Search results for: phenomenological method

Authors: S. De Curtis, L. Delle Rose, S. Moretti, K. Yagyu

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Supersymmetry and compositeness are the two prevalent paradigms providing both a solution to the hierarchy problem and motivation for a light Higgs boson state. An open door towards the solution is found in the context of 2-Higgs Doublet Models (2HDMs), which are necessary to supersymmetry and natural within compositeness in order to enable Electro-Weak Symmetry Breaking. In scenarios of compositeness, the two isospin doublets arise as pseudo Nambu-Goldstone bosons from the breaking of SO(6). By calculating the Higgs potential at one-loop level through the Coleman-Weinberg mechanism from the explicit breaking of the global symmetry induced by the partial compositeness of fermions and gauge bosons, we derive the phenomenological properties of the Higgs states and highlight the main signatures of this Composite 2-Higgs Doublet Model at the Large Hadron Collider. These include modifications to the SM-like Higgs couplings as well as production and decay channels of heavier Higgs bosons. We contrast the properties of this composite scenario to the well-known ones established in supersymmetry, with the MSSM being the most notorious example. We show how 2HDM spectra of masses and couplings accessible at the Large Hadron Collider may allow one to distinguish between the two paradigms.

Keywords: beyond the standard model, composite Higgs, supersymmetry, Two-Higgs Doublet Model

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Authors: C. Bunsanit

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This paper presents the refinement method for two beams formation of wideband smart antenna. The refinement method for weighting coefficients is based on Fully Spatial Signal Processing by taking Inverse Discrete Fourier Transform (IDFT), and its simulation results are presented using MATLAB. The radiation pattern is created by multiplying the incoming signal with real weights and then summing them together. These real weighting coefficients are computed by IDFT method; however, the range of weight values is relatively wide. Therefore, for reducing this range, the refinement method is used. The radiation pattern concerns with five input parameters to control. These parameters are maximum weighting coefficient, wideband signal, direction of mainbeam, beamwidth, and maximum of minor lobe level. Comparison of the obtained simulation results between using refinement method and taking only IDFT shows that the refinement method works well for wideband two beams formation.

Keywords: fully spatial signal processing, beam forming, refinement method, smart antenna, weighting coefficient, wideband

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Authors: Lewis Wallace, William Dempster, David Nash, Alexandros Boukis, Craig Maclean

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This paper, through traditional test methods and close adherence to international standards, presents a characterization study of a woven Polyethylene Terephthalate (PET). Testing is undergone in the axial, shear, and out-of-plane (bend) directions, and the results are fitted to the *FABRIC material model with ABAQUS FEA. The non-linear behaviors of the fabric in the axial and shear directions and behaviors on the macro scale are explored at the meso scale level. The medical grade bio-fabric is tested in untreated and heat-treated forms, and deviations are closely analyzed at the micro, meso, and macro scales to determine the effects of the process. The heat-treatment process was found to increase the stiffness of the fabric during axial and bending stiffness testing but had a negligible effect on the shear response. The ability of *FABRIC to capture behaviors unique to fabric deformation is discussed, whereby the unique phenomenological input can accurately represent the experimentally derived inputs.

Keywords: experimental techniques, FEA modelling, materials characterization, post-processing techniques

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Anastasiya Paltarzhitskaya

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Subjective time plays an important role in consciousness processes and self-awareness at the moment. The concept of intrinsic neural timescales (INT) explains the difference in perceiving various time intervals. The capacity to experience the present builds on the fundamental properties of temporal cognition. The challenge that both philosophy and neuroscience try to answer is how the brain differentiates the present from the past and future. In our work, we analyze papers which describe mechanisms involved in the perception of ‘present’ and ‘non-present’, i.e., future and past moments. Taking into account that we perceive time intervals even during rest or relaxation, we suppose that the default-mode network activity can code time features, including the present moment. We can compare some results of time perceptual studies, where brain activity was shown in states with different flows of time, including resting states and during “mental time travel”. According to the concept of mental traveling, we employ a range of scenarios which demand episodic memory. However, some papers show that the hippocampal region does not activate during time traveling. It is a controversial result that is further complicated by the phenomenological aspect that includes a holistic set of information about the individual’s past and future.

Keywords: temporal consciousness, time perception, memory, present

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: S. J. Yune, K. H. Park

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The purpose of this study was to understand the experiences of medical students in volunteer activities and to draw implications for medical education. For this purpose, the questionnaire and the reflection essay on the volunteer experience of 54 students in the first year and 57 students in the second year were analyzed and analyzed. As a result, the participation of the students in the volunteer activities was the highest in the first semester and once a month in the second grade. Activities were mostly through volunteer organizations. The essence of the volunteering activities experience revealed through reflection essays was 'I want to avoid with fear' and 'I feel far away' in the recognition before volunteering activities. In terms of knowledge after participating in volunteer activities, 'breaking eggs and getting to know the world' and 'intellectual growth through social experience' appeared. In terms of attitude, it revealed 'deep reflection on me and others', 'understanding of service life'. And in terms of behavior, 'Begin preparing for a life of service' appeared. The results of this study revealed that volunteering activities provide students with opportunities for growth and development. In order to obtain more meaningful results, consciousness education related to social service should be done in advance.

Keywords: volunteering activity, pre-medical school student, reflection essay, qualitative analysis

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Muhammad Fajar Suardi, Fathimatufzzahra, Dela Isnaini Sendra

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Learning is an activity that has been used to do, especially for a student or academics. But a handful of people have not been using and maximizing their brains work and some also do not know a good brain work time in capturing the lessons, so that knowledge is absorbed is also less than the maximum. