Search results for: finite word length

Authors: Sakol Udomsiri, Masahiro Iwahashi

Abstract:

This paper presents comparative study on recent integer DCTs and a new method to construct a low sensitive structure of integer DCT for colored input signals. The method refers to sensitivity of multiplier coefficients to finite word length as an indicator of how word length truncation effects on quality of output signal. The sensitivity is also theoretically evaluated as a function of auto-correlation and covariance matrix of input signal. The structure of integer DCT algorithm is optimized by combination of lower sensitive lifting structure types of IRT. It is evaluated by the sensitivity of multiplier coefficients to finite word length expression in a function of covariance matrix of input signal. Effectiveness of the optimum combination of IRT in integer DCT algorithm is confirmed by quality improvement comparing with existing case. As a result, the optimum combination of IRT in each integer DCT algorithm evidently improves output signal quality and it is still compatible with the existing one.

Keywords: DCT, sensitivity, lossless, wordlength.

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Authors: Jamal Laaouine, Mohammed Elhassani Charkani

Abstract:

Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

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Authors: Yidan Shao

Abstract:

With the advancement of the economy, technology promotes online teaching, and learning has become one of the common features in the educational field. Meanwhile, the dramatic expansion of the online environment provides opportunities for more learners, including second language learners. A greater command of vocabulary improves students’ learning capacity, and word acquisition and development play a critical role in learning. Furthermore, the Word Wall is an effective tool to improve students’ knowledge of words, which works for a wide range of age groups. Therefore, this study is going to use the Word Wall as an intervention to examine whether it can bring some memorization changes in an online English language class for a second language learner based on the word morphology method. The participant will take ten courses in the experiment as it plans. The findings show that the Word Wall activity plays a slight role in improving word memorizing, but it does affect instant memorization. If longer periods and more comprehensive designs of research can be applied, it is expected to have more value.

Keywords: Second language acquisition, word morphology, word memorization, the Word Wall.

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Authors: Eleni Galiotou, Angela Ralli

Abstract:

In this paper we propose a computational model for the representation and processing of morpho-phonological phenomena in a natural language, like Modern Greek. We aim at a unified treatment of inflection, compounding, and word-internal phonological changes, in a model that is used for both analysis and generation. After discussing certain difficulties cuase by well-known finitestate approaches, such as Koskenniemi-s two-level model [7] when applied to a computational treatment of compounding, we argue that a morphology-based model provides a more adequate account of word-internal phenomena. Contrary to the finite state approaches that cannot handle hierarchical word constituency in a satisfactory way, we propose a unification-based word grammar, as the nucleus of our strategy, which takes into consideration word representations that are based on affixation and [stem stem] or [stem word] compounds. In our formalism, feature-passing operations are formulated with the use of the unification device, and phonological rules modeling the correspondence between lexical and surface forms apply at morpheme boundaries. In the paper, examples from Modern Greek illustrate our approach. Morpheme structures, stress, and morphologically conditioned phoneme changes are analyzed and generated in a principled way.

Keywords: Morpho-Phonology, Natural Language Processing.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.

Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.

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Authors: Chutchada Nusai, Yoshimi Suzuki, Haruaki Yamazaki

Abstract:

Selecting the word translation from a set of target language words, one that conveys the correct sense of source word and makes more fluent target language output, is one of core problems in machine translation. In this paper we compare the 3 methods of estimating word translation probabilities for selecting the translation word in Thai – English Machine Translation. The 3 methods are (1) Method based on frequency of word translation, (2) Method based on collocation of word translation, and (3) Method based on Expectation Maximization (EM) algorithm. For evaluation we used Thai – English parallel sentences generated by NECTEC. The method based on EM algorithm is the best method in comparison to the other methods and gives the satisfying results.

Keywords: Machine translation, EM algorithm.

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Authors: Ibrahim A. El rube, Mohamed T. El Sonni, Soha S. Saleh

Abstract:

the cursive nature of the Arabic writing makes it difficult to accurately segment characters or even deal with the whole word efficiently. Therefore, in this paper, a printed Arabic sub-word recognition system is proposed. The suggested algorithm utilizes geometrical moments as descriptors for the separated sub-words. Three types of moments are investigated and applied to the printed sub-word images after dividing each image into multiple parts using windowing. Since moments are global descriptors, the windowing mechanism allows the moments to be applied to local regions of the sub-word. The local-global mixture of the proposed scheme increases the discrimination power of the moments while keeping the simplicity and ease of use of moments.

Keywords: Arabic sub-word recognition, windowing, aspectratio, moments.

