Search results for: block size

Authors: Hesam Sedaghat Nejad, Navid Hosseini, Arash Nikvar Hassani

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Determination of the optimum block size with high profitability is one of the significant parameters in designation of the building stone mines. The aim of this study was to determine the optimum dimensions of building stone blocks in Delichai travertine mine of Damavand in Tehran province through combining the effective parameters proven in determination of the optimum dimensions in building stones such as the spacing of joints and gaps, extraction tools constraints with the help of modeling by Gemcom software. To this end, following simulation of the topography of the mine, the block model was prepared and then in order to use spacing joints and discontinuities as a limiting factor, the existing joints set was added to the model. Since only one almost horizontal joint set with a slope of 5 degrees was available, this factor was effective only in determining the optimum height of the block, and thus to determine the longitudinal and transverse optimum dimensions of the extracted block, the power of available loader in the mine was considered as the secondary limiting factor. According to the aforementioned factors, the optimal block size in this mine was measured as 3.4×4×7 meter.

Keywords: building stone, optimum block size, Delichay travertine mine, loader power

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Malika Yaici, Kamel Hariche

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In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Zhan Chen, Wenquan Bi, Xiaoyun Wang

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The Midori family of light weight block cipher is proposed in ASIACRYPT2015. It has attracted the attention of numerous cryptanalysts. There are two versions of Midori: Midori64 which takes a 64-bit block size and Midori128 the size of which is 128-bit. In this paper an improved 10-round impossible differential attack on Midori64 is proposed. Pre-whitening keys are considered in this attack. A better impossible differential path is used to reduce time complexity by decreasing the number of key bits guessed. A hash table is built in the pre-computation phase to reduce computational complexity. Partial abort technique is used in the key seiving phase. The attack requires 259 chosen plaintexts, 214.58 blocks of memory and 268.83 10-round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: Hooman Dabirmanesh, Attila M. Zsaki

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The toppling failure mode in a rock mass is considerably different from the most common sliding failure type along an existing or an induced slip plane. Block toppling is observed in a rock mass which consists of both a widely-spaced basal cross-joint set and a closely-spaced discontinuity set dipping into the slope. For this case, failure occurs when the structure cannot bear the tensile portion of bending stress, and the columns or blocks overturn by their own weight. This paper presents a particle-based discrete element model of rock blocks subjected to a toppling failure where geometric conditions and interaction among blocks are investigated. A series of parametric studies have been conducted on particles’ size, arrangement and bond contact among of particles which are made the blocks. Firstly, a numerical investigation on a one-block system was verified. Afterward, a slope consisting of multi-blocks was developed to study toppling failure and interaction forces between blocks. The results show that the formation of blocks, especially between the block and basal plane surface, can change the process of failure. The results also demonstrate that the initial configuration of particles used to form the blocks has a significant role in achieving accurate simulation results. The size of particles and bond contacts have a considerable influence to change the progress of toppling failure.

Keywords: block toppling failure, contact interaction, discrete element, particle size, random generation

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Authors: Gaurav Bansod, Swapnil Sutar, Abhijit Patil, Jagdish Patil

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This paper proposes an ultra-lightweight cipher NUX. NUX is a generalized Feistel network. It supports 128/80 bit key length and block length of 64 bit. For 128 bit key length, NUX needs only 1022 GEs which is less as compared to all existing cipher design. NUX design results into less footprint area and minimal memory size. This paper presents security analysis of NUX cipher design which shows cipher’s resistance against basic attacks like Linear and Differential Cryptanalysis. Advanced attacks like Biclique attack is also mounted on NUX cipher design. Two different F function in NUX cipher design results in high diffusion mechanism which generates large number of active S-boxes in minimum number of rounds. NUX cipher has total 31 rounds. NUX design will be best-suited design for critical application like smart grid, IoT, wireless sensor network, where memory size, footprint area and the power dissipation are the major constraints.

