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Mathematical modelling of the in-host dynamics of malaria and the effects of treatment
Mathematical modelling of the in-host dynamics of malaria and the effects of treatment
en
en
Malaria research and mathematical models have mainly concentrated on malaria Plasmodium at the blood stage. This
has left many questions concerning models of parasite dynamics in the liver and within the mosquito. These concerns are
anticipated to keep scientists busy trying to understand the biology of the parasite for some more years to come. Thorough
knowledge of parasite biology helps in designing appropriate drugs targeting particular stages of Plasmodium. To achieve
this, there is need to study the transmission dynamics of malaria and the interaction between the infection in the liver, blood
and mosquito using a mathematical model. In this study, a within-host mathematical model is proposed and considers the
dynamics of P. falciparum malaria from the liver to the blood in the human host and then to the mosquito. Several techniques,
including center manifold theory and sensitivity analysis are used to understand relevant features of the model dynamics like
basic reproduction number, local and global stability of the disease-free equilibrium and conditions for existence of the endemic
equilibrium. Results indicate that the infection rate of merozoites, the rate of sexual reproduction in gametocytes, burst size of
both hepatocytes and erythrocytes are more sensitive parameters for the onset of the disease. However, a treatment strategy
using highly effective drugs against such parameters can reduce on malaria progression and control the disease. Numerical
simulations show that drugs with an efficacy above 90% boost healthy cells, reduce infected cells and clear parasites in human
host. Therefore more needs to be done such as research in parasite biology and using highly effective drugs for treatment of
malaria.
1
21
Zadoki
Tabo
Livingstone S.
Luboobi
Joseph
Ssebuliba
Malaria
malaria Plasmodium
sexual and asexual stages
stability and sensitivity analysis
treatment.
Article.1.pdf
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Two improved classes of Broyden's methods for solving nonlinear systems of equations
Two improved classes of Broyden's methods for solving nonlinear systems of equations
en
en
In this paper, we propose two efficient algorithms based on Broyden’s methods by using the central finite difference and
modification of Newton’s method for solving systems of nonlinear equations. The most significant features of these algorithms
are their simplicity and excellent accuracy. Some numerical examples are given to test the validity of the proposed algorithms
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improvements in Broyden’s methods.
22
31
Mohammad H.
Al-Towaiq
Yousef S. Abu
hour
Nonlinear systems of equations
Newton’s method
Broyden’s methods
quasi Newton method
finite difference
secant equation.
Article.2.pdf
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Y. Abu-Hour, Improved Classes of Broyden methods for solving a nonlinear systems of equations, MSc. thesis, Department of Mathematics and Statistics, Jordan University of Science and Technology, Jordan (2016)
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en
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32
40
Hossein
Piri
Samira
Rahrovi
Hamidreza
Marasi
Poom
Kumam
Fixed point
asymmetric metric spaces
F-contraction.
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Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments
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en
en
The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation \begin{equation*}
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\end{equation*}
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41
52
M. Tamer
Senel
Nadide
Utku
Oscillation
third order quasilinear neutral dynamic equation with distributed deviating arguments
time scales.
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]
Numerical study of time-fractional hyperbolic partial differential equations
Numerical study of time-fractional hyperbolic partial differential equations
en
en
In this study, a numerical scheme is developed for the solution of time-fractional hyperbolic partial differential equation.
In the proposed scheme, cubic B-spline collocation is used for space discretization and time discretization is obtained by using
central difference formula. Caputo fractional derivative is used for time-fractional derivative. The stability and convergence
of the developed scheme, have also been proved. The numerical examples support the theoretical results.
53
65
Saima
Arshed
Time-fractional hyperbolic equation
cubic B-spline
collocation method
convergence analysis
stability analysis.
