Abstract and Applied Analysis Articles (Project Euclid)
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The latest articles from Abstract and Applied Analysis on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTMon, 01 Nov 2010 10:13 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces
http://projecteuclid.org/euclid.aaa/1267538585
<strong>Siwaporn Saewan</strong>, <strong>Poom Kumam</strong>, <strong>Kriengsak Wattanawitoon</strong><p><strong>Source: </strong>Abstr. Appl. Anal., Volume 2010, 25 pages.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of
the variational inequality for an $\alpha$ -inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature.
</p>projecteuclid.org/euclid.aaa/1267538585_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTA Variational Approach to Perturbed Discrete Anisotropic Equationshttp://projecteuclid.org/euclid.aaa/1481943747<strong>Amjad Salari</strong>, <strong>Giuseppe Caristi</strong>, <strong>David Barilla</strong>, <strong>Alfio Puglisi</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 12 pages.</p><p><strong>Abstract:</strong><br/> We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory. </p>projecteuclid.org/euclid.aaa/1481943747_20161216220306Fri, 16 Dec 2016 22:03 ESTA Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transformhttp://projecteuclid.org/euclid.aaa/1455115144<strong>Mawardi Bahri</strong>, <strong>Ryuichi Ashino</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 11 pages.</p><p><strong>Abstract:</strong><br/> We provide a short and simple proof of an uncertainty principle associated with the quaternion linear canonical transform (QLCT) by considering the fundamental relationship between the QLCT and the quaternion Fourier transform (QFT). We show how this relation allows us to derive the inverse transform and Parseval and Plancherel formulas associated with the QLCT. Some other properties of the QLCT are also studied. </p>projecteuclid.org/euclid.aaa/1455115144_20170124220641Tue, 24 Jan 2017 22:06 ESTLocal Hypoellipticity by Lyapunov Functionhttp://projecteuclid.org/euclid.aaa/1455115145<strong>E. R. Aragão-Costa</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 8 pages.</p><p><strong>Abstract:</strong><br/> We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: ${L}_{j}=\partial /\partial {t}_{j}+(\partial \varphi /\partial {t}_{j})(t,A)A$ , $j=\mathrm{1,2},\dots ,n$ , where $A:D(A)\subset H\to H$ is a self-adjoint linear operator, positive with $\mathrm{0}\in \rho (A)$ , in a Hilbert space $H$ , and $\varphi =\varphi (t,A)$ is a series of nonnegative powers of ${A}^{-\mathrm{1}}$ with coefficients in ${C}^{\mathrm{\infty }}(\mathrm{\Omega })$ , $\mathrm{\Omega }$ being an open set of ${\mathbb{R}}^{n}$ , for any $n\in \mathbb{N}$ , different from what happens in the work of Hounie (1979) who studies the problem only in the case $n=\mathrm{1}$ . We provide sufficient condition to get the local hypoellipticity for that complex in the elliptic region, using a Lyapunov function and the dynamics properties of solutions of the Cauchy problem $t$ ′ $(s)=-\nabla \mathrm{R}\mathrm{e}\mathrm{}{\varphi }_{\mathrm{0}}(t(s))$ , $s\ge \mathrm{0}$ , $t(\mathrm{0})={t}_{\mathrm{0}}\in \mathrm{\Omega },{\varphi }_{\mathrm{0}}:\mathrm{\Omega }\to \mathbb{C}$ being the first coefficient of $\varphi (t,A)$ . Besides, to get over the problem out of the elliptic region, that is, in the points $t$ ∗ $\in \mathrm{\Omega }$ such that $\nabla \mathrm{R}\mathrm{e}{\varphi }_{\mathrm{0}}(t$ ∗ $)$ = 0, we will use the techniques developed by Bergamasco et al. (1993) for the particular operator $A=\mathrm{1}-\mathrm{\Delta }:{H}^{\mathrm{2}}({\mathbb{R}}^{N})\subset {L}^{\mathrm{2}}({\mathbb{R}}^{N})\to {L}^{\mathrm{2}}({\mathbb{R}}^{N})$ . </p>projecteuclid.org/euclid.aaa/1455115145_20170124220641Tue, 24 Jan 2017 22:06 ESTGeneration and Identification of Ordinary Differential Equations of Maximal Symmetry Algebrahttp://projecteuclid.org/euclid.aaa/1485313541<strong>J. C. Ndogmo</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2016, 9 pages.</p><p><strong>Abstract:</strong><br/> An effective method for generating linear ordinary differential equations of maximal symmetry in their most general form is found, and an explicit expression for the point transformation reducing the equation to its canonical form is obtained. New expressions for the general solution are also found, as well as several identification and other results and a direct proof of the fact that a linear ordinary differential equation is iterative if and only if it is reducible to the canonical form by a point transformation. New classes of solvable equations parameterized by an arbitrary function are also found, together with simple algebraic expressions for the corresponding general solution. </p>projecteuclid.org/euclid.aaa/1485313541_20170124220641Tue, 24 Jan 2017 22:06 ESTA Variation on Uncertainty Principle and Logarithmic Uncertainty Principle
for Continuous Quaternion Wavelet Transformshttp://projecteuclid.org/euclid.aaa/1488423778<strong>Mawardi Bahri</strong>, <strong>Ryuichi Ashino</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
The continuous quaternion wavelet transform(CQWT) is a generalization of the classical continuous wavelet transformwithin the
context of quaternion algebra. First of all, we show that the directional quaternion Fourier transform (QFT) uncertainty principle
can be obtained using the component-wise QFT uncertainty principle. Based on this method, the directional QFT uncertainty
principle using representation of polar coordinate form is easily derived. We derive a variation on uncertainty principle related
to the QFT. We state that the CQWT of a quaternion function can be written in terms of the QFT and obtain a variation on
uncertainty principle related to the CQWT. Finally, we apply the extended uncertainty principles and properties of the CQWT to
establish logarithmic uncertainty principles related to generalized transform.
