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Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth
Issue:
Volume 7, Issue 4, August 2019
Pages:
90-97
Received:
14 July 2019
Accepted:
27 August 2019
Published:
9 September 2019
Abstract: In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.
Abstract: In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting e...
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Differential Incremental Equilibrium Geometry - Spatial Folding of Protein Particles, Genome Expression and Bidirectional Semiconservative Replication of Ring Chromosomes
Issue:
Volume 7, Issue 4, August 2019
Pages:
98-113
Received:
13 July 2019
Accepted:
31 July 2019
Published:
12 September 2019
Abstract: The research direction of this paper is to study the interdisciplinary subjects of life science, mathematics and computer science at the molecular level from the life science Molecular Cell Biology. On the basis of mathematical primitive innovation "Differential Incremental Balanced Geometry", the cell modification of normal chromosome mitosis was established at the molecular level, and the normal cell tissue spatial morphology with initial boundary was established. DNA is used to unravel double helix and separate double strands to solve the protein skeleton structure of bi-directional Semi-Reserved replication of cyclic chromosomes in life sciences at the molecular level. Therefore, it establishes and reveals the duplication fork and bidirectional duplication of molecular cell biology model, the internal structure and regularity of cyclic chromosomes bound by cyclic DNA double helix and many proteins. New mathematics is integrated into the micro-activities of cell modification in life sciences. The topological geometric image of the solitary wavelet with supersymmetric structure is constructed, which reflects the correct abstract model of cell modification and provides dynamic structure for DNA gene sequencing, etc. It also provides a mature mathematical basis for reliable predictability of gene editing.
Abstract: The research direction of this paper is to study the interdisciplinary subjects of life science, mathematics and computer science at the molecular level from the life science Molecular Cell Biology. On the basis of mathematical primitive innovation "Differential Incremental Balanced Geometry", the cell modification of normal chromosome mitosis was ...
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Existence and Uniqueness of Entropy Solution for an Elliptic Problem with Nonlinear Boundary Conditions and Measure-data
Issue:
Volume 7, Issue 4, August 2019
Pages:
114-126
Received:
15 July 2019
Accepted:
29 August 2019
Published:
16 September 2019
Abstract: In this paper, we study a class of elliptic equations on a bounded domain with nonlinear boundary conditions of type graph and measure - data. First of all, give some spaces and basic assumptions. Next, we apply the classical variational approach. So, we need an essentially bounded estimate on the solution, which is not evident to obtain directly in our problem. The obstacles which we encounter is that we cannot get rid of the non-linear term evaluated as a zero gradient and it appear at the boundary, for the part of the measure-data, a term which cannot vanish, when one uses the integration by parts formula. To overcome this difficulties, we first redefine and extend the function which appears in the third Leray-Lions-type conditions and we add a penalization term on the boundary. Secondly, we consider a smooth domain in order to work with the Sobolev spaces that are the closure of indefinitely differentiable and null functions on the bounary, and to going back later to the classical Sobolev space. Then, we assume that the domain is extensible. Next, we obtain a priori estimates and convergence results in the approach problem, which allow us to delete the penalization term. To finish, we introduce a notion of entropy solution for our main problem and prove that it is the limit of the solution obtained in the variational case.
Abstract: In this paper, we study a class of elliptic equations on a bounded domain with nonlinear boundary conditions of type graph and measure - data. First of all, give some spaces and basic assumptions. Next, we apply the classical variational approach. So, we need an essentially bounded estimate on the solution, which is not evident to obtain directly i...
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Modeling and Analysis of Population Dynamics of Human Cells Pertaining to HIV/AIDS with Treatment
Kumama Regassa,
Purnachandra Rao Koya
Issue:
Volume 7, Issue 4, August 2019
Pages:
127-136
Received:
28 June 2019
Accepted:
3 August 2019
Published:
20 September 2019
Abstract: In this paper, a mathematical model has been formulated to describe the population dynamics of human cells pertaining to the HIV/AIDS disease with ART as treatment and is analyzed. The human cells have been divided into four compartments Susceptible – Asymptomatic – Symptomatic – AIDS (SAIV). The well posedness of the four dimensional dynamical system is proved and the steady states of the model are identified. Additionally, parametric expression for the basic reproduction number is constructed following next generation matrix method and analyzed its stability using Routh Hurwitz criterion. From the analytical and numerical simulation studies it is observed that if the basic reproduction is less than one unit then the solution converges to the disease free steady state i.e., disease will wipe out and thus the treatment is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the treatment is said to be unsuccessful. Sensitivity analysis of the model parameters is conducted and their impact on the reproduction number is analyzed. Finally, the model of the present study simulated using MATLAB. The results and observations have been included in the text of this paper lucidly.
Abstract: In this paper, a mathematical model has been formulated to describe the population dynamics of human cells pertaining to the HIV/AIDS disease with ART as treatment and is analyzed. The human cells have been divided into four compartments Susceptible – Asymptomatic – Symptomatic – AIDS (SAIV). The well posedness of the four dimensional dynamical sys...
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