]>
2018
18
3
132
Turing instability in two-patch predator-prey population dynamics
Turing instability in two-patch predator-prey population dynamics
en
en
In this paper, a spatio-temporal model as systems of ODE which describe
two-species Beddington-DeAngelis type predator-prey system living in
a habitat of two identical patches linked by migration is
investigated. It is assumed in the model that the per capita
migration rate of each species is influenced not only by its own but
also by the other one's density, i.e., there is cross diffusion
present. We show that a standard (self-diffusion) system may be
either stable or unstable, a cross-diffusion response can stabilize
an unstable standard system and destabilize a stable standard
system. For the diffusively stable model, numerical studies show
that at a critical value of the bifurcation parameter the system
undergoes a Turing bifurcation and the cross migration response is
an important factor that should not be ignored when pattern emerges.
255
261
Ali
Al-Qahtani
Ali
Al-Qahtani
King Khalid University
King Khalid University
Saudi Arabia
Aesha
Almoeed
Aesha
Almoeed
King Khalid University
King Khalid University
Saudi Arabia
Bayan
Najmi
Bayan
Najmi
King Khalid University
King Khalid University
Saudi Arabia
Shaban
Aly
Shaban
Aly
King Khalid University
Azhar University
King Khalid University
Azhar University
Saudi Arabia
Egypt
Self-diffusion
cross-diffusion
diffusive instability
pattern formation
turing-instability-in-two-patch-predator-prey-population-dynamics.pdf
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[1]
U. Dieckmann, R. Law, J. A. Metz, The Geometry of Ecological Interaction: Simplifying Spatial Complexity, Cambridge University Press, Cambridge (2005)
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M. Farkas, Two ways of modeling cross diffusion, Nonlinear Anal., 30 (1997), 1225-1233
##[3]
M. Farkas, Dynamical Models in Biology, Academic Press, San Diego (2001)
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Y. Huang, O. Diekmann, Interspecific influence on mobility and Turing instability, Bull. Math. Biol., 65 (2003), 143-156
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J. D. Murray , Mathematical Biology, Springer-Verlag, Berlin (1989)
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Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra system, World Scientific Publishing Co., Singapore (1996)
##[7]
A. M. Turing, The chemical basis of morphogenesis, Philos. Trans. Roy. Soc. London Ser. B, 237 (1952), 37-72
]
\(F_{m}\)-contractive and \(F_{m}\)-expanding mappings in \(M\)-metric spaces
\(F_{m}\)-contractive and \(F_{m}\)-expanding mappings in \(M\)-metric spaces
en
en
Inspired by the work of Górnicki in his recent article [J. Górnicki, Fixed Point Theory Appl., \({\bf 2017}\) (2017), 10 pages], where he introduced a new class of self mappings
called \(F\)-expanding mappings, in this paper we introduce the concept of \(F_{m}\)-contractive and
\(F_{m}\)-expanding mappings in \(M\)-metric spaces. Also, we prove the existence and uniqueness of fixed point for such mappings.
262
271
Nabil
Mlaiki
Nabil
Mlaiki
Prince Sultan University
Prince Sultan University
Saudi Arabia
\(M\)-metric spaces
\(F_{m}\)-contractive
\(F_{m}\)-expanding mappings
f-m-contractive-and-f-m-expanding-mappings-in-m-metric-spaces.pdf
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[1]
K. Abodayeh, N. Mlaiki, T. Abdeljawad, W. Shatanawi , Relations between partial metric spaces and M-metric spaces, Caristi Kirk’s Theorem in M-metric type spaces , J. Math. Anal., 7 (2016), 1-12
##[2]
M. Asadi, E. Karapınar, P. Salimi , New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014 ), 1-9
##[3]
J. Górnicki , Fixed points theorems for F-expanding mappings , Fixed Point Theory Appl., 2017 (2017), 1-10
##[4]
R. H. Haghi, S. Rezapour, N. Shahzad , Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450-454
##[5]
S. G. Matthews, Partial metric topology, Ann. New York Acad. Sci., 728 (1994), 183-197
##[6]
N. Mlaiki, N. Souayah, K. Abodayeh, T. Abdeljawad , Contraction principles in Ms-metric spaces , J. Nonlinear Sci. Appl., 10 (2017), 575-582
##[7]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012 ), 1-6
]
Explicit solution for some generalized fluids in laminar flow with slip boundary conditions
Explicit solution for some generalized fluids in laminar flow with slip boundary conditions
en
en
In this study, we present a new approximation method to give an explicit solution of a laminar flow using a Sisko
model. This is a problem of a generalized Newtonian fluid with slip boundary conditions. The proposed method
is based on the variational iteration method (VIM) combined with an approximation step. This method is validated
where the exact solution is available. In addition, in order to enrich the discussion, a numerical method is
presented. The results illustrate that the VIM may be more effective that the finite difference method for a dilatant
fluid. However, the VIM will be inappropriate for pseudoplastic fluid cases.
272
281
Mourad
Chamekh
Mourad
Chamekh
University of Jeddah
University of Tunis El Manar
University of Jeddah
University of Tunis El Manar
KSA
Tunisia
Tarig. M.
Elzaki
Tarig. M.
Elzaki
University of Jeddah
University of Jeddah
KSA
Sisko model
variational iteration method
dilatant fluid
pseudoplastic fluid
explicit-solution-for-some-generalized-fluids-in-laminar-flow-with-slip-boundary-conditions.pdf
[
[1]
N. Ali, A. Zaman, M. Sajid, Unsteady blood flow through a tapered stenotic artery using Sisko model, Comput. & Fluids, 101 (2014), 42-49
##[2]
M. M. Bhatti, T. Abbas, M. M. Rashidi, Numerical Study of Entropy Generation with Nonlinear Thermal Radiation on Magnetohydrodynamics non-Newtonian Nanofluid Through a Porous Shrinking Sheet, J. Magnet., 21 (2016), 468-475
##[3]
M. M. Bhatti, R. Ellahi, A. Zeeshan, Study of variable magnetic field on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls, J. Mol. Liq., 222 (2016), 101-108
##[4]
M. M. Bhatti, A. Zeeshan, Analytic study of heat transfer with variable viscosity on solid particle motion in dusty Jeffery fluid, Modern Phys. Lett. B, 2016 (2016), 1-13
##[5]
M. M. Bhatti, A. Zeeshan, R. Ellahi, Endoscope analysis on peristaltic blood flow of Sisko fluid with Titanium magnetonanoparticles, Comput. Biol. Med., 78 (2016), 29-41
##[6]
M. M. Bhatti, A. Zeeshan, N. Ijaz, O. A. Beg, A. Kadir , Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct, Eng. Sci. Tech. Int. J., 20 (2017), 1129-1139
##[7]
R. Ellahi, M. M. Bhatti, I. Pop, Effects of Hall and Ion Slip on MHD peristaltic flow of Jeffrey fluid in a non-Uniform rectangular duct, Internat. J. Numer. Methods Heat Fluid Flow, 26 (2016), 1802-1820
##[8]
R. Ellahi, E. Shivanian, S. Abbasbandy, T. Hayat, Numerical study of magnetohydrodynamics generalized Couette flow of Eyring-Powell fluid with heat transfer and slip condition, Internat. J. Numer. Methods Heat Fluid Flow, 26 (2016), 1433-1445
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L. L. Ferrás, J. M. Nóbrega, F. T. Pinho, Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip, J. Non-Newtonian Fluid Mech., 175–176 (2012), 76-88
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J.-H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech., 34 (1999), 699-708
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O. Martin, Modified variational iteration method for the analysis of viscoelastic beams, Appl. Math. Model., 40 (2016), 7988-7995
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A. D. Polyanin, V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Second edition, Chapman & Hall/CRC, Boca Raton, London, New York (2003)
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S. U. Rahman, R. Ellahi, S. Nadeem, Q. M. Zaigham Zia, Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis, J. Mol. Liq., 218 (2016), 484-493
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A. W. Sisko, The flow of lubricating greases, Ind. Eng. Chem., 50 (1958), 1789-1792
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A.-M. Wazwaz , The variational iteration method for solving a system of PDES, Comput. Math. Appl., 54 (2007), 895-902
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]
On upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions
On upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions
en
en
This paper deals with the concepts of upper and lower
\((\tau_1,\tau_2)\)-precontinuous multifunctions.
