Search results for: The direct AnsAz method.

Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

Abstract:

Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: Convergence, iteration, line search, running time, steepest descent, unconstrained optimization.

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Authors: Georgi Bebrov, Rozalina Dimova

Abstract:

In the field of quantum secure communication, there is no evaluation that characterizes quantum secure communication (QSC) protocols in a complete, general manner. The current paper addresses the problem concerning the lack of such an evaluation for QSC protocols by introducing an optimality evaluation, which is expressed as the average over the three main parameters of QSC protocols: efficiency, security, and practicality. For the efficiency evaluation, the common expression of this parameter is used, which incorporates all the classical and quantum resources (bits and qubits) utilized for transferring a certain amount of information (bits) in a secure manner. By using criteria approach whether or not certain criteria are met, an expression for the practicality evaluation is presented, which accounts for the complexity of the QSC practical realization. Based on the error rates that the common quantum attacks (Measurement and resend, Intercept and resend, probe attack, and entanglement swapping attack) induce, the security evaluation for a QSC protocol is proposed as the minimum function taken over the error rates of the mentioned quantum attacks. For the sake of clarity, an example is presented in order to show how the optimality is calculated.

Keywords: Quantum cryptography, quantum secure communcation, quantum secure direct communcation security, quantum secure direct communcation efficiency, quantum secure direct communcation practicality.

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Authors: Nicholas Kyriazis, Emmanouil Marios L. Economou, Jr, Loukas Zachilas

Abstract:

In the present essay, a model of choice by actors is analysedby utilizing the theory of chaos to explain how change comes about. Then, by using ancient and modern sources of literature, the theory of the social contract is analysed as a historical phenomenon that first appeared during the period of Classical Greece. Then, based on the findings of this analysis, the practice of direct democracy and public choice in ancient Athens is analysed, through two historical cases: Eubulus and Lycurgus political program in the second half of the 4th century. The main finding of this research is that these policies can be interpreted as an implementation of a social contract, through which citizens were taking decisions based on rational choice according to economic considerations.

Keywords: Chaos theory, public choice, social contract, 4th century BC. Athens.

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Authors: Ju-Seok Kim, Sun-Ae Moon, Tae-Gu Lee, Seung-Jae Moon, Jae-Heon Lee

Abstract:

As a simple to method estimate the plant heating energy capacity of an apartment complex, a new load calculation method has been proposed. The method which can be called as unit building method, predicts the heating load of the entire complex instead of summing up that of each apartment belonging to complex. Comparison of the unit heating load for various floor sizes between the present method and conventional approach shows a close agreement with dynamic load calculation code. Some additional calculations are performed to demonstrate it-s application examples.

Keywords: Unit Building Method, Unit Heating Load, TFMLoad.

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Authors: Thulane Paepae, Tumisang Seodigeng

Abstract:

This paper demonstrates the use of a method of synthesizing process flowsheets using a graphical tool called the GH-plot and in particular, to look at how it can be used to compare the reactions of a combined simultaneous process with regard to their thermodynamics. The technique uses fundamental thermodynamic principles to allow the mass, energy and work balances locate the attainable region for chemical processes in a reactor. This provides guidance on what design decisions would be best suited to developing new processes that are more effective and make lower demands on raw material and energy usage.

Keywords: Attainable region, dimethyl ether synthesis, mass balance, optimal reaction networks.

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Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

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In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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Authors: Yunjia Wang, Zhihong Zhao, Erxiang Song

Abstract:

Rockfills are widely used in civil engineering, such as dams, railways, and airport foundations in mountain areas. A significant long-term post-construction settlement may affect the serviceability or even the safety of rockfill infrastructures. The creep behavior of rockfills is influenced by a number of factors, such as particle size, strength and shape, water condition and stress level. However, the effect of particle shape on rockfill creep still remains poorly understood, which deserves a careful investigation. Particle-based discrete element method (DEM) was used to simulate the creep behavior of rockfills under different boundary conditions. Both angular and rounded particles were considered in this numerical study, in order to investigate the influence of particle shape. The preliminary results showed that angular particles experience more breakages and larger creep strains under one-dimensional compression than rounded particles. On the contrary, larger creep strains were observed in he rounded specimens in the direct shear test. The mechanism responsible for this difference is that the possibility of the existence of key particle in rounded particles is higher than that in angular particles. The above simulations demonstrate that the influence of particle shape on the creep behavior of rockfills can be simulated by DEM properly. The method of DEM simulation may facilitate our understanding of deformation properties of rockfill materials.

Keywords: Rockfills, creep behavior, particle crushing, discrete element method, boundary conditions.

