Displaying publications 401 - 420 of 761 in total

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  1. Setapa A, Ahmad N, Mohd Mahali S, Mohd Amin MCI
    Polymers (Basel), 2020 Dec 05;12(12).
    PMID: 33291495 DOI: 10.3390/polym12122921
    Various swelling drug delivery devices are promising materials for control drug delivery because of their ability to swell and release entrapped therapeutics, in response to physiological stimuli. Previously, many mathematical models have been developed to predict the mechanism of drug release from a swelling device. However, some of these models do not consider the changes in diffusion behaviour as the device swells. Therefore, we used a two-phase approach to simplify the mathematical model considering the effect of swelling on the diffusion coefficient. We began by defining a moving boundary problem to consider the swelling process. Landau transformation was used for mitigating the moving boundary problem. The transformed problem was analytically solved using the separation of variables method. Further, the analytical solution was extended to include the drug release in two phases where each phase has distinct diffusion coefficient and continuity condition was applied. The newly developed model was validated by the experimental data of bacterial cellulose hydrogels using the LSQCURVEFIT function in MATLAB. The numerical test showed that the new model exhibited notable improvement in curve fitting, and it was observed that the initial effective diffusion coefficient of the swelling device was lower than the later effective diffusion coefficient.
    Matched MeSH terms: Models, Theoretical
  2. Eghbali Babadi F, Yunus R, Masoudi Soltani S, Shotipruk A
    ACS Omega, 2021 May 04;6(17):11144-11154.
    PMID: 34056270 DOI: 10.1021/acsomega.0c04353
    In this study, a mineral-based coated urea was fabricated in a rotary pan coater using a mixture of gypsum/sulfur/zeolite (G25S25Z50) as an effective and low-cost coating material. The effects of different coating compositions on the dissolution rate of urea and the crushing strength and morphology of the coated urea were investigated. A 25:25:50 (wt %) mixture of gypsum/sulfur/zeolite (G25S25Z50) increased the coating effectiveness to 34.1% with the highest crushing strength (31.06 N). The effectiveness of coated urea was further improved to 46.6% with the addition of a microcrystalline wax (3%) as a sealant. Furthermore, the release mechanisms of various urea fertilizers were determined by fitting the release profiles with six mathematical models, namely, the zeroth-order, first-order, second-order, Higuchi, Ritger & Peppas, and Kopcha models. The results showed that the release mechanism of the uncoated urea and all other coated urea followed the Ritger & Peppas model, suggesting the diffusional release from nonswellable delivery systems. In addition, due to the increased mass-transfer resistance, the kinetic constant was decreased from 0.2233 for uncoated urea to 0.1338 for G25S25Z50-coated urea and was further decreased to 0.0985 when 3% Witcovar 146 sealant was applied.
    Matched MeSH terms: Models, Theoretical
  3. Ghalambaz M, Mehryan SAM, Hajjar A, Shdaifat MYA, Younis O, Talebizadehsardari P, et al.
    Molecules, 2021 Mar 09;26(5).
    PMID: 33803488 DOI: 10.3390/molecules26051496
    A wavy shape was used to enhance the thermal heat transfer in a shell-tube latent heat thermal energy storage (LHTES) unit. The thermal storage unit was filled with CuO-coconut oil nano-enhanced phase change material (NePCM). The enthalpy-porosity approach was employed to model the phase change heat transfer in the presence of natural convection effects in the molten NePCM. The finite element method was applied to integrate the governing equations for fluid motion and phase change heat transfer. The impact of wave amplitude and wave number of the heated tube, as well as the volume concertation of nanoparticles on the full-charging time of the LHTES unit, was addressed. The Taguchi optimization method was used to find an optimum design of the LHTES unit. The results showed that an increase in the volume fraction of nanoparticles reduces the charging time. Moreover, the waviness of the tube resists the natural convection flow circulation in the phase change domain and could increase the charging time.
    Matched MeSH terms: Models, Theoretical
  4. Ahmad, M.H., Norzaie, J., Al Qbadi, F., Daniel, B.D.
    ASM Science Journal, 2009;3(1):17-26.