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]
Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems
Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems
en
en
In this paper, Bernstein polynomial method applied to the solutions of generalized Emden-Fowler equations as singular
initial value problems is presented. Firstly, the singular differential equations are converted to Volterra integro-differential
equations and then solved by the Bernstein polynomials method. The properties of Bernstein polynomials via Gauss-Legendre
rule are used to reduce the integral equations to a system of algebraic equations which can be solved numerically. Some
illustrative examples are discussed to demonstrate the validity and applicability of the present method.
66
75
Abdelkrim
Bencheikh
Lakhdar
Chiter
Hocine
Abbassi
Bernstein polynomials
Volterra integro-differential equations
Emden-Fowler equation
Gaussian integrations.
Article.6.pdf
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]
Generalization of Khan fixed point theorem
Generalization of Khan fixed point theorem
en
en
In this paper, we study some results of existence and uniqueness of fixed points for a class of mappings satisfying an
inequality of rational expressions. Our main result extends and unifies the well-known results of Khan [M. S. Khan, Rend. Inst.
Math. Univ. Trieste, 8 (1976), 69–72].
76
83
Hossein
Piri
Samira
Rahrovi
Poom
Kumam
Fixed point
metric space
Khan theorem.
Article.7.pdf
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[1]
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##[2]
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##[3]
N. Redjel, A. Dehici, E. Karapinar, I. M. Erhan, Fixed point theorems for (\(alpha, psi\))-Meir-Keeler-Khan mappings, J. Nonlinear Sci. Appl., 8 (2015), 955-964
##[4]
B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683-2693
]
Thermal boundary layer analysis of nanofluid flow past over a stretching flat plate in different transpiration conditions by using DTM-Pade method
Thermal boundary layer analysis of nanofluid flow past over a stretching flat plate in different transpiration conditions by using DTM-Pade method
en
en
In this paper, Differential Transformation Method (DTM) is applied on governing equations of heat and fluid flow for
a nanofluid over a horizontal flat plate. After obtaining the governing equations and solving them by DTM, the accuracy of
results is examined by fourth order Runge-kutta numerical method. Due to infinite boundary condition for the stretching plate,
outcomes need to an improvement method to be converged. For this aim, Padé approximation is applied on the obtained results
which [10,10] Padé order had the best accuracy compared to numerical method. The influence of relevant parameters such
as the transpiration parameter on temperature and nanoparticle concentration profile is discussed and it is concluded that by
increasing this parameter, nanoparticles concentration over the plate decrease due to more fluid penetration from pores and this
is the main reason of lower thermal boundary layer caused by fewer nanoparticles over the plate.
84
95
M. A.
Yousif
M.
Hatami
B. A.
Mahmood
M. M.
Rashidi
Nanofluid
DTM-Pad´e
boundary layer
Lewis number
heat transfer.
Article.8.pdf
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]
Numerical methods for piecewise constant Robin coefficient
Numerical methods for piecewise constant Robin coefficient
en
en
In this paper, we consider a numerical method for reconstructing piecewise constant Robin coefficients from boundary
measurements. An adaptive total variation functional is proposed. The boundary integral equation method is utilized for
discretizing the functional, and the Gauss-Newton method is employed for solving the non-linear problem.
96
105
Yanbo
Ma
Inverse problem
ill-posedness
boundary integral equations
total variation
Robin coefficient
Article.9.pdf
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S. Chaabane, C. Elhechmi, M. Jaoua, A stable recovery method for the Robin inverse problem, Math. Comput. Simulation, 66 (2004), 367-383
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S. Chaabane, I. Feki, N. Mars, Numerical reconstruction of a piecewise constant Robin parameter in the two- or threedimensional case, Inverse Problems, 28 (2012), 1-19
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S. Chaabane, M. Jaoua, Identification of Robin coefficients by the means of boundary measurements, Inverse Problems, 15 (1999), 1425-1438
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S. Chaabane, M. Jaoua, J. Leblond, Parameter identification for Laplace equation and approximation in Hardy classes, J. Inverse Ill-Posed Probl., 11 (2003), 33-57
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W.-F. Fang, F. Cumberbatch, Inverse problems for metal oxide semiconductor field-effect transistor contact resistivity, SIAM J. Appl. Math., 52 (1992), 699-709
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W.-F. Fang, M.-Y. Lu, A fast collocation method for an inverse boundary value problem, Internat. J. Numer. Methods Engrg., 59 (2004), 1563-1585
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W.-F. Fang, S.-X. Zeng, A direct solution of the Robin inverse problem, J. Integral Equations Appl., 21 (2009), 545-557
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W.-F. Fang, S.-X. Zeng, Numerical recovery of Robin boundary from boundary measurements for the Laplace equation, J. Comput. Appl. Math., 224 (2009), 573-580
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D. Fasino, G. Inglese, An inverse Robin problem for Laplace’s equation: theoretical results and numerical methods, Conference on Inverse Problems, Control and Shape Optimization, Carthage, (1998), Inverse Problems, 15 (1999), 41-48
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]
New computational method for solving fractional Riccati equation
New computational method for solving fractional Riccati equation
en
en
In this work, we implement the residual power series (RPS) method for solving the time fractional nonlinear Riccati initial
value problem
\[
\begin{cases}
D^{\alpha}_t y(t)+a y(t)+b y^2(t)=c,\,\,\,\,\,0<\alpha \leq 1, \,0\leq t < R,\\
y(0)=d,
\end{cases}
\]
where \(a, b, c, d\) are constants and \(D^\alpha_t\)
is the Caputo fractional derivative. An analytical solution of \(y(t)\) is obtained as a convergent
fractional power series in \(t\). To demonstrate the dependability of the proposed method, three illustrative examples are offered and
the obtained results are compared with some existing results in the literature. Moreover, the results show that the approximate
solutions are continuously communicate, as \(\alpha \) increases, until the first derivative is reached.
106
114
Mohammed
Ali
Imad
Jaradat
Marwan
Alquran
Fractional Riccati
Caputo derivative
residual power series.
Article.10.pdf
[
[1]
O. Abu Arqub, Series solution of fuzzy differential equations under strongly generalized differentiability, J. Adv. Res. Appl. Math., 5 (2013), 31-52
##[2]
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]
Bifurcations of heteroclinic loops with nonresonant eigenvalues
Bifurcations of heteroclinic loops with nonresonant eigenvalues
en
en
In this paper, we use the way of local coordinates instead of the Floquet method to study the problems of homoclinic
and periodic orbits bifurcated from heteroclinic loop for high-dimensional system. Under some transversal conditions and the
non-twisted or twisted conditions, we discuss the existence, uniqueness, coexistence, and non-coexistence of 1-periodic orbit,
1-homoclinic orbit, and 1-heteroclinic orbit near the heteroclinic loop. We get some general conclusions only under the basic
hypotheses, and the other conclusions under the two hyperbolic ratios of the heteroclinic loop are greater than 1. Meanwhile,
the bifurcation surfaces and existence regions are given.
115
132
Zheng
Guo
Yinlai
Jin
Yuerang
Gao
Dandan
Xie
Heteroclinic loop
Poincar´e map
periodic orbit
bifurcation surface
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Motion analysis and fuzzy-PID control algorithm designing for the pitch angle of an underwater glider
Motion analysis and fuzzy-PID control algorithm designing for the pitch angle of an underwater glider
en
en
Underwater gliders are used for deep-water gliding to observe large areas with minimal energy consumption. The pitch
angle of the underwater glider is an important control parameter. This study involved designing a fuzzy-PID controller for the
pitch angle of an underwater glider based on hydrodynamics analysis. The formula of pitch angle is obtained and a system
identification method was used to identify the transfer function based on the time-domain equation and initial experimental data.
