2017
9
4
0
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Gframes in Hilbert Modules Over ProC*algebras
2
2
Gframes are natural generalizations of frames which provide more choices on analyzing functions from frame expansion coefficients. First, they were defined in Hilbert spaces and then generalized on C*Hilbert modules. In this paper, we first generalize the concept of gframes to Hilbert modules over proC*algebras. Then, we introduce the gframe operators in such spaces and show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that, by having a gframe and an invertible operator in this spaces, we can produce the corresponding dual gframe. Finally we introduce the canonical dual gframes and provide a reconstruction formula for the elements of such Hilbert modules.
1

259
267


N.
Haddadzadeh
Department of Mathematics, Abadan Branch, Islamic Azad University, Abadan, Iran.
Department of Mathematics, Abadan Branch,
Iran
nhaddad25@gmail.com
ProC*algebra
Hilbert modules
Gframes
Frame operators
A New Group Data Envelopment Analysis Method for Ranking Design Requirements in Quality Function Deployment
2
2
Data envelopment analysis (DEA) is an objective method for priority determination of decision making units (DMUs) with the same multiple inputs and outputs. DEA is an efficiency estimation technique, but it can be used for solving many problems of management such as rankig of DMUs. Many researchers have found similarity between DEA and MCDM techniques. One of the earliest techniques in MCDM is Quality Function Deployment (QFD) which is a teambased and disciplined approach to product design, engineering and production and provides indepth evaluation of a product. The QFD team is responsible for assessing the relationships between costumer requirements (CRs) and design requirements (DRs) and the interrelationships between DRs. In practice, each member demonstrates significantly different behavior from the others and generates different assessment results, leading to the QFD with uncertainty. In this paper data envelopment analysis is used to overcome this uncertainty. Each member's subjective assessment is taken into account directly and a new data envelopment analysis method in group situation is constructed which differs from multiobjective decision making models. Then, without using CharnesCooper transformation, the proposed model is transformed into a linear programing problem in a completely different manner. We will call the proposed model "GroupedQFDEA".
1

269
278


J.
Pourmahmoud
Department of Applied Mathematics, Azarbaijan Shahid madani University, Tabriz, Iran.
Department of Applied Mathematics, Azarbaijan
Iran
pourmahmoud@azaruniv.ac.ir


E.
Babazadeh
Department of Applied Mathematics, Azarbaijan Shahid madani University, Tabriz, Iran.
Department of Applied Mathematics, Azarbaijan
Iran
Data Envelopment Analysis (DEA)
Quality function deployment (QFD)
Group situation
Multiobjective decision making models
Ranking
On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation
2
2
In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara differentiability, the analytical solution of an exact second order fuzzy initial value problem is derived in two senses of differentiability. Also, several properties for generalized Hukuhara differentiability are obtained on the topics, such as, the univariate fuzzy chain rules, fuzzy integration by parts, among others. At the end, some illustrative examples are presented and these examples show the behavior of the solutions.
1

279
288


A.
Armand
Young Researchers and Elites Club, YadegareImam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran.
Young Researchers and Elites Club, YadegareImam
Iran


Z.
Gouyandeh
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Department of Mathematics, Science and Research
Iran
zgouyandeh@yahoo.com
Generalized Hukuhara differentiability
Switching point
Fuzzy first order differential equation
Second order exact fuzzy initial value problem
Effect of Hall Current and Wall Conductance on Hydromagnetic Natural Convective Flow Between Vertical Walls
2
2
This paper has examined the analytical solution of steady fully developed natural convective flow of a viscous incompressible and electrically conducting fluid between vertical channel by taking the Hall current and induced magnetic field into account. We have obtained the nondimensional simultaneous ordinary differential equations using the suitable nondimensional variables and parameters in the governing equations of the model. By obtaining the analytical solution of the simultaneous ordinary differential equations, the effects of the Hall current and the Hartmann number on the primary and secondary components of the velocity, induced magnetic field and induced current density are presented by the graphs. The influence of the Hall current is to increase both the primary and secondary components of the velocity and induced magnetic field profiles but decrease the components of induced current density. It is found that the effect of Hartmann number is to decrease both the primary and secondary components of velocity and induced current density but increase the components of the induced magnetic field.
1