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Authors: Zeynep Orhan, Zeynep Altan

Abstract:

Word sense disambiguation is an important intermediate stage for many natural language processing applications. The senses of an ambiguous word are the classification of usages for that specific word. This paper deals with the methodologies of determining the senses for a given word if they can not be obtained from an already available resource like WordNet. We offer a method that helps us to determine the sense boundaries gradually. In this method, first we decide on some features that are thought to be effective on the senses and divide the instances first into two, then according to the results of evaluations we continue dividing instances gradually. In a second method we use the pseudo words. We devise artificial words depending on some criteria and evaluate classification algorithms on these previously classified words.

Keywords: Word sense disambiguation, sense determination, pseudo words, sense granularity.

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied.

The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length.

To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed.

Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition.

The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work.

The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: Buckling, Finite Strip, Different Sides Support, Plates on Foundation.

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Authors: B. Singh, B. K. Nanda

Abstract:

The characterization and modeling of the dynamic behavior of many built-up structures under vibration conditions is still a subject of current research. The present study emphasizes the theoretical investigation of slip damping in layered and jointed welded cantilever structures using finite element approach. Application of finite element method in damping analysis is relatively recent, as such, some problems particularly slip damping analysis has not received enough attention. To validate the finite element model developed, experiments have been conducted on a number of mild steel specimens under different initial conditions of vibration. Finite element model developed affirms that the damping capacity of such structures is influenced by a number of vital parameters such as; pressure distribution, kinematic coefficient of friction and micro-slip at the interfaces, amplitude, frequency of vibration, length and thickness of the specimen. Finite element model developed can be utilized effectively in the design of machine tools, automobiles, aerodynamic and space structures, frames and machine members for enhancing their damping capacity.

Keywords: Amplitude, finite element method, slip damping, tack welding.

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Authors: S. Jalaja, A. M. Vijaya Prakash

Abstract:

Recursive combination of an algorithm based on Karatsuba multiplication is exploited to design a generalized transpose and parallel Finite Impulse Response (FIR) Filter. Mid-range Karatsuba multiplication and Carry Save adder based on Karatsuba multiplication reduce time complexity for higher order multiplication implemented up to n-bit. As a result, we design modified N-tap Transpose and Parallel Symmetric FIR Filter Structure using Karatsuba algorithm. The mathematical formulation of the FFA Filter is derived. The proposed architecture involves significantly less area delay product (APD) then the existing block implementation. By adopting retiming technique, hardware cost is reduced further. The filter architecture is designed by using 90 nm technology library and is implemented by using cadence EDA Tool. The synthesized result shows better performance for different word length and block size. The design achieves switching activity reduction and low power consumption by applying with and without retiming for different combination of the circuit. The proposed structure achieves more than a half of the power reduction by adopting with and without retiming techniques compared to the earlier design structure. As a proof of the concept for block size 16 and filter length 64 for CKA method, it achieves a 51% as well as 70% less power by applying retiming technique, and for CSA method it achieves a 57% as well as 77% less power by applying retiming technique compared to the previously proposed design.

Keywords: Carry save adder Karatsuba multiplication, mid-range Karatsuba multiplication, modified FFA, transposed filter, retiming.

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

Abstract:

This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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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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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: T.C. Manjunath, B. Bandyopadhyay

Abstract:

This paper features the modeling and design of a Fast Output Sampling (FOS) Feedback control technique for the Active Vibration Control (AVC) of a smart flexible aluminium cantilever beam for a Single Input Single Output (SISO) case. Controllers are designed for the beam by bonding patches of piezoelectric layer as sensor / actuator to the master structure at different locations along the length of the beam by retaining the first 2 dominant vibratory modes. The entire structure is modeled in state space form using the concept of piezoelectric theory, Euler-Bernoulli beam theory, Finite Element Method (FEM) and the state space techniques by dividing the structure into 3, 4, 5 finite elements, thus giving rise to three types of systems, viz., system 1 (beam divided into 3 finite elements), system 2 (4 finite elements), system 3 (5 finite elements). The effect of placing the sensor / actuator at various locations along the length of the beam for all the 3 types of systems considered is observed and the conclusions are drawn for the best performance and for the smallest magnitude of the control input required to control the vibrations of the beam. Simulations are performed in MATLAB. The open loop responses, closed loop responses and the tip displacements with and without the controller are obtained and the performance of the proposed smart system is evaluated for vibration control.

Keywords: Smart structure, Finite element method, State spacemodel, Euler-Bernoulli theory, SISO model, Fast output sampling, Vibration control, LMI

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Authors: A.R.Nezamabadi, M.Mansouri Gavari, S.Mansouri, M.Mansouri Gavari

Abstract:

This article considers the positional buckling of composite thick plates under thermal loading . For this purpose , the complex finite strip method is used . In analysis of complex finite strip, harmonic complex function in longitudinal direction , cubic functions in transversal direction and parabola distribution of transverse shear strain in thickness of thick plate based on higherorder shear deformation theory are used . In given examples , the effect of angles of stratification , number of layers , dimensions ratio and length – to – thick ratio across critical temperature are considered.

