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Abstract This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points’ stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model’s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system’s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

This paper aims to design a quadratic optimization model of an investment portfolio based on value-at-risk (VaR) by entering risk-free assets and company liabilities. The designed model develops Markowitz’s investment portfolio optimization model with risk aversion. Model development was carried out using vector and matrix equations. The entry of risk-free assets and liabilities is essential. Risk-free assets reduce the loss risk, while liabilities accommodate a fundamental analysis of the company’s condition. The model can be applied in various sectors of capital markets worldwide. This study applied the model to Indonesia’s mining and energy sector. The application results show that risk aversion negatively correlates with the mean and VaR of the return of investment portfolios. Assuming that risk aversion is in the 5.1% to 8.2% interval, the maximum mean and VaR obtained for the next month are 0.0103316 and 0.0138270, respectively, while the minimum mean and VaR are 0.0102964 and 0.0137975, respectively. The finding of this study is that the vector equation for investment portfolio weights is obtained, which can facilitate calculating investment portfolio weight optimization. This study is expected to help investors control the quality of appropriate investment, especially in some stocks in Indonesia’s mining and energy sector.

According to the World Health Organization (WHO), traumatic brain injury (TBI) will mainly contribute to disability and death by 2020. Facial fractures associated with TBI are a significant public health concern worldwide. The main etiological factors are road traffic accidents, violence, and falls. Neurological injury associated with facial fractures has been reported to be as high as 76%. Therefore, we retrospectively evaluated facial fracture patterns in patients with a traumatic brain injury in Hospital Universiti Sains Malaysia and evaluated their associations in our study. Ordinal regression was used to examine the facial fracture patterns in patients with traumatic brain injuries. The confounding variables were controlled using ordinal regression analysis, and probabilities of p < 0.1 were considered significant associations. The results found that zygomatic arch fracture −1.141 (95% CI, −2.487 to 0.204, p-value = 0.096), Le Fort II fracture −1.080 (95% CI, −2.138 to −0.022, p-value = 0.045), maxillary bone fracture 2.924 (95% CI, 1.784 to 4.063, p-value .001), nasal bone fracture 4.047 (95% CI, 1.243 to 6.851, p-value = 0.005), and mandibular bone fracture 1.501 (95% CI, 0.711 to 2.291, p-value .001) were the most common facial fracture types associated with traumatic brain injury (TBI). This study provides valuable data for creating prevention plans and gives a chance to discover the epidemiology, prevalence, and connection between TBI and facial fracture.

In Indonesia, natural disasters cases have significantly increased from time to time and have the largest impact on economic losses. To avoid losses in the future due to natural disasters, the insurance company needs to estimate the risk and determine the rate of premium that would be charged to the policyholder. In conjunction with the present issue, this study seeks to determine the premium rate and estimate the size claim of insurance by considering the mitigation fund reserve decisions using The Collective Risk Model (CRM). The data was analyzed using the Poisson process with Weibull distribution to determine the natural disaster frequency and losses. The distribution of losses is estimated using Maximum Likelihood Estimation (MLE), and the magnitude of losses was estimated using the CRM. Also, the mean and variance estimators of the aggregate risk were used to estimate the premium charged. The results indicated that expectation and variance of the frequency of incident claims have the same value, i.e., 2562. Also, the loss claims follow the Weibull distribution with the expected value and variance of 5.81309×1010 and 2.5301×1022, respectively. The mean and variance of the aggregate (collective) claims are 148,931,365,800,000 and 7.35×1025, respectively. In conclusion, this study has successfully determined the efficient pure premium model through the Standard Deviation Principle (SDP). SDP provides a much cheaper premium than the Expected Value Principle with the same loading factor. In addition, SDP considers the standard deviation of the collective risk of natural disasters. The implications of the results of the premium determination are expected to be the basis for decision-making for insurance companies and the government in determining insurance policies for natural disaster mitigation.

