Search results for: primal-dual interior point method

Authors: Yun-Ho Ahn, Hyery Kang, Dong-Yeun Koh, Huen Lee

Abstract:

In this study, we demonstrate the production of natural gas hydrates from permeable marine sediments with simultaneous mechanisms for methane recovery and methane-air or methane-air/carbon dioxide replacement. The simultaneous melting happens until the chemical potentials become equal in both phases as natural gas hydrate depletion continues and self-regulated methane-air replacement occurs over an arbitrary point. We observed certain point between dissociation and replacement mechanisms in the natural gas hydrate reservoir, and we call this boundary as critical methane concentration. By the way, when carbon dioxide was added, the process of chemical exchange of methane by air/carbon dioxide was observed in the natural gas hydrate. The suggested process will operate well for most global natural gas hydrate reservoirs, regardless of the operating conditions or geometrical constraints.

Keywords: Air injection, Carbon dioxide sequestration, Hydrate production, Natural gas hydrate.

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Authors: F. Yildiz, S. Y. Oturanc

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Advances technology in the field of photogrammetry replaces analog cameras with reflection on aircraft GPS/IMU system with a digital aerial camera. In this system, when determining the position of the camera with the GPS, camera rotations are also determined by the IMU systems. All around the world, digital aerial cameras have been used for the photogrammetry applications in the last ten years. In this way, in terms of the work done in photogrammetry it is possible to use time effectively, costs to be reduced to a minimum level, the opportunity to make fast and accurate. Geo-referencing techniques that are the cornerstone of the GPS / INS systems, photogrammetric triangulation of images required for balancing (interior and exterior orientation) brings flexibility to the process. Also geo-referencing process; needed in the application of photogrammetry targets to help to reduce the number of ground control points. In this study, the use of direct and indirect georeferencing techniques on the accuracy of the points was investigated in the production of photogrammetric mapping.

Keywords: Photogrammetry, GPS/IMU Systems, Geo- Referencing.

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Authors: Salim Istyaq, Mohammad Sarosh Umar

Abstract:

Today, the mankind is in the stage of development, every day comes with new proposal of technology, in order to secure these types of technology, we also prepare high yielding security modules to conserve these resources. The capacity of human brain to recognize anything is far more than any species; this is all due to our developing cycle of curiosity. In this paper, we proposed a scheme based on graphical password using QR Code which provides more security to the recent online system. It also contains a supportive sound signature. In this system, authentication is done using sequence of images in QR code form. Users select one click-point per image with the help of QR scanner or recognizer. The encoded phrase in a QR code emphasizes the minimum probability of attacking via shoulder surfing or other attacks.

Keywords: Graphical password, QR code, sound signature, image authentication, cued click point.

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Authors: Theerawat Songyot, Tham Manjing, Bunyarit Uyyanonvara, Chanjira Sinthanayothin

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Corner detection and optical flow are common techniques for feature-based video stabilization. However, these algorithms are computationally expensive and should be performed at a reasonable rate. This paper presents an algorithm for discarding irrelevant feature points and maintaining them for future use so as to improve the computational cost. The algorithm starts by initializing a maintained set. The feature points in the maintained set are examined against its accuracy for modeling. Corner detection is required only when the feature points are insufficiently accurate for future modeling. Then, optical flows are computed from the maintained feature points toward the consecutive frame. After that, a motion model is estimated based on the simplified affine motion model and least square method, with outliers belonging to moving objects presented. Studentized residuals are used to eliminate such outliers. The model estimation and elimination processes repeat until no more outliers are identified. Finally, the entire algorithm repeats along the video sequence with the points remaining from the previous iteration used as the maintained set. As a practical application, an efficient video stabilization can be achieved by exploiting the computed motion models. Our study shows that the number of times corner detection needs to perform is greatly reduced, thus significantly improving the computational cost. Moreover, optical flow vectors are computed for only the maintained feature points, not for outliers, thus also reducing the computational cost. In addition, the feature points after reduction can sufficiently be used for background objects tracking as demonstrated in the simple video stabilizer based on our proposed algorithm.

Keywords: background object tracking, feature point reduction, low cost tracking, video stabilization.