Keywords: lightweight cryptography, Feistel cipher, block cipher, IoT, encryption, embedded security, ubiquitous computing

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Authors: Ki-Ro Kim, Seung-Jun Yu, Hyoung-Kyu Song

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Recently, the wireless communication systems are required to have high quality and provide high bit rate data services. Researchers have studied various multiple antenna scheme to meet the demand. In practical application, it is difficult to deploy multiple antennas for limited size and cost. Cooperative diversity techniques are proposed to overcome the limitations. Cooperative communications have been widely investigated to improve performance of wireless communication. Among diversity schemes, space-time block code has been widely studied for cooperative communication systems. In this paper, we propose a new cooperative scheme using pre-coding and space-time block code. The proposed cooperative scheme provides improved error performance than a conventional cooperative scheme using space-time block coding scheme.

Keywords: cooperative communication, space-time block coding, pre-coding

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Authors: Maciej Major, Izabela Major

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The aim of this paper is a numerical analysis of three-layered block design to walls construction subjected to the dynamic load. The block consists of the layers: concrete with rubber pads in shape of crosses, space filled with air and concrete with I-shape rubber pads. The main purpose of rubber inserts embedded during the production process is additional protection against the transversal dynamic load. For the analysis, as rubber, the Zahorski hyperelastic incompressible material model was assumed. A concentrated force as dynamic load applied to the external block surface was investigated. The results for the considered block observed as the stress distribution plot were compared to the results obtained for the solid concrete block. In order to estimate the percentage damping of proposed composite, rubber-concrete block in relation to the solid block the numerical analysis with the use of finite element method based on ADINA software was performed.

Keywords: dynamics, composite, rubber, Zahorski

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Authors: Hae-Yeoun Lee

Abstract:

Mosaic refers to a technique that makes image by gathering lots of small materials in various colours. This paper presents an automatic algorithm that makes the photomosaic image using photos. The algorithm is composed of four steps: Partition and feature extraction, block matching, redundancy removal and colour adjustment. The input image is partitioned in the small block to extract feature. Each block is matched to find similar photo in database by comparing similarity with Euclidean difference between blocks. The intensity of the block is adjusted to enhance the similarity of image by replacing the value of light and darkness with that of relevant block. Further, the quality of image is improved by minimizing the redundancy of tiles in the adjacent blocks. Experimental results support that the proposed algorithm is excellent in quantitative analysis and qualitative analysis.

Keywords: photomosaic, Euclidean distance, block matching, intensity adjustment

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Authors: Mustahsan Mir, Ahmed Hassanin, Mohammed A. Al-Saleh

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The layout optimization of building blocks of unequal areas has applications in many disciplines including VLSI floorplanning, macrocell placement, unequal-area facilities layout optimization, and plant or machine layout design. A number of heuristics and some analytical and hybrid techniques have been published to solve this problem. This paper presents an efficient high-quality building-block layout design technique especially suited for solving large-size problems. The higher efficiency and improved quality of optimized solutions are made possible by introducing the concept of Promising Infant Clusters in a constructive placement procedure. The results presented in the paper demonstrate the improved performance of the presented technique for benchmark problems in comparison with published heuristic, analytic, and hybrid techniques.

Keywords: block layout problem, building-block layout design, CAD, optimization, search techniques

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Authors: Omaima N. Ahmad AL-Allaf

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Over communication networks, images can be easily copied and distributed in an illegal way. The copyright protection for authors and owners is necessary. Therefore, the digital watermarking techniques play an important role as a valid solution for authority problems. Digital image watermarking techniques are used to hide watermarks into images to achieve copyright protection and prevent its illegal copy. Watermarks need to be robust to attacks and maintain data quality. Therefore, we discussed in this paper two approaches for image watermarking, first is based on Particle Swarm Optimization (PSO) and the second approach is based on Genetic Algorithm (GA). Discrete wavelet transformation (DWT) is used with the two approaches separately for embedding process to cover image transformation. Each of PSO and GA is based on co-relation coefficient to detect the high energy coefficient watermark bit in the original image and then hide the watermark in original image. Many experiments were conducted for the two approaches with different values of PSO and GA parameters. From experiments, PSO approach got better results with PSNR equal 53, MSE equal 0.0039. Whereas GA approach got PSNR equal 50.5 and MSE equal 0.0048 when using population size equal to 100, number of iterations equal to 150 and 3×3 block. According to the results, we can note that small block size can affect the quality of image watermarking based PSO/GA because small block size can increase the search area of the watermarking image. Better PSO results were obtained when using swarm size equal to 100.