Some characterizations of upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions are investigated. The relationships between upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions and the other types of continuity are discussed.
282
293
Chawalit
Boonpok
Chawalit
Boonpok
Mahasarakham University
Mahasarakham University
Thailand
Chokchai
Viriyapong
Chokchai
Viriyapong
Mahasarakham University
Mahasarakham University
Thailand
Montri
Thongmoon
Montri
Thongmoon
Mahasarakham University
Mahasarakham University
Thailand
\(\tau_1\tau_2\)-preopen
lower $(\tau_1,\tau_2)$-precontinuous multifunction
upper $(\tau_1,\tau_2)$-precontinuous multifunction
on-upper-and-lower-tau-1tau-2-precontinuous-multifunctions.pdf
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E. Ekici, S. Jafari, V. Popa, On contra-precontinuous and almost contra-precontinuous multifunctions, J. Adv. Res. Pure Math., 2 (2010), 11-25
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T. Noiri, V. Popa , On weakly precontinuous functions in bitopological spaces, Soochow J. Math., 33 (2007), 87-100
]
Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)
Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)
en
en
The main goal of this paper is to develop a mathematical model to study the dynamic of malaria transmission, and the direct effects of congenital malaria on the spread of malaria.
In this study, we have clarified the significant impact of malaria on the human community through their impact on the newborn, and that directly increases spread of the malaria in the human community, especially in the newborns with the lower and inexperienced immunity systems.
The existence and stability of the disease-free points of the system is analyzed. We established that the disease-free equilibrium point is locally asymptotically stable when the reproduction number \(R_{0}<1\) and the disease always dies out. For \(R_{0}>1\) the disease-free equilibrium becomes unstable and there exists a unique endemic equilibrium.
294
305
Ebrahim
As-Shareef
Ebrahim
As-Shareef
Central China Normal University
Central China Normal University
P. R. China
Arif
Saif
Arif
Saif
Central China Normal University
Central China Normal University
P. R. China
Cui-Hong
Yang
Cui-Hong
Yang
Central China Normal University
Central China Normal University
P. R. China
Xin-An
Zhang
Xin-An
Zhang
Central China Normal University
Central China Normal University
P. R. China
Congenital malaria
vertical transmission
basic reproduction number
stability
mathematical-models-of-the-spread-of-malaria-with-the-vertical-transmission-congenital-malaria.pdf
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]
Construction of multi-layered QR codes utilizing partitions of positive integers
Construction of multi-layered QR codes utilizing partitions of positive integers
en
en
Multi-layered QR (MLQR) codes are created by superimposing many black and white QR codes, all of which are assigned their white areas with the colors in RGB color space. These colors must be different enough to enable distinguishing each layer of a MLQR code. This makes a MLQR code be able to hold more data than a common QR code.
In this work, the procedures for generating and un-layering MLQR codes were proposed and the according graphical user interfaces (GUIs) were created with MATLAB. They use the property of a partition of the number 255, constructed by the geometric sequence \(\left\{2^{n-1}\right\}_{n\in\mathbb{N}}\), to compute the collection of suitable colors for assigning to black and white QR codes in the generating process. Our developed procedures can promote better intercommunication between human and computers, therefore ensure easier computer programming and being more flexible in the number of layers of created MLQR codes. We found that the developed GUIs could work accurately up to 15 layers because more QR code layers require the use of more colors, which diminish an ability to clearly distinguish the color of each QR code layer.