The fuzzy-PID control algorithm was used to design the controller. Lake and sea trials indicated that the minimum overshoot
reached 0% and the settling time was about 34s when the change of the angle was \(15^o\)
. The minimum steady-state error was
\(0.8^o\)
. These advantages could reduce the consumption of energy and improve the accuracy of gliding trajectory. Therefore, this
control algorithm should be applied to control the pitch of the gliders.
133
147
Yu-hai
Liu
Zhi-qiang
Su
Xin
Luan
Da-lei
Song
Lei
Han
Underwater glider
pitch angle
fuzzy-PID control
mathematical mode
Article.12.pdf
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]
Another class of warped product CR-submanifolds in Kenmotsu manifolds
Another class of warped product CR-submanifolds in Kenmotsu manifolds
en
en
Recently, Arslan et al. [K. Arslan, R. Ezentas, I. Mihai, C. Murathan, J. Korean Math. Soc., 42 (2005), 1101–1110] studied
contact CR-warped product submanifolds of the form \(M_\top \times_f M_\bot\) of a Kenmotsu manifold \(\widetilde{M}\), where \(M_\top\) and \(M_\bot\) are invariant
and anti-invariant submanifolds of \(\widetilde{M}\), respectively. In this paper, we study the warped product submanifolds by reversing these
two factors, i.e., the warped products of the form \(M_\bot \times_f M_\top\) which have not been considered in earlier studies. On the existence
of such warped products, a characterization is given. A sharp estimation for the squared norm of the second fundamental form
is obtained, and in the statement of inequality, the equality case is considered. Finally, we provide two examples of non-trivial
warped product submanifolds.
148
157
Siraj
Uddin
Azeb
Alghanemi
Monia Fouad
Naghi
Falleh Rijaullah
Al-Solamy
Warped products
contact CR-submanifolds
mixed totally geodesic
contact CR-warped products
Kenmotsu manifolds.
Article.13.pdf
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[1]
K. Arslan, R. Ezentas, I. Mihai, C. Murathan, Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42 (2005), 1101-1110
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M. Atçeken, Contact CR-warped product submanifolds in Kenmotsu space forms, Bull. Iranian Math. Soc., 39 (2013), 415-429
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]
Noise correction algorithm for nonlinear turbulent shear velocity time series based on energy spectrum of singular values
Noise correction algorithm for nonlinear turbulent shear velocity time series based on energy spectrum of singular values
en
en
Shear velocity time series are essential in characterizing ocean turbulent flows. The moored platform is mounted with two
orthogonal shear probes (PNS06) to measure shear data for calculating velocity spectra. However, the shear probes are inevitably
contaminated by instrument noise and the complex marine environments. In this paper, a method based on singular spectra
decomposition was proposed to attenuate vibration noise by neglecting the higher-order modes in time-series reconstruction.
First, this method constructed a Hankel matrix with shear velocity data, then decomposed and reconstructed the shear signals
based on the method of conducting inverse singular value decomposition transformation on the values and their corresponding
vectors to achieve the purpose of signal de-noising. The corrected spectra match well with the empirical Nasmyth spectrum and
dissipation rates calculated from the noise-reduced shear spectra have dropped nearly one order of magnitude. The experimental
results show that the proposed method provides an effective and straightforward approach for eliminating the noise signals in
shear velocity spectra in ocean dynamics.
158
168
Xiuyan
Liu
Xin
Luan
Dalei
Song
Turbulent flows
shear spectra
singular values decomposition
noise correction
dissipation rates.
Article.14.pdf
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I. Fer, M. B. Paskyabi, Autonomous ocean turbulence measurements using shear probes on a moored instrument, J. Atmos. Oceanic Technol., 31 (2014), 474-490
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]
Using differential transform method and Pade approximation for solving MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet
Using differential transform method and Pade approximation for solving MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet
en
en
The problem of MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet is investigated analytically.
