Search results for: quadratic residue

Authors: Ahmet Tekcan

Abstract:

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

Keywords: Elliptic curve, conic, rational points.

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Authors: Nazli Yildiz İkikardes, Gokhan Soydan, Musa Demirci, Ismail Naci Cangul

Abstract:

In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.

Keywords: Elliptic curves over finite fields, quadratic residue, cubic residue.

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Authors: Musa Demirci, Nazlı Yıldız İkikardeş, Gökhan Soydan, İsmail Naci Cangül

Abstract:

In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a.

Keywords: Elliptic curves over finite fields, rational points, quadratic residue.

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Authors: Ahmet Tekcan, Arzu Özkoç

Abstract:

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indefinite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the first section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some specific values of Q and P.

Keywords: Quadratic irrationals, quadratic ideals, indefinite quadratic forms, extended modular group.

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Authors: Naruemon Prapasuwannakul

Abstract:

Soymilk residue is obtained as a byproduct from soymilk and tofu production with little economic value. It contains high protein and fiber as well as various minerals and phyto-chemical compounds. The objective of this research was to substitute soymilk residue for wheat flour in gyoza skin in order to enhance value of soymilk residue and increase protein and fiber content of gyoza skin. Wheat flour was replaced with soymilk residue from 0 to 40%. The soy milk residue prepared in this research contains 26.92%protein, 3.58% fiber, 2.88% lipid, 6.29% ash and 60.33% carbohydrate. The results showed that increasing soymilk residue decreased lightness (L*value), tensile strength and sensory attributes but increased redness (a*), yellowness (b*), protein and fiber contents of product. The result also showed that the gyoza skin substituted with 30% soymilk residue was the most acceptable (p≤0.05) and its protein and fiber content increased up to 45 % and 867 % respectively.

Keywords: Gyoza skin, sensory, soymilk residue, wheat flour.

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Authors: Ahmet Tekcan

Abstract:

Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Keywords: Binary quadratic form, elliptic curves, cubic congruence.

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.

Keywords: Impulsive systems, switched systems, quadratic stabilization, robust stabilization.

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Authors: M. I. Youssef, A. E. Emam, M. Abd Elghany

Abstract:

In this paper, a residue number arithmetic is used in direct sequence spread spectrum system, this system is evaluated and the bit error probability of this system is compared to that of non residue number system. The effect of channel bandwidth, PN sequences, multipath effect and modulation scheme are studied. A Matlab program is developed to measure the signal-to-noise ratio (SNR), and the bit error probability for the various schemes.

Keywords: Spread Spectrum, Direct sequence, Bit errorprobability and Residue number system.

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Authors: Dávid Csercsik, Péter Kádár

Abstract:

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: Economic dispatch, optimization, quadratic programming, MATLAB.

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Authors: Yongzhong Wu, Ping Ji

Abstract:

This paper proposes a genetic algorithm based on a new replacement strategy to solve the quadratic assignment problems, which are NP-hard. The new replacement strategy aims to improve the performance of the genetic algorithm through well balancing the convergence of the searching process and the diversity of the population. In order to test the performance of the algorithm, the instances in QAPLIB, a quadratic assignment problem library, are tried and the results are compared with those reported in the literature. The performance of the genetic algorithm is promising. The significance is that this genetic algorithm is generic. It does not rely on problem-specific genetic operators, and may be easily applied to various types of combinatorial problems.

Keywords: Quadratic assignment problem, Genetic algorithm, Replacement strategy, QAPLIB.

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Authors: Hossein Khademolhosseini, Mehdi Hosseinzadeh

Abstract:

The residue number system (RNS), due to its properties, is used in applications in which high performance computation is needed. The carry free nature, which makes the arithmetic, carry bounded as well as the paralleling facility is the reason of its capability of high speed rendering. Since carry is not propagated between the moduli in this system, the performance is only restricted by the speed of the operations in each modulus. In this paper a novel method of number representation by use of redundancy is suggested in which {rn- 2,rn-1,rn} is the reference moduli set where r=2k+1 and k =1, 2,3,.. This method achieves fast computations and conversions and makes the circuits of them much simpler.