Keywords: Thermal buckling , Thick plate , Complex finite strip , Higher – order shear deformation theory.

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Authors: Faaza A, Almarsoomi, James D, O'Shea, Zuhair A, Bandar, Keeley A, Crockett

Abstract:

This paper is concerned with the production of an Arabic word semantic similarity benchmark dataset. It is the first of its kind for Arabic which was particularly developed to assess the accuracy of word semantic similarity measurements. Semantic similarity is an essential component to numerous applications in fields such as natural language processing, artificial intelligence, linguistics, and psychology. Most of the reported work has been done for English. To the best of our knowledge, there is no word similarity measure developed specifically for Arabic. In this paper, an Arabic benchmark dataset of 70 word pairs is presented. New methods and best possible available techniques have been used in this study to produce the Arabic dataset. This includes selecting and creating materials, collecting human ratings from a representative sample of participants, and calculating the overall ratings. This dataset will make a substantial contribution to future work in the field of Arabic WSS and hopefully it will be considered as a reference basis from which to evaluate and compare different methodologies in the field.

Keywords: Arabic categories, benchmark dataset, semantic similarity, word pair, stimulus Arabic words

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Authors: Atilla Akpinar

Abstract:

In this paper, we study on finite projective Hjelmslev planes M(Zq) coordinatized by Hjelmslev ring Zq (where prime power q = pk). We obtain finite hyperbolic Klingenberg planes from these planes under certain conditions. Also, we give a combinatorical result on M(Zq), related by deleting a line from lines in same neighbour.

Keywords: Finite Klingenberg plane, finite hyperbolic Klingenberg plane.

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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: Mahdi Sadeghian, Mahmoud Hassanlourad, Alireza Ardakani, Reza Dinarvand

Abstract:

In this research, the behavior of monopiles, under lateral loads, was investigated with vertical and oblique piles by Finite Element Method. In engineering practice when soil-pile interaction comes to the picture some simplifications are applied to reduce the design time. As a simplified replacement of soil and pile interaction analysis, pile could be replaced by a column. The height of the column would be equal to the free length of the pile plus a portion of the embedded length of it. One of the important factors studied in this study was that columns with an equivalent length (free length plus a part of buried depth) could be used instead of soil and pile modeling. The results of the analysis show that the more internal friction angle of the soil increases, the more the bearing capacity of the soil is achieved. This additional length is 6 to 11 times of the pile diameter in dense soil although in loose sandy soil this range might increase.

Keywords: Lateral bearing capacity, pile group, oblique pile, soil-structure interaction, depth of fixity.

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Authors: Theologos Athanaselis, Stelios Bakamidis, Ioannis Dologlou, Konstantinos Mamouras

Abstract:

This paper presents an approach for repairing word order errors in English text by reordering words in a sentence and choosing the version that maximizes the number of trigram hits according to a language model. A possible way for reordering the words is to use all the permutations. The problem is that for a sentence with length N words the number of all permutations is N!. The novelty of this method concerns the use of an efficient confusion matrix technique for reordering the words. The confusion matrix technique has been designed in order to reduce the search space among permuted sentences. The limitation of search space is succeeded using the statistical inference of N-grams. The results of this technique are very interesting and prove that the number of permuted sentences can be reduced by 98,16%. For experimental purposes a test set of TOEFL sentences was used and the results show that more than 95% can be repaired using the proposed method.

Keywords: Permutations filtering, Statistical language model N-grams, Word order errors, TOEFL

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Authors: M. S. Salwani, B. B. Sahari, Aidy Ali, A. A. Nuraini

Abstract:

In this study, optimization is carried out to find the optimized design of a foam-filled column for the best Specific Energy Absorption (SEA) and Crush Force Efficiency (CFE). In order to maximize SEA, the optimization gives the value of 2.3 for column thickness and 151.7 for foam length. On the other hand to maximize CFE, the optimization gives the value of 1.1 for column thickness and 200 for foam length. Finite Element simulation is run by using this value and the SEA and CFE obtained 1237.76 J/kg and 0.92.

Keywords: Crash, foam, oblique loading.