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Authors: T. Matsubayashi, T. Yamada

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In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.

Keywords: visualization, graph drawing, Internet Map

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Authors: Hui-Yu Huang, Shih-Hsu Chang

Abstract:

In this paper, we propose a high capacity image hiding technology based on pixel prediction and the difference of modified histogram. This approach is used the pixel prediction and the difference of modified histogram to calculate the best embedding point. This approach can improve the predictive accuracy and increase the pixel difference to advance the hiding capacity. We also use the histogram modification to prevent the overflow and underflow. Experimental results demonstrate that our proposed method within the same average hiding capacity can still keep high quality of image and low distortion

Keywords: data hiding, predictor

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Authors: Ie-jung Choi

Abstract:

Since the feasibility study of R&D programs have been initiated for efficient public R&D investments, year 2008, feasibility studies have improved in terms of precision. Although experience related to these studies of R&D programs have increased to a certain point, still methodological improvement is required. The feasibility studies of R&D programs are consisted of various viewpoints, such as technology, policy, and economics. This research is to provide improvement methods to the economic perspective; especially the cost estimation process of R&D activities. First of all, the fundamental concept of cost estimation is reviewed. After the review, a statistical and econometric analysis method is applied as empirical analysis. Conclusively, limitations and further research directions are provided.

Keywords: Cost Estimation, R&D Program, Feasibility AnalysisStudy.

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Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

Abstract:

Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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Authors: Mohsen Keyvanfard

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A new, simple and highly sensitive kinetic spectrophotometric method was developed for the determination of trace amounts of Ru(III) in the range of 0.06-20 ng/ml .The method is based on the inhibitory effect of ruthenium(III) on the oxidation of Rhodamine B by bromate in acidic and micellar medium. The reaction was monitored spectrophotometrically by measuring the decreasing in absorbance of Rhodamine B at 554 nm with a fixedtime method..The limit of detection is 0.04 ng/ml Ru(III).The relative standard deviation of 5 and 10 ng/ml Ru(III) was 2.3 and 2.7 %, respectively. The method was applied to the determination of ruthenium in real water samples

Keywords: Ruthenium ;Inhibitory; Rhodamine B; bromate

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: Exponential smoothing method, open data, operation estimation, train schedule.

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Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

Abstract:

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: Finite Volume Methods, Central Schemes, Fortran 90, Relativistic Astrophysics, Jet.

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Authors: Minjeong Kim, Seungchul Lee, Iman Janghorban Esfahani, Jeong Tai Kim, Chang Kyoo Yoo

Abstract:

This study was carried out for an underground subway station at Seoul Metro, Korea. The optimal set-points of the ventilation control system are determined every 3 hours, then, the ventilation controller adjusts the ventilation fan speed according to the optimal set-point changes. Compared to manual ventilation system which is operated irrespective of the OAQ, the IDP-based ventilation control system saves 3.7% of the energy consumption. Compared to the fixed set-point controller which is operated irrespective of the IAQ diurnal variation, the IDP-based controller shows better performance with a 2% decrease in energy consumption, maintaining the comfortable IAQ range inside the station.

Keywords: Indoor air quality, iterative dynamic algorithm, outdoor air information, ventilation control system.

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Authors: J. A. Michline Rupa, S. Ganesh

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This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

Keywords: Backward/Forward sweep method, Distribution system, Load flow analysis.

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Authors: Kemalettin Erbatur, Özer Koca, Evrim Taşkıran, Metin Yılmaz, Utku Seven

Abstract:

Recent fifteen years witnessed fast improvements in the field of humanoid robotics. The human-like robot structure is more suitable to human environment with its supreme obstacle avoidance properties when compared with wheeled service robots. However, the walking control for bipedal robots is a challenging task due to their complex dynamics. Stable reference generation plays a very important role in control. Linear Inverted Pendulum Model (LIPM) and the Zero Moment Point (ZMP) criterion are applied in a number of studies for stable walking reference generation of biped walking robots. This paper follows this main approach too. We propose a natural and continuous ZMP reference trajectory for a stable and human-like walk. The ZMP reference trajectories move forward under the sole of the support foot when the robot body is supported by a single leg. Robot center of mass trajectory is obtained from predefined ZMP reference trajectories by a Fourier series approximation method. The Gibbs phenomenon problem common with Fourier approximations of discontinuous functions is avoided by employing continuous ZMP references. Also, these ZMP reference trajectories possess pre-assigned single and double support phases, which are very useful in experimental tuning work. The ZMP based reference generation strategy is tested via threedimensional full-dynamics simulations of a 12-degrees-of-freedom biped robot model. Simulation results indicate that the proposed reference trajectory generation technique is successful.