Keywords: Binary to RNS converter, Carry save adder, Computer arithmetic, Residue number system.

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Authors: Mehdi Hosseinzadeh, Amir Sabbagh Molahosseini, Keivan Navi

Abstract:

The residue number system (RNS) is popular in high performance computation applications because of its carry-free nature. The challenges of RNS systems design lie in the moduli set selection and in the reverse conversion from residue representation to weighted representation. In this paper, we proposed a fully parallel reverse conversion algorithm for the moduli set {rn - 2, rn - 1, rn}, based on simple mathematical relationships. Also an efficient hardware realization of this algorithm is presented. Our proposed converter is very faster and results to hardware savings, compared to the other reverse converters.

Keywords: Reverse converter, residue to weighted converter, residue number system, multiple-valued logic, computer arithmetic.

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Authors: Ahmet Tekcan

Abstract:

In this paper, we derive some algebraic identities on right and left neighbors R(F) and L(F) of an indefinite binary quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant Δ = b2 -4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F.

Keywords: Quadratic form, indefinite form, cycle, proper cycle, right neighbor, left neighbor.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

Abstract:

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: Belkacem Brahmi, Mohand Ouamer Bibi

Abstract:

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

Keywords: Convex quadratic programming, dual support methods, active set methods.

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Authors: Pitcha Wongskeo, Pramoch Rangsunvigit, Sumaeth Chavadej

Abstract:

The possibility of using cassava residue containing 49.66% starch, 21.47% cellulose, 12.97% hemicellulose, and 21.86% lignin as a raw material to produce glucose using enzymatic hydrolysis was investigated. In the experiment, each reactor contained the cassava residue, bacteria cells, and production medium. The effects of particles size (40 mesh and 60 mesh) and strains of bacteria (A002 and M015) isolated from Thai higher termites, Microcerotermes sp., on the glucose concentration at 37°C were focused. High performance liquid chromatography (HPLC) with a refractive index detector was used to determine the quantity of glucose. The maximum glucose concentration obtained at 37°C using strain A002 and 60 mesh of the cassava residue was 1.51 g/L at 10 h.

Keywords: Hydrolysis, termites, glucose, cassava

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Authors: Mamoun F. Al-Mistarihi

Abstract:

We have previously introduced an ultrasonic imaging approach that combines harmonic-sensitive pulse sequences with a post-beamforming quadratic kernel derived from a second-order Volterra filter (SOVF). This approach is designed to produce images with high sensitivity to nonlinear oscillations from microbubble ultrasound contrast agents (UCA) while maintaining high levels of noise rejection. In this paper, a two-step algorithm for computing the coefficients of the quadratic kernel leading to reduction of tissue component introduced by motion, maximizing the noise rejection and increases the specificity while optimizing the sensitivity to the UCA is presented. In the first step, quadratic kernels from individual singular modes of the PI data matrix are compared in terms of their ability of maximize the contrast to tissue ratio (CTR). In the second step, quadratic kernels resulting in the highest CTR values are convolved. The imaging results indicate that a signal processing approach to this clinical challenge is feasible.

Keywords: Volterra Filter, Pulse Inversion, Ultrasonic Imaging, Contrast Agent.

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Authors: Chan Weng Howe, Mohd Saberi Mohamad

Abstract:

Protein residue contact map is a compact representation of secondary structure of protein. Due to the information hold in the contact map, attentions from researchers in related field were drawn and plenty of works have been done throughout the past decade. Artificial intelligence approaches have been widely adapted in related works such as neural networks, genetic programming, and Hidden Markov model as well as support vector machine. However, the performance of the prediction was not generalized which probably depends on the data used to train and generate the prediction model. This situation shown the importance of the features or information used in affecting the prediction performance. In this research, support vector machine was used to predict protein residue contact map on different combination of features in order to show and analyze the effectiveness of the features.