    MyJurnal
    The functions of dams are for water supply, flood control and hydroelectric power generation. A concrete faced rockfill dam (CFRD) is preferred by dam consultants due to its many advantages. It is designed to withstand all applied loads, namely gravity load due to its massive weight and hydrostatic load due to water thrust from the reservoir. The structural response of the Bakun CFRD which is the second highest dam in the world after the Shuibuya Dam, was analyzed using finite element method. A two-dimensional plane strain finite element analysis of the non-linear Duncan-Chang hyperbolic model was used in the study of the dam in respect to the deformation and stresses of the main dam of Bakun CFRD project. The Dead-Birth-Ghost element technique was used to simulate sequences of the construction of the dam. The comparison of rigid and flexible foundation on the behaviour of the dam is discussed in this study. In the finite element modeling, the concrete slab on the upstream was represented through a six-noded element, while the interface characteristic between the dam body and the concrete slab was modeled using an interface element. The maximum settlement and stresses of the cross-section were found and their distribution was discussed and tabulated in the form of contours. The effect of reservoir filling loading had a gradual effect on the dam response behaviour. Comparisons with no water impoundment in the dam were also discussed.
    Matched MeSH terms: Models, Theoretical
  5. Syafiq, A., Amir, I.Z., Sharon, W.X.R.
    MyJurnal
    The impacts on both rheological parameters; Casson yield stress and Casson viscosity were determined. The interactions among blend’s components; xanthan gum (XG), corn starch (CS), glycerin (GL) and their relationship with both flow parameters were also investigated by using D-Optimal mixture design. Three levels of cocoa butter substitution assigned in chocolate production were at 5%, 10% and 15% level with random proportions of each component generated by Design Expert software. An appropriate mathematical model was applied to evaluate each response as a function of the proportions of the components enabling in prediction of future response by using any blend of components. As the incorporation of the blends (XG/CS/GL) in chocolate production was elevated from 5% to 15%, both parameters; viscosity and yield stress of chocolate were gradually increased, as in range 7.819 to 10.529 Pa, and 2.372 to 3.727 Pa.s, respectively. Neither binary nor ternary component-component interaction exhibited synergistic effect. Nevertheless, strongest antagonistic effect on both rheological parameters of substituted chocolate at 5% level and 10% level were respectively observed at ternary interaction region for the former, and at binary interaction area of CS:GL, closer to CS corner as for the latter. This study somehow provides ideas on how component-component interactions influence experimented response.
    Matched MeSH terms: Models, Theoretical
  6. Goudarzi S, Haslina Hassan W, Abdalla Hashim AH, Soleymani SA, Anisi MH, Zakaria OM
    PLoS One, 2016;11(7):e0151355.
    PMID: 27438600 DOI: 10.1371/journal.pone.0151355
    This study aims to design a vertical handover prediction method to minimize unnecessary handovers for a mobile node (MN) during the vertical handover process. This relies on a novel method for the prediction of a received signal strength indicator (RSSI) referred to as IRBF-FFA, which is designed by utilizing the imperialist competition algorithm (ICA) to train the radial basis function (RBF), and by hybridizing with the firefly algorithm (FFA) to predict the optimal solution. The prediction accuracy of the proposed IRBF-FFA model was validated by comparing it to support vector machines (SVMs) and multilayer perceptron (MLP) models. In order to assess the model's performance, we measured the coefficient of determination (R2), correlation coefficient (r), root mean square error (RMSE) and mean absolute percentage error (MAPE). The achieved results indicate that the IRBF-FFA model provides more precise predictions compared to different ANNs, namely, support vector machines (SVMs) and multilayer perceptron (MLP). The performance of the proposed model is analyzed through simulated and real-time RSSI measurements. The results also suggest that the IRBF-FFA model can be applied as an efficient technique for the accurate prediction of vertical handover.
    Matched MeSH terms: Models, Theoretical
  7. Schaefer A, Buratto LG, Goto N, Brotherhood EV
    PLoS One, 2016 09 22;11(9):e0163150.