Keywords: Biped robot, Linear Inverted Pendulum Model, Zero Moment Point, Fourier series approximation.

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Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.

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Authors: G. Revathi, P. Saikrishnan

Abstract:

In the present analysis an unsteady laminar forced convection water boundary layer flow is considered. The fluid properties such as viscosity and Prandtl number are taken as variables such that those are inversely proportional to temperature. By using quasi-linearization technique the nonlinear coupled partial differential equations are linearized and the numerical solutions are obtained by using implicit finite difference scheme with the appropriate selection of step sizes. Non-similar solutions have been obtained from the starting point of the stream-wise coordinate to the point where skin friction value vanishes. The effect non-uniform mass transfer along the surface of the cylinder through slot is studied on the skin friction and heat transfer coefficients.

Keywords: Boundary layer, heat transfer, non-similar solution, non-uniform mass, unsteady flow.

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Authors: Meng-Hao Tsai, Tsuei-Chiang Huang

Abstract:

Interior brick-infill partitions are usually considered as non-structural components and only their weight is accounted for in practical structural design. In this study, their effect on the progressive collapse resistance of an RC building subjected to sudden column loss is investigated. Three notional column loss conditions with four different brick-infill locations are considered. Column-loss response analyses of the RC building with and without brick infills are carried out. Analysis results indicate that the collapse resistance is only slightly influenced by the brick infills due to their brittle failure characteristic. Even so, they may help to reduce the inelastic displacement response under column loss. For practical engineering, it is reasonably conservative to only consider the weight of brick-infill partitions in the structural analysis.

Keywords: Progressive collapse, column loss, brick-infill partition, compression strut.

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Authors: A. Shahsavari, M. Nili-Ahmadabadi

Abstract:

This paper presents an innovative one-dimensional optimization of a transonic compressor based on the radial equilibrium theory by means of increasing blade loading. Firstly, the rotor blade of the transonic compressor is redesigned based on the constant span-wise deHaller number and diffusion. The code is applied to extract compressor meridional plane and blade to blade geometry containing rotor and stator in order to design blade three-dimensional view. A structured grid is generated for the numerical domain of fluid. Finer grids are used for regions near walls to capture boundary layer effects and behavior. RANS equations are solved by finite volume method for rotating zones (rotor) and stationary zones (stator). The experimental data, available for the performance map of NASA Rotor67, is used to validate the results of simulations. Then, the capability of the design method is validated by CFD that is capable of predicting the performance map. The numerical results of new geometry show about 19% increase in pressure ratio and 11% improvement in overall efficiency of the transonic stage; however, the design point mass flow rate of the new compressor is 5.7% less than that of the original compressor.

Keywords: One dimensional design, deHaller number, radial equilibrium, transonic compressor.

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Authors: Tayfun Gundogdu, Guven Komurgoz

Abstract:

This paper presents design, analysis and comparison of the different rotor type permanent magnet machines. The presented machines are designed as having same geometrical dimensions and same materials for comparison. The main machine parameters of interior and exterior rotor type machines including eddy current effect, torque-speed characteristics and magnetic analysis are investigated using MAXWELL program. With this program, the components of the permanent magnet machines can be calculated with high accuracy. Six types of Permanent machines are compared with respect to their topology, size, magnetic field, air gap flux, voltage, torque, loss and efficiency. The analysis results demonstrate the effectiveness of the proposed machines design methodology. We believe that, this study will be a helpful resource in terms of examination and comparison of the basic structure and magnetic features of the PM (Permanent magnet) machines which have different rotor structure.

