Search results for: Effective Length

Authors: Petar Sarajcev, Josip Vasilj, Damir Jakus

Abstract:

This paper presents a novel statistical description of the counterpoise effective length due to lightning surges, where the (impulse) effective length had been obtained by means of regressive formulas applied to the transient simulation results. The effective length is described in terms of a statistical distribution function, from which median, mean, variance, and other parameters of interest could be readily obtained. The influence of lightning current amplitude, lightning front duration, and soil resistivity on the effective length has been accounted for, assuming statistical nature of these parameters. A method for determining the optimal counterpoise length, in terms of the statistical impulse effective length, is also presented. It is based on estimating the number of dangerous events associated with lightning strikes. Proposed statistical description and the associated method provide valuable information which could aid the design engineer in optimising physical lengths of counterpoises in different grounding arrangements and soil resistivity situations.

Keywords: Counterpoise, Grounding conductor, Effective length, Lightning, Monte Carlo method, Statistical distribution.

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Authors: Mohsen Solimani Babarsad, Habib Musavi Jahromi

Abstract:

Behavior of turbulent jet is relying on jet parameters, environmental and geometric parameters. In this research, it has attempt to Study effect of jet parameters of internal angle on maximum effective length and velocity on centerline from nozzle experimentally. Toward this end, four internal angles 30, 45, 60 and 90-degree are considered for this study in a flume with 600cm as long, 100cm as high and 150cm in width. Various discharges were used to evaluate effective length for a wide range of densimetric Froude numbers F0, from 17.9 to 39.4 that is defined at the nozzle. As a result, It is revealed that both velocity on centerline and effective length decreases when nozzle angle decreased from 90° to 30°. The results show that, for all range of Fr0 the Um/U0 ratio for nozzle with α=90° on centerline increases 20% - 27% than nozzle with α=30° that has lowest velocity on centerline than other nozzle.

Keywords: Turbulent jet, velocity, effective length, Froude number.

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Authors: Amin Eslami, Jafar Bolouri Bazaz

Abstract:

Excavation and retaining walls are of challenging issues in civil engineering. In this study, the behavior of one important type of supporting systems called Contiguous Bored Pile (CBP) retaining wall is investigated using a physical model. Besides, a comparison is made between two modes of free end piles (soft bed) and fixed end piles (stiff bed). Also a back calculation of effective length (the real free length of pile) is done by measuring lateral deflection of piles in different stages of excavation in both aforementioned cases. Based on observed results, for the fixed end mode, the effective length to free length ratio (Leff/L0) is equal to unity in initial stages of excavation and less than 1 in its final stages in a decreasing manner. While this ratio for free end mode, remains constant during all stages of excavation and is always less than unity.

Keywords: Contiguous Bored Pile Wall, Effective Length, Fixed End, Free End, Free Length.

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Authors: Muhammad Naeem, Asif Hussain Bhatti, Muhammad Fahad Nouman

Abstract:

115 samples of Labeo calbasu ranged 8.0-17.9cm length with mean11.90±1.96 and 4.9-68.5g weight with mean 22.25±12.54 from the River Chenab, Southern Punjab, Pakistan were analyzed to investigate length-weight relationships (LWR) of fish in relation to condition factor (K). Standard length (SL), fork length (FL), head length (HL) head width (HW), body girth (BG), dorsal fin length (DFL), dorsal fin base (DFB), pectoral fin length (PcFL), pelvic fin length (PvFL) and anal fin length (AFL) are found to be highly correlated with increasing total length and wet body weight (r > 0.500). Wet body weight has positive (r=0.540) and total length has no correlation (r=0.344) with calculated Condition factor (K). The slope “b" in the relationship is 3.27 and intercepts -2.2258.

Keywords: Labeo calbasu, Length-weight relationship, Body weight, condition factor

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Authors: Maharavo Randrianarivony

Abstract:

The length  of a given rational B'ezier curve is efficiently estimated. Since a rational B'ezier function is nonlinear, it is usually impossible to evaluate its length exactly. The length is approximated by using subdivision and the accuracy of the approximation n is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis of the rate of convergence of n to  is given. The required number of subdivisions to attain a prescribed accuracy is also analyzed. An application to CAD parametrization is briefly described. Numerical results are reported to supplement the theory.