289
299


D.
Kumar
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi221005, India.
Department of Mathematics, Institute of Science,
Iran
dileepyadav02april@gmail.com


A. K.
Singh
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi221005, India.
Department of Mathematics, Institute of Science,
Iran


Mr.
Sarveshanand
Department of Mathematics, K. N. Govt. P. G. College, Gyanpur, Bhadohi 221304, India.
Department of Mathematics, K. N. Govt. P.
Iran
Hall current
Induced magnetic field
Natural convection
Hydromagnetic
Induced current density
Solving Volterra's Population Model via Rational Christov Functions Collocation Method
2
2
The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integrodifferential equation. First, the Volterra's Population Model is converted to a nonlinear ordinary differential equation (ODE), then researchers solve this equation (ODE). The accuracy of method is tested in terms of $RES$ error and compare the obtained results with some wellknown results.The numerical results obtained show that the proposed method produces a convergent solution.
1

301
306


K.
Parand
Department of Computer Sciences, Faculty of Mathematical, Shahid Beheshti University, Tehran, Iran.
Department of Computer Sciences, Faculty
Iran
k\_parand@sbu.ac.ir


E.
Hajizadeh
Department of Computer Sciences, Faculty of Mathematical, Shahid Beheshti University, Tehran, Iran.
Department of Computer Sciences, Faculty
Iran


A.
Jahangiri
Department of Computer Sciences, Salman Farsi University of Kazerun, Kazerun, Iran.
Department of Computer Sciences, Salman Farsi
Iran


S.
Khaleqi
Department of Computer Sciences, Faculty of Mathematical, Shahid Beheshti University, Tehran, Iran.
Department of Computer Sciences, Faculty
Iran
Volterra's Population Model
Collocation method
Rational Christov Functions
Nonlinear ODE
Environmental Assessment and Congestion for DMUs With Undesirable Outputs
2
2
In recent years, the assessment of environmental performance has been received considerable attention by environmental policy indicators and decision makers. In this regard, this paper applies data envelopment analysis (DEA) as a management tool for evaluating the environmental performance of the firms and uses the extended bounded adjusted measure (extended BAM) for including undesirable outputs in the environmental assessment. On the other hand, congestion points to a situation where inputs are excessively used. The previous studies of congestion mainly considered the framework of desirable outputs, and undesirable outputs have been disregarded in the evaluation. To overcome these shortcomings, this paper introduces an alternative definition and approach to treat congestion in the simultaneous presence of desirable and undesirable outputs. Then, the presented method is applied on 31 administrative regions of China. As a result of this application, it is observed that seven industries are environmentally efficient and also do not show congestion. Four industries evidence congestion in one or both of their inputs. By reducing the amount of congestion in each input, these industries can increase their desirable output and decrease their undesirable outputs.
1

307
318


M.
Khodadadi
Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.
Department of Mathematics, Urmia Branch,
Iran
m.khodadadi@iaurmia.ac.ir


H.
Zare Haghighi
Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.
Department of Mathematics, Urmia Branch,
Iran
data envelopment analysis
environmental performance
Congestion
Undesirable output
Impact of Outliers in Data Envelopment Analysis
2
2
This paper will examine the relationship between "Data Envelopment Analysis" and a statistical concept ``Outlier". Data envelopment analysis (DEA) is a method for estimating the relative efficiency of decision making units (DMUs) having similar tasks in a production system by multiple inputs to produce multiple outputs. An important issue in statistics is to identify the outliers. In this paper, we attempt to investigate the concept of the outliers determination by data envelopment analysis and assess the manner of decision making units when a sample contains an outlier. We will start by providing a review literature. We will then proceed with our proposed method and discuss the strengths and weaknesses of our method. We will provide some numerical results to demonstrate the applicability of our method.
1

319
332


A.
Gholam Abri
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.
Department of Mathematics, Firoozkooh Br
Iran
Data Envelopment Analysis (DEA)
Statistics
Outlier
efficiency
Normal Distribution
Production Possibility Set (PPS)
Another Method for Defuzzification Based On Characterization of Fuzzy Numbers
2
2
Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middlepoint and the spread of each $gamma$cut of a fuzzy number, respectively. We use the value of a as the weight of the signal/noise ratio of each $gamma$cut of a fuzzy number to calculate the ranking index of each fuzzy number. The proposed method can rank any kinds of fuzzy numbers with different kinds of membership functions.
1

