains to highlight fundamental motion patterns, coupled with employing competitive weighting for More >

Osman Zeki Okuyucu^*

CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 653-671, 2022, DOI:10.32604/cmes.2022.021081

Abstract In this study, we examine the possible relations between the Frenet planes of any given two curves in three dimensional Lie groups with left invariant metrics. We explain these possible relations in nine cases and then introduce the conditions that must be met to coincide with the planes of these curves in nine theorems. More >

Eman M. A. Hilal¹, E. M. Khalil^2,3,*, S. Abdel-Khalek^2,4

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1227-1236, 2021, DOI:10.32604/cmc.2020.012659

Abstract The effect of the field–field interaction on a cavity containing two qubit (TQ) interacting with a two mode of electromagnetic field as parametric amplifier type is investigated. After performing an appropriate transformation, the constants of motion are calculated. Using the Schrödinger differential equation a system of differential equations was obtained, and the general solution was obtained in the case of exact resonance. Some statistical quantities were calculated and discussed in detail to describe the features of this system. The collapses and revivals phenomena have been discussed in details. The Shannon information entropy has been applied… More >

Chein-Shan Liu ^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 73-94, 2007, DOI:10.3970/cmes.2007.017.073

Abstract The primary objectives of the present exposition focus on five different types of representations of the plastic equations obtained from an elastic-perfectly plastic model by employing different corotational stress rates. They are (a) an affine nonlinear system with a finite-dimensional Lie algebra, (b) a canonical linear system in the Minkowski space, (c) a non-canonical linear system in the Minkowski space, (d) the Lie-Poisson bracket formulation, and (e) a two-generator and two-bracket formulation. For the affine nonlinear system we prove that the Lie algebra of the vector fields is so(5,1), which has dimensions fifteen, and by the… More >

C.-S. Liu^1,2, C.-W. Chang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 277-294, 2004, DOI:10.3970/cmes.2004.006.277

Abstract This paper delivers several new types of representations of the convex plasticity equation and realizes them by numerical discretizations. In terms of the Gaussian unit vector and the Weingarten map techniques in differential geometry, we prove that the plastic equation exhibits a Lie group symmetry. We convert the nonlinear constitutive equations to a quasilinear equations system X = AX, X ∈ Mⁿ⁺¹, A ∈ so(n,1) in local. In this way the inherent symmetry of the constitutive model of convex plasticity is brought out. The underlying structure is found to be a cone in the Minkowski space Mⁿ⁺¹ More >