    PMID: 27658301 DOI: 10.1371/journal.pone.0163150
    A large body of evidence shows that buying behaviour is strongly determined by consumers' price expectations and the extent to which real prices violate these expectations. Despite the importance of this phenomenon, little is known regarding its neural mechanisms. Here we show that two patterns of electrical brain activity known to index prediction errors-the Feedback-Related Negativity (FRN) and the feedback-related P300 -were sensitive to price offers that were cheaper than participants' expectations. In addition, we also found that FRN amplitude time-locked to price offers predicted whether a product would be subsequently purchased or not, and further analyses suggest that this result was driven by the sensitivity of the FRN to positive price expectation violations. This finding strongly suggests that ensembles of neurons coding positive prediction errors play a critical role in real-life consumer behaviour. Further, these findings indicate that theoretical models based on the notion of prediction error, such as the Reinforcement Learning Theory, can provide a neurobiologically grounded account of consumer behavior.
    Matched MeSH terms: Models, Theoretical
  8. Abdul-Kadir NA, Mat Safri N, Othman MA
    Comput Methods Programs Biomed, 2016 Nov;136:143-50.
    PMID: 27686711 DOI: 10.1016/j.cmpb.2016.08.021
    BACKGROUND: Atrial fibrillation (AF) can cause the formation of blood clots in the heart. The clots may move to the brain and cause a stroke. Therefore, this study analyzed the ECG features of AF and normal sinus rhythm signals for AF recognition which were extracted by using a second-order dynamic system (SODS) concept.
    OBJECTIVE: To find the appropriate windowing length for feature extraction based on SODS and to determine a machine learning method that could provide higher accuracy in recognizing AF.
    METHOD: ECG features were extracted based on a dynamic system (DS) that uses a second-order differential equation to describe the short-term behavior of ECG signals according to the natural frequency (ω), damping coefficient, (ξ), and forcing input (u). The extracted features were windowed into 2, 3, 4, 6, 8, and 10 second episodes to find the appropriate windowing size for AF signal processing. ANOVA and t-tests were used to determine the significant features. In addition, pattern recognition machine learning methods (an artificial neural network (ANN) and a support vector machine (SVM)) with k-fold cross validation (k-CV) were used to develop the ECG recognition system.
    RESULTS: Significant differences (p 
    Matched MeSH terms: Models, Theoretical
  9. Jaafar, M.S., Thanoon, Waleed A., Mohammed, T.A., Huda, A.M., Noorzaei, J.
    MyJurnal
    An attempt was made in this investigation to trace the dynamic response of roller compacted concrete dam, which is subjected to horizontal ground motion by considering the interactions between flexible foundations, reservoir water, and bottom reservoir sediments. Two-dimensional finiteinfinite element was used for the non-linear elasto-plastic dynamic analysis. In this analysis, special emphasis was given to the non-linear behaviour of discontinuities along RCC dam-bedding rock foundation which was modelled by thin layer interface. Analysis was first carried out under static loading (self-weight and hydrostatic pressure), and this this was followed by seismic analysis, with hydrodynamic pressure effect in a dam-reservoir system. Based on the numerical dynamic results, it is concluded that the bottom reservoir sediment has significant effect on the seismic response of the RCC gravity dam. Moreover, there is a redistribution of the stresses at thin layer interface with significant stresses reduction, which is resulted from the release of energy through different modes of deformation in this region.
    Matched MeSH terms: Models, Theoretical
  10. Al-Shamiry, Faisal Mohammed Seif, Desa Ahmad
    MyJurnal
    Natural ventilation is defined as the number of air exchanges per hour per unit floor area necessary
    to reduce high indoor air temperature and humidity. In addition, it maintains the concentration of carbon dioxide. Natural ventilation is preferred in mechanical system as the ventilation opening is built into the greenhouse, with lower construction cost and no energy and maintenance inputs are required. A mathematical model to quantify natural ventilation rates was developed and verified in large-scale greenhouse structures. For this purpose, four Naturally Ventilated Tropical Greenhouse Structures were designed and constructed at the Malaysian Agricultural Research and Development Institute (MARDI). These were single, double, triple, and quadruple span structures with floor areas of 500 m2, 1000 m2, 1500 m2 and 2000 m2, respectively. This paper presents the validation of a mathematical model which was developed to quantify natural ventilation rates which are very crucial to reduce high in-house temperature built up in the tropics. Regression equations of natural ventilation against wind speed were found to be Φw = 0.0632V, Φw= 0.0395V, Φw= 0.0316Vand Φw=0.0276V for the single, double, triple and quadruple spans, respectively. Meanwhile, coefficients of determination showed strong relationships between ventilation rate and wind speed, with R2 = 0.9999 for all structures. Larger floor area was found to have higher in-house temperature than smaller ones. Ventilation rate inside the single-span structure was found to be higher compared to the multi-span structures, which increased linearly with the increasing wind speed at the eaves of structure.