Keywords: Adaptivity, Length, Parametrization, Rational Bezier

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Authors: Varun Setia, Vinod Kumar

Abstract:

In present paper we proposed a simple and effective method to compress an image. Here we found success in size reduction of an image without much compromising with it-s quality. Here we used Haar Wavelet Transform to transform our original image and after quantization and thresholding of DWT coefficients Run length coding and Huffman coding schemes have been used to encode the image. DWT is base for quite populate JPEG 2000 technique.

Keywords: Lossy compression, DWT, quantization, Run length coding, Huffman coding, JPEG2000.

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Authors: Rafet Akdeniz, Pınar Tüfekçi, B.Sıddık Yarman

Abstract:

In this study, to compress ECG signals, KLT (Karhunen- Loeve Transform) method has been used. The purpose of this method is to perform effective ECG coding by a correlation between the length of frames and the number of vectors of ECG signals.

Keywords: ECG Compression, EKG Compression.

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Authors: Sri Wahjuningsih, Hermanto, Nuryadi, Agus Budiarto, Panji Bhintoro

Abstract:

The objective of the present study was to determine the effect of different concentration of spermatozoa and length of storage in 5 0C on sperm motility. Semen was collected using artificial vagina from goat aged 2 to 2.5 years. Fresh goat semen with sperm motility ≥ 70% was used as material. Semen was divided into 4 treatments of concentration (40 x 10 6 / ml, 50 x 106/ml, 60x106/ml, 70x106/ml) with length of storage 0,12,24,36 h. in 5 0C. There were interactions (P <0.05) between concentration and length of storage on individual motility of spermatozoa. Concentration of spermatozoa and length of storage affect the motility of individual (P <0.05). It was concluded that Sperm motility will decrease with increasing concentration and length of storage in 5 0C. Concentration of sperm 40x106/ ml and length of storage 0 h in 50C showed the highest motility of spermatozoa

Keywords: Goat, Length of storage, Motility, Sperm Concentration

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Authors: Jer-Huan Jang, Han-Chieh Chiu, Wei-Chung Yeih, Jia-Jui Yang, Chien-Sheng Huang

Abstract:

In this paper, numerical simulation is used to investigate the thermal performance of liquid cooling heatsink with microchannels due to geometric arrangement. Commercial software ICEPAK is utilized for the analysis. The considered parameters include aspect ratio, porosity and the length and height of microchannel. The aspect ratio varies from 3 to 16 and the length of microchannel is 10mm, 14mm, and 18mm. The height of microchannel is 2mm, 3mm and 4mm. It is found short channel have better thermal efficiency than long channel at 490Pa. No matter the length of channel the best aspect ratio is 4. It is also noted that pressure difference at 2940Pa the best aspect ratio from 4 to 8, it means pressure difference affect aspect ratio, effective thermal resistance at low pressure difference but lower effective thermal resistance at high pressure difference.

Keywords: thermal resistance, liquid cooling, microchannels, numerical analysis, pressure difference

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Authors: Ehab Hasan Ahmed Hasan Ali

Abstract:

The calculation of buckling length factor (K) for steel frames columns is a major and governing processes to determine the dimensions steel frame columns cross sections during design. The buckling length of steel frames columns has a direct effect on the cost (weight) of using cross section. A new formula is required to determine buckling length factor (K) by simplified way. In this research a new formula for buckling length factor (K) was established to determine by accurate method for a limited interval of columns ends rigidity (GA, GB). The new formula can be used ease to evaluate the buckling length factor without needing to complicated equations or difficult charts.

Keywords: Buckling length, New formula, Curve fitting, Simplification, Steel column design.

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Authors: Brian H. Marsh

Abstract:

Self-propelled forage harvesters in the 850 horsepower range were tested over three years for fuel consumption, throughput and quality of chop for corn silage. Cut length had a significant effect on fuel consumption, throughput and some aspects of chop quality. Measure cut length was often different than theoretical length of cut. Where cut length was equivalent fuel consumption and throughput were equivalent across brands. Shortening cut length from 17 to 11mm increases fuel consumption 53 percent measured as Mg of silage harvested per gallon of fuel used and a 42 percent decrease in capacity as tons of fresh material per hour run time.

Keywords: Corn silage, forage harvester, fuel use, length of cut.