Keywords: Motor design, Permanent Magnet, Finite-Elementmethod.

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Authors: M. Caramihai, Irina Severin, H. Balan, A. Blidaru, V. Balanica

Abstract:

Accurate assessment of the primary tumor response to treatment is important in the management of breast cancer. This paper introduces a new set of treatment evaluation indicators for breast cancer cases based on the computational process of three known metrics, the Euclidian, Hamming and Levenshtein distances. The distance principals are applied to pairs of mammograms and/or echograms, recorded before and after treatment, determining a reference point in judging the evolution amount of the studied carcinoma. The obtained numerical results are indeed very transparent and indicate not only the evolution or the involution of the tumor under treatment, but also a quantitative measurement of the benefit in using the selected method of treatment.

Keywords: Breast cancer, Distance metrics, Cancer treatment evaluation.

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Authors: Javier Rivas, Olga Gimeno, Maria Carbajo, Teresa Borralho

Abstract:

The elimination of ranitidine (a pharmaceutical compound) has been carried out in the presence of UV-C radiation. After some preliminary experiments, it has been experienced the no influence of the gas nature (air or oxygen) bubbled in photolytic experiments. From simple photolysis experiments the quantum yield of this compound has been determined. Two photolytic approximation has been used, the linear source emission in parallel planes and the point source emission in spherical planes. The quantum yield obtained was in the proximity of 0.05 mol Einstein-1 regardless of the method used. Addition of free radical promoters (hydrogen peroxide) increases the ranitidine removal rate while the use of photocatalysts (TiO2) negatively affects the process.

Keywords: Quantum yield, photolysis, ranitidine, watertreatment.

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: A. Won-Yong Chae, B. Hyung-Nam Kim, C. Kyoung-Jun Lee, D. Hee-Je Kim

Abstract:

The renewable energy has been attracting attention as a new alternative energy due to the problem of environmental pollution and resource depletion. In particular, daylighting and PV system are regarded as the solutions. In this paper, the hybrid dimming control system supplied by solar cell and daylighting system was designed. Daylighting system is main source and PV system is spare source. PV system operates the LED lamp which supports daylighting system because daylighting system is unstable due to the variation of irradiance. In addition, PV system has a role charging batteries. Battery charging has a benefit that PV system operate LED lamp in the bad weather. However, LED lamp always can`t turn on that-s why dimming control system was designed. In particular, the solar charging robot was designed to check the interior irradiance intensity. These systems and the application of the solar charging robot are expected to contribute developing alternative energy in the near future.

Keywords: Daylighting system, PV system, LED lamp, Suntracking robot.

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

Abstract:

The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: Control, limits cycle, robot, stability.

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Authors: S. K. Gupta, Richa Bansal

Abstract:

In a deregulated power system structure, power producers and customers share a common transmission network for wheeling power from the point of generation to the point of consumption. All parties in this open access environment may try to purchase the energy from the cheaper source for greater profit margins, which may lead to overloading and congestion of certain corridors of the transmission network. This may result in violation of line flow, voltage and stability limits and thereby undermine the system security. Utilities therefore need to determine adequately their available transfer capability (ATC) to ensure that system reliability is maintained while serving a wide range of bilateral and multilateral transactions. This paper presents power transfer distribution factor based on AC load flow for the determination and enhancement of ATC. The study has been carried out for IEEE 24 bus Reliability Test System.

Keywords: Available Transfer Capability, FACTS devices, Power Transfer Distribution Factors.

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Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: Mir Shahriar Emami

Abstract:

Although it is fully impossible to ensure that a software system is quite secure, developing an acceptable secure software system in a convenient platform is not unreachable. In this paper, we attempt to analyze software development life cycle (SDLC) models from the hardware systems and circuits point of view. To date, the SDLC models pay merely attention to the software security from the software perspectives. In this paper, we present new features for SDLC stages to emphasize the role of systems and circuits in developing secure software system through the software development stages, the point that has not been considered previously in the SDLC models.

Keywords: Systems and circuits security, software security, software process engineering, SDLC, SSDLC.

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Authors: Li Jiang, Baoguang Tian

Abstract:

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

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

Abstract:

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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