COVID-19 has spread to more than a hundred countries worldwide since the first case reported in late 2019 in Wuhan, China. As one of the countries affected by the spread of COVID-19 cases, the local government of Malaysia has issued several policies to reduce the spread of this outbreak. One of the measures taken by the Malaysian government, namely the Movement Control Order, has been carried out since March 18, 2020. In order to provide precise information to the government so that it can take the appropriate measures, many researchers have attempted to predict and create the model for these cases to identify the number of cases each day and the peak of this pandemic. Therefore, hospitals and health workers can anticipate a surge in COVID-19 patients. In this research, confirmed, recovered, and death cases prediction was performed using the neural network as one of the machine learning methods with high accuracy. The neural network model used is the Multi-Layer Perceptron, Neural Network Auto-Regressive, and Extreme Learning Machine. The three models calculated the average percentage error (APE) values for 7 days and obtained APE values for most cases less than 10%; only 1 case in the last day of one method had an APE value of approximately 11%. Furthermore, based on the best model, then the forecast is made for the next 7 days. In conclusion, this study identified that the MLP model is the best model for 7-step ahead forecasting for confirmed, recovered, and death cases in Malaysia. However, according to the result of testing data, the ELM performs better than the MLP model.

The Spectral conjugate gradient (SCG) methods are among the efficient variants of CG algorithms which are obtained by combining the spectral gradient parameter and CG parameter. The success of SCG methods relies on effective choices of the step-size $\alpha _{k}$ and the search direction $d_{k}$ . This paper presents an SCG method for unconstrained optimization models. The search directions generated by the new method possess sufficient descent property without the restart condition and independent of the line search procedure used. The global convergence of the new method is proved under the weak Wolfe line search. Preliminary numerical results are presented which show that the method is efficient and promising, particularly for large-scale problems. Also, the method was applied to solve the robotic motion control problem and portfolio selection problem.

In this work, we devise a new 5-D hyperchaotic dynamo system by adding two feedback controllers to the Rikitake 2-disk dynamo system (1958). We show that the new 5-D hyperchaotic system does not possess any equilibrium point and deduce that the new 5-D system has a hidden hyperchaotic attractor. Using Multisim, we develop an electronic circuit design of the new 5-D hyperchaotic dynamo system for practical applications. We also exhibit the implementation of the new 5-D hyperchaotic dynamo system by using a field-programmable gate array (FPGA), which requires adders, subtractors and multipliers. The hardware resources are given for the application of three numerical methods, all of them providing results in good agreement with MATLAB simulations. As an application, we devise a dual core high speed hybrid true random number generator (TRNG) using Ring and Heun algorithm based on the new 5-D hyperchaotic oscillator on FPGA. Based on the hyperchaotic features of the proposed 5-D hyperchaotic dynamo system, we suggest a new encryption approach for colour images. Simulation outcomes of the presented encryption approach confirm that our chaotic system has good cryptographic properties and its usability in different cryptographic purposes.

In this work, we describe the model of a new 4-D hyperchaotic system with no balance point and deduce that the new hyperchaotic system has a hidden attractor. We present a detailed bifurcation analysis for the new hyperchaotic dynamo system with respect to the system parameters and also exhibit that the new hyperchaotic system displays multistability with coexisting attractors. Using NI Multisim 14.0, we design an electronic circuit for the implementation of the new 4-D hyperchaotic system and present the circuit simulation results. We also show the implementation of the new 4-D hyperchaotic system by using a field programmable gate array (FPGA). The hardware resources are reduced by designing single-constant multipliers, adders, subtractors and multipliers. The FPGA design is done for three numerical methods, namely: Forward-Euler, Backward-Euler and fourth-order Runge-Kutta. We demonstrate that experimental chaotic attractors are in good agreement with theoretical simulations. To verify the ability of the presented hyperchaotic system for designing robust cryptosystems, we suggest a novel image cryptosystem using the proposed hyperchaotic system. Simulation outcomes confirm the effectiveness of the proposed image cryptosystem, and consequently, the effectiveness of the proposed 4-D hyperchaotic system in designing diverse cryptographic purposes.