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Authors: Zina Saheb, Ezz El-Masry

Abstract:

As the Silicon oxide scaled down in MOSFET technology to few nanometers, gate Direct Tunneling (DT) in Floating gate (FGMOSFET) devices has become a major concern for analog designers. FGMOSFET has been used in many low-voltage and low-power applications, however, there is no accurate model that account for DT gate leakage in nano-scale. This paper studied and analyzed different simulation models for FGMOSFET using TSMC 90-nm technology. The simulation results for FGMOSFET cascade current mirror shows the impact of DT on circuit performance in terms of current and voltage without the need for fabrication. This works shows the significance of using an accurate model for FGMOSFET in nan-scale technologies.

Keywords: CMOS transistor, direct-tunneling current, floatinggate, gate-leakage current, simulation model.

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Authors: Sadegh Papari, Mohammad Kazemeini, Moslem Fattahi

Abstract:

In the present study, a heterogeneous and homogeneous gas flow dispersion model for simulation and optimisation of a large-scale catalytic slurry reactor for the direct synthesis of dimethyl ether (DME) from syngas and CO2, using a churn-turbulent regime was developed. In the heterogeneous gas flow model the gas phase was distributed into two bubble phases: small and large, however in the homogeneous one, the gas phase was distributed into only one large bubble phase. The results indicated that the heterogeneous gas flow model was in more agreement with experimental pilot plant data than the homogeneous one.

Keywords: Modelling, Slurry bubble column, Dimethyl ether synthesis, Homogeneous gas flow, Heterogeneous gas flow

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Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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Authors: A. Ourici

Abstract:

This paper proposes a direct power control for doubly-fed induction machine for variable speed wind power generation. It provides decoupled regulation of the primary side active and reactive power and it is suitable for both electric energy generation and drive applications. In order to control the power flowing between the stator of the DFIG and the network, a decoupled control of active and reactive power is synthesized using PI controllers.The obtained simulation results show the feasibility and the effectiveness of the suggested method

Keywords: Doubly fed induction machine , decoupled power control , vector control , active and reactive power, PWM inverter

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Authors: Fatma Belghith, Hassen Loukil, Nouri Masmoudi

Abstract:

This paper presents the hardware design of a unified architecture to compute the 4x4, 8x8 and 16x16 efficient twodimensional (2-D) transform for the HEVC standard. This architecture is based on fast integer transform algorithms. It is designed only with adders and shifts in order to reduce the hardware cost significantly. The goal is to ensure the maximum circuit reuse during the computing while saving 40% for the number of operations. The architecture is developed using FIFOs to compute the second dimension. The proposed hardware was implemented in VHDL. The VHDL RTL code works at 240 MHZ in an Altera Stratix III FPGA. The number of cycles in this architecture varies from 33 in 4-point- 2D-DCT to 172 when the 16-point-2D-DCT is computed. Results show frequency improvements reaching 96% when compared to an architecture described as the direct transcription of the algorithm.

Keywords: HEVC, Modified Integer Transform, FPGA.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

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: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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Authors: Chutarat Boontho

Abstract:

The purposes of this study were as follows to evaluate the economic value of Phu Kradueng National Park by the travel cost method (TCM) and the contingent valuation method (CVM) and to estimate the demand for traveling and the willingness to pay. The data for this study were collected by conducting two large scale surveys on users and non-users. A total of 1,016 users and 1,034 non-users were interviewed. The data were analyzed using multiple linear regression analysis, logistic regression model and the consumer surplus (CS) was the integral of demand function for trips. The survey found, were as follows: 1)Using the travel cost method which provides an estimate of direct benefits to park users, we found that visitors- total willingness to pay per visit was 2,284.57 bath, of which 958.29 bath was travel cost, 1,129.82 bath was expenditure for accommodation, food, and services, and 166.66 bath was consumer surplus or the visitors -net gain or satisfaction from the visit (the integral of demand function for trips). 2) Thai visitors to Phu Kradueng National Park were further willing to pay an average of 646.84 bath per head per year to ensure the continued existence of Phu Kradueng National Park and to preserve their option to use it in the future. 3) Thai non-visitors, on the other hand, are willing to pay an average of 212.61 bath per head per year for the option and existence value provided by the Park. 4) The total economic value of Phu Kradueng National Park to Thai visitors and non-visitors taken together stands today at 9,249.55 million bath per year. 5) The users- average willingness to pay for access to Phu Kradueng National Park rises from 40 bath to 84.66 bath per head per trip for improved services such as road improvement, increased cleanliness, and upgraded information. This paper was needed to investigate of the potential market demand for bio prospecting in Phu Kradueng national Park and to investigate how a larger share of the economic benefits of tourism could be distributed income to the local residents.

Keywords: Contingent Valuation Method, Travel Cost Method, Consumer surplus.

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Authors: Osama Yusuf Ababneh

Abstract:

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

Keywords: Third-order convergence, non-linear equations, root finding, iterative method.