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Authors: Zahra Ghadampour, Gholamreza Rakhshandehroo

Abstract:

A concern that researchers usually face in different applications of Artificial Neural Network (ANN) is determination of the size of effective domain in time series. In this paper, trial and error method was used on groundwater depth time series to determine the size of effective domain in the series in an observation well in Union County, New Jersey, U.S. different domains of 20, 40, 60, 80, 100, and 120 preceding day were examined and the 80 days was considered as effective length of the domain. Data sets in different domains were fed to a Feed Forward Back Propagation ANN with one hidden layer and the groundwater depths were forecasted. Root Mean Square Error (RMSE) and the correlation factor (R2) of estimated and observed groundwater depths for all domains were determined. In general, groundwater depth forecast improved, as evidenced by lower RMSEs and higher R2s, when the domain length increased from 20 to 120. However, 80 days was selected as the effective domain because the improvement was less than 1% beyond that. Forecasted ground water depths utilizing measured daily data (set #1) and data averaged over the effective domain (set #2) were compared. It was postulated that more accurate nature of measured daily data was the reason for a better forecast with lower RMSE (0.1027 m compared to 0.255 m) in set #1. However, the size of input data in this set was 80 times the size of input data in set #2; a factor that may increase the computational effort unpredictably. It was concluded that 80 daily data may be successfully utilized to lower the size of input data sets considerably, while maintaining the effective information in the data set.

Keywords: Neural networks, groundwater depth, forecast.

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Authors: Reza Bazargan Lari, Mohammad H. Fattahi

Abstract:

Natural resources management including water resources requires reliable estimations of time variant environmental parameters. Small improvements in the estimation of environmental parameters would result in grate effects on managing decisions. Noise reduction using wavelet techniques is an effective approach for preprocessing of practical data sets. Predictability enhancement of the river flow time series are assessed using fractal approaches before and after applying wavelet based preprocessing. Time series correlation and persistency, the minimum sufficient length for training the predicting model and the maximum valid length of predictions were also investigated through a fractal assessment.

Keywords: Wavelet, de-noising, predictability, time series fractal analysis, valid length, ANN.

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Authors: Mohammad Hamdan, Emad Elnajjar

Abstract:

The LHP is a two-phase device with extremely high effective thermal conductivity that utilizes the thermodynamic pressure difference to circulate a cooling fluid. A thermodynamics analytical model is developed to explore different parameters effects on a Loop Heat Pipe (LHP).. The effects of pipe length, pipe diameter, condenser temperature, and heat load are reported. As pipe length increases and/or pipe diameter decreases, a higher temperature is expected in the evaporator.

Keywords: Loop Heat Pipe, LHP, Passive Cooling, CapillaryForce.

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Authors: Seema Sharma Kaushik, Dhananjoy Shaw

Abstract:

Various length dimensions of the body have been a variable of interest in the research areas of kinanthropometry. However the inclusion of length measurements in various studies remains restricted to reflect characteristics of a particular game/sport at a particular time. Hence, the present investigation was conducted to study various length dimensions correlates of a longitudinal physical conditioning program on Indian male youth. The study was conducted on 90 Indian male youth. The sample was equally divided into three groups namely, progressive load training (PLT), constant load training (CLT) and no load training (NL). The variables included sitting height, leg length, arm length and foot length. The study was conducted by adopting the multi group repeated measure design. Three different groups were measured four times after completion of each of the three meso-cycles of six-weeks duration each. The measurements were taken using the standard landmarks and procedures. Mean, standard deviation and analysis of co-variance were computed to analyze the data statistically. The post-hoc analysis was conducted for the significant F-ratios at 0.05 level. The study concluded that the followed longitudinal physical conditioning program had significant effect on various length dimensions of Indian male youth.

Keywords: Indian male youth, longitudinal, length dimensions, physical conditioning.

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Authors: R. Nandikeswari, M. Sambasivam, V. Anandan

Abstract:

The present study investigates the length-weight relationship of Terapon jarbua from Puducherry (East coast of India). A total of 370 individuals of different sizes were collected from Puducherry landings centre. Length-weight relationships were calculated for all specimens sampled. The length weight relationship equations are W = 0.0050 L3.2742; W = 0.0035 L3.3616; W = 0.0736 L2.4076; W = 0.0098 L3.0807; W = 0.0088 L3.0914; W = 0.0038 L3.3776 for immature male, immature female, matured male, matured female, total male, and total female respectively. The growth exponential (b) values were found to be positively allometric for all the stages except matured male.