306
313
Passawan
Noppakaew
Passawan
Noppakaew
Silpakorn University
Silpakorn University
Thailand
Sukanya
Khomkuth
Sukanya
Khomkuth
Silpakorn University
Silpakorn University
Thailand
Sureepat
Sriwilas
Sureepat
Sriwilas
Silpakorn University
Silpakorn University
Thailand
Quick response codes
preinvex function
geometric sequences
partitions of positive integers
construction-of-multi-layered-qr-codes-utilizing-partitions-of-positive-integers.pdf
[
[1]
T. Dean, C. Dunn, Quick Layered Response (QLR) Codes , Informally published manuscript, Electrical Engineering, Stanford University, Stanford (2012)
##[2]
G. Jancke, High Capacity Color Barcodes (HCCB), Available Online, (2007)
##[3]
H. Kato, Mobile Multi-Color Composite: A Novel Color 2D-Barcode for True Ubiquitous Computing, Doctoral thesis, School of Computer and Information Science, Edith Cowan University (2009)
##[4]
C. Nessen, Encoding Multi-layered Data into QR Codes for Increased Capacity and Security, Research Experience for Undergraduates Summer, South Dakota School of Mines and Technology (2013)
]
Symplectic properties research for finite element methods of Hamiltonian system
Symplectic properties research for finite element methods of Hamiltonian system
en
en
In this paper, we first apply properties of the wedge product and continuous finite element methods to prove that the
linear, quadratic element
methods are symplectic algorithms to the linear
Hamiltonian systems, i.e., the symplectic condition \(dp_{j+1}\wedge dq_{j+1}=dp_{j}\wedge dq_{j}\) is preserved exactly and the linear element method is an approximately symplectic integrator to nonlinear
Hamiltonian systems, i.e., \(dp_{j+1}\wedge dq_{j+1}=dp_{j}\wedge dq_{j}+O(h^2)\), as
well as energy conservative.
314
327
Qiong
Tang
Qiong
Tang
Hunan University of Technology
Hunan University of Technology
P. R. China
Yangfan
Liu
Yangfan
Liu
Xiang Tan University
Xiang Tan University
P. R. China
Yujun
Zheng
Yujun
Zheng
Hunan University of Science and Engineering
Hunan University of Science and Engineering
P. R. China
Hongping
Cao
Hongping
Cao
Shanghai University of Engineering Science
Shanghai University of Engineering Science
P. R. China
Hamiltonian systems
continuous finite element methods
energy conservative
wedge product
symplectic algorithm
symplectic-properties-research-for-finite-element-methods-of-hamiltonian-system.pdf
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S. D. Bond, B. J. Leimkuhler, Molecular dynamics and the accuracy of numerically computed averages, Acta Numer., 16 (2007), 1-65
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C. M. Chen, Finite element superconvergence construction theory, Hunan Press of Science and Technology, Changsha (2001)
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K. Feng, Collected Works of Feng Kang, National Defence Industry Press, Beijing (1995)
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K. Feng, M. Z. Qin, Symplectic Geometry Algorithm for Hamiltonian systems , ZheJiang Press of Science and Technology, HangZhou (2004)
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E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer-Verlag Berlin Heidelberg, Berlin (2006)
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C. Kane, J. E. Marsden, M. Ortiz, Symplectic-Energy-Momentum Preserving Variational Integrators, J. Math. Phys., 40 (1999), 3353-3371
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B. Leimkuhler, S. Reich, Simulating Hamiltonian Dynamics, Cambridge Universty Press, Cambridge (2004)
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Lyapunov functions to Caputo reaction-diffusion fractional neural networks with time-varying delays
Lyapunov functions to Caputo reaction-diffusion fractional neural networks with time-varying delays
en
en
A reaction diffusion equation with a Caputo fractional derivative in time and with time-varying
delays is considered. Stability properties of the solutions are studied via the direct Lyapunov method and arbitrary Lyapunov functions (usually quadratic Lyapunov functions are used). In this paper we give a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of reaction-diffusion fractional neural network with variable coefficients and time-varying delays. We show the quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability are obtained and we illustrate our theory on a particular nonlinear Caputo reaction-diffusion fractional neural network with time dependent delays.
