Search results for: generalized Lorenz model
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7658

Search results for: generalized Lorenz model

7658 New Insight into Fluid Mechanics of Lorenz Equations

Authors: Yu-Kai Ting, Jia-Ying Tu, Chung-Chun Hsiao

Abstract:

New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work.

Keywords: Galerkin method, Lorenz equations, Navier-Stokes equations.

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7657 Modeling Bessel Beams and Their Discrete Superpositions from the Generalized Lorenz-Mie Theory to Calculate Optical Forces over Spherical Dielectric Particles

Authors: Leonardo A. Ambrosio, Carlos. H. Silva Santos, Ivan E. L. Rodrigues, Ayumi K. de Campos, Leandro A. Machado

Abstract:

In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.

Keywords: Bessel Beams and Frozen Waves, Generalized Lorenz-Mie Theory, Numerical Methods, Optical Forces.

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7656 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

Authors: Chao Yuan, Bao Guang Tian

Abstract:

A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

Keywords: Generalized linear model, generalized relative coefficient, least eigenvalue, relative efficiency.

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7655 On Deterministic Chaos: Disclosing the Missing Mathematics from the Lorenz-Haken Equations

Authors: Belkacem Meziane

Abstract:

The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.

Keywords: chaos, Lorenz-Haken equations, laser dynamics, nonlinearities

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7654 Adaptive Functional Projective Lag Synchronization of Lorenz System

Authors: Tae H. Lee, J.H. Park, S.M. Lee, H.Y. Jung

Abstract:

This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results.

Keywords: Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method

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7653 Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller

Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi

Abstract:

In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.

Keywords: Chaotic system, Fuzzy control, Lorenz equation.

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7652 2D Numerical Analysis of Sao Paulo Tunnel

Authors: A.H. Akhaveissy

Abstract:

Nonlinear finite element method and Serendipity eight nodes element are used for determining of ground surface settlement due to tunneling. Linear element with elastic behavior is used for modeling of lining. Modified Generalized plasticity model with nonassociated flow rule is applied for analysis of a tunnel in Sao Paulo – Brazil. The tunnel had analyzed by Lades- model with 16 parameters. In this work modified Generalized Plasticity is used with 10 parameters, also Mohr-Coulomb model is used to analysis the tunnel. The results show good agreement with observed results of field data by modified Generalized Plasticity model than other models. The obtained result by Mohr-Coulomb model shows less settlement than other model due to excavation.

Keywords: Non-associated flow rule, Generalized plasticity, tunnel excavation, Excavation method.

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7651 Implementation of Generalized Plasticity in Load-Deformation Behavior of Foundation with Emphasis on Localization Problem

Authors: A. H. Akhaveissy

Abstract:

Nonlinear finite element method with eight noded isoparametric quadrilateral element is used for prediction of loaddeformation behavior including bearing capacity of foundations. Modified generalized plasticity model with non-associated flow rule is applied for analysis of soil-footing system. Also Von Mises and Tresca criterions are used for simulation of soil behavior. Modified generalized plasticity model is able to simulate load-deformation including softening behavior. Localization phenomena are considered by different meshes. Localization phenomena have not been seen in the examples. Predictions by modified generalized plasticity model show good agreement with laboratory data and theoretical prediction in comparison the other models.

Keywords: Localization phenomena, Generalized plasticity, Non-associated Flow Rule

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7650 Complex-Valued Neural Network in Signal Processing: A Study on the Effectiveness of Complex Valued Generalized Mean Neuron Model

Authors: Anupama Pande, Ashok Kumar Thakur, Swapnoneel Roy

Abstract:

A complex valued neural network is a neural network which consists of complex valued input and/or weights and/or thresholds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in signal processing. In Neural networks, generalized mean neuron model (GMN) is often discussed and studied. The GMN includes a new aggregation function based on the concept of generalized mean of all the inputs to the neuron. This paper aims to present exhaustive results of using Generalized Mean Neuron model in a complex-valued neural network model that uses the back-propagation algorithm (called -Complex-BP-) for learning. Our experiments results demonstrate the effectiveness of a Generalized Mean Neuron Model in a complex plane for signal processing over a real valued neural network. We have studied and stated various observations like effect of learning rates, ranges of the initial weights randomly selected, error functions used and number of iterations for the convergence of error required on a Generalized Mean neural network model. Some inherent properties of this complex back propagation algorithm are also studied and discussed.