The very high demand for chaotic systems in the fields of sciences, particularly in secure communication, leads numerous researchers to build novel systems. This work announces a new easy to implement 3D chaotic system with five quadratic nonlinearities and three positive parameters, the proposed system is complex with larger bandwidth compared to at least 50 other systems that have been described. It contains eight terms and it can generate chaotic, periodic and quasi-periodic behaviors. The main dynamical properties of the proposed system are studied using Kaplan-Yorke dimension (KYD), Lyapunov exponents, bifurcation diagrams, multistability, equilibrium points stability and dissipativity. Then, the eight terms system feasibility is verified using Multisim software by designing its electronic circuit. In addition, active controllers are designed for leading the proposed system to achieve stability, tracking a desired dynamic and synchronizing with an identical model. Finally, using drive response synchronization, a novel secure communication electrical circuit design is built based on the suggested approach. The findings from numerical experiment demonstrated the new system’s success in completing the encryption/decryption process, as well as its secured transmission technique.

The conjugate gradient (CG) scheme is regarded as among the efficient methods for large-scale optimization problems. Several versions of CG methods have been presented recently owing to their rapid convergence, simplicity, and their less memory requirements. In this article, we construct a new CG algorithm via the combination of the classical methods of Fletcher-Reeves (FR), and Hestenes-Stiefel (HS). The new CG method possesses the descent properties and converge globally provided the exact minimization condition is satisfied. The tests of the new CG method using MATLAB are analysed in terms of iteration number and CPU time. Numerical results have been reported which shows that the proposed CG method performs better compare to other CG methods.

In this paper, we are interested in the numerical solution of nonlinear equations, particularly, when the coefficients are fuzzy numbers rather than crisp numbers. These problems often arise in numerous applications and have recently been the subject of several studies, where many researchers parameterized the fuzzy coefficients and proposed numerical method for obtaining the solutions. Most of the numerical methods applied for solving the parameterized fuzzy equations are Newton-like methods that require the computation of Jacobian matrix at every iteration or after every few iterations. However, the Newton search direction may not be a descent direction if the Jacobian J ( x k ) is not positive definite, and, when J ( x k ) is singular, the method may fail to converge. Also, there are limited literatures on numerical methods for solution of dual fuzzy nonlinear equations. This paper proposed a variant of Newton’s method for solving parameterized dual fuzzy nonlinear equations. This method introduces a new parameter μ k to the Newton’s method to ensure that the search direction is a descent direction even when J ( x k ) is not positive definite. The proposed method was further applied to solve an application problem. Preliminary results on the considered benchmark and application problems show that the new algorithm effective and promising.

In Wireless Sensor Networks (WSN), energy efficiency is a fundamental issue that requires attention in the design of communication protocols. Energy waste occurs as a result of collision and idle listening. The widely used mechanism for energy saving in WSN is duty cycling. Duty cycling coordinates the sleep/wake-up time of sensor nodes to maximize the network lifetime while achieving specific application goals such as high throughput or low latency. Most existing works focused more on static duty cycle, which cannot guarantee the desired end-to-end delay at varying network conditions. In applications with specified delay requirements, the duty cycle of every node should be adjusted separately at runtime depending on the network conditions to achieve the desired delay and energy efficiency. In this paper, we present an Energy Efficient and QoS-aware (EEQ) MAC protocol with a duty cycle scheme that adapts the node's duty cycle to the queue size and priority class of a packet to reduce the delay of high priority packets and support time-bounded delivery of priority packets. By checking the queue size and the priority class of packets in the message queue of each node, the node determines whether or not to adjust its duty cycle. In this approach, a node increases the length of its active period in the event of high traffic which provides less waiting time for the packets in the queue. The sender node informs the receiver the duration for which it has to stay awake at the beginning of data transmission, both the sending and the receiver's duty cycle is controlled based on the queue length and the priority of the packets. This approach saves energy and lessen packet latency. Finally, extensive simulation experiments were conducted to evaluate its energy performance within different network topologies. Comparisons with the existing energy-aware MAC protocol verified the effect of EEQ on improving the energy efficiency and extending the lifespan of WSNs.

