Search results for: Square Matrix Bipartition

Authors: J. Kavitha, S. Sowmyayani, P. Arockia Jansi Rani

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In this paper, a shot boundary detection method is presented using octagon square search pattern. The color, edge, motion and texture features of each frame are extracted and used in shot boundary detection. The motion feature is extracted using octagon square search pattern. Then, the transition detection method is capable of detecting the shot or non-shot boundaries in the video using the feature weight values. Experimental results are evaluated in TRECVID video test set containing various types of shot transition with lighting effects, object and camera movement within the shots. Further, this paper compares the experimental results of the proposed method with existing methods. It shows that the proposed method outperforms the state-of-art methods for shot boundary detection.

Keywords: Content-based indexing and retrieval, cut transition detection, discrete wavelet transform, shot boundary detection, video source.

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Authors: Z. Sadeghi, M. R. Omidkhah, M. E. Masoomi

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The purpose of this paper is to examine gas transport behavior of mixed matrix membranes (MMMs) combined with porous particles. Main existing models are categorized in two main groups; two-phase (ideal contact) and three-phase (non-ideal contact). A new coefficient, J, was obtained to express equations for estimating effect of the particle porosity in two-phase and three-phase models. Modified models evaluates with existing models and experimental data using Matlab software. Comparison of gas permeability of proposed modified models with existing models in different MMMs shows a better prediction of gas permeability in MMMs.

Keywords: Mixed Matrix Membrane, Permeation Models, Porous particles, Porosity.

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Authors: Ling Zhang, Feng Liu

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A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

Keywords: Spectrally arbitrary, Nilpotent matrix, Ray patterns, sign patterns.

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Authors: Samsiah Abdul Razak, Daud Mohamad

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Molodstov-s soft sets theory was originally proposed as general mathematical tool for dealing with uncertainty problems. The matrix form has been introduced in soft set and some of its properties have been discussed. However, the formulation of soft matrix in group decision making problem only with equal importance weights of criteria, which does not show the true opinion of decision maker on each criteria. The aim of this paper is to propose a method for solving group decision making problem incorporating the importance of criteria by using soft matrices in a more objective manner. The weight of each criterion is calculated by using the Analytic Hierarchy Process (AHP) method. An example of house selection process is given to illustrate the effectiveness of the proposed method.

Keywords: Soft set, Soft Matrix, Soft max-min decision making (SMmDM), Analytic hierarchy process (AHP)

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Authors: Bharatendra Rai

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Predictive data analysis and modeling involving machine learning techniques become challenging in presence of too many explanatory variables or features. Presence of too many features in machine learning is known to not only cause algorithms to slow down, but they can also lead to decrease in model prediction accuracy. This study involves housing dataset with 79 quantitative and qualitative features that describe various aspects people consider while buying a new house. Boruta algorithm that supports feature selection using a wrapper approach build around random forest is used in this study. This feature selection process leads to 49 confirmed features which are then used for developing predictive random forest models. The study also explores five different data partitioning ratios and their impact on model accuracy are captured using coefficient of determination (r-square) and root mean square error (rsme).

Keywords: Housing data, feature selection, random forest, Boruta algorithm, root mean square error.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

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In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Xu Zhao

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Text categorization techniques are widely used to many Information Retrieval (IR) applications. In this paper, we proposed a simple but efficient method that can automatically find the relationship between any pair of terms and documents, also an indexing matrix is established for text categorization. We call this method Indexing Matrix Categorization Machine (IMCM). Several experiments are conducted to show the efficiency and robust of our algorithm.

Keywords: Text categorization, Sub-space learning, Latent Semantic Space

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Authors: Sanaz Ahmadzadeh Siyahrood, Arghavan Ebrahimi, Mohammadjavad Mahdavinejad

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Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.

Keywords: Angle, architecture, design, equal triangle, generating, grammar, square and structural hierarchy.

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Authors: Amal Kr Sarma, H Zeen Devi, N Nimai Singh

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The Constraints imposed by non-thermal leptogenesis on the survival of the neutrino mass models describing the presently available neutrino mass patterns, are studied numerically. We consider the Majorana CP violating phases coming from right-handed Majorana mass matrices to estimate the baryon asymmetry of the universe, for different neutrino mass models namely quasi-degenerate, inverted hierarchical and normal hierarchical models, with tribimaximal mixings. Considering two possible diagonal forms of Dirac neutrino mass matrix as either charged lepton or up-quark mass matrix, the heavy right-handed mass matrices are constructed from the light neutrino mass matrix. Only the normal hierarchical model leads to the best predictions of baryon asymmetry of the universe, consistent with observations in non-thermal leptogenesis scenario.

Keywords: Thermal leptogenesis, Non-thermal leptogenesis.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

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In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.