</p>projecteuclid.org/euclid.aaa/1488423778_20170301220315Wed, 01 Mar 2017 22:03 ESTBoundedness Criteria and Norm of Some Multilinear Hilbert-Type Operatorshttp://projecteuclid.org/euclid.aaa/1491962535<strong>Justice S. Bansah</strong>, <strong>Benoît F. Sehba</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 13 pages.</p><p><strong>Abstract:</strong><br/>
We consider two families of multilinear Hilbert-type operators for which we give exact relations between the parameters so that they are bounded. We also find the exact norm of these operators.
</p>projecteuclid.org/euclid.aaa/1491962535_20170411220232Tue, 11 Apr 2017 22:02 EDTModification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell Line Searchhttp://projecteuclid.org/euclid.aaa/1491962536<strong>Ahmad Alhawarat</strong>, <strong>Zabidin Salleh</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 6 pages.</p><p><strong>Abstract:</strong><br/>
Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional methods.
</p>projecteuclid.org/euclid.aaa/1491962536_20170411220232Tue, 11 Apr 2017 22:02 EDTSome Notes about the Continuous-in-Time Financial Modelhttp://projecteuclid.org/euclid.aaa/1491962537<strong>Tarik Chakkour</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the properties of operators in the continuous-in-time model which is designed to be used for the finances of public institutions. These operators are involved in the inverse problem of this model. We discuss this inverse problem in Schwartz space that we prove the uniqueness theorem.
</p>projecteuclid.org/euclid.aaa/1491962537_20170411220232Tue, 11 Apr 2017 22:02 EDTOn Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothnesshttp://projecteuclid.org/euclid.aaa/1491962538<strong>Nimete Sh. Berisha</strong>, <strong>Faton M. Berisha</strong>, <strong>Mikhail K. Potapov</strong>, <strong>Marjan Dema</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities.
</p>projecteuclid.org/euclid.aaa/1491962538_20170411220232Tue, 11 Apr 2017 22:02 EDTNew Conditions for the Exponential Stability of Nonlinear Differential Equationshttp://projecteuclid.org/euclid.aaa/1494468086<strong>Rigoberto Medina</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration.
</p>projecteuclid.org/euclid.aaa/1494468086_20170510220138Wed, 10 May 2017 22:01 EDTItô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scaleshttp://projecteuclid.org/euclid.aaa/1494468087<strong>Wenqing Hu</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 13 pages.</p><p><strong>Abstract:</strong><br/>
We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale ( $q$ -time scale).
</p>projecteuclid.org/euclid.aaa/1494468087_20170510220138Wed, 10 May 2017 22:01 EDTNonnegative Infinite Matrices that Preserve $(p,q)$ -Convexity of Sequenceshttp://projecteuclid.org/euclid.aaa/1497578540<strong>Chikkanna R. Selvaraj</strong>, <strong>Suguna Selvaraj</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 9 pages.</p><p><strong>Abstract:</strong><br/>
This paper deals with matrix transformations that preserve the $(p,q)$ -convexity of sequences. The main result gives the necessary
and sufficient conditions for a nonnegative infinite matrix $A$ to preserve the $(p,q)$ -convexity of sequences. Further, we give examples of such
matrices for different values of $p$ and $q$ .