This work introduce a new high dimensional 10-D hyperchaotic system with high complexity and many of coexisting attractors. With the adjustment of its parameters and initial points, the novel system can generate periodic, quasi-periodic, chaotic, and hyperchaotic behaviours. For special values of parameters, we show that the proposed 10-D system has a very high Kaplan-Yorke fractal dimension, which can reach up to 9.067 indicating the very complexity of the 10-D system dynamics. In addition, the proposed system is shown to exhibit at least six varied attractors for the same values of parameters due to its multistability. Regions of multistability are identified by analysing the bifurcation diagrams of the proposed model versus its parameters and for six different values of initial points. Many of numerical plots are given to show the appearance of different dynamical behaviours and the existence of multiple coexisting attractors. The main problem with controlling chaos/hyperchaos systems is that they are not always fully synchronized. therefore, some powerful synchronization techniques should be considered. The synchronization between the high-dimensional 10-D system and a set of three low-dimensional chaotic and hyperchaotic systems is proposed. Ten control functions are designed using the active control method, ensuring synchronisation between the collection of systems and the 10-D hyperchaotic system. Finally, using Multisim 13.0 software to construct the new system’s electronic circuit, the feasibility of the new system with its extremely complicated dynamics is verified. Therefore, the novel 10-D hyperchaotic system can be applied to different chaotic-based application due to its large dimension, complex dynamics, and simple circuit architecture.

Climate change that occurs causes the risk of natural disasters to continue to increase throughout the world. Economic losses are unavoidable, leading to the need for continuous innovation in post-disaster economic recovery efforts. Insurance is one of the offers in providing funding for the economic recovery that occurs. This study aimed to develop innovations and models for determining natural disaster insurance premiums with a subsidy and tax system. In addition, the developed model considers the disaster risk index in the form of the level of risk distribution, the frequency of events, and economic losses. In this study, the data used were the frequency of events and economic losses obtained from the Indonesian National Disaster Management Agency. The data used were 20 database periods from 2000 to 2019. This study used the collective risk method from the index of natural disaster risk parameters. From the results of the analysis, it was found that the level of distribution of disaster risk affected the determination of insurance premiums. The amount of insurance premiums is increasing along with the increase in the magnitude of the spread of disaster risk. In addition, if taxes and subsidies are reduced, then for high-risk areas, there will be a decrease in the burden of insurance premiums, and for low-risk areas, there will be an increase in the premium burden that must be paid. On the basis of the results of the analysis on the insurance model, it was found that the insurance premiums in each province varied. The results of this study are expected to be a reference for the government and private companies in implementing disaster insurance in Indonesia. In addition, the results of this study can be a means of developing innovations for disaster risk management that occurs.

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time.

Penentuan koordinat kanonik merupakan hal yang diperlukan dalam penentuan solusi persamaan diferensial dengan menggunakan metode simetri Lie. Pada tulisan ini dibahas penentuan koordinat kanonik dari persamaan diferensial Painleve Ince dan mereduksinya menjadi persamaan diferensial orde satu. Berdasarkan hasil pembahasan metode simetri Lie dapat digunakan untuk menentukan solusi eksak persamaan diferensial Painleve Ince.

This research work reports a double-wing chaotic system with a line of equilibrium points and constructs an electronic circuit via MultiSIM for practical implementation. Explicitly, the new chaotic system has a total of six terms with two quadratic nonlinearities and absolute function nonlinearity. Using the phase plots in MATLAB, we demonstrate that the new chaotic system has double-wing chaotic attractor. We describe the Lyapunov exponents and the Kaplan-Yorke fractal dimension of the new chaotic system. A novel feature of the new chaotic system is that the system has rest points located on the z-axis as well as two rest points not on the z-axis. Thus, the new system has infinite number of rest points and hidden attractor. We also exhibit that the new double-wing chaotic system has multi-stability and we illustrate the coexistence of attractors for two different sets of initial conditions. Some interesting dynamical properties such as offset boosting are also presented. Finally, we build an electronic circuit of the new chaotic system and show that the theoretical model has practical feasibility for implementation.