Keywords: image watermarking, genetic algorithm, particle swarm optimization, discrete wavelet transform

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Authors: Young-Hun Ko, Seung-Jun Kim, Khaqan Baluch, Hyung- Sik Yang

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In this study, the polymer gel was used as coupling material in a blasting hole and its comparison was made with other coupling materials like sand, water, and air. Trazul lead block test and AUTODYN numerical analysis were conducted to analyze the effects of the coupling materials on the intensity of the explosion, as well as the verification tests were conducted by using concrete block test. The emulsion explosives were used in decoupling conditions, sand, water, and polymer gel were used as the coupling materials. The lead block test and the numerical analysis showed that the expansion of the blast hole in the lead block was similar to that of the water and gelatin and followed by sand and air conditions. The validation of concrete block test result showed the similar result as Trazul lead block test and the explosion strength was measured at 0.8 for polymer gel, 0.7 for sand, and 0.6 for no coupling material, in comparison to the full charge (1.0) case.

Keywords: Trazul lead block test, AUTODYN numerical analysis, coupling material, polymer gel, soil covering concrete block explosion test

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Authors: Abubakar Danbaba

Abstract:

Sudoku squares have been widely used to design an experiment where each treatment occurs exactly once in each row, column or sub-block. For some experiments, the size of row (or column or sub-block) may be larger than the number of treatments. Since each treatment appears only once in each row (column or sub-block) with an additional empty cell such designs are partially balanced Sudoku designs (PBSD) with NP-complete structures. This paper proposed methods for constructing PBSD of prime order of treatments by a modified Kronecker product and swap of matrix row (or column) in cyclic order. In addition, linear model and procedure for the analysis of data for PBSD are proposed.

Keywords: sudoku design, partial sudoku, NP-complete, Kronecker product, row and column swap

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Authors: Khairil I. Othman, Mahfuzah Mahayaddin, Zarina Bibi Ibrahim

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We develop and demonstrate a computationally efficient numerical technique to solve first order stiff differential equations. This technique is based on block method whereby three approximate points are calculated. The Cholistani of varied step sizes are presented in divided difference form. Stability regions of the formulae are briefly discussed in this paper. Numerical results show that this block method perform very well compared to existing methods.

Keywords: block method, divided difference, stiff, computational

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Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Beghdadi Lotfi, Bouziane Abdelhafid

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A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Li Li, Ahmed A. Abd El-Latif, Aya El-Fatyany, Mohamed Amin

Abstract:

This paper proposes a new secret image sharing method based on integer discrete cosine transform (IntDCT). It first transforms the original image into the frequency domain (DCT coefficients) using IntDCT, which are operated on each block with size 8*8. Then, it generates shares among each DCT coefficients in the same place of each block, that is, all the DC components are used to generate DC shares, the ith AC component in each block are utilized to generate ith AC shares, and so on. The DC and AC shares components with the same number are combined together to generate DCT shadows. Experimental results and analyses show that the proposed method can recover the original image lossless than those methods based on traditional DCT and is more sensitive to tiny change in both the coefficients and the content of the image.

Keywords: secret image sharing, integer DCT, lossless recovery, sensitivity

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Authors: Antwi Kwaku Dei, Lyford Conrad Power

Abstract:

This paper investigates the outcome of participating in the government of Ghana block farm program on rural households’ farm productivity, income, food security and nutritional status in Northern Ghana using cross-sectional data. Data analysis was done using the Instrumental Variable and the Heckman Selection Bias procedures. Our analysis indicates that participation in the block farm program significantly increased directly the productivity of maize, rice, and soybean by 21.3 percent, 15.8 percent, and 12.3 percent respectively. Also, the program participation was found to increase households’ farm income by 20 percent in northern Ghana. Furthermore, program participation was found to improve household food security and nutrition by 19 percent and 14 percent respectively through income effect. Based on the benefit-cost ratio of 1.59 the results from the study recommends that the program is expanded to other communities in the northern region. Further analysis indicates that rural households’ decision to participate in food security intervention programs is significantly influenced by factors including the gender of the household head, the age of the household head, and household size. Results of the study further show that gender of household head, household size, household monthly income, household assets, women educational status, the age of women, marital status of women, are significant determinants of food security and nutrition status in Northern Ghana.