    Matched MeSH terms: Models, Theoretical
  11. Sirageldin, Abubakr, Baharum Baharudin, Low, Tang Jung
    MyJurnal
    Developing a trust management scheme in mobile computing environment is increasingly important,
    and the effective trust management model is a challenging task. Business, education, military, and
    entertainment have motivated the growth of ubiquitous and pervasive computing environments, which are always available due to the widespread of portable and embedded devices. Wireless and mobile computing are good example of ubiquitous and pervasive computing environments. Due to the uncertainty and mobility in such environments, the issue of trust has been regarded as an important security problem. Malicious nodes are a major threat to these networks; the trust system can monitor the behaviour of nodes and accordingly rewards well-behaved nodes and punishes misbehaving ones. At present, there are a lot of endeavours on the trust model of the pervasive computing environment. In this paper, a trust management framework for mobile computing is presented. The hybrid framework is based on a fusion of the support vector machine (SVM) and fuzzy logic system. From the results, it can be stated that the framework is effective, dynamic, lightweight, and applicable.
    Matched MeSH terms: Models, Theoretical
  12. Akhtar M, Hannan MA, Begum RA, Basri H, Scavino E
    Waste Manag, 2017 Mar;61:117-128.
    PMID: 28153405 DOI: 10.1016/j.wasman.2017.01.022
    Waste collection is an important part of waste management that involves different issues, including environmental, economic, and social, among others. Waste collection optimization can reduce the waste collection budget and environmental emissions by reducing the collection route distance. This paper presents a modified Backtracking Search Algorithm (BSA) in capacitated vehicle routing problem (CVRP) models with the smart bin concept to find the best optimized waste collection route solutions. The objective function minimizes the sum of the waste collection route distances. The study introduces the concept of the threshold waste level (TWL) of waste bins to reduce the number of bins to be emptied by finding an optimal range, thus minimizing the distance. A scheduling model is also introduced to compare the feasibility of the proposed model with that of the conventional collection system in terms of travel distance, collected waste, fuel consumption, fuel cost, efficiency and CO2 emission. The optimal TWL was found to be between 70% and 75% of the fill level of waste collection nodes and had the maximum tightness value for different problem cases. The obtained results for four days show a 36.80% distance reduction for 91.40% of the total waste collection, which eventually increases the average waste collection efficiency by 36.78% and reduces the fuel consumption, fuel cost and CO2 emission by 50%, 47.77% and 44.68%, respectively. Thus, the proposed optimization model can be considered a viable tool for optimizing waste collection routes to reduce economic costs and environmental impacts.
    Matched MeSH terms: Models, Theoretical
  13. Ahmad MS, Mehmood MA, Al Ayed OS, Ye G, Luo H, Ibrahim M, et al.
    Bioresour Technol, 2017 Jan;224:708-713.
    PMID: 27838316 DOI: 10.1016/j.biortech.2016.10.090
    The biomass of Urochloa mutica was subjected to thermal degradation analyses to understand its pyrolytic behavior for bioenergy production. Thermal degradation experiments were performed at three different heating rates, 10, 30 and 50°Cmin-1 using simultaneous thermogravimetric-differential scanning calorimetric analyzer, under an inert environment. The kinetic analyses were performed using isoconversional models of Kissenger-Akahira-Sunose (KAS) and Flynn-Wall-Ozawa (FWO). The high heating value was calculated as 15.04MJmol-1. The activation energy (E) values were shown to be ranging from 103 through 233 kJmol-1. Pre-exponential factors (A) indicated the reaction to follow first order kinetics. Gibbs free energy (ΔG) was measured to be ranging from 169 to 173kJmol-1 and 168 to 172kJmol-1, calculated by KAS and FWO methods, respectively. We have shown that Para grass biomass has considerable bioenergy potential comparable to established bioenergy crops such as switchgrass and miscanthus.
    Matched MeSH terms: Models, Theoretical
  14. Mirza IA, Abdulhameed M, Vieru D, Shafie S
    Comput Methods Programs Biomed, 2016 Dec;137:149-166.
