Microwave Imaging of 3-D Dielectric–Magnetic Penetrable Objects Based on Integral Equation Method

He, Yuan; Zhang, Li; Tong, Mei Song

doi:10.1109/tap.2023.3262299

Cited by 22 publications

(6 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the function a 1 +b 1 −ξ 1 D 2 q f is convex on [0, 1]. Thus, by using Theorem 3 and Definition 4, we have [2] q + 9 16 [3] q − 1 8 [4] q .…”

Section: New Mercer Quantum Midpoint-type Auxiliary Resultsmentioning

confidence: 96%

“…Then, by inequality (22), we have 27 64 − 27 32 [2] q + 9 16 [3] q − 1 8 [4] q − (1 + 3q) 3 64[2] 3 q ≤ q 3 4 [2] 5 q [3] q 1 2 6 + 3q − 6q 2 − 3q 3 2 + 10 + 11q + 2q 2 + q 3 2 16[2] 3 q [3] q…”

Section: Remarkmentioning

confidence: 99%

“…The definition of convex functions is as follows: Convex function analysis provides an excellent starting point for creating and improving numerical tools to address challenging mathematical problems. Its theory of optimization is one of its greatest advantages, playing a significant role in constructing applications in differential equations to facilitate boundary conditions [2,3]. Moreover, in approximation theory and data analysis, convex functions play a significant role in solving regression statistical models [4,5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen–Mercer Inequality

2023

View full text Add to dashboard Cite

The objective of this study is to identify novel quantum midpoint-type inequalities for twice q-differentiable functions by utilizing Mercer’s approach. We introduce a new auxiliary variant of the quantum Mercer midpoint-type identity related to twice q-differentiable functions. By applying the theory of convex functions to this identity, we introduce new bounds using well-known inequalities, such as H"older’s inequality and power-mean inequality. We provide explicit examples along with graphical demonstrations. The findings of this study explain previous studies on midpoint-type inequalities. Analytic inequalities of this type, as well as related strategies, have applications in various fields where symmetry plays an important role.

show abstract

“…Thus, the function a 1 +b 1 −ξ 1 D 2 q f is convex on [0, 1]. Thus, by using Theorem 3 and Definition 4, we have [2] q + 9 16 [3] q − 1 8 [4] q .…”

Section: New Mercer Quantum Midpoint-type Auxiliary Resultsmentioning

confidence: 96%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen–Mercer Inequality

2023

View full text Add to dashboard Cite

show abstract

“…Formally, dynamical systems concern the analysis, prediction, and understanding of the behavior of systems of differential equations or iterative mappings that describe the evolution of the state of a system [1]. A considerable amount of literature has been published [2][3][4] as robust tools, models, and algorithms to describe the recent research results in the directory of dynamical systems and [5] is an application of integral equation methods for solving microwave imaging of threedimensional (3D) dielectric-magnetic penetrable objects. As a special case of integral equations, Abel's integral equation occurs in many areas of physics and engineering [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A new Abel inversion algorithm by using legendre polynomials

Pang¹,

Shi

Liu

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

Abel’s integral equation is frequently used in many areas of physics to reconstruct the radial physical quantity distribution from its projection data. In this paper, a new effective and accurate Abel inversion algorithm based on shifted Legendre polynomials is proposed and analyzed. The proposed method is derivative-free and singularity-free. Both the input projection data and the unknown solutions of the Abel’s integral equation are approximately expressed as Legendre expansions. A Legendre operational matrix of integral is constructed and then reduced to a discrete algebraic sum, which makes it easy and fast to compute the coefficients matrix of approximate solutions for the inverse Abel transform. Finally, the accuracy and stability are proved and then illustrated by some numerical experiments widely used in plasma diagnostics.

show abstract

“…Some of authors 44 – 46 presented Eyring-Powell liquid via SS. He et al 47 presented microwave imaging of 3D dielectric-magnetic penetrable objects. Tamoor et al 48 exhibited the MHD Casson liquid motion induced by stretched cylinder.…”

Section: Introductionmentioning

confidence: 99%

Convective heat and mass transfer rate on 3D Williamson nanofluid flow via linear stretching sheet with thermal radiation and heat absorption

Jagadeesh

Reddy

Tarakaramu³

et al. 2023

Sci Rep

View full text Add to dashboard Cite

A mathematical analysis is communicated to the thermal radiation and heat absorption effects on 3D MHD Williamson nanoliquid (NFs) motion via stretching sheet. The convective heat and mass boundary conditions are taken in sheet when liquid is motion. As a novelty, the effects of thermal radiation, heat absorption and heat and mass convection are incorporated. The aim is to develop heat transfer. Williamson NFs are most important source of heat absorption, it having many significant applications in “energy generation, HT, aircraft, missiles, electronic cooling systems, gas turbines” etc. The suitable similarity transformations have been utilized for reduce basic governing P.D. E’s into coupled nonlinear system of O.D. E’s. Obtained O.D. Es are calculated by help of R–K–F (“Runge–Kutta–Fehlberg”)4th order procedure with shooting technique in MATLAB programming. We noticed that, the skin friction coefficient is more effective in Williamson liquid motion when compared with NFs motion with higher numerical values of stretching ratio parameter, Williamson liquid motion is high when compared to NFs motion for large values of magnetic field. We compared with present results into previous results for various conditions. Finally, in the present result is good invention of previous results.

show abstract

Microwave Imaging of 3-D Dielectric–Magnetic Penetrable Objects Based on Integral Equation Method

Cited by 22 publications

References 45 publications

New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen–Mercer Inequality

New Study on the Quantum Midpoint-Type Inequalities for Twice q-Differentiable Functions via the Jensen–Mercer Inequality

A new Abel inversion algorithm by using legendre polynomials

Convective heat and mass transfer rate on 3D Williamson nanofluid flow via linear stretching sheet with thermal radiation and heat absorption

Contact Info

Product

Resources

About