Keywords: Complex valued neural network, Generalized Meanneuron model, Signal processing.

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7649 An Approach to Correlate the Statistical-Based Lorenz Method, as a Way of Measuring Heterogeneity, with Kozeny-Carman Equation

Authors: H. Khanfari, M. Johari Fard

Abstract:

Dealing with carbonate reservoirs can be mind-boggling for the reservoir engineers due to various digenetic processes that cause a variety of properties through the reservoir. A good estimation of the reservoir heterogeneity which is defined as the quality of variation in rock properties with location in a reservoir or formation, can better help modeling the reservoir and thus can offer better understanding of the behavior of that reservoir. Most of reservoirs are heterogeneous formations whose mineralogy, organic content, natural fractures, and other properties vary from place to place. Over years, reservoir engineers have tried to establish methods to describe the heterogeneity, because heterogeneity is important in modeling the reservoir flow and in well testing. Geological methods are used to describe the variations in the rock properties because of the similarities of environments in which different beds have deposited in. To illustrate the heterogeneity of a reservoir vertically, two methods are generally used in petroleum work: Dykstra-Parsons permeability variations (V) and Lorenz coefficient (L) that are reviewed briefly in this paper. The concept of Lorenz is based on statistics and has been used in petroleum from that point of view. In this paper, we correlated the statistical-based Lorenz method to a petroleum concept, i.e. Kozeny-Carman equation and derived the straight line plot of Lorenz graph for a homogeneous system. Finally, we applied the two methods on a heterogeneous field in South Iran and discussed each, separately, with numbers and figures. As expected, these methods show great departure from homogeneity. Therefore, for future investment, the reservoir needs to be treated carefully.

Keywords: Carbonate reservoirs, heterogeneity, homogeneous system, Dykstra-Parsons permeability variations (V), Lorenz coefficient (L).

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7648 Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.

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7647 Investigation on Machine Tools Energy Consumptions

Authors: Shiva Abdoli, Daniel T. Semere

Abstract:

Several researches have been conducted to study consumption of energy in cutting process. Most of these researches are focusing to measure the consumption and propose consumption reduction methods. In this work, the relation between the cutting parameters and the consumption is investigated in order to establish a generalized energy consumption model that can be used for process and production planning in real production lines. Using the generalized model, the process planning will be carried out by taking into account the energy as a function of the selected process parameters. Similarly, the generalized model can be used in production planning to select the right operational parameters like batch sizes, routing, buffer size, etc. in a production line. The description and derivation of the model as well as a case study are given in this paper to illustrate the applicability and validity of the model.

Keywords: Process parameters, cutting process, energy efficiency, Material Removal Rate (MRR).

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7646 Application of a Generalized Additive Model to Reveal the Relations between the Density of Zooplankton with Other Variables in the West Daya Bay, China

Authors: Weiwen Li, Hao Huang, Chengmao You, Jianji Liao, Lei Wang, Lina An

Abstract:

Zooplankton are a central issue in the ecology which makes a great contribution to maintaining the balance of an ecosystem. It is critical in promoting the material cycle and energy flow within the ecosystems. A generalized additive model (GAM) was applied to analyze the relationships between the density (individuals per m³) of zooplankton and other variables in West Daya Bay. All data used in this analysis (the survey month, survey station (longitude and latitude), the depth of the water column, the superficial concentration of chlorophyll a, the benthonic concentration of chlorophyll a, the number of zooplankton species and the number of zooplankton species) were collected through monthly scientific surveys during January to December 2016. GLM model (generalized linear model) was used to choose the significant variables’ impact on the density of zooplankton, and the GAM was employed to analyze the relationship between the density of zooplankton and the significant variables. The results showed that the density of zooplankton increased with an increase of the benthonic concentration of chlorophyll a, but decreased with a decrease in the depth of the water column. Both high numbers of zooplankton species and the overall total number of zooplankton individuals led to a higher density of zooplankton.

Keywords: Density, generalized linear model, generalized additive model, the West Daya Bay, zooplankton.

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7645 Generalized Chaplygin Gas and Varying Bulk Viscosity in Lyra Geometry

Authors: A. K. Sethi, R. N. Patra, B. Nayak

Abstract:

In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: Bulk viscosity, Lyra geometry, generalized Chaplygin gas, cosmology.