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Authors: R.Goudarzizadeh, N.Hedayat, S.H.Mousavi Jahromi

Abstract:

Channel junctions can be analyzed in two ways of division (lateral intake) and combined flows (confluence). The present paper investigates 3D flow pattern at lateral intake using Navier-Stokes equation and κ -ε (RNG) turbulent model. The equations are solved by Finite-Volume Method (FVM) and results are compared with the experimental data of (Barkdoll, B.D., 1997) to test the validity of the findings. Comparison of the results with the experimental data indicated a close proximity between the two sets of data which suggest a very close simulation. Results further indicated an inverse relation between the effects of discharge ratio ( r Q ) on the length and width of the separation zone. In other words, as the discharge ration increases, the length and width of separation zone decreases.

Keywords: 900 junction, flow division, turbulent flow, numerical modeling, flow separation zone.

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Authors: Zöhre Kara Kayikci, Günther Palm

Abstract:

A word recognition architecture based on a network of neural associative memories and hidden Markov models has been developed. The input stream, composed of subword-units like wordinternal triphones consisting of diphones and triphones, is provided to the network of neural associative memories by hidden Markov models. The word recognition network derives words from this input stream. The architecture has the ability to handle ambiguities on subword-unit level and is also able to add new words to the vocabulary during performance. The architecture is implemented to perform the word recognition task in a language processing system for understanding simple command sentences like “bot show apple".

Keywords: Hebbian learning, hidden Markov models, neuralassociative memories, word recognition.

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Authors: Theologos Athanaselis, Stelios Bakamidis, Ioannis Dologlou

Abstract:

There are multiple reasons to expect that detecting the word order errors in a text will be a difficult problem, and detection rates reported in the literature are in fact low. Although grammatical rules constructed by computer linguists improve the performance of grammar checker in word order diagnosis, the repairing task is still very difficult. This paper presents an approach for repairing word order errors in English text by reordering words in a sentence and choosing the version that maximizes the number of trigram hits according to a language model. The novelty of this method concerns the use of an efficient confusion matrix technique for reordering the words. The comparative advantage of this method is that works with a large set of words, and avoids the laborious and costly process of collecting word order errors for creating error patterns.

Keywords: Permutations filtering, Statistical languagemodel N-grams, Word order errors

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Authors: Fares Jnaid, Riyad Aboutaha

Abstract:

In this paper, a nonlinear Finite Element Analysis (FEA) was carried out using ANSYS software to build a model able of predicting the behavior of Reinforced Concrete (RC) beams with unbonded reinforcement. The FEA model was compared to existing experimental data by other researchers. The existing experimental data consisted of 16 beams that varied from structurally sound beams to beams with unbonded reinforcement with different unbonded lengths and reinforcement ratios. The model was able to predict the ultimate flexural strength, load-deflection curve, and crack pattern of concrete beams with unbonded reinforcement. It was concluded that when the when the unbonded length is less than 45% of the span, there will be no decrease in the ultimate flexural strength due to the loss of bond between the steel reinforcement and the surrounding concrete regardless of the reinforcement ratio. Moreover, when the reinforcement ratio is relatively low, there will be no decrease in ultimate flexural strength regardless of the length of unbond.

Keywords: FEA, ANSYS, Unbond, Strain.

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Authors: R. M. Barron, B. Zogheib

Abstract:

A new numerical method for solving the twodimensional, steady, incompressible, viscous flow equations on a Curvilinear staggered grid is presented in this paper. The proposed methodology is finite difference based, but essentially takes advantage of the best features of two well-established numerical formulations, the finite difference and finite volume methods. Some weaknesses of the finite difference approach are removed by exploiting the strengths of the finite volume method. In particular, the issue of velocity-pressure coupling is dealt with in the proposed finite difference formulation by developing a pressure correction equation in a manner similar to the SIMPLE approach commonly used in finite volume formulations. However, since this is purely a finite difference formulation, numerical approximation of fluxes is not required. Results obtained from the present method are based on the first-order upwind scheme for the convective terms, but the methodology can easily be modified to accommodate higher order differencing schemes.

Keywords: Curvilinear, finite difference, finite volume, SIMPLE.

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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: Juárez-Luna Gelacio, Ayala Gustavo, Retama-Velasco Jaime

Abstract:

This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constitutive model to describe the behavior of the material in the symmetric formulation is a traction-displacement jump relationship equipped with softening after reaching the failure surface.

To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented. It is shown that the non-symmetric family may over or underestimate the energy required to create a discontinuity, as this effect is related with the total length of the discontinuity, fact that is not noticed when the discontinuity path is a straight line.

Keywords: Variational formulation, strong discontinuity, embedded discontinuities, strain localization.

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Authors: Shitian Liu, Deqin Chen

Abstract:

Let G be a finite group, and let F be a formation of finite group. We say that a subgroup H of G is p F -normal in G if there exists a normal subgroup T of G such that HT is a permutable Hall subgroup of G and G G (H

Keywords: Finite group, Fp -normal subgroup, Sylowsubgroup, Maximal subgroup

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