Keywords: contact map, protein residue contact, support vector machine, protein structure prediction

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Authors: Mehdi Hosseinzadeh, Amir Sabbagh Molahosseini, Keivan Navi

Abstract:

In this paper, a new reverse converter for the moduli set {2n, 2n–1, 2n–1–1} is presented. We improved a previously introduced conversion algorithm for deriving an efficient hardware design for reverse converter. Hardware architecture of the proposed converter is based on carry-save adders and regular binary adders, without the requirement for modular adders. The presented design is faster than the latest introduced reverse converter for moduli set {2n, 2n–1, 2n–1–1}. Also, it has better performance than the reverse converters for the recently introduced moduli set {2n+1–1, 2n, 2n–1}

Keywords: Residue arithmetic, Residue number system, Residue-to-Binary converter, Reverse converter

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

Abstract:

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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Authors: Liping Zhou, Liang Bao, Yiqin Lin, Yimin Wei, Qinghua Wu

Abstract:

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.

Keywords: Quadratic eigenvalue problem, Generalized secondorder Krylov subspace, Generalized second-order Arnoldi process, Projection technique, Refined technique, Restarting.

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Authors: Ali Fellah Jahromi, Wen Fang Xie, Rama B. Bhat

Abstract:

A semi-active control strategy for suspension systems of passenger cars is presented employing Magnetorheological (MR) dampers. The vehicle is modeled with seven DOFs including the, roll pitch and bounce of car body, and the vertical motion of the four tires. In order to design an optimal controller based on the actuator constraints, a Linear-Quadratic Regulator (LQR) is designed. The design procedure of the LQR consists of selecting two weighting matrices to minimize the energy of the control system. This paper presents a hybrid optimization procedure which is a combination of gradient-based and evolutionary algorithms to choose the weighting matrices with regards to the actuator constraint. The optimization algorithm is defined based on maximum comfort and actuator constraints. It is noted that utilizing the present control algorithm may significantly reduce the vibration response of the passenger car, thus, providing a comfortable ride.

Keywords: Full car model, Linear Quadratic Regulator, Sequential Quadratic Programming, Genetic Algorithm

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Authors: Satjaporn Tungsong, Gun Srijuntongsiri

Abstract:

This research seeks to investigate the frequency and profitability of index arbitrage opportunities involving the SET50 futures, SET50 component stocks, and the ThaiDEX SET50 ETF (ticker symbol: TDEX). In particular, the frequency and profit of arbitrage are measured in the following three arbitrage tests: (1) SET50 futures vs. ThaiDEX SET50 ETF, (2) SET50 futures vs. SET50 component stocks, and (3) ThaiDEX SET50 ETF vs. SET50 component stocks are investigated. For tests (2) and (3), the problems involve conic optimization and quadratic programming as subproblems. This research is first to apply conic optimization and quadratic programming techniques in the context of index arbitrage and is first to investigate such index arbitrage in the Thai equity and derivatives markets. Thus, the contribution of this study is twofold. First, its results would help understand the contribution of the derivatives securities to the efficiency of the Thai markets. Second, the methodology employed in this study can be applied to other geographical markets, with minor adjustments.

Keywords: Conic optimization, Equity index arbitrage, Executionlags, Quadratic programming, SET50 index futures, ThaiDEX SET50ETF, Transaction costs

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Authors: Muthu Solayappan, Kien Ming Ng, Kim Leng Poh

Abstract:

This paper presents a perturbation based search method to solve the unconstrained binary quadratic programming problem. The proposed algorithm was tested with some of the standard test problems and the results are reported for 10 instances of 50, 100, 250, & 500 variable problems. A comparison of the performance of the proposed algorithm with other heuristics and optimization software is made. Based on the results, it was found that the proposed algorithm is computationally inexpensive and the solutions obtained match the best known solutions for smaller sized problems. For larger instances, the algorithm is capable of finding a solution within 0.11% of the best known solution. Apart from being used as a stand-alone method, this algorithm could also be incorporated with other heuristics to find better solutions.