</p>projecteuclid.org/euclid.aaa/1497578540_20170615220243Thu, 15 Jun 2017 22:02 EDTOn the Boundedness of the Fractional Bergman Operatorshttp://projecteuclid.org/euclid.aaa/1497578541<strong>Benoît F. Sehba</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 3 pages.</p><p><strong>Abstract:</strong><br/>
We give a necessary and sufficient condition for the boundedness of the
Bergman fractional operators.
</p>projecteuclid.org/euclid.aaa/1497578541_20170615220243Thu, 15 Jun 2017 22:02 EDTCorrigendum to “Existence of Solutions for a Coupled System of
Second and Fourth Order Elliptic Equations”http://projecteuclid.org/euclid.aaa/1497578542<strong>Fanglei Wang</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 1 page.</p>projecteuclid.org/euclid.aaa/1497578542_20170615220243Thu, 15 Jun 2017 22:02 EDTOn the Convergence of the Uniform Attractor for the 2D Leray- α
Modelhttp://projecteuclid.org/euclid.aaa/1497578543<strong>Gabriel Deugoué</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 11 pages.</p><p><strong>Abstract:</strong><br/>
We consider a nonautonomous 2D Leray- $\alpha $ model of fluid turbulence. We prove the existence of the
uniform attractor ${\mathcal{A}}^{\alpha }$ . We also study the convergence of ${\mathcal{A}}^{\alpha }$ as $\alpha $ goes to zero. More precisely, we prove that the uniform
attractor ${\mathcal{A}}^{\alpha }$ converges to the uniform attractor of the 2D Navier-Stokes
system as $\alpha $ tends to zero.
</p>projecteuclid.org/euclid.aaa/1497578543_20170615220243Thu, 15 Jun 2017 22:02 EDTApproximation of Durrmeyer Type Operators Depending on Certain
Parametershttp://projecteuclid.org/euclid.aaa/1497578544<strong>Neha Malik</strong>, <strong>Serkan Araci</strong>, <strong>Man Singh Beniwal</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 9 pages.</p><p><strong>Abstract:</strong><br/>
Motivated by a number of recent investigations, we consider a new
analogue of Bernstein-Durrmeyer operators based on certain variants.
We derive some approximation properties of these operators. We also
compute local approximation and Voronovskaja type asymptotic formula.
We illustrate the convergence of aforementioned operators by making
use of the software MATLAB which we stated in the paper.
</p>projecteuclid.org/euclid.aaa/1497578544_20170615220243Thu, 15 Jun 2017 22:02 EDTA New Class of Contraction in $b$ -Metric Spaces and Applicationshttp://projecteuclid.org/euclid.aaa/1500429779<strong>Preeti Kaushik</strong>, <strong>Sanjay Kumar</strong>, <strong>Kenan Tas</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 10 pages.</p><p><strong>Abstract:</strong><br/>
A novel class of $\alpha $ - $\beta $ -contraction for a pair of mappings is introduced in the setting of $b$ -metric spaces. Existence and uniqueness of coincidence and common fixed
points for such kind of mappings are investigated. Results are supported with
relevant examples. At the end, results are applied to find the solution of an
integral equation.
</p>projecteuclid.org/euclid.aaa/1500429779_20170718220321Tue, 18 Jul 2017 22:03 EDTWeak and Strong Solutions for a Strongly Damped Quasilinear Membrane
Equationhttp://projecteuclid.org/euclid.aaa/1500429780<strong>Jin-soo Hwang</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 9 pages.</p><p><strong>Abstract:</strong><br/>
We consider a strongly damped quasilinear membrane equation with Dirichlet
boundary condition. The goal is to prove the well-posedness of the equation in
weak and strong senses. By setting suitable function spaces and making use of
the properties of the quasilinear term in the equation, we have proved the
fundamental results on existence, uniqueness, and continuous dependence on data
including bilinear term of weak and strong solutions.
</p>projecteuclid.org/euclid.aaa/1500429780_20170718220321Tue, 18 Jul 2017 22:03 EDTGeneralized Hölder’s and Minkowski’s Inequalities for
Jackson’s $q$ -Integral and Some Applications to the Incomplete $q$ -Gamma Functionhttp://projecteuclid.org/euclid.aaa/1502762543<strong>Kwara Nantomah</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 6 pages.</p><p><strong>Abstract:</strong><br/>
We establish some generalized Hölder’s and Minkowski’s
inequalities for Jackson’s $q$ -integral. As applications, we derive some inequalities involving the
incomplete $q$ -Gamma function.
</p>projecteuclid.org/euclid.aaa/1502762543_20170814220252Mon, 14 Aug 2017 22:02 EDTThe Approximation Szász-Chlodowsky Type Operators Involving Gould-Hopper
Type Polynomialshttp://projecteuclid.org/euclid.aaa/1502762544<strong>Behar Baxhaku</strong>, <strong>Artan Berisha</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 8 pages.</p><p><strong>Abstract:</strong><br/>
We introduce the Szász and Chlodowsky operators based on Gould-Hopper
polynomials and study the statistical convergence of these operators in a
weighted space of functions on a positive semiaxis. Further, a Voronovskaja type
result is obtained for the operators containing Gould-Hopper polynomials.
