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 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 EDTNumerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditionshttps://projecteuclid.org/euclid.aaa/1521252087<strong>Pawarisa Samalerk</strong>, <strong>Nopparat Pochai</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 7 pages.</p><p><strong>Abstract:</strong><br/>
The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one-dimensional water-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with nonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference technique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by the quadratic interpolation technique. The approximated solutions to the model are verified by a comparison with the analytical solution. The proposed numerical technique worked very well to give dependable and accurate solutions to these kinds of several real-world applications.
</p>projecteuclid.org/euclid.aaa/1521252087_20180918220240Tue, 18 Sep 2018 22:02 EDTSolution of Sequential Hadamard Fractional Differential Equations by Variation of Parameter Techniquehttps://projecteuclid.org/euclid.aaa/1521252086<strong>Mohammed M. Matar</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 7 pages.</p><p><strong>Abstract:</strong><br/>
We obtain in this article a solution of sequential differential equation involving the Hadamard fractional derivative and focusing the orders in the intervals $(\mathrm{1,2})$ and $(\mathrm{2,3})$ . Firstly, we obtain the solution of the linear equations using variation of parameter technique, and next we investigate the existence theorems of the corresponding nonlinear types using some fixed-point theorems. Finally, some examples are given to explain the theorems.
</p>projecteuclid.org/euclid.aaa/1521252086_20180918220240Tue, 18 Sep 2018 22:02 EDTNumerical Simulation for a Three-Dimensional Air Pollution Measurement Model in a Heavy Traffic Area under the Bangkok Sky Train Platformhttps://projecteuclid.org/euclid.aaa/1523498522<strong>Kewalee Suebyat</strong>, <strong>Nopparat Pochai</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 10 pages.</p><p><strong>Abstract:</strong><br/>
Air pollutant levels in Bangkok are generally high in street tunnels. They are particularly elevated in almost closed street tunnels such as an area under the Bangkok sky train platform with high traffic volume where dispersion is limited. There are no air quality measurement stations in the vicinity, while the human population is high. In this research, the numerical simulation is used to measure the air pollutant levels. The three-dimensional air pollution measurement model in a heavy traffic area under the Bangkok sky train platform is proposed. The finite difference techniques are employed to approximate the modelled solutions. The vehicle air pollutant emission due to the high traffic volume is mathematically assumed by the pollutant sources term. The simulation is also considered in averaged and moving pollutant sources due to manner vehicle emission. The proposed approximated air pollutant concentration indicators can be replaced by user required gaseous pollutants indices such as NOx, SO2, CO, and PM2.5.
</p>projecteuclid.org/euclid.aaa/1523498522_20180918220240Tue, 18 Sep 2018 22:02 EDTAn Extended Generalized $q$ -Extensions for the Apostol Type Polynomialshttps://projecteuclid.org/euclid.aaa/1537322513<strong>Letelier Castilla</strong>, <strong>William Ramírez</strong>, <strong>Alejandro Urieles</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 13 pages.</p><p><strong>Abstract:</strong><br/>
Through a modification on the parameters associated with generating function of the $q$ -extensions for the Apostol type polynomials of order $\alpha $ and level $m$ , we obtain some new results related to a unified presentation of the $q$ -analog of the generalized Apostol type polynomials of order $\alpha $ and level $m$ . In addition, we introduce some algebraic and differential properties for the $q$ -analog of the generalized Apostol type polynomials of order $\alpha $ and level $m$ and the relation of these with the $q$ -Stirling numbers of the second kind, the generalized $q$ -Bernoulli polynomials of level $m$ , the generalized $q$ -Apostol type Bernoulli polynomials, the generalized $q$ -Apostol type Euler polynomials, the generalized $q$ -Apostol type Genocchi polynomials of order $\alpha $ and level $m$ , and the $q$ -Bernstein polynomials.
</p>projecteuclid.org/euclid.aaa/1537322513_20180918220240Tue, 18 Sep 2018 22:02 EDTOn the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervalshttps://projecteuclid.org/euclid.aaa/1537322514<strong>Jukkrit Daengsaen</strong>, <strong>Anchalee Khemphet</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 6 pages.</p><p><strong>Abstract:</strong><br/>
We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.