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Authors: Aziza Benaboud, Alfred Rufer

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In this paper the authors propose a flexible electronic solution, to improve the energetic efficiency of a thermo plant. This is achieved by replacing the mechanical gear box, placed traditionally between a gas turbine and a synchronous generator; by a power electronic converter. After reminding problematic of gear boxes and interest of a proposed electronic solution in high power plants, the authors describe a new control strategy for an indirect frequency converter, which is characterized by its high efficiency due to the use of SWM: Square Wave Modulation. The main advantage of this mode is the quasi absence of switching losses. A control method is also proposed to resolve some problems incurred by using square wave modulation, in particular to reduce the harmonics distortion of the output inverter voltage and current. Simulation examples as well as experimental results are included.

Keywords: Angle shift, high efficiency, indirect converter, gas turbine, NPC three level converter, square wave modulation SWM, switching angle.

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Authors: Sajjad Dehghanpour, Ali Yousefi

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Impact is one of very important subjects which always have been considered in mechanical science. Nature of impact is such that which makes its control a hard task. Therefore it is required to present the transfer of impact to other vulnerable part of a structure, when it is necessary, one of the best method of absorbing energy of impact, is by using Thin-walled tubes these tubes collapses under impact and with absorption of energy, it prevents the damage to other parts.Purpose of recent study is to survey the deformation and energy absorption of tubes with different type of cross section (rectangular or square) and with similar volumes, height, mean cross section thickness, and material under loading with different speeds. Lateral loading of tubes are quasi-static type and beside as numerical analysis, also experimental experiences has been performed to evaluate the accuracy of the results. Results from the surveys is indicates that in a same conditions which mentioned above, samples with square cross section ,absorb more energy compare to rectangular cross section, and also by increscent in speed of loading, energy absorption would be more.

Keywords: absorbed energy, lateral loading, quasi-static.

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Authors: Oluwagbenga B. Fatile, Felix U. Idu, Olajide T. Sanya

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This paper reports the viability of developing Zn-27Al alloy matrix hybrid composites reinforced with alumina, graphite and fly ash (solid waste bye product of coal in thermal power plants). This research work was aimed at developing low cost-high performance Zn-27Al matrix composite with low density. Alumina particulates (Al2O3), graphite added with 0, 2, 3, 4 and 5 wt% fly ash were utilized to prepare 10wt% reinforcing phase with Zn-27Al alloy as matrix using two-step stir casting method. Density measurement, estimated percentage porosity, tensile testing, micro hardness measurement and optical microscopy were used to assess the performance of the composites produced. The results show that the hardness, ultimate tensile strength, and percent elongation of the hybrid composites decrease with increase in fly ash content. The maximum decrease in hardness and ultimate tensile strength of 13.72% and 15.25% respectively were observed for composite grade containing 5wt% fly ash. The percentage elongation of composite sample without fly ash is 8.9% which is comparable with that of the sample containing 2wt% fly ash with percentage elongation of 8.8%. The fracture toughness of the fly ash containing composites was however superior to those of composites without fly ash with 5wt% fly ash containing composite exhibiting the highest fracture toughness. The results show that fly ash can be utilized as complementary reinforcement in ZA-27 alloy matrix composite to reduce cost.

Keywords: Fly ash, hybrid composite, mechanical behaviour, stir-cast.

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Authors: Mario Mastriani, Marcelo Naiouf

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This paper introduces a Quantum Correlation Matrix Memory (QCMM) and Enhanced QCMM (EQCMM), which are useful to work with quantum memories. A version of classical Gram-Schmidt orthogonalisation process in Dirac notation (called Quantum Orthogonalisation Process: QOP) is presented to convert a non-orthonormal quantum basis, i.e., a set of non-orthonormal quantum vectors (called qudits) to an orthonormal quantum basis, i.e., a set of orthonormal quantum qudits. This work shows that it is possible to improve the performance of QCMM thanks QOP algorithm. Besides, the EQCMM algorithm has a lot of additional fields of applications, e.g.: Steganography, as a replacement Hopfield Networks, Bilevel image processing, etc. Finally, it is important to mention that the EQCMM is an extremely easy to implement in any firmware.

Keywords: Quantum Algebra, correlation matrix memory, Dirac notation, orthogonalisation.

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Authors: Vladimir Simovic, Matija Varga, Tonco Marusic

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This research paper shows matrix technology models and examples of information systems in education (in the Republic of Croatia and in the Germany) in support of business, education (when learning and teaching) and e-learning. Here we researched and described the aims and objectives of the main process in education and technology, with main matrix classes of data. In this paper, we have example of matrix technology with detailed description of processes related to specific data classes in the processes of education and an example module that is support for the process: ‘Filling in the directory and the diary of work’ and ‘evaluation’. Also, on the lower level of the processes, we researched and described all activities which take place within the lower process in education. We researched and described the characteristics and functioning of modules: ‘Fill the directory and the diary of work’ and ‘evaluation’. For the analysis of the affinity between the aforementioned processes and/or sub-process we used our application model created in Visual Basic, which was based on the algorithm for analyzing the affinity between the observed processes and/or sub-processes.