Finally, some graphical examples for the convergence of this type of operator
are given.
</p>projecteuclid.org/euclid.aaa/1502762544_20170814220252Mon, 14 Aug 2017 22:02 EDTOn Weighted Montgomery Identity for $k$ Points and Its Associates on Time Scaleshttp://projecteuclid.org/euclid.aaa/1502762545<strong>Eze R. Nwaeze</strong>, <strong>Ana M. Tameru</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to establish a weighted Montgomery identity for
$k$ points and then use this identity to prove a new weighted Ostrowski type
inequality. Our results boil down to the results of Liu and Ngô if we take
the weight function to be the identity map. In addition, we also generalize an
inequality of Ostrowski-Grüss type on time scales for $k$ points. For $k=\mathrm{2},$ we recapture a result of Tuna and Daghan. Finally, we apply our results
to the continuous, discrete, and quantum calculus to obtain more results in this
direction.
</p>projecteuclid.org/euclid.aaa/1502762545_20170814220252Mon, 14 Aug 2017 22:02 EDTBifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Termshttps://projecteuclid.org/euclid.aaa/1505786568<strong>V. Hadžiabdić</strong>, <strong>M. R. S. Kulenović</strong>, <strong>E. Pilav</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 19 pages.</p><p><strong>Abstract:</strong><br/>
We investigate global dynamics of the following systems of difference equations ${x}_{n+\mathrm{1}}={x}_{n}/({A}_{\mathrm{1}}+{B}_{\mathrm{1}}{x}_{n}+{C}_{\mathrm{1}}{y}_{n})$ , ${y}_{n+\mathrm{1}}={y}_{n}^{\mathrm{2}}/({A}_{\mathrm{2}}+{B}_{\mathrm{2}}{x}_{n}+{C}_{\mathrm{2}}{y}_{n}^{\mathrm{2}})$ , $n=\mathrm{0,1},\dots $ , where the parameters ${A}_{\mathrm{1}}$ , ${A}_{\mathrm{2}}$ , ${B}_{\mathrm{1}}$ , ${B}_{\mathrm{2}}$ , ${C}_{\mathrm{1}}$ , and ${C}_{\mathrm{2}}$ are positive numbers and the initial conditions ${x}_{\mathrm{0}}$ and ${y}_{\mathrm{0}}$ are arbitrary nonnegative numbers. This system is a version of the Leslie-Gower competition model for two species. We show that this system has rich dynamics which depends on the part of parametric space.
</p>projecteuclid.org/euclid.aaa/1505786568_20170918220316Mon, 18 Sep 2017 22:03 EDTA Degree Theory for Compact Perturbations of Monotone Type Operators and
Application to Nonlinear Parabolic Problemhttps://projecteuclid.org/euclid.aaa/1507687470<strong>Teffera M. Asfaw</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 13 pages.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a real locally uniformly convex reflexive Banach space with
locally uniformly convex dual space ${X}^{*}$ . Let $T:X\supseteq D(T)\to {\mathrm{2}}^{{X}^{*}}$ be maximal monotone, $S:X\to {\mathrm{2}}^{{X}^{*}}$ be bounded and of type $({S}_{+}),$ and $C:D(C)\to {X}^{*}$ be compact with $D(T)\subseteq D(C)$ such that $C$ lies in ${\mathrm{\Gamma }}_{\sigma }^{\tau }$ (i.e., there exist $\sigma \ge \mathrm{0}$ and $\tau \ge \mathrm{0}$ such that $‖Cx‖\le \tau ‖x‖+\sigma $ for all $x\in D(C)$ ). A new topological degree theory is developed for operators
of the type $T+S+C$ . The theory is essential because no degree theory and/or
existence result is available to address solvability of operator
inclusions involving operators of the type $T+S+C$ , where $C$ is not defined everywhere. Consequently, new existence
theorems are provided. The existence theorem due to Asfaw and
Kartsatos is improved. The theory is applied to prove existence of
weak solution (s) for a nonlinear parabolic problem in appropriate
Sobolev spaces.