</p>projecteuclid.org/euclid.aaa/1537322514_20180918220240Tue, 18 Sep 2018 22:02 EDTExistence Theorems on Solvability of Constrained Inclusion Problems and Applicationshttps://projecteuclid.org/euclid.aaa/1537322515<strong>Teffera M. Asfaw</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 10 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 a maximal monotone operator and $C:X\supseteq D(C)\to {X}^*$ be bounded and continuous with $D(T)\subseteq D(C)$ . The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the type $T+C$ provided that $C$ is compact or $T$ is of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition on $T+C$ . The operator $C$ is neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems.
</p>projecteuclid.org/euclid.aaa/1537322515_20180918220240Tue, 18 Sep 2018 22:02 EDTEstimates on the Bergman Kernels in a Tangential Direction on Pseudoconvex Domains in ${\mathbb{C}}^{3}$https://projecteuclid.org/euclid.aaa/1537322516<strong>Sanghyun Cho</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 13 pages.</p><p><strong>Abstract:</strong><br/>
Let $\mathrm{\Omega }$ be a smoothly bounded pseudoconvex domain in ${\mathbb{C}}^{\mathrm{3}}$ and assume that ${T}_{\mathrm{\Omega }}^{reg}({z}_{\mathrm{0}})<\mathrm{\infty }$ where ${z}_{\mathrm{0}}\in b\mathrm{\Omega }$ , the boundary of $\mathrm{\Omega }$ . Then we get optimal estimates of the Bergman kernel function along some “almost tangential curve” ${C}_{b}({z}_{\mathrm{0}},{\mathrm{\delta }}_{\mathrm{0}})\subset \mathrm{\Omega }\cup \{{z}_{\mathrm{0}}\}$ .
</p>projecteuclid.org/euclid.aaa/1537322516_20180918220240Tue, 18 Sep 2018 22:02 EDTGlobal Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latencyhttps://projecteuclid.org/euclid.aaa/1537322517<strong>Rodrigue Yves M’pika Massoukou</strong>, <strong>Suares Clovis Oukouomi Noutchie</strong>, <strong>Richard Guiem</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 21 pages.</p><p><strong>Abstract:</strong><br/>
Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number ${\mathfrak{R}}_{\mathrm{0}}$ .
</p>projecteuclid.org/euclid.aaa/1537322517_20180918220240Tue, 18 Sep 2018 22:02 EDTA New Method of Hypothesis Test for Truncated Spline Nonparametric Regression Influenced by Spatial Heterogeneity and Applicationhttps://projecteuclid.org/euclid.aaa/1539137013<strong> Sifriyani</strong>, <strong>I. N. Budiantara</strong>, <strong>S. H. Kartiko</strong>, <strong> Gunardi</strong>. <p><strong>Source: </strong>Abstract and Applied Analysis, Volume 2018, 13 pages.</p><p><strong>Abstract:</strong><br/>
This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H 0 whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics $V$ and verified that each of the numerators and denominators in the statistic test $V$ followed a distribution of ${\chi }^{\mathrm{2}}$ . Since there was a symmetric and idempotent matrix S, it could be proved that ${\stackrel{~}{\mathrm{Y}}}^{\mathrm{T}}S \stackrel{~}{\mathrm{Y}}/{\sigma }^{\mathrm{2}}~{\chi }_{(n-lm-\mathrm{1})}^{\mathrm{2}}$ . Matrix $D({u}_{i},{v}_{i})$ was positive semidefinite and contained weighting matrix $\mathbf{W}({u}_{i},{v}_{i})$ which had different values in every location; therefore matrix $D({u}_{i},{v}_{i})$ was not idempotent. If ${\stackrel{~}{\mathrm{Y}}}^{\mathrm{T}}D({u}_{i},{v}_{i})\stackrel{~}{\mathrm{Y}}\ge \mathrm{0}$ and $D({u}_{i},{v}_{i})$ was not idempotent and also $\stackrel{~}{\mathrm{Y}}$ was a $N(\mathbf{0},\mathbf{I})$ distributed random vector, then there were constants $k$ and $r$ ; hence ${\stackrel{~}{\mathrm{Y}}}^{\mathrm{T}}D({u}_{i},{v}_{i})\stackrel{~}{\mathrm{Y}}~k{\chi }_{r}^{\mathrm{2}}$ ; therefore it was concluded that test statistic $V$ followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia.
</p>projecteuclid.org/euclid.aaa/1539137013_20181009220356Tue, 09 Oct 2018 22:03 EDT