Keywords: unconstrained binary quadratic programming, perturbation, interior point methods

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Authors: Yin Yin Pey, Leok Poh Chua, Wei Long Siauw

Abstract:

Linear stochastic estimation and quadratic stochastic estimation techniques were applied to estimate the entire velocity flow-field of an open cavity with a length to depth ratio of 2. The estimations were done through the use of instantaneous velocity magnitude as estimators. These measurements were obtained by Particle Image Velocimetry. The predicted flow was compared against the original flow-field in terms of the Reynolds stresses and turbulent kinetic energy. Quadratic stochastic estimation proved to be more superior than linear stochastic estimation in resolving the shear layer flow. When the velocity fluctuations were scaled up in the quadratic estimate, both the time-averaged quantities and the instantaneous cavity flow can be predicted to a rather accurate extent.

Keywords: Open cavity, Particle Image Velocimetry, Stochastic estimation, Turbulent kinetic energy.

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Authors: Girija Chetty, Renuka Biswas

Abstract:

In this paper, we propose novel algorithmic models based on information fusion and feature transformation in crossmodal subspace for different types of residue features extracted from several intra-frame and inter-frame pixel sub-blocks in video sequences for detecting digital video tampering or forgery. An evaluation of proposed residue features – the noise residue features and the quantization features, their transformation in cross-modal subspace, and their multimodal fusion, for emulated copy-move tamper scenario shows a significant improvement in tamper detection accuracy as compared to single mode features without transformation in cross-modal subspace.

Keywords: image tamper detection, digital forensics, correlation features image fusion

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Authors: Shahana T. K., Babita R. Jose, K. Poulose Jacob, Sreela Sasi

Abstract:

The modern telecommunication industry demands higher capacity networks with high data rate. Orthogonal frequency division multiplexing (OFDM) is a promising technique for high data rate wireless communications at reasonable complexity in wireless channels. OFDM has been adopted for many types of wireless systems like wireless local area networks such as IEEE 802.11a, and digital audio/video broadcasting (DAB/DVB). The proposed research focuses on a concatenated coding scheme that improve the performance of OFDM based wireless communications. It uses a Redundant Residue Number System (RRNS) code as the outer code and a convolutional code as the inner code. Here, a direct conversion of analog signal to residue domain is done to reduce the conversion complexity using sigma-delta based parallel analog-to-residue converter. The bit error rate (BER) performances of the proposed system under different channel conditions are investigated. These include the effect of additive white Gaussian noise (AWGN), multipath delay spread, peak power clipping and frame start synchronization error. The simulation results show that the proposed RRNS-Convolutional concatenated coding (RCCC) scheme provides significant improvement in the system performance by exploiting the inherent properties of RRNS.

Keywords: Analog-to-residue converter, Concatenated codes, OFDM, Redundant Residue Number System, Sigma-delta modulator, Wireless communication

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: Kamil Aida-zade, C. Ardil

Abstract:

In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.

Keywords: dynamic objects, ordinary differential equations, multipoint unshared edge conditions, quadratic programming, conditions shift

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Authors: Cheewaphongphan P., Garivait S., Pongpullponsak A., Patumsawad S.

Abstract:

Thailand is one of the world-s leaders of rice producers and exporters. Farmers have to increase the rice cultivation frequency for serving the national increasing of export-s demand. It leads to an elimination of rice residues by open burning which is the quickest and costless management method. The open burning of rice residue is one of the major causes of air pollutants and greenhouse gas (GHG) emission. Under ASEAN agreement on trans-boundary haze, Thailand set the master plan to mitigate air pollutant emission from open burning of agricultural residues. In this master plan, residues incorporation is promoted as alternative management method to open burning. However, the assessment of both options in term of GHG emission in order to investigate their contribution to long-term global warming is still scarce or inexistent. In this study, a method on rice residues assessment was first developed in order to estimate and compare GHG emissions from rice cultivation under rice residues open burning and the case with incorporation of the same amount of rice residues, using 2006 IPCC guidelines for emission estimation and Life Cycle Analysis technique. The emission from rice cultivation in different preparing area practice was also discussed.

Keywords: Greenhouse gases, Incorporation, Rice cultivation, Rice field residue, Rice residue management

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