One of the most significant problems in fuzzy set theory is solving fuzzy nonlinear equations. Numerous researches have been done on numerical methods for solving these problems, but numerical investigation indicates that most of the methods are computationally expensive due to computing and storage of Jacobian or approximate Jacobian at every iteration. This paper presents the Shamanskii algorithm, a variant of Newton method for solving nonlinear equation with fuzzy variables. The algorithm begins with Newton’s step at first iteration, followed by several Chord steps thereby reducing the high cost of Jacobian or approximate Jacobian evaluation during the iteration process. The fuzzy coe?cients of the nonlinear systems are parameterized before applying the proposed algorithm to obtain their solutions. Preliminary results of some benchmark problems and comparisons with existing methods show that the proposed method is promising.

Conjugate gradient (CG) methods are among the most efficient numerical methods for solving unconstrained optimization problems. This is due to their simplicty and less computational cost in solving large-scale nonlinear problems. In this paper, we proposed some spectral CG methods using the classical CG search direction. The proposed methods are applied to real-life problems in regression analysis. Their convergence proof was establised under exact line search. Numerical results has shown that the proposed methods are efficient and promising.

Natural convection boundary layer flow over a solid sphere in micropolar nanofluid with prescribed wall temperature is studied. Copper (Cu) and alumina (Al2O3) in water-based micropolar nanofluid has been considered. Tiwari and Das’s nanofluid model with realistic empirical correlations are considered to analyze the nanoparticles effects on natural convective flow. The nonlinear partial differential equations of the boundary layer are first transformed into a non-dimensional form and then solved numerically using an implicit finite difference scheme known as Keller-box method. The effects of nanoparticles volume fraction, Prandtl number, micro-rotation parameter on temperature, velocity and angular velocity are plotted and discussed. Further, numerical results for the local Nusselt number and the local skin friction coefficient are obtained. It is found that Cu has a low heat transfer rate as compare to Al2O3 water-based micropolar nanofluid with increasing micro-rotation parameter. The present results of local Nusselt number and the local skin friction for viscous fluid are found to be in good agreement with the literature. Keywords: Micropolar nanofluid, Natural convection, Solid sphere, Keller-box method

This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA).

The Likert scale is commonly used in survey research using primary and secondary data to measure the respondent attitude by asking insofar to which they agree or disagree with a particular questions. In generals, Likert scale would be preferred in the questionnaire development stage to ascertain the researchers conducting their research needed. However, the researchers nowadays are abuse to understand the nature of measurement scale in data analysis and thus causes the finding obtained are meaningless. This article is aimed to compare the performance of two categories of measurement scales which are 5 point and 10 points of Likert scales using the same sample size and research subject that would pave the way to understand the real different between both of these ranges using Structural Equation Modeling (SEM). Moreover, this study also interested to clarify briefly between two types of measurement scale namely ordinal and interval data. The findings reveal that 10 points of Likert scale is more efficient than 5 points of Likert scale in operating of measurement model

This study employs exact line search iterative algorithms for solving large scale unconstrained optimization problems in which the direction is a three-term modification of iterative method with two different scaled parameters. The objective of this research is to identify the effectiveness of the new directions both theoretically and numerically. Sufficient descent property and global convergence analysis of the suggested methods are established. For numerical experiment purposes, the methods are compared with the previous well-known three-term iterative method and each method is evaluated over the same set of test problems with different initial points. Numerical results show that the performances of the proposed three-term methods are more efficient and superior to the existing method. These methods could also produce an approximate linear regression equation to solve the regression model. The findings of this study can help better understanding of the applicability of numerical algorithms that can be used in estimating the regression model.

In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this paper is to analyze the phase portraits, the Lyapunov exponents, the Poincaré maps and the bifurcation diagrams. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the bidirectional coupling scheme between two identical Jerk circuits in a secure communication system is presented in details. Finally, the simulation results are shown to demonstrate that the proposed method is correct and feasible

This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs.