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Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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Authors: B. Ghanbarian-Alavijeh, A.M. Liaghat, S. Sohrabi

Abstract:

Saturated hydraulic conductivity is one of the soil hydraulic properties which is widely used in environmental studies especially subsurface ground water. Since, its direct measurement is time consuming and therefore costly, indirect methods such as pedotransfer functions have been developed based on multiple linear regression equations and neural networks model in order to estimate saturated hydraulic conductivity from readily available soil properties e.g. sand, silt, and clay contents, bulk density, and organic matter. The objective of this study was to develop neural networks (NNs) model to estimate saturated hydraulic conductivity from available parameters such as sand and clay contents, bulk density, van Genuchten retention model parameters (i.e. r θ , α , and n) as well as effective porosity. We used two methods to calculate effective porosity: : (1) eff s FC φ =θ -θ , and (2) inf φ =θ -θ eff s , in which s θ is saturated water content, FC θ is water content retained at -33 kPa matric potential, and inf θ is water content at the inflection point. Total of 311 soil samples from the UNSODA database was divided into three groups as 187 for the training, 62 for the validation (to avoid over training), and 62 for the test of NNs model. A commercial neural network toolbox of MATLAB software with a multi-layer perceptron model and back propagation algorithm were used for the training procedure. The statistical parameters such as correlation coefficient (R2), and mean square error (MSE) were also used to evaluate the developed NNs model. The best number of neurons in the middle layer of NNs model for methods (1) and (2) were calculated 44 and 6, respectively. The R2 and MSE values of the test phase were determined for method (1), 0.94 and 0.0016, and for method (2), 0.98 and 0.00065, respectively, which shows that method (2) estimates saturated hydraulic conductivity better than method (1).

Keywords: Neural network, Saturated hydraulic conductivity, Soil physical properties.

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Authors: V. Chahal, A. Nagpal, Y. B. Pakade, J. K. Katnoria

Abstract:

Soil is a complex physical and biological system that provides support, water, nutrients and oxygen to the plants. Apart from these, it acts as a connecting link between inorganic, organic and living components of the ecosystem. In recent years, presence of xenobiotics, alterations in the natural soil environment, application of pesticides/inorganic fertilizers, percolation of contaminated surface water as well as leachates from landfills to subsurface strata and direct discharge of industrial wastes to the land have resulted in soil pollution which in turn has posed severe threats to human health especially in terms of causing carcinogenicity by direct DNA damage. The present review is an attempt to summarize literature on sources of soil pollution, characterization of pollutants and their consequences in different living systems.

Keywords: Soil Pollution, Contaminants, Heavy metals, Pesticides, Bioassays.

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Authors: Jeong Yup Han, Su Kyung Lee, Hong Bae Park

Abstract:

In this paper, we propose a method to reduce the various kinds of noise while gathering and recording the electrocardiogram (ECG) signal. Because of the defects of former method in the noise elimination of ECG signal, we use translation invariant (TI) multiwavelet denoising method to the noise elimination. The advantage of the proposed method is that it may not only remain the geometrical characteristics of the original ECG signal and keep the amplitudes of various ECG waveforms efficiently, but also suppress impulsive noise to some extent. The simulation results indicate that the proposed method are better than former removing noise method in aspects of remaining geometrical characteristics of ECG signal and the signal-to-noise ratio (SNR).

Keywords: ECG, TI multiwavelet, denoise.

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Authors: Corné J. Coetzee, Etienne Horn

Abstract:

One of the main challenges in using the Discrete Element Method (DEM) is to specify the correct input parameter values. In general, the models are sensitive to the input parameter values and accurate results can only be achieved if the correct values are specified. For the linear contact model, micro-parameters such as the particle density, stiffness, coefficient of friction, as well as the particle size and shape distributions are required. There is a need for a procedure to accurately calibrate these parameters before any attempt can be made to accurately model a complete bulk materials handling system. Since DEM is often used to model applications in the mining and quarrying industries, a calibration procedure was developed for materials that consist of relatively large (up to 40 mm in size) particles. A coarse crushed aggregate was used as the test material. Using a specially designed large shear box with a diameter of 590 mm, the confined Young’s modulus (bulk stiffness) and internal friction angle of the material were measured by means of the confined compression test and the direct shear test respectively. DEM models of the experimental setup were developed and the input parameter values were varied iteratively until a close correlation between the experimental and numerical results was achieved. The calibration process was validated by modelling the pull-out of an anchor from a bed of material. The model results compared well with experimental measurement.

Keywords: Discrete Element Method (DEM), calibration, shear box, anchor pull-out.