Keywords: block farm program, farm productivity, , household food security, Northern Ghana

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Authors: B. Saripah, A. Alias

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Cocoa Theobroma cacao (Linnaeus) (Malvales: Sterculiaceae) is subjected to be infested by various numbers of insect pests, and Conopomorpha cramerella Snellen (Lepidoptera: Gracillariidae) is the most serious pest of cocoa in Malaysia. The pest was indigenous to the South East Asia. Several control measures have been implemented and the chemicals have been a major approach if not unilateral, in the management of CPB. Despite extensive use of insecticides, CPB continues to cause an unacceptable level of damage; thus, the combination of several control approaches should be sought. The study was commenced for 12 months at three blocks; Block 18C with complete management practices which include insecticide application, pruning, fertilization and frequent harvesting, Block 17C was treated with frequent harvesting at intervals of 7-8 days, and Block 19C was served as control block. The results showed that the mean numbers of CPB eggs were recorded higher in Block 17C compared with Block 18C in all sampling occasions. Block 18C shows the lowest mean number of CPB eggs in both sampling plots, outside and core plots and it was found significantly different (p ≤ 0. 05) compared to the other blocks. The mean number of CPB eggs was fluctuated throughout sampling occasions, the lowest mean number of eggs was recorded in January (17C) and November (18C), while the highest was recorded in April (17C) and December 2012 (18C). Frequent spraying with insecticides at the adjacent block (18C) helps in reducing CPB eggs in the control block (Block 19C), although there was no spraying was implemented Block 19C. In summary, the combination of complete management practices at Block 18C seems to have some effect on the CPB population at Blocks 17 and 19C because all blocks are adjacent to each other.

Keywords: cocoa, theobroma cacao, cocoa pod borer, conopomorpha cramerella

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Wang Ye, Wei Wei

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Residential block construction of big cities in China began in the 1950s, and four models had far-reaching influence on modern residential block in its development process, including unit compound and residential district in 1950s to 1980s, and gated community and open community in 1990s to now. Based on analysis of the four models’ fabric, the article takes residential blocks in Hangzhou west area as an example and carries on the studies from urban structure level and block special level, mainly including urban road network, land use, community function, road organization, public space and building fabric. At last, the article puts forward semi-open sub-community strategy to improve the current fabric.

Keywords: Hangzhou west area, residential block model, residential block fabric, semi-open sub-community strategy

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Authors: Rita SahaRay, Ganesh Dutta

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In this article, experimental situations are considered where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks, not necessarily of same size. Assuming the block sizes to be even for all blocks, for the case n ≡ 2 (mod 4), optimal designs are obtained with respect to type 1 and type 2 optimality criteria in the class of designs providing estimation of all main effects orthogonal to the block effects. In practice, such orthogonal estimation of main effects is often a desirable condition. In the wider class of all available m two level even sized blocked main effects plans, where the factors do not occur at high and low levels equally often in each block, E-optimal designs are also characterized. Simple construction methods based on Hadamard matrices and Kronecker product for these optimal designs are presented.

Keywords: design matrix, Hadamard matrix, Kronecker product, type 1 criteria, type 2 criteria

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Authors: J. C. Cheng, Y. L. Tsay, Z. D. Chan, C. H. Yang

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In this study the physical system under consideration is a three-dimensional (3-D) cabinet with arrays of block heat sources mounted on one of the walls of the cabinet. The block heat sources dissipate heat to the cabinet surrounding through the conjugate conduction and natural convection. The results illustrate that the difference in hot spot temperatures of the system (θH) for the situations with and without consideration of thermal interaction is higher for smaller Rayleigh number (Ra), and can be up to 94.73% as Ra=10^5. In addition, the heat transfer characteristics depends strongly on the dimensionless heat conductivity of cabinet wall (Kwf), heat conductivity of block (Kpf) and length of cabinet (Ax). The maximum reduction in θH is 70.01% when Kwf varies from 10 to 1000, and it is 30.07% for Ax from 0.5 to 1. While the hot spot temperature of system is not sensitive to the cabinet angle (Φ).