328
345
R. P.
Agarwal
R. P.
Agarwal
M University-Kingsville
Distinguished University Professor of Mathematics
M University-Kingsville
Distinguished University Professor of Mathematics
USA
USA
S.
Hristova
S.
Hristova
University of Plovdiv Paisii Hilendarski
University of Plovdiv Paisii Hilendarski
Bulgaria
Donal
O'Regan
Donal
O'Regan
National University of Ireland
National University of Ireland
Ireland
Reaction-diffusion fractional neural networks
delays
Caputo derivatives
Lyapunov functions
stability
fractional derivative of Lyapunov functions
lyapunov-functions-to-caputo-reaction-diffusion-fractional-neural-networks-with-time-varying-delays.pdf
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[1]
R. Agarwal, S. Hristova, D. O’Regan, Lyapunov functions and strict stability of Caputo fractional differential equations, Adv. Difference Equ., 2015 (2015), 1-20
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R. Agarwal, S. Hristova, D. O’Regan, Lyapunov functions and stability of Caputo fractional differential equations with delays, , (to be published), -
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R. Agarwal, S. Hristova, D. O’Regan, A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations, Fract. Calc. Appl. Anal., 19 (2016), 290-318
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R. Agarwal, D. O’Regan, S. Hristova, Stability of Caputo fractional differential equations by Lyapunov functions, Appl. Math., 60 (2015), 653-676
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R. Agarwal, D. O’Regan, S. Hristova, M. Cicek, Practical stability with respect to initial time difference for Caputo fractional differential equations, Commun. Nonlinear Sci. Numer. Simul., 42 (2017), 106-120
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H. Bao, J. H. Park, J. Cao, Synchronization of fractional-order complex-valued neural networks with time delay, Neural Netw., 81 (2016), 16-28
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L. Chen, Y. Chai, R. Wu, T. Ma, H. Zhai, Dynamic analysis of a class of fractional-order neural networks with delay, Neurocomputing, 111 (2013), 190-194
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]
Some new fixed point theorems for compatible mappings in partial metric spaces
Some new fixed point theorems for compatible mappings in partial metric spaces
en
en
The aim of this paper is to prove common fixed point theorems for compatible
mappings of type (A) for three self mappings satisfying certain contractive
conditions and its topological properties in partial metric spaces.
346
356
Laila A.
Alnaser
Laila A.
Alnaser
Taibah University
Taibah University
Kingdom of Saudi Arabia
Durdana
Lateef
Durdana
Lateef
Taibah University
Taibah University
Kingdom of Saudi Arabia
Jamshaid
Ahmad
Jamshaid
Ahmad
University of Jeddah
University of Jeddah
Kingdom of Saudi Arabia
Fixed point
self mappings
compatibility of type (A)
partial metric space
some-new-fixed-point-theorems-for-compatible-mappings-in-partial-metric-spaces.pdf
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[1]
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Z. Mustafa, M. Arshad, S. U. Khan, J. Ahmad, M. M. M. Jaradat , Common fixed point for multivalued mappings in G-metric spaces with applications, J. Nonlinear Sci. Appl., 10 (2017), 2550-2564
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]
On the inclusion graphs of \(S\)-acts
On the inclusion graphs of \(S\)-acts
en
en
In this paper, we define the inclusion graph \({\Bbb{Inc}}(A)\) of an \(S\)-act \(A\) which is a graph whose vertices are non-trivial subacts of \(A\) and two distinct vertices \(B_1,B_2\) are adjacent if \(B_1 \subset B_2\) or \(B_2 \subset B_1\). We investigate the relationship between the algebraic properties of an \(S\)-act \(A\) and the properties of the graph \(\Bbb{Inc}(A)\). Some properties of \(\Bbb{Inc}(A)\) including girth, diameter and connectivity are studied. We characterize some classes of graphs which are the inclusion graphs of \(S\)-acts. Finally, some results concerning the domination number of such graphs are given.