Keywords: Designing, education management, information systems, matrix technology, process affinity.

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Authors: O. Altuntaş, A. Güral

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The hardness-microstructure relationships of spherical cementite in bainitic matrix obtained by a different heat treatment cycles carried out to high carbon powder metallurgy (P/M) steel were investigated. For this purpose, 1.5 wt.% natural graphite powder admixed in atomized iron powders and the mixed powders were compacted under 700 MPa at room temperature and then sintered at 1150 °C under a protective argon gas atmosphere. The densities of the green and sintered samples were measured via the Archimedes method. A density of 7.4 g/cm³ was obtained after sintering and a density of 94% was achieved. The sintered specimens having primary cementite plus lamellar pearlitic structures were fully quenched from 950 ^°C temperature and then over-tempered at 705 °C temperature for 60 minutes to produce spherical-fine cementite particles in the ferritic matrix. After by this treatment, these samples annealed at 735 °C temperature for 3 minutes were austempered at 300 °C salt bath for a period of 1 to 5 hours. As a result of this process, it could be able to produced spherical cementite particle in the bainitic matrix. This microstructure was designed to improve wear and toughness of P/M steels. The microstructures were characterized and analyzed by SEM and micro and macro hardness.

Keywords: Powder metallurgy steel, heat treatment, bainite, spherical cementite.

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Authors: D. R. Jain

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The aim of this paper is to use matrix representation of Fuzzy soft sets for proving some equalities connected with Fuzzy soft sets based on set-operations.

Keywords: Equality, Fuzzy soft matrix, Fuzzy soft sets, operations.

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Authors: Ji Hoon Kim, Hyung Gi Min, Jae Dong Cho, Jae Hoon Jang, Sung-Ha Kwon, Eun Tae Jeung

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Since MEMS gyro sensors measure not angle of rotation but angular rate, an estimator is designed to estimate the angles in many applications. Gyro and accelerometer are used to improve estimating accuracy of the angle. This paper presents a method of finding filter coefficients of the well-known estimator which is to get rotation angles from gyro and accelerometer data. In order to verify the performance of our method, the estimated angle is compared with the encoder output in a rotary pendulum system.

Keywords: gyro, accelerometer, estimator, least square.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

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Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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Authors: Mohamed Amine Belmiloud, Nord Eddine Sad Chemloul

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In this study, we investigated numerically heat transfer by mixed convection coupled to radiation in a square cavity; the upper horizontal wall is movable. The purpose of this study is to see the influence of the emissivity ε and the varying of the Richardson number Ri on the variation of average Nusselt number Nu. The vertical walls of the cavity are differentially heated, the left wall is maintained at a uniform temperature higher than the right wall, and the two horizontal walls are adiabatic. The finite volume method is used for solving the dimensionless Governing Equations. Emissivity values used in this study are ranged between 0 and 1, the Richardson number in the range 0.1 to 10. The Rayleigh number is fixed to Ra=104 and the Prandtl number is maintained constant Pr=0.71. Streamlines, isothermal lines and the average Nusselt number are presented according to the surface emissivity. The results of this study show that the Richardson number Ri and emissivity ε affect the average Nusselt number.

Keywords: Numerical study, mixed convection, square cavity, wall emissivity, lid-driven.

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.

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Authors: Wudhichai Assawinchaichote

Abstract:

This paper examines the problem of designing robust H controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (S) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the system. A sufficient condition of the controller for this system is given in term of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through simulation results. It has been shown that the anti-HIV vaccines are critically important in reducing the infected cells.

Keywords: H∞ Fuzzy control; Takagi-Sugeno (TS) fuzzy model; Linear Matrix Inequalities (LMIs); HIV/AIDS infection system

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Authors: S. Nazhan, Hassan K. Al-Musawi, Khalid A. Humood

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This paper reports on an experimental investigation into the influence of current modulation on the properties of a vertical-cavity surface-emitting laser (VCSEL) with a direct square wave modulation. The optical output power response, as a function of the pumping current, modulation frequency, and amplitude, is measured for an 850 nm VCSEL. We demonstrate that modulation frequency and amplitude play important roles in reducing the VCSEL’s power consumption for optical generation. Indeed, even when the biasing current is below the static threshold, the VCSEL emits optical power under the square wave modulation. The power consumed by the device to generate light is significantly reduced to > 50%, which is below the threshold current, in response to both the modulation frequency and amplitude. An operating VCSEL device at low power is very desirable for less thermal effects, which are essential for a high-speed modulation bandwidth.

Keywords: VCSELs, optical power generation, power consumption, square wave modulation.