333
339


Rahim
Saneifard
Department of Mathematics, Urmia Branch, Urmia, Iran
Department of Mathematics, Urmia Branch,
Iran
srsaneeifard@yahoo.com
Ranking
Fuzzy number
Defuzzification
Signal/noise ratios
Comparison Between Different Methods of Feature Extraction in BCI Systems Based on SSVEP
2
2
There are different feature extraction methods in braincomputer interfaces (BCI) based on SteadyState Visually Evoked Potentials (SSVEP) systems. This paper presents a comparison of five methods for stimulation frequency detection in SSVEPbased BCI systems. The techniques are based on Power Spectrum Density Analysis (PSDA), Fast Fourier Transform (FFT), Hilbert Huang Transform (HHT), Cross Correlation and Canonical Correlation Analysis (CCA). The results demonstrate that the CCA and FFT can be successfully applied for stimulus frequency detection by considering the highest accuracy and minimum consuming time.
1

341
347


S.
Sheykhivand
Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
Faculty of Electrical and Computer Engineering,
Iran


T.
Yousefi Rezaii
Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran.
Faculty of Electrical and Computer Engineering,
Iran


A.
Naderi Saatlo
Department of ElectricalElectronics Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran.
Department of ElectricalElectronics Engineering,
Iran


N.
Romooz
Department of ElectricalElectronics Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran.
Department of ElectricalElectronics Engineering,
Iran
BCI
CCA
Cross Correlation
FFT
fuzzy
HHT
PSDA
SSVEP
Numerical Solution of Fredholm Integrodifferential Equations By Using Hybrid Function Operational Matrix of Differentiation
2
2
In this paper, first, a numerical method is presented for solving a class of linear Fredholm integrodifferential equation. The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Blockpulse functions. The application of the proposed operational matrix with tau method is then utilized to transform the integrodifferential equations to the algebraic equations. Finally, show the efficiency of the proposed method is indicated by some numerical examples.
1

349
358


R.
Jafri
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj
Iran


R.
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj
Iran
ezati@ kiau.ac.ir


K.
Maleknejad
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Department of Mathematics, Karaj
Iran
Fredholm integrodifferential equation
Hybrid function
Chebyshev polynomial
Blockpulse function
Operational matrix of derivative
Solving Some InitialBoundary Value Problems Including Nonclassical Cases of Heat Equation By Spectral and Countour Integral Methods
2
2
In this paper, we consider some initialboundary value problems which contain onedimensional heat equation in nonclassical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and FourierBirkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the solution and also satisfying the solution in the given P.D.E and satisfing the given initial and boundary conditions are established by complex analysis theory and Countour integral method.
1

359
364


M.
Jahanshahi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Department of Mathematics, Azarbaijan Shahid
Iran
jahanshahi@azaruniv.edu


N.
Aliev
Department of Mathematics, Bakue State University, Baku, Azarbaijan.
Department of Mathematics, Bakue State University,
Iran


F.
Jahanshahi
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Department of Mathematics, Azarbaijan Shahid
Iran
InitialBoundary Value Problem
Laplace Line
Countor Integral
Heat Equation.
Classical Center Location Problem Under Uncertain Environment
2
2
This paper investigates the $p$center location problem on a network in which vertex weights and distances between vertices are uncertain. The concepts of the $alpha$$p$center and the expected $p$center are introduced. It is shown that the $alpha$$p$center and the expected $p$center models can be transformed into corresponding deterministic models. Finally, linear time algorithms for finding the 1center and \2center of uncertain unweighted trees are proposed.
1

365
374


A.
Soltanpour
Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
Department of Applied Mathematics, Faculty
Iran


F.
Baroughi
Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
Department of Applied Mathematics, Faculty
Iran


B.
Alizadeh
Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
Department of Applied Mathematics, Faculty
Iran
Location Problem
$p$center
Uncertainty theory
Uncertain Programming