Governing equations are reduced to a set of nonlinear ordinary differential equations using the similarity transformations, and
solved via an efficient and suitable mathematical technique, named the differential transform method (DTM), in the form of
convergent series, by applying Pad´e approximation. The results are compared with the results obtained by the shooting method
of MATHEMATICA and with the fourth-order Runge-Kutta-Fehlberg results. The results of DTM-Pad´e are closer to numerical
solutions than the results of DTM are. A comparison of our results with existing published results shows good agreement
between them. Suitability end effectiveness of our method are illustrated graphically for various parameters. Moreover, it is
also observed that the Casson fluid parameter, stretching parameter, Hartmann number and porosity parameter increase with
increment in the velocity profiles.
169
178
M. A.
Yousif
B. A.
Mahmood
M. M.
Rashidi
Casson model
three-dimensional flow
MHD flow
porous sheet
DTM- Pad´e.
Article.15.pdf
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[1]
T. Abbas, M. Ayub, M. M. Bhatti, M. M. Rashidi, M. E. S. Ali , Entropy generation on nanofluid flow through a horizontal riga plate, Entropy, 18 (2016), 1-223
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M. M. Al-Sawalha, M. S. M. Noorani, Application of the differential transformation method for the solution of the hyperchaotic Rössler system , Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 1509-1514
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M. Ayub, T. Abbas, M. M. Bhatti, Inspiration of slip effects on electromagnetohydrodynamics (EMHD) nanofluid flow through a horizontal Riga plate , Eur. Phys. J. Plus, 131 (2016), 1-9
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M. M. Bhatti, T. Abbas, M. M. Rashidi, A new numerical simulation of MHD stagnation-point flow over a permeable stretching/shrinking sheet in porous media with heat transfer, Iran. J. Sci. Technol. Trans. A Sci., (2016), 1-7
##[8]
M. M. Bhatti, T. Abbas, M. M. Rashidi, M. E. S. Ali, Numerical simulation of entropy generation with thermal radiation on MHD Carreau nanofluid towards a shrinking sheet , Entropy, 18 (2016), 1-200
##[9]
M. M. Bhatti, T. Abbas, M. M. Rashidi, M. E. S. Ali, Z. G. Yang, Entropy generation on MHD Eyring-Powell nanofluid through a permeable stretching surface, Entropy, 18 (2016), 1-224
##[10]
M. M. Bhatti, M. M. Rashidi, Entropy generation with nonlinear thermal radiation in MHD boundary layer flow over a permeable shrinking/stretching sheet: numerical solution , J. Nanofluids, 5 (2016), 543-548
##[11]
M. M. Bhatti, M. M. Rashidi, Numerical simulation of entropy generation on MHD nanofluid towards a stagnation point flow over a stretching surface, Int. J. Appl. Comput. Math., 2 (2016), 1-15
##[12]
M. M. Bhatti, A. Zeeshan, Heat and mass transfer analysis on peristaltic flow of particle-fluid suspension with slip effects, J. Mech. Med. Biol., 17 (2016), 1-16
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##[18]
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R. Ellahi, S. Aziz, A. Zeeshan, Non-Newtonian nanofluid flow through a porous medium between two coaxial cylinders with heat transfer and variable viscosity, J. Porous Media, 16 (2013), 205-216
##[20]
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]
The Chebyshev collocation solution of the time fractional coupled Burgers' equation
The Chebyshev collocation solution of the time fractional coupled Burgers' equation
en
en
This paper is concerned with the numerical solution of the time fractional coupled Burgers’ equation. The proposed hybrid
solution is based on Chebyshev collection method for space variable, and the trapezoidal quadrature technique. Finally the error
analysis is discussed and some test examples are presented to demonstrate the applicability and efficiency of the method.
179
193
Basim
Albuohimad
Hojatollah
Adibi
Fractional coupled Burgers’ equation
trapezoidal quadrature
finite difference
Chebyshev polynomials
spectral collection method.
Article.16.pdf
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