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Authors: P. S. Bhowmik, D. V. Rajan, S. P. Bose

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The load flow study in a power system constitutes a study of paramount importance. The study reveals the electrical performance and power flows (real and reactive) for specified condition when the system is operating under steady state. This paper gives an overview of different techniques used for load flow study under different specified conditions.

Keywords: Load Flow Studies, Y-matrix and Z-matrix iteration, Newton-Raphson method, Fast Decoupled method, Fuzzy logic, Artificial Neural Network.

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Authors: Nripjit, Anand K Tyagi, Nirmal Singh

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The present work consecutively on synthesis and characterization of composites, Al/Al alloy A 384.1 as matrix in which the main ingredient as Al/Al-5% MgO alloy based metal matrix composite. As practical implications the low cost processing route for the fabrication of Al alloy A 384.1 and operational difficulties of presently available manufacturing processes based in liquid manipulation methods. As all new developments, complete understanding of the influence of processing variables upon the final quality of the product. And the composite is applied comprehensively to the acquaintance for achieving superiority of information concerning the specific heat measurement of a material through the aid of thermographs. Products are evaluated concerning relative particle size and mechanical behavior under tensile strength. Furthermore, Taguchi technique was employed to examine the experimental optimum results are achieved, owing to effectiveness of this approach.

Keywords: MMC, Thermographs, Tensile strength, Taguchi technique, Optimal parameters

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Authors: M. T. Anwar, P. K. Lala, P. Thenappan

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This paper presents the decoder design for the single error correcting and double error detecting code proposed by the authors in an earlier paper. The speed of error detection and correction of a code is largely dependent upon the associated encoder and decoder circuits. The complexity and the speed of such circuits are determined by the number of 1?s in the parity check matrix (PCM). The number of 1?s in the parity check matrix for the code proposed by the authors are fewer than in any currently known single error correcting/double error detecting code. This results in simplified encoding and decoding circuitry for error detection and correction.

Keywords: Decoder, Hsiao code, Parity Check Matrix, Syndrome Pattern.

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Authors: S. Raja Balachandar, K.Kannan

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This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: Combinatorial Optimization Problem, Generalized Assignment Problem, Intercept Matrix, Heuristic, Computational Complexity, NP-Hard Problems.

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

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The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: Eigenvalues/Eigenvectors, Latent values/vectors, Matrix fraction description, State space description.

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Authors: Jonmichael A. Weaver, David A. Miller

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Ultra High Molecular Weight Polyethylene (UHMWPE) presents several distinct advantages as a material with a high strength to weight ratio, durability, and neutron stability. Understanding the change in the mechanical performance of UHMWPE due to environmental exposure is key to safety for future applications. Dyneema® HB-210, a 15 µm diameter UHMWPE multi-filament fiber laid up in a polyurethane matrix in [0/ 90]2, with a thickness of 0.17 mm is compared to the same fiber and orientation system, HB-212, with a rubber-based matrix under UV aging conditions. UV aging tests according to ASTM-G154 were performed on both HB-210 and HB-212 to interrogate the change in mechanical properties, as measured through dynamic mechanical analysis and imaged using a scanning electron microscope. These results showed a decrease in both the storage modulus and loss modulus of the aged material compared to the unaged, even though the tan δ slightly increased. Material degradation occurred at a higher rate in Dyneema® HB-212 compared to HB-210. The HB-210 was characterized for the effects of 100 hours of UV aging via dynamic mechanical analysis. Scanning electron microscope images were taken of the HB-210 and HB-212 to identify the primary damage mechanisms in the matrix. Embrittlement and matrix spall were the products of prolonged UV exposure and erosion, resulting in decreased mechanical properties.

Keywords: Composite materials, material characterization, UV aging, UHMWPE.

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Authors: Hironori Karachi, Haruka Yamashita

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Recently, the system of quick response (QR) code is getting popular. Many companies introduce new QR code payment services and the services are competing with each other to increase the number of users. For increasing the number of users, we should grasp the difference of feature of the demographic information, usage information, and value of users between services. In this study, we conduct an analysis of real-world data provided by Nomura Research Institute including the demographic data of users and information of users’ usages of two services; LINE Pay, and PayPay. For analyzing such data and interpret the feature of them, Nonnegative Matrix Factorization (NMF) is widely used; however, in case of the target data, there is a problem of the missing data. EM-algorithm NMF (EMNMF) to complete unknown values for understanding the feature of the given data presented by matrix shape. Moreover, for comparing the result of the NMF analysis of two matrices, there is Discriminant NMF (DNMF) shows the difference of users features between two matrices. In this study, we combine EMNMF and DNMF and also analyze the target data. As the interpretation, we show the difference of the features of users between LINE Pay and Paypay.

Keywords: Data science, non-negative matrix factorization, missing data, quality of services.

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