</p>projecteuclid.org/euclid.aaa/1507687470_20171010220505Tue, 10 Oct 2017 22:05 EDTOn Singular Solutions to PDEs with Turning Point Involving a Quadratic
Nonlinearityhttps://projecteuclid.org/euclid.aaa/1507687471<strong>Stéphane Malek</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 32 pages.</p><p><strong>Abstract:</strong><br/>
We study a singularly perturbed PDE with quadratic nonlinearity depending
on a complex perturbation parameter $\mathrm{ϵ}$ . The problem involves an irregular singularity in time, as in
a recent work of the author and A. Lastra, but possesses also, as a
new feature, a turning point at the origin in $\mathbb{C}$ . We construct a family of sectorial meromorphic solutions
obtained as a small perturbation in $\mathrm{ϵ}$ of a slow curve of the equation in some time scale. We show
that the nonsingular parts of these solutions share common formal
power series (that generally diverge) in $\mathrm{ϵ}$ as Gevrey asymptotic expansion of some order depending on data
arising both from the turning point and from the irregular singular
point of the main problem.
</p>projecteuclid.org/euclid.aaa/1507687471_20171010220505Tue, 10 Oct 2017 22:05 EDTThree Different Methods for New Soliton Solutions of the Generalized NLS Equationhttps://projecteuclid.org/euclid.aaa/1510801630<strong>Anwar Ja’afar Mohamad Jawad</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 8 pages.</p><p><strong>Abstract:</strong><br/>
Three different methods are applied to construct new types of solutions of nonlinear evolution equations. First, the Csch method is used to carry out the solutions; then the Extended Tanh-Coth method and the modified simple equation method are used to obtain the soliton solutions. The effectiveness of these methods is demonstrated by applications to the RKL model, the generalized derivative NLS equation. The solitary wave solutions and trigonometric function solutions are obtained. The obtained solutions are very useful in the nonlinear pulse propagation through optical fibers.
</p>projecteuclid.org/euclid.aaa/1510801630_20171115220745Wed, 15 Nov 2017 22:07 ESTThe Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Priceshttps://projecteuclid.org/euclid.aaa/1510801634<strong>L. Gómez-Valle</strong>, <strong>Z. Habibilashkary</strong>, <strong>J. Martínez-Rodríguez</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 10 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we analyze the role of the jump size distribution in the US natural gas prices when valuing natural gas futures traded at New York Mercantile Exchange (NYMEX) and we observe that a jump-diffusion model always provides lower errors than a diffusion model. Moreover, we also show that although the Normal distribution offers lower errors for short maturities, the Exponential distribution is quite accurate for long maturities. We also price natural gas options and we see that, in general, the model with the Normal jump size distribution underprices these options with respect to the Exponential distribution. Finally, we obtain the futures risk premia in both cases and we observe that for long maturities the term structure of the risk premia is negative. Moreover, the Exponential distribution provides the highest premia in absolute value.
</p>projecteuclid.org/euclid.aaa/1510801634_20171115220745Wed, 15 Nov 2017 22:07 ESTApplications of the $g$ -Drazin Inverse to the Heat Equation and a Delay Differential Equationhttps://projecteuclid.org/euclid.aaa/1513220438<strong>Alrazi Abdeljabbar</strong>, <strong>Trung Dinh Tran</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 4 pages.</p><p><strong>Abstract:</strong><br/>
We consider applications of the $g$ -Drazin inverse to some classes of abstract Cauchy problems, namely, the heat equation with operator coefficient and delay differential equations in Banach space.
</p>projecteuclid.org/euclid.aaa/1513220438_20171213220130Wed, 13 Dec 2017 22:01 ESTCorrigendum to “Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems”https://projecteuclid.org/euclid.aaa/1513220443<strong>Teffera M. Asfaw</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 1 page.</p>projecteuclid.org/euclid.aaa/1513220443_20171213220130Wed, 13 Dec 2017 22:01 ESTImproving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Functionhttps://projecteuclid.org/euclid.aaa/1513220444<strong>Beong In Yun</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
We introduce a generalized sigmoidal transformation ${w}_{m}(r;x)$ on a given interval $[a,b]$ with a threshold at $x=r\in (a,b)$ . Using ${w}_{m}(r;x)$ , we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.
</p>projecteuclid.org/euclid.aaa/1513220444_20171213220130Wed, 13 Dec 2017 22:01 ESTOn the Output Controllability of Positive Discrete Linear Delay Systemshttps://projecteuclid.org/euclid.aaa/1513220445<strong>Mouhcine Naim</strong>, <strong>Fouad Lahmidi</strong>, <strong>Abdelwahed Namir</strong>, <strong>Mostafa Rachik</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 12 pages.</p><p><strong>Abstract:</strong><br/>
Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability.