Keywords: block heat sources, 3-D cabinet, thermal interaction, heat transfer

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Authors: Presto Tri Sambodo, Suharjana, Galih Yoga Santiko

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Having an ideal body shape healthy body are the desire of everyone, both young and old. The purpose of this study was to determine: (1) the effect of block circuit training on aerobic fitness and body fat percentage, (2) the effect of non-block circuit training on aerobic fitness and body fat percentage, and (3) differences in the effect of exercise on block and non-circuit training block against aerobic fitness and body fat percentage. This research is an experimental research with the prestest posttest design Two groups design. The population in this study were 57 members of fat loss at GOR UNY Fitness Center. The retrieval technique uses purposive random sampling with a sample of 20 people. The instruments with rockport test (1.6 KM) and body fat percentage with a scale of bioelectrical impedance analysis omron (BIA). So it can be concluded the circuit training between block and non-block has a significant effect on aerobic fitness and body fat percentage. And for differences in the effect of circuit training between blocks and non-blocks, it is more influential on aerobic fitness than the percentage of body fat.

Keywords: circuit training, aerobic fitness, body fat percentage, healthy body

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Authors: M. Panahian

Abstract:

A global challenge which is of paramount significance today is the issue of devising innovative solutions to tackle the environmental issues, as well as more intelligent and foresightful consumption of and management of natural resources. Changes in global climate resulting from the burning of fossil fuel and the rise in the level of energy consumption are a few examples of environmental issues detrimental to any form of life on earth, which are aggravated year by year. Overall, energy-efficient designs and construction strategies can be studied at three scales: building, block, and city. Nevertheless, as the available literature suggests, the greatest emphasis has been on building and city scales, and little has been done as to the energy-efficient designs at block scale. Therefore, the aim of the current research is to investigate the influences of residential block scale envelope on the energy consumption in buildings. To this end, a case study of residential block scale has been selected in the city of Isfahan, in Iran, situated in a hot and dry climate with cold winters. Eventually, the most effective variables in energy consumption, concerning the block scale envelope, will be concluded.

Keywords: sustainability, passive energy saving solutions, residential block scale, energy efficiency

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Authors: Kamonwat Suksumek, Seeronk Prichanont

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Access block refers to the situation where Emergency Department (ED) patients requiring hospital admission spend an unreasonable holding time in an ED because their access to a ward is blocked by the full utilization of the ward’s beds. Not only it delays the proper treatments required by the patients, but access block is also the cause of ED’s overcrowding. Clearly, access block is an inter-departmental problem that needs to be brought to management’s attention. This paper focuses on the analysis of strategies to address the access block problem, both in the operational and intermediate levels. These strategies were analyzed through a simulation model with a real data set from a university hospital in Thailand. The paper suggests suitable variable levels for each strategy so that the management will make the final decisions.

Keywords: access block, emergency department, health system analysis, simulation

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Authors: Nazia Nazir

Abstract:

Background: The benefits of regional anesthetic techniques are well established. Use of additives to local anesthetics can prolong these benefits. The aim of this study was to observe the effect of adding dexmedetomidine to bupivacaine for the supraclavicular block. Methods (Design): In this randomized, double-blind study, seventy ASA I & II patients of either sex undergoing elective surgeries on the upper limb were given supraclavicular block under ultrasound guidance. Group C (n=35), received 38 mL 0.25% bupivacaine + 2mL normal saline and group D received 38 mL 0.25% bupivacaine + 1 µg/kg dexmedetomidine (2mL). Patients were observed for onset, duration of motor and sensory block, duration of analgesia, sedation score, hemodynamic changes and any adverse events. Results: In group D the onset was faster (P < 0.001), duration of sensory and motor block, as well as duration of analgesia, was prolonged as compared to group C (P < 0.0001). There was significant drop in heart rate (HR) from the baseline in group D (P < 0.05) at 30, 60, 90 and 120 min, however, none of the patients dropped HR below 50/min. Mean arterial Pressure (MAP) remained unaffected. The patients in group D were effectively sedated than those in group C (P < 0.05). No adverse event was reported in either group. Conclusion: Dexmedetomidine as adjuvant to bupivacaine in supraclavicular block resulted in faster action, prolonged motor and sensory block, prolonged analgesia with hemodynamic stability and adequate sedation.

Keywords: Analgesia, bupivacaine, dexmedetomidine, supraclavicular block

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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