357
363
Abdolhossein
Delfan
Abdolhossein
Delfan
Islamic Azad University
Islamic Azad University
Iran
Hamid
Rasouli
Hamid
Rasouli
Islamic Azad University
Islamic Azad University
Iran
Abolfazl
Tehranian
Abolfazl
Tehranian
Islamic Azad University
Islamic Azad University
Iran
\(S\)-Act
inclusion graph
diameter
girth
domination number
on-the-inclusion-graphs-of-s-acts.pdf
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]
A class of shape preserving 5-point \(n\)-ary approximating schemes
A class of shape preserving 5-point \(n\)-ary approximating schemes
en
en
A new class of shape preserving relaxed 5-point \(n\)-ary approximating subdivision schemes is presented. Further, the conditions on the initial data assuring monotonicity, convexity and concavity preservation of the limit functions are derived. Furthermore, some significant properties of ternary and quaternary subdivision schemes have been elaborated such as continuity, Hölder exponent, polynomial generation, polynomial reproduction, approximation order, and support of basic limit function. Moreover the visual performance of schemes has also been demonstrated through several examples.
364
380
Robina
Bashir
Robina
Bashir
The Islamia University of Bahawalpur
The Islamia University of Bahawalpur
Pakistan
Ghulam
Mustafa
Ghulam
Mustafa
The Islamia University of Bahawalpur
The Islamia University of Bahawalpur
Pakistan
Praveen
Agarwal
Praveen
Agarwal
Anand International College of Engineering
Anand International College of Engineering
India
Approximating scheme
shape preserving
monotonicity
convexity
concavity
polynomial reproduction and generation
a-class-of-shape-preserving-5-point-n-ary-approximating-schemes.pdf
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G. Mustafa, F. Khan, A new 4-point quaternary approximating subdivision scheme, Abstr. Appl. Anal., 2009 (2009), 1-14
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]
On the reversible geodesics of a Finsler space with special \((\alpha,\beta)\)-metric
On the reversible geodesics of a Finsler space with special \((\alpha,\beta)\)-metric
en
en
This paper deals with the existence of reversible geodesics on a Finsler space with some \((\alpha,\beta)\)-metrics. The conditions for a Finsler space \((M,F)\) to be with reversible geodesics are obtained. We study some geometrical properties of \(F\) with reversible geodesics and prove that the Finsler metric \(F\) induces a weighted quasi-metric \(d_F\) on \(M\).
381
387
Mohammad
Rafee
Mohammad
Rafee
I. K. Gujral Punjab Technical University
I. K. Gujral Punjab Technical University
India
Avdhesh
Kumar
Avdhesh
Kumar
I. K. Gujral Punjab Technical University
I. K. Gujral Punjab Technical University
India
G. C.
Chaubey
G. C.
Chaubey
V. B. S. Purvanchal University
V. B. S. Purvanchal University
India
Reversible geodesics
\((\alpha,\beta)\)-metric
distance
quasi-metric
weighted quasi-metric
on-the-reversible-geodesics-of-a-finsler-space-with-special-alphabeta-metric.pdf
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M. Crampin, Randers spaces with reversible geodesics, Publ. Math. Debrecen, 67 (2005), 401-409
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I. Masca, S. V. Sabau, H. Shimada, Two dimensional (\(\alpha,\beta\))-metrics with reversible geodesics, Publ. Math. Debrecen, 82 (2013), 485-501
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S. V. Sabau, H. Shimada, Finsler manifolds with reversible geodesics, Rev. Roumaine Math. Pures Appl., 57 (2012), 91-103
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]