    PMID: 28110721 DOI: 10.1016/j.cmpb.2016.09.014
    Therapies with magnetic/electromagnetic field are employed to relieve pains or, to accelerate flow of blood-particles, particularly during the surgery. In this paper, a theoretical study of the blood flow along with particles suspension through capillary was made by the electro-magneto-hydrodynamic approach. Analytical solutions to the non-dimensional blood velocity and non-dimensional particles velocity are obtained by means of the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The study of thermally transfer characteristics is based on the energy equation for two-phase thermal transport of blood and particles suspension with viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect. The solution of the nonlinear heat transfer problem is derived by using the velocity field and the integral transform method. The influence of dimensionless system parameters like the electrokinetic width, the Hartman number, Prandtl number, the coefficient of heat generation due to Joule heating and Eckert number on the velocity and temperature fields was studied using the Mathcad software. Results are presented by graphical illustrations.
    Matched MeSH terms: Models, Theoretical
  15. Ahmed M. Mbarib, Mohammad Hamiruce Marhaban, Abdul Rahman Ramli
    MyJurnal
    Skin colour is an important visual cue for face detection, face recogmtlon, hand segmentation for gesture analysis and filtering of objectionable images. In this paper, the adaptive skin color detection model is proposed, based on two bivariate normal distribution models of the skin chromatic subspace, and on image segmentation using an automatic and adaptive multi-thresholding technique. Experimental results on images presenting a wide range of variations in lighting condition and background demonstrate the efficiency of the proposed skin-segmentation algorithm.
    Matched MeSH terms: Models, Theoretical
  16. Mas Ezatul Nadia Mohd Ruah, Nor Fazila Rasaruddin, Fong, Sim Siong, Mohd Zuli Jaafar
    MyJurnal
    This paper outlines the application of chemometrics and pattern recognition tools to classify palm oil using Fourier Transform Mid Infrared spectroscopy (FT-MIR). FT-MIR spectroscopy is used as an effective analytical tool in order to categorise the oil into the category of unused palm oil and used palm oil for frying. The samples used in this study consist of 28 types of pure palm oil, and 28 types of frying palm oils. FT-MIR spectral was obtained in absorbance mode at the spectral range from 650 cm -1 to 4000 cm -1 using FT-MIR-ATR sample handling. The aim of this work is to develop fast method in discriminating the palm oils by implementing Partial Least Square Discriminant Analysis (PLS-DA), Learning Vector Quantisation (LVQ) and Support Vector Machine (SVM). Raw FT-MIR spectra were subjected to Savitzky-Golay smoothing and standardized before developing the classification models. The classification model was validated through finding the value of percentage correctly classified by test set for every model in order to show which classifier provided the best classification. In order to improve the performance of the classification model, variable selection method known as t-statistic method was applied. The significant variable in developing classification model was selected through this method. The result revealed that PLSDA classifier of the standardized data with application of t-statistic showed the best performance with highest percentage correctly classified among the classifiers.
    Matched MeSH terms: Models, Theoretical
  17. Ujjal Kumar Ghosh, Chiu, Choon Hong, Jobrun Nandong, Shufeng, Shen
    MyJurnal
    In this paper, a mathematical model is developed based on mass and momentum balance for carbon dioxide absorption into aqueous ammonia solution. The model is simplified based on the assumption that the CO2 absorption into aqueous ammonia is a pseudo-first-order reaction. Laplace transform method is applied in order to solve the partial differential model equation. Finally, the CO2 molar flux is expressed as a function of partial pressure of CO2, concentration of aqueous ammonia, temperature and gas-liquid contact area. Variation of CO2 molar flux with partial pressure of CO2 and temperature is discussed and a comparison is performed with experimental data from literature. Variation of CO2 molar flux is also shown with gas-liquid contact area. The calculated flux from the model follows the same trend as that of the experimental data reported in literature and the accuracy is within the accepted limit. The mathematical model is very helpful to predict the CO2 molar flux as a function of partial pressure of CO2, concentration of aqueous ammonia, temperature and gas-liquid contact area.
    Matched MeSH terms: Models, Theoretical
  18. Woon YL, Hor CP, Lee KY, Mohd Anuar SFZ, Mudin RN, Sheikh Ahmad MK, et al.
    BMC Public Health, 2018 08 02;18(1):946.