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Authors: Mahmoud R. Shaghaghian

Abstract:

Amount of dissolve oxygen in a river has a great direct affect on aquatic macroinvertebrates and this would influence on the region ecosystem indirectly. In this paper it is tried to predict dissolved oxygen in rivers by employing an easy Fuzzy Logic Modeling, Wang Mendel method. This model just uses previous records to estimate upcoming values. For this purpose daily and hourly records of eight stations in Au Sable watershed in Michigan, United States are employed for 12 years and 50 days period respectively. Calculations indicate that for long period prediction it is better to increase input intervals. But for filling missed data it is advisable to decrease the interval. Increasing partitioning of input and output features influence a little on accuracy but make the model too time consuming. Increment in number of input data also act like number of partitioning. Large amount of train data does not modify accuracy essentially, so, an optimum training length should be selected.

Keywords: Dissolved oxygen, Au Sable, fuzzy logic modeling, Wang Mendel.

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Authors: Tanapat Brikshavana, Anirut Luadsong

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Keywords: donor-cell scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: Fahad Alsharari, Mohd Salmi Md Noorani

Abstract:

A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron- Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift, x will be in the Motzkin subshift M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, a new direct method of calculating the topological entropy of the Motzkin shift is given without any measure theoretical discussion.

Keywords: Motzkin shift, topological entropy.

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Authors: Seyed Saeid Tabaee, Omid Bahar

Abstract:

Nowadays, energy dissipation devices are commonly used in structures. High rate of energy absorption during earthquakes is the benefit of using such devices, which results in damage reduction of structural elements, specifically columns. The hysteretic damping capacity of energy dissipation devices is the key point that it may adversely make analysis and design process complicated. This effect may be generally represented by Equivalent Viscous Damping (EVD). The equivalent viscous damping might be obtained from the expected hysteretic behavior regarding to the design or maximum considered displacement of a structure. In this paper, the hysteretic damping coefficient of a steel Moment Resisting Frame (MRF), which its performance is enhanced by a Buckling Restrained Brace (BRB) system has been evaluated. Having foresight of damping fraction between BRB and MRF is inevitable for seismic design procedures like Direct Displacement-Based Design (DDBD) method. This paper presents an approach to calculate the damping fraction for such systems by carrying out the dynamic nonlinear time history analysis (NTHA) under harmonic loading, which is tuned to the natural system frequency. Two MRF structures, one equipped with BRB and the other without BRB are simultaneously studied. Extensive analysis shows that proportion of each system damping fraction may be calculated by its shear story portion. In this way, contribution of each BRB in the floors and their general contribution in the structural performance may be clearly recognized, in advance.

Keywords: Buckling restrained brace, Direct displacement based design, Dual systems, Hysteretic damping, Moment resisting frames.

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Authors: Sudipta Majumdar, Harish Parthasarathy

Abstract:

In this paper, a wavelet based method is proposed to identify the constant coefficients of a second order linear system and is compared with the least squares method. The proposed method shows improved accuracy of parameter estimation as compared to the least squares method. Additionally, it has the advantage of smaller data requirement and storage requirement as compared to the least squares method.

Keywords: Least squares method, linear system, system identification, wavelet transform.

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Authors: Venugopal Kummamuru

Abstract:

Corporate Governance (CG) is of utmost importance for running a company ethically. It is essential for the growth and success of the corporation. It is intended to increase the accountability of an organization to the larger context of the business environment. The general principles of CG include and are related to Shareholder recognition, Stakeholder interests, and focus on Corporate Social Responsibility (CSR), Clear Board responsibilities, Ethical behavior, and Business transparency. Network Marketing Organizations (NMOs) focus on marketing through direct-sales using people who are associated with the organization but are not their employees. This paper tries to study the importance of Ethics and CSR in an NMO and suggest a basic guideline for CG in NMO(s). This paper could be used as a basis or starting point for conducting an in-depth research to understand the difference in CG practices between NMO(s) and other organizations and define a standard set of guidelines for CG practice.

Keywords: Corporate governance, corporate responsibility, direct selling, network marketing.

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Authors: Sudeshna Bhattacharya, Pratyush Pandey, Pradeep Kumar K

Abstract:

We propose a decoy-pulse protocol for frequency-coded implementation of B92 quantum key distribution protocol. A direct extension of decoy-pulse method to frequency-coding scheme results in security loss as an eavesdropper can distinguish between signal and decoy pulses by measuring the carrier photon number without affecting other statistics. We overcome this problem by optimizing the ratio of carrier photon number of decoy-to-signal pulse to be as close to unity as possible. In our method the switching between signal and decoy pulses is achieved by changing the amplitude of RF signal as opposed to modulating the intensity of optical signal thus reducing system cost. We find an improvement by a factor of 100 approximately in the key generation rate using decoy-state protocol. We also study the effect of source fluctuation on key rate. Our simulation results show a key generation rate of 1.5×10-4/pulse for link lengths up to 70km. Finally, we discuss the optimum value of average photon number of signal pulse for a given key rate while also optimizing the carrier ratio.

Keywords: B92, decoy-pulse, frequency-coding, quantum key distribution.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

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