</p>projecteuclid.org/euclid.aaa/1513220445_20171213220130Wed, 13 Dec 2017 22:01 ESTCorrigendum to “A Three-Point Boundary Value Problem with an Integral Condition for a Third-Order Partial Differential Equation”https://projecteuclid.org/euclid.aaa/1513220446<strong>C. Latrous</strong>, <strong>A. Memou</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 1 page.</p>projecteuclid.org/euclid.aaa/1513220446_20171213220130Wed, 13 Dec 2017 22:01 ESTApproximation Properties of $q$ -Bernoulli Polynomialshttps://projecteuclid.org/euclid.aaa/1515466879<strong>M. Momenzadeh</strong>, <strong>I. Y. Kakangi</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 6 pages.</p><p><strong>Abstract:</strong><br/>
We study the $q$ -analogue of Euler-Maclaurin formula and by introducing a new $q$ -operator we drive to this form. Moreover, approximation properties of $q$ -Bernoulli polynomials are discussed. We estimate the suitable functions as a combination of truncated series of $q$ -Bernoulli polynomials and the error is calculated. This paper can be helpful in two different branches: first we solve the differential equations by estimating functions and second we may apply these techniques for operator theory.
</p>projecteuclid.org/euclid.aaa/1515466879_20180108220206Mon, 08 Jan 2018 22:02 ESTFinite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systemshttps://projecteuclid.org/euclid.aaa/1515466880<strong>Xiaoxing Chen</strong>, <strong>Manfeng Hu</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 12 pages.</p><p><strong>Abstract:</strong><br/>
Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS-) based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP) solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.
</p>projecteuclid.org/euclid.aaa/1515466880_20180108220206Mon, 08 Jan 2018 22:02 ESTContractibility of Fixed Point Sets of Mean-Type Mappingshttps://projecteuclid.org/euclid.aaa/1515466882<strong>S. Iampiboonvatana</strong>, <strong>P. Chaoha</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2017, 7 pages.</p><p><strong>Abstract:</strong><br/>
We establish a convergence theorem and explore fixed point sets of certain continuous quasi-nonexpansive mean-type mappings in general normed linear spaces. We not only extend previous works by Matkowski to general normed linear spaces, but also obtain a new result on the structure of fixed point sets of quasi-nonexpansive mappings in a nonstrictly convex setting.
</p>projecteuclid.org/euclid.aaa/1515466882_20180108220206Mon, 08 Jan 2018 22:02 ESTNecessary and Sufficient Conditions for Set-Valued Maps with Set Optimizationhttps://projecteuclid.org/euclid.aaa/1518577260<strong>Abdessamad Oussarhan</strong>, <strong>Ikram Daidai</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of $S$ -derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions.
</p>projecteuclid.org/euclid.aaa/1518577260_20180213220118Tue, 13 Feb 2018 22:01 ESTSoliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearityhttps://projecteuclid.org/euclid.aaa/1518577262<strong>Anwar Ja’afar Mohamad Jawad</strong>, <strong>Mahmood Jawad Abu-AlShaeer</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 8 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.
</p>projecteuclid.org/euclid.aaa/1518577262_20180213220118Tue, 13 Feb 2018 22:01 ESTGeneralized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusionshttps://projecteuclid.org/euclid.aaa/1518577263<strong>G. M. N’Guérékata</strong>, <strong>Marko Kostić</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 17 pages.</p><p><strong>Abstract:</strong><br/>
The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
</p>projecteuclid.org/euclid.aaa/1518577263_20180213220118Tue, 13 Feb 2018 22:01 ESTMultiobjective Optimization, Scalarization, and Maximal Elements of Preordershttps://projecteuclid.org/euclid.aaa/1518577264<strong>Paolo Bevilacqua</strong>, <strong>Gianni Bosi</strong>, <strong>Magalì Zuanon</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.
</p>projecteuclid.org/euclid.aaa/1518577264_20180213220118Tue, 13 Feb 2018 22:01 ESTTwo Sufficient Conditions for Convex Ordering on Risk Aggregationhttps://projecteuclid.org/euclid.aaa/1521252060<strong>Dan Zhu</strong>, <strong>Chuancun Yin</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 5 pages.</p><p><strong>Abstract:</strong><br/>
We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.
</p>projecteuclid.org/euclid.aaa/1521252060_20180316220113Fri, 16 Mar 2018 22:01 EDTStability for Linear Volterra Difference Equations in Banach Spaceshttps://projecteuclid.org/euclid.aaa/1523498503<strong>Rigoberto Medina</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.
</p>projecteuclid.org/euclid.aaa/1523498503_20180411220152Wed, 11 Apr 2018 22:01 EDTTime Scale Inequalities of the Ostrowski Type for Functions Differentiable on the Coordinateshttps://projecteuclid.org/euclid.aaa/1523498504<strong>Eze R. Nwaeze</strong>, <strong>Seth Kermausuor</strong>, <strong>Ana M. Tameru</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 10 pages.</p><p><strong>Abstract:</strong><br/>
In 2016, some inequalities of the Ostrowski type for functions (of two variables) differentiable on the coordinates were established. In this paper, we extend these results to an arbitrary time scale by means of a parameter $\lambda \in [\mathrm{0,1}]$ . The aforementioned results are regained for the case when the time scale $\mathbb{T}=\mathbb{R}$ . Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction.