    PMID: 30068318 DOI: 10.1186/s12889-018-5849-z
    BACKGROUND: Epidemiologic measures of the dengue burden such as prevalence and incidence are important for policy-making and monitoring the progress of disease control. It is a common practice where epidemiologic and economic research estimate dengue burden based on notification data. However, a basic challenge in estimating the incidence of dengue is that a significant proportion of infected population are asymptomatic. It can be overcome by using mathematical models that relate observed prevalence and mortality to incidence. In this study, we estimate the trend of dengue incidence and hospitalization in Malaysia.

    METHODS: This study is based entirely on the available secondary data sources on dengue in Malaysia. The age-specific incidence of dengue between 2001 and 2013 was estimated using the prevalence and mortality estimates in an incidence-prevalence-mortality (IPM) model. Data on dengue prevalence were extracted from six sero-surveys conducted in Malaysia between 2001 and 2013; while statistics on dengue notification and Case Fatality Rate were derived from National Dengue Surveillance System. Dengue hospitalization data for the years 2009 to 2013 were extracted from the Health Informatics Centre and the volumes of dengue hospitalization for hospitals with missing data were estimated with Poisson models.

    RESULTS: The dengue incidence in Malaysia varied from 69.9 to 93.4 per 1000 population (pkp) between 2001 and 2013.The temporal trend in incidence rate was decreasing since 2001. It has been reducing at an average rate of 2.57 pkp per year from 2001 to 2013 (p = 0.011). The age-specific incidence of dengue decreased steadily with dengue incidence reaching zero by age > 70 years. Dengue notification rate has remained stable since 2001 and the number of notified cases each year was only a small fraction of the incident cases (0.7 to 2.3%). Similarly, the dengue hospitalization was larger but still a small fraction of the incident cases (3.0 to 5.6%).

    CONCLUSION: Dengue incidence can be estimated with the use of sero-prevalence surveys and mortality data. This study highlights a reducing trend of dengue incidence in Malaysia and demonstrates the discrepancy between true dengue disease burden and cases reported by national surveillance system. Sero-prevalence studies with representative samples should be conducted regularly to allow better estimation of dengue burden in Malaysia.

    Matched MeSH terms: Models, Theoretical
  19. Bashir MJK, Wei CJ, Aun NC, Abu Amr SS
    J Environ Manage, 2017 May 15;193:458-469.
    PMID: 28262420 DOI: 10.1016/j.jenvman.2017.02.031
    Malaysia alone produces more than 49 million m3 palm oil mill effluent per year. Biological treated palm oil mill effluent via ponding system often fails to fulfill the regulatory discharge standards. This is due to remaining of non-biodegradable organics in the treated effluent. Thus, the aim of this study was to resolve such issue by using electro persulphate oxidation process, for the first time, as a post treatment of palm oil mill effluent. Central composite design in response surface methodology was used to analyze and optimize the interaction of operational variables (i.e., current density, contact time, initial pH and persulphate dosage) targeted on maximum treatment efficiency. The significance of quadratic model of each response was determined by analysis of variance, where all models indicated sufficient significance with p-value 
    Matched MeSH terms: Models, Theoretical
  20. Geok TK, Hossain F, Chiat ATW
    PLoS One, 2018;13(8):e0201905.
    PMID: 30086170 DOI: 10.1371/journal.pone.0201905
    Radio propagation prediction simulation methods based on deterministic technique such as ray launching is extensively used to accomplish radio channel characterization. However, the superiority of the simulation depends on the number of rays launched and received. This paper presented the indoor three-dimensional (3D) Minimum Ray Launching Maximum Accuracy (MRLMA) technique, which is applicable for an efficient indoor radio wave propagation prediction. Utilizing the novel MRLMA technique in the simulation environment for ray lunching and tracing can drastically reduce the number of rays that need to be traced, and improve the efficiency of ray tracing. Implementation and justification of MRLMA presented in the paper. An indoor office 3D layouts are selected and simulations have been performed using the MRLMA and other reference techniques. Results showed that the indoor 3D MRLMA model is appropriate for wireless communications network systems design and optimization process with respect to efficiency, coverage, number of rays launching, number of rays received by the mobile station, and simulation time.
    Matched MeSH terms: Models, Theoretical
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