Keywords: Allometry, Length weight relationship, Puducherry waters, Terapon jarbua.

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Authors: M. M. M. Jaradat, M. K. Al-Qeyyam

Abstract:

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

Keywords: Cycle space, minimum cycle basis, wreath product.

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Authors: M. Khairulmazidah, A. B. Nurul Nadiah, A. R. Rumiza

Abstract:

Formulation of biological profile is one of the modern roles of forensic anthropologist. The present study was conducted to estimate height using foot and shoeprint length of Malaysian population. The present work can be very useful information in the process of identification of individual in forensic cases based on shoeprint evidence. It can help to narrow down suspects and ease the police investigation. Besides, stature is important parameters in determining the partial identify of unidentified and mutilated bodies. Thus, this study can help the problem encountered in cases of mass disaster, massacre, explosions and assault cases. This is because it is very hard to identify parts of bodies in these cases where people are dismembered and become unrecognizable. Samples in this research were collected from 200 Malaysian adults (100 males and 100 females) with age ranging from 20 to 45 years old. In this research, shoeprint length were measured based on the print of the shoes made from the flat shoes. Other information like gender, foot length and height of subject were also recorded. The data was analyzed using IBM® SPSS Statistics 19 software. Results indicated that, foot length has a strong correlation with stature than shoeprint length for both sides of the feet. However, in the unknown, where the gender was undetermined have shown a better correlation in foot length and shoeprint length parameter compared to males and females analyzed separately. In addition, prediction equations are developed to estimate the stature using linear regression analysis of foot length and shoeprint length. However, foot lengths give better prediction than shoeprint length. 

Keywords: Forensic anthropology, foot length, shoeprints, stature estimation.

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Authors: Reneiloe Seodigeng, Malwandla Hanabe, Haleden Chiririwa, Hilary Rutto, Tumisang Seodigeng

Abstract:

Neutralisation of acid-mine drainage (AMD) using limestone is cost effective, and good results can be obtained. However, this process has its limitations; it cannot be used for highly acidic water which consists of Fe(III). When Fe(III) reacts with CaCO₃, it results in armoring. Armoring slows the reaction, and additional alkalinity can no longer be generated. Limestone is easily accessible, so this problem can be easily dealt with. Experiments were carried out to evaluate the effect of PVC pipe length on ferric and ferrous ions. It was found that the shorter the pipe length the more these dissolved metals precipitate. The effect of the pipe length on the hydrogen ions was also studied, and it was found that these two have an inverse relationship. Experimental data were further compared with the model prediction data to see if they behave in a similar fashion. The model was able to predict the behaviour of 1.5m and 2 m pipes in ferric and ferrous ion precipitation.

Keywords: Acid mine drainage, neutralization, limestone, modeling.

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Authors: Shahadat Uddin, Md Ekramul Hossain, Arif Khan

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The collaboration among physicians during episodes of care for a hospitalised patient has a significant contribution towards effective health outcome. This research aims at improving this health outcome by analysing the attributes of patient-sharing physician collaboration network (PCN) on hospital data. To accomplish this goal, we present a research framework that explores the impact of several types of attributes (such as clique and clan) of PCN on hospitalisation cost and hospital length of stay. We use electronic health insurance claim dataset to construct and explore PCNs. Each PCN is categorised as ‘low’ and ‘high’ in terms of hospitalisation cost and length of stay. The results from the proposed model show that the clique and clan of PCNs affect the hospitalisation cost and length of stay. The clique and clan of PCNs show the difference between ‘low’ and ‘high’ PCNs in terms of hospitalisation cost and length of stay. The findings and insights from this research can potentially help the healthcare stakeholders to better formulate the policy in order to improve quality of care while reducing cost.

Keywords: Clique, clan, electronic health records, physician collaboration.

