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Optimal Sequential Third Order Rotatable Designs in Three, Four and Five Dimensions
Nyakundi Omwando Cornelious,
Evans Mbuthi Kilonzo
Issue:
Volume 6, Issue 2, June 2021
Pages:
35-39
Received:
6 April 2021
Accepted:
19 April 2021
Published:
29 April 2021
Abstract: Response surface methodology (RSM) is a statistical technique used to evaluate the relationship between multiple input variables and one or more response variables with the aim of optimizing the response variables. Sequential experiments are very economical and useful in practice. Therefore, rotatable designs such as the third order rotatable design (TORD) may be run sequentially in three stages with three or four blocks depending on the model adequacy. Normally, the first section consisting of first order is run and the response function is approximated using a first order model. If the first order model is found to be adequate, as the representation of the unknown function by noting the evidence of the goodness of fit, the experiment may be stopped at this stage. However, if the first model is found to be unfit, the trials of the second order are run and ultimately, proceed to fit a third order if a second order model is also found to be inadequate. In this paper, two sets of second order rotatable designs are combined to form sequential third order rotatable designs (TORD) in three, four and five dimensions. The TORDs are then evaluated on their alphabetic optimality criteria with the aim of reducing the costs of experimentation. The classical optimality criteria includes; D-criterion, A-criterion, T-criterion and E- criterion.
Abstract: Response surface methodology (RSM) is a statistical technique used to evaluate the relationship between multiple input variables and one or more response variables with the aim of optimizing the response variables. Sequential experiments are very economical and useful in practice. Therefore, rotatable designs such as the third order rotatable desig...
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Global Existence of a Virus Infection Model with Saturated Chemotaxis
Issue:
Volume 6, Issue 2, June 2021
Pages:
40-54
Received:
26 April 2021
Accepted:
11 May 2021
Published:
27 May 2021
Abstract: In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus particles, respectively. By virtue of regularized approximation technique and fixed point theorem, the local solvability of the regularized system corresponding to the original system is established. Then by extracting a suitable sequence along which the respective approximate solutions approach a limit in convenient topologies, with addition of Gagliardo-Nirenberg interpolation inequality as well as Lp-estimate techniques, we show that the original system describing the virus infection model exists at least one global weak solution. To illustrate the application of our theoretical results, an optimal control problem of the epidemic system is considered, where the admissible control domain is assumed to be a bounded closed convex subset. With the help of Aubin compactness theorem and lower semicontinuous of the cost functional, the existence of the optimal pair is proved. Our results generalize and improve partial previously known ones, and moreover, we first prove that the optimal control problem has at least one optimal pair.
Abstract: In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus parti...
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Electrostatic and Dynamic Analysis of P+PNP Double Junction Type and P+PNPN Triple Junction Type Pinned Photodiodes
Issue:
Volume 6, Issue 2, June 2021
Pages:
55-76
Received:
28 May 2021
Accepted:
10 June 2021
Published:
16 June 2021
Abstract: This paper explains the device structure and operation of image sensors and solar cells. Both are semiconductor devices operating with the same physical principle of detecting photons. A high efficiency of the photon to electron energy conversion is very much desired in both devices. Image sensors now use a very advanced and scaled down CMOS fabrication process technology to achieve high performance features such as the excellent short wave blue light sensitivity for good color reproduction, the low noise and the no image lag picture quality for filmless and mechanical free action cameras. On the other hand, solar cells are still now built with the primitive floating N+P single junction type photodiode to minimize the fabrication process cost but with very low energy conversion efficiency of about 20%. It is explained in details that the depletion region of the PN junction is not the only place where we can achieve photo electron and hole pair separations effectively. The short-wave blue light has only 1000 Å silicon crystal penetration depth. The pinned surface P+P Gaussian doping profile has a very important role to achieve a better photon to energy conversion efficiency, especially for the short-wave blue light. Electrostatic and dynamic behaviors of Pinned Surface P+PNP Double Junction type Dynamic Photo Transistor and Pinned Surface P+PNPN Triple Junction type Dynamic Photo Thyristor are analyzed in details. Both of them are shown to be expected to have much excellent photon-to-electron energy conversion efficiency.
Abstract: This paper explains the device structure and operation of image sensors and solar cells. Both are semiconductor devices operating with the same physical principle of detecting photons. A high efficiency of the photon to electron energy conversion is very much desired in both devices. Image sensors now use a very advanced and scaled down CMOS fabric...
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