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7644 Dynamic Model of a Buck Converter with a Sliding Mode Control

Authors: S. Chonsatidjamroen , K-N. Areerak, K-L. Areerak

Abstract:

This paper presents the averaging model of a buck converter derived from the generalized state-space averaging method. The sliding mode control is used to regulate the output voltage of the converter and taken into account in the model. The proposed model requires the fast computational time compared with those of the full topology model. The intensive time-domain simulations via the exact topology model are used as the comparable model. The results show that a good agreement between the proposed model and the switching model is achieved in both transient and steady-state responses. The reported model is suitable for the optimal controller design by using the artificial intelligence techniques.

Keywords: Generalized state-space averaging method, buck converter, sliding mode control, modeling, simulation.

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7643 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

Authors: Xingping Sheng

Abstract:

Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn iteration steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.

Keywords: Generalized inverse A(2) T, S, Restricted inner product, Iterative method, Orthogonal projection.

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7642 Kalman Filter for Bilinear Systems with Application

Authors: Abdullah E. Al-Mazrooei

Abstract:

In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real measurements is introduced to illustrate the efficiency of the proposed algorithm.

Keywords: Bilinear systems, state space model, Kalman filter.

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7641 Unsteady Rayleigh-Bénard Convection of Nanoliquids in Enclosures

Authors: P. G. Siddheshwar, B. N. Veena

Abstract:

Rayleigh-B´enard convection of a nanoliquid in shallow, square and tall enclosures is studied using the Khanafer-Vafai-Lightstone single-phase model. The thermophysical properties of water, copper, copper-oxide, alumina, silver and titania at 3000 K under stagnant conditions that are collected from literature are used in calculating thermophysical properties of water-based nanoliquids. Phenomenological laws and mixture theory are used for calculating thermophysical properties. Free-free, rigid-rigid and rigid-free boundary conditions are considered in the study. Intractable Lorenz model for each boundary combination is derived and then reduced to the tractable Ginzburg-Landau model. The amplitude thus obtained is used to quantify the heat transport in terms of Nusselt number. Addition of nanoparticles is shown not to alter the influence of the nature of boundaries on the onset of convection as well as on heat transport. Amongst the three enclosures considered, it is found that tall and shallow enclosures transport maximum and minimum energy respectively. Enhancement of heat transport due to nanoparticles in the three enclosures is found to be in the range 3% - 11%. Comparison of results in the case of rigid-rigid boundaries is made with those of an earlier work and good agreement is found. The study has limitations in the sense that thermophysical properties are calculated by using various quantities modelled for static condition.

Keywords: Enclosures, free-free, rigid-rigid and rigid-free boundaries, Ginzburg-Landau model, Lorenz model.

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7640 Generalized Chebyshev Collocation Method

Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

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7639 (T1, T2)*- Semi Star Generalized Locally Closed Sets

Authors: M. Sundararaman, K. Chandrasekhara Rao

Abstract:

The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

Keywords: (T1, T2)*-semi star generalized locally closed sets, T1T2-semi star generalized closed sets.

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7638 Forecasting Electricity Spot Price with Generalized Long Memory Modeling: Wavelet and Neural Network

Authors: Souhir Ben Amor, Heni Boubaker, Lotfi Belkacem

Abstract:

This aims of this paper is to forecast the electricity spot prices. First, we focus on modeling the conditional mean of the series so we adopt a generalized fractional -factor Gegenbauer process (k-factor GARMA). Secondly, the residual from the -factor GARMA model has used as a proxy for the conditional variance; these residuals were predicted using two different approaches. In the first approach, a local linear wavelet neural network model (LLWNN) has developed to predict the conditional variance using the Back Propagation learning algorithms. In the second approach, the Gegenbauer generalized autoregressive conditional heteroscedasticity process (G-GARCH) has adopted, and the parameters of the k-factor GARMA-G-GARCH model has estimated using the wavelet methodology based on the discrete wavelet packet transform (DWPT) approach. The empirical results have shown that the k-factor GARMA-G-GARCH model outperform the hybrid k-factor GARMA-LLWNN model, and find it is more appropriate for forecasts.

Keywords: k-factor, GARMA, LLWNN, G-GARCH, electricity price, forecasting.

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7637 The Baer Radical of Rings in Term of Prime and Semiprime Generalized Bi-ideals

Authors: Rattiya Boonruang, Aiyared Iampan

Abstract:

Using the idea of prime and semiprime bi-ideals of rings, the concept of prime and semiprime generalized bi-ideals of rings is introduced, which is an extension of the concept of prime and semiprime bi-ideals of rings and some interesting characterizations of prime and semiprime generalized bi-ideals are obtained. Also, we give the relationship between the Baer radical and prime and semiprime generalized bi-ideals of rings in the same way as of biideals of rings which was studied by Roux.