</p>projecteuclid.org/euclid.aaa/1523498504_20180411220152Wed, 11 Apr 2018 22:01 EDTOn Solvability Theorems of Second-Order Ordinary Differential Equations with Delayhttps://projecteuclid.org/euclid.aaa/1525744868<strong>Nai-Sher Yeh</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
For each ${x}_{\mathrm{0}}\in [\mathrm{0,2}\pi )$ and $k\in \mathbf{N}$ , we obtain some existence theorems of periodic solutions to the two-point boundary value problem ${u}^{\mathrm{\prime }\mathrm{\prime }}(x)+{k}^{\mathrm{2}}u(x-{x}_{\mathrm{0}})+g(x,u(x-{x}_{\mathrm{0}}))=h(x)$ in $(\mathrm{0},\mathrm{2}\pi )$ with $u(\mathrm{0})-u(\mathrm{2}\pi )={u}^{\mathrm{\prime }}(\mathrm{0})-{u}^{\mathrm{\prime }}(\mathrm{2}\pi )=\mathrm{0}$ when $g:(\mathrm{0,2}\pi )\times\mathbf{R}\to \mathbf{R}$ is a Caratheodory function which grows linearly in $u$ as $|u|\to \mathrm{\infty }$ , and $h\in {L}^{\mathrm{1}}(\mathrm{0,2}\pi )$ may satisfy a generalized Landesman-Lazer condition $(\mathrm{1}+\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}(\beta )){\int }_{\mathrm{0}}^{\mathrm{2}\pi }h(x)v(x)dx<{\int }_{v(x)>\mathrm{0}}{g}_{\beta }^{+}(x){|v(x)|}^{\mathrm{1}-\beta }dx+{\int }_{v(x)<\mathrm{0}}{g}_{\beta }^{-}(x){|v(x)|}^{\mathrm{1}-\beta }dx$ for all $v\in N(L)\\{\mathrm{0}\}$ . Here $N(L)$ denotes the subspace of ${L}^{\mathrm{1}}(\mathrm{0,2}\pi )$ spanned by $\mathrm{sin}kx$ and $\mathrm{cos}kx$ , $-\mathrm{1}<\beta \le \mathrm{0}$ , ${g}_{\beta }^{+}(x)={\mathrm{l}\mathrm{i}\mathrm{m} \mathrm{i}\mathrm{n}\mathrm{f}}_{u\to \mathrm{\infty }}(g(x,u)u/{|u|}^{\mathrm{1}-\beta })$ , and ${g}_{\beta }^{-}(x)={\mathrm{l}\mathrm{i}\mathrm{m} \mathrm{i}\mathrm{n}\mathrm{f}}_{u\to -\mathrm{\infty }}(g(x,u)u/{|u|}^{\mathrm{1}-\beta })$ .
</p>projecteuclid.org/euclid.aaa/1525744868_20180507220114Mon, 07 May 2018 22:01 EDTOptimal Rational Approximations by the Modified Fourier Basishttps://projecteuclid.org/euclid.aaa/1525744869<strong>Arnak V. Poghosyan</strong>, <strong>Tigran K. Bakaryan</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 21 pages.</p><p><strong>Abstract:</strong><br/>
We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis.
</p>projecteuclid.org/euclid.aaa/1525744869_20180507220114Mon, 07 May 2018 22:01 EDTA Version of Uncertainty Principle for Quaternion Linear Canonical Transformhttps://projecteuclid.org/euclid.aaa/1528855378<strong>Mawardi Bahri</strong>, <strong> Resnawati</strong>, <strong>Selvy Musdalifah</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 7 pages.</p><p><strong>Abstract:</strong><br/>
In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain.
</p>projecteuclid.org/euclid.aaa/1528855378_20180612220317Tue, 12 Jun 2018 22:03 EDTA Deposition Model: Riemann Problem and Flux-Function Limits of Solutionshttps://projecteuclid.org/euclid.aaa/1528855379<strong>Hongjun Cheng</strong>, <strong>Shiwei Li</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 14 pages.</p><p><strong>Abstract:</strong><br/>
The Riemann solutions of a deposition model are shown. A singular flux-function limit of the obtained Riemann solutions is considered. As a result, it is shown that the Riemann solutions of the deposition model just converge to the Riemann solutions of the limit system, the scalar conservation law with a linear flux function involving discontinuous coefficient. Especially, for some initial data, the two-shock Riemann solution of the deposition model tends to the delta-shock Riemann solution of the limit system; by contrast, for some initial data, the two-rarefaction-wave Riemann solution of the deposition model tends to the vacuum Riemann solution of the limit system. Some numerical results exhibiting the formation processes of delta-shocks and vacuum states are presented.