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Authors: Tom Snir, Eitan Rubin

Abstract:

Mendelian Disease Genes represent a collection of single points of failure for the various systems they constitute. Such genes have been shown, on average, to encode longer proteins than 'non-disease' proteins. Existing models suggest that this results from the increased likeli-hood of longer genes undergoing mutations. Here, we show that in saturated mutagenesis experiments performed on model organisms, where the likelihood of each gene mutating is one, a similar relationship between length and the probability of a gene being lethal was observed. We thus suggest an extended model demonstrating that the likelihood of a mutated gene to produce a severe phenotype is length-dependent. Using the occurrence of conserved domains, we bring evidence that this dependency results from a correlation between protein length and the number of functions it performs. We propose that protein length thus serves as a proxy for protein cardinality in different networks required for the organism's survival and well-being. We use this example to argue that the collection of Mendelian Disease Genes can, and should, be used to study the rules governing systems vulnerability in living organisms.

Keywords: Systems Biology, Protein Length

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Authors: Namal A. Senanayake, A. Beg, Withana C. Prasad

Abstract:

This paper analyzes the patterns of the Monte Carlo data for a large number of variables and minterms, in order to characterize the circuit path length behavior. We propose models that are determined by training process of shortest path length derived from a wide range of binary decision diagram (BDD) simulations. The creation of the model was done use of feed forward neural network (NN) modeling methodology. Experimental results for ISCAS benchmark circuits show an RMS error of 0.102 for the shortest path length complexity estimation predicted by the NN model (NNM). Use of such a model can help reduce the time complexity of very large scale integrated (VLSI) circuitries and related computer-aided design (CAD) tools that use BDDs.

Keywords: Monte Carlo data, Binary decision diagrams, Neural network modeling, Shortest path length estimation.

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Authors: N. AboulAtta, G. Ezizah, N. Yousif , S. Fathy

Abstract:

The stilling basins are commonly used to dissipate the energy and protect the downstream floor from erosion. The aim of the present experimental work is to improve the roughened stilling basin using T-shape roughness instead of the regular cubic one and design this new shape. As a result of the present work the best intensity and the best roughness length are identified. Also, it is found that the T-shape roughness save materials and reduce the jump length compared to the cubic one. Sensitivity analysis was performed and it was noticed that the change in the length of jump is more sensitive to the change in roughness length than the change in intensity.

Keywords: hydraulic jump, energy dissipater, roughened bed, stilling basin.

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Authors: Ivan Pavic, Fran Galetic, Tomislava Pavic Kramaric

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The purpose of this article is to analyze the degree of concentration in the banking market in EU member states as well as to determine the impact of the length of EU membership on the degree of concentration. In that sense several analysis were conducted, specifically, panel analysis, calculation of correlation coefficient and regression analysis of the impact of the length of EU membership on the degree of concentration. Panel analysis was conducted to determine whether there is a similar trend of concentration in three groups of countries - countries with a low, moderate and high level of concentration. The conducted panel analysis showed that in EU countries with a moderate level of concentration, the level of concentration decreases. The calculation of correlation showed that, to some extent, with other influential factors, the length of EU membership negatively affects the market concentration of the banking market. Using the regression analysis for investigation of the influence of the length of EU membership on the level of concentration in the banking sector in a particular country, the results reveal that there is a negative effect of the length in EU membership on market concentration, although it is not significantly influential variable.

Keywords: Banking sector, concentration, EU

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Authors: Dariush Semnani, Mohammad Sheikhzadeh

Abstract:

Circular knitting machine makes the fabric with more than two knitting tools. Variation of yarn tension between different knitting tools causes different loop length of stitches duration knitting process. In this research, a new intelligent method is applied to control loop length of stitches in various tools based on ideal shape of stitches and real angle of stitches direction while different loop length of stitches causes stitches deformation and deviation those of angle. To measure deviation of stitch direction against variation of tensions, image processing technique was applied to pictures of different fabrics with constant front light. After that, the rate of deformation is translated to needed compensation of loop length cam degree to cure stitches deformation. A fuzzy control algorithm was applied to loop length modification in knitting tools. The presented method was experienced for different knitted fabrics of various structures and yarns. The results show that presented method is useable for control of loop length variation between different knitting tools based on stitch deformation for various knitted fabrics with different fabric structures, densities and yarn types.