Dalam dekade terakhir ini, perkembangan saham syariah meningkat secara signifikan. Hal ini ditunjukkan dengan makin banyaknya saham-saham yang berbasis syariah. Selain itu, munculnya indeks yang menjadi benchmark saham syariah di bursa efek menambah menariknya kegiatan investasi bagi para investor. Seperi harga saham pada umumnya, harga saham syariah juga sering berubah-ubah (berfluktuasi), sehingga investasi pada saham syariah pun dihadapkan pada risiko investasi. Berdasarkan karakteristik tingkat risiko, kinerja investasi pada suatu saham syariah perlu dilakukan analisis. Oleh karena itu, dalam paper ini dilakukan analisis kinerja beberapa saham syariah dengan pendekatan rata-rata dan volatilitas tak konstan. Rata-rata tak konstan dimodelkan dengan menggunakan model-model Autoregressive Moving Average (ARMA), sedangkan Volatilitas tak konstan dianalisis menggunakan model-model Generalized Autoregressive Conditional Heteroscedastic (GARCH). Sedangkan untuk menganalisis kinerja investasi pada saham syariah dilakukan dengan menggunakan model Sharpe’s measure. Sebagai ilustrasi numeric, metode tersebut digunakan untuk menganalisis beberapa saham syariah di Indonesia. Hasil yang diharapkan adalah dapat diketahuinya kinerja investasi saham syariah untuk beberapa periode mendatang.

Poor eating behavior has been identified as one of the core contributory factors of the childhood obesity epidemic. The consequences of obesity on numerous aspects of life are thoroughly explored in the existing literature. For instance, evidence shows that obesity is linked to incidences of diseases such as heart disease, type-2 diabetes, and some cancers, as well as psychosocial problems. To respond to the increasing trends in the UK, in 2008 the government set a target to reverse the prevalence of obesity (POB) back to 2000 levels by 2020. This paper will outline the application of system dynamics (SD) optimization to simulate the effect of changes in the eating behavior of British children (aged 2 to 15 years) on weight and obesity. This study also will identify how long it will take to achieve the government's target. This paper proposed a simulation model called Intervention Childhood Obesity Dynamics (ICOD) by focusing the interrelations between various strands of knowledge in one complex human weight regulation system. The model offers distinct insights into the dynamics by capturing the complex interdependencies from the causal loop and feedback structure, with the intention to better understand how eating behaviors influence children's weight, body mass index (BMI), and POB measurement. This study proposed a set of equations that are revised from the original (baseline) equations. The new functions are constructed using a RAMP function of linear decrement in portion size and number of meal variables from 2013 until 2020 in order to achieve the 2020 desired target. Findings from the optimization analysis revealed that the 2020 target won't be achieved until 2026 at the earliest, six years late. Thus, the model suggested that a longer period may be needed to significantly reduce obesity in this population.

In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, a new hybrid method, known as the BFGS-CG method, has been created based on these properties, combining the search direction between conjugate gradient methods and quasi-Newton methods. In comparison to standard BFGS methods and conjugate gradient methods, the BFGS-CG method shows significant improvement in the total number of iterations and CPU time required to solve large scale unconstrained optimization problems. We also prove that the hybrid method is globally convergent.

We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant.

Makalah ini bertujuan untuk mengukur kecekapan relatif industri saham amanah di Malaysia menggunakan kaedah Analisis Sempadan Stokastik (ASS) bagi tahun 2003 dan 2004 yang terdiri daripada 65 buah dana daripada 16 buah syarikat pengurusan dana saham amanah di Malaysia. Dana yang dikaji dibahagikan kepada tiga jenis, iaitu pertumbuhan, pendapatan dan Islam/Syariah menggunakan spesifi kasi Batt ese dan Coelli (1992). Analisis data dan keputusan kajian menggunakan program Frontier Versi 4.1 (Coelli, 1996). Kecekapan merupakan pengukuran penting yang boleh digunakan untuk menilai perkembangan dan pertumbuhan ekonomi sesebuah negara.

Instead of using standard analytical techniques, like Buckley and Qu method, which are not suitable for solving a system of fuzzy nonlinear equations where the coefficient is fuzzy number, Broyden's method is proposed for solving fuzzy nonlinear equations. In this paper, an eight-step algorithm is used to solve fuzzy nonlinear equations. Two numerical examples are given to illustrate the proposed method.