Keywords: ring, prime and semiprime (generalized) bi-ideal, Baer radical.

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7636 The Gerber-Shiu Functions of a Risk Model with Two Classes of Claims and Random Income

Authors: Shan Gao

Abstract:

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

Keywords: Poisson process, generalized Erlang risk process, Gerber-Shiu function, generating function, generalized Lundberg equation.

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7635 Generalized d-q Model of n-Phase Induction Motor Drive

Authors: G. Renukadevi, K. Rajambal

Abstract:

This paper presents a generalized d-q model of n- phase induction motor drive. Multi -phase (n-phase) induction motor (more than three phases) drives possess several advantages over conventional three-phase drives, such as reduced current/phase without increasing voltage/phase, lower torque pulsation, higher torque density, fault tolerance, stability, high efficiency and lower current ripple. When the number of phases increases, it is also possible to increase the power in the same frame. In this paper, a generalized dq-axis model is developed in Matlab/Simulink for an n-phase induction motor. The simulation results are presented for 5, 6, 7, 9 and 12 phase induction motor under varying load conditions. Transient response of the multi-phase induction motors are given for different number of phases. Fault tolerant feature is also analyzed for 5-phase induction motor drive.

Keywords: d-q model, dynamic Response, fault tolerant feature, Matlab/Simulink, multi-phase induction motor, transient response.

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7634 Convergence Analysis of the Generalized Alternating Two-Stage Method

Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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7633 Modelling Extreme Temperature in Malaysia Using Generalized Extreme Value Distribution

Authors: Husna Hasan, Norfatin Salam, Mohd Bakri Adam

Abstract:

Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is linear for the location parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Keywords: Extreme temperature, extreme value, return level.

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7632 Regular Generalized Star Star closed sets in Bitopological Spaces

Authors: K. Kannan, D. Narasimhan, K. Chandrasekhara Rao, R. Ravikumar

Abstract:

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.

Keywords: τ1τ2-regular closed sets, τ1τ2-regular open sets, τ1τ2-regular generalized closed sets, τ1τ2-regular generalized star closed sets, τ1τ2-regular generalized star star closed sets.

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7631 A Generalized Framework for Working with Multiagent Systems

Authors: Debal Saha, NirmalBaranHui

Abstract:

The present paper discusses the basic concepts and the underlying principles of Multi-Agent Systems (MAS) along with an interdisciplinary exploitation of these principles. It has been found that they have been utilized for lots of research and studies on various systems spanning across diverse engineering and scientific realms showing the need of development of a proper generalized framework. Such framework has been developed for the Multi-Agent Systems and it has been generalized keeping in mind the diverse areas where they find application. All the related aspects have been categorized and a general definition has been given where ever possible.

Keywords: Generalized framework, multiagent systems.

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7630 Study of Rayleigh-Bénard-Brinkman Convection Using LTNE Model and Coupled, Real Ginzburg-Landau Equations

Authors: P. G. Siddheshwar, R. K. Vanishree, C. Kanchana

Abstract:

A local nonlinear stability analysis using a eight-mode expansion is performed in arriving at the coupled amplitude equations for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence of LTNE effects. Streamlines and isotherms are obtained in the two-dimensional unsteady finite-amplitude convection regime. The parameters’ influence on heat transport is found to be more pronounced at small time than at long times. Results of the Rayleigh-Bénard convection is obtained as a particular case of the present study. Additional modes are shown not to significantly influence the heat transport thus leading us to infer that five minimal modes are sufficient to make a study of RBBC. The present problem that uses rolls as a pattern of manifestation of instability is a needed first step in the direction of making a very general non-local study of two-dimensional unsteady convection. The results may be useful in determining the preferred range of parameters’ values while making rheometric measurements in fluids to ascertain fluid properties such as viscosity. The results of LTE are obtained as a limiting case of the results of LTNE obtained in the paper.

Keywords: Rayleigh-Bénard convection, heat transport, porous media, generalized Lorenz model, coupled Ginzburg-Landau model.

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7629 On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings

Authors: Teerayut Chomchuen, Aiyared Iampan

Abstract:

The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

Keywords: Γ-semiring, bi-Γ-ideal, generalized bi-Γ-ideal.

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