Keywords: Circular knitting, Radon transformation, Knittedfabric, Regularity, Fuzzy control

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Authors: Mehmet Alpaslan Köroğlu, Musa Hakan Arslan, Muslu Kazım Körez

Abstract:

Basic objective of this study is to create a regression analysis method that can estimate the length of a plastic hinge which is an important design parameter, by making use of the outcomes of (lateral load-lateral displacement hysteretic curves) the experimental studies conducted for the reinforced square concrete columns. For this aim, 170 different square reinforced concrete column tests results have been collected from the existing literature. The parameters which are thought affecting the plastic hinge length such as crosssection properties, features of material used, axial loading level, confinement of the column, longitudinal reinforcement bars in the columns etc. have been obtained from these 170 different square reinforced concrete column tests. In the study, when determining the length of plastic hinge, using the experimental test results, a regression analysis have been separately tested and compared with each other. In addition, the outcome of mentioned methods on determination of plastic hinge length of the reinforced concrete columns has been compared to other methods available in the literature.

Keywords: Columns, plastic hinge length, regression analysis, reinforced concrete.

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Authors: Yu Zhang, Nao-Aki Noda, Kentaro Takaishi

Abstract:

This paper discusses effects of adhesive thickness, overlap length and material combinations on the single-lap joints strength from the point of singular stress fields. A useful method calculating the ratio of intensity of singular stress is proposed using FEM for different adhesive thickness and overlap length. It is found that the intensity of singular stress increases with increasing adhesive thickness, and decreases with increasing overlap length. The increment and decrement are different depending on material combinations between adhesive and adherent.

Keywords: Adhesive thickness, Overlap length, Intensity ofsingular stress, Single-lap joint

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Authors: Sajjad Seifoori

Abstract:

Impact behavior of striker on graphene sheet and carbon nanotube is investigated based on molecular dynamics (MD) simulations. A MD simulation is conducted to obtain the maximum dynamic deflections of a square and rectangular single-layered graphene sheets (SLGSs) with various values of side-length and striker parameter. Effect of (i) chirality, (ii) graphene side-length and nanotube length, (iii) striker mass on the maximum dynamic deflections of graphene and nanotube are investigated. The effect of different types of boundary condition on the maximum dynamic deflections is studied for zigzag and armchair SWCNTs with various aspect ratios (Length/Diameter).

Keywords: Impact, molecular dynamic, graphene, nanotube.

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Authors: F. M. Nor, N. Abdullah, Al-M. Mustapa, L. Q. Wen, N. A. Faisal, D. A. A. Ahmad Nazari

Abstract:

Estimation of stature is an important step in developing a biological profile for human identification. It may provide a valuable indicator for unknown individual in a population. The aim of this study was to analyses the relationship between stature and lower limb dimensions in the Malaysian population. The sample comprised 100 corpses, which included 69 males and 31 females between age ranges of 20 to 90 years old. The parameters measured were stature, thigh length, lower leg length, leg length, foot length, foot height and foot breadth. Results showed that mean values in males were significantly higher than those in females (P < 0.05). There were significant correlations between lower limb dimensions and stature. Cross-validation of the equation on 100 individuals showed close approximation between known stature and estimated stature. It was concluded that lower limb dimensions were useful for estimation of stature, which should be validated in future studies. 

Keywords: Forensic anthropology population data, lower leg length, Malaysian, stature.

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Authors: Abhijit Mitra

Abstract:

This paper proposes an efficient finite precision block floating point (BFP) treatment to the fixed coefficient finite impulse response (FIR) digital filter. The treatment includes effective implementation of all the three forms of the conventional FIR filters, namely, direct form, cascaded and par- allel, and a roundoff error analysis of them in the BFP format. An effective block formatting algorithm together with an adaptive scaling factor is pro- posed to make the realizations more simple from hardware view point. To this end, a generic relation between the tap weight vector length and the input block length is deduced. The implementation scheme also emphasises on a simple block exponent update technique to prevent overflow even during the block to block transition phase. The roundoff noise is also investigated along the analogous lines, taking into consideration these implementational issues. The simulation results show that the BFP roundoff errors depend on the sig- nal level almost in the same way as floating point roundoff noise, resulting in approximately constant signal to noise ratio over a relatively large dynamic range.

Keywords: Finite impulse response digital filters, Cascade structure, Parallel structure, Block floating point arithmetic, Roundoff error.

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