</p>projecteuclid.org/euclid.aaa/1528855379_20180612220317Tue, 12 Jun 2018 22:03 EDT${C}^{\mathrm{1}}$ Hermite Interpolation with PH Curves Using the Enneper Surfacehttps://projecteuclid.org/euclid.aaa/1528855380<strong>Hyun Chol Lee</strong>, <strong>Jae Hoon Kong</strong>, <strong>Gwangil Kim</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 10 pages.</p><p><strong>Abstract:</strong><br/>
We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular ${C}^{\mathrm{1}}$ Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four interpolants on each surface. Examples of these interpolants were found to be better, in terms of bending energy and arc-length, than those obtained using a previous PH-preserving mapping.
</p>projecteuclid.org/euclid.aaa/1528855380_20180612220317Tue, 12 Jun 2018 22:03 EDTThe Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Methodhttps://projecteuclid.org/euclid.aaa/1528855381<strong>Yousef Alnafisah</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 7 pages.</p><p><strong>Abstract:</strong><br/>
Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE.
</p>projecteuclid.org/euclid.aaa/1528855381_20180612220317Tue, 12 Jun 2018 22:03 EDTControllability and Observability of Nonautonomous Riesz-Spectral Systemshttps://projecteuclid.org/euclid.aaa/1528855382<strong>Sutrima Sutrima</strong>, <strong>Christiana Rini Indrati</strong>, <strong>Lina Aryati</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 10 pages.</p><p><strong>Abstract:</strong><br/>
There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a ${C}_{\mathrm{0}}$ -quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.
</p>projecteuclid.org/euclid.aaa/1528855382_20180612220317Tue, 12 Jun 2018 22:03 EDTGeneralized Fractional Integral Operators Involving Mittag-Leffler Functionhttps://projecteuclid.org/euclid.aaa/1531274540<strong>Hafte Amsalu</strong>, <strong>D. L. Suthar</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 8 pages.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s $H$ -function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and $K$ -transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters.
</p>projecteuclid.org/euclid.aaa/1531274540_20180710220243Tue, 10 Jul 2018 22:02 EDTThe Existence and Structure of Rotational Systems in the Circlehttps://projecteuclid.org/euclid.aaa/1531274541<strong>Jayakumar Ramanathan</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 11 pages.</p><p><strong>Abstract:</strong><br/>
By a rotational system, we mean a closed subset $X$ of the circle, $\mathbb{T}=\mathbb{R}/\mathbb{Z}$ , together with a continuous transformation $f:X\to X$ with the requirements that the dynamical system $(X,f)$ be minimal and that $f$ respect the standard orientation of $\mathbb{T}$ . We show that infinite rotational systems $(X,f)$ , with the property that map $f$ has finite preimages, are extensions of irrational rotations of the circle. Such systems have been studied when they arise as invariant subsets of certain specific mappings, $F:\mathbb{T}\to \mathbb{T}$ . Because our main result makes no explicit mention of a global transformation on $\mathbb{T}$ , we show that such a structure theorem holds for rotational systems that arise as invariant sets of any continuous transformation $F:\mathbb{T}\to \mathbb{T}$ with finite preimages. In particular, there are no explicit conditions on the degree of $F$ . We then give a development of known results in the case where $F(\theta )=d·\theta \mathrm{mod}\mathrm{1}$ for an integer $d>\mathrm{1}$ . The paper concludes with a construction of infinite rotational sets for mappings of the unit circle of degree larger than one whose lift to the universal cover is monotonic.
</p>projecteuclid.org/euclid.aaa/1531274541_20180710220243Tue, 10 Jul 2018 22:02 EDTMultiresolution Analysis Applied to the Monge-Kantorovich Problemhttps://projecteuclid.org/euclid.aaa/1531274542<strong>Armando Sánchez-Nungaray</strong>, <strong>Carlos González-Flores</strong>, <strong>Raquiel R. López-Martínez</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem.
</p>projecteuclid.org/euclid.aaa/1531274542_20180710220243Tue, 10 Jul 2018 22:02 EDTA Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systemshttps://projecteuclid.org/euclid.aaa/1531274543<strong>Mohammad Hossein Daliri Birjandi</strong>, <strong>Jafar Saberi-Nadjafi</strong>, <strong>Asghar Ghorbani</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions.
</p>projecteuclid.org/euclid.aaa/1531274543_20180710220243Tue, 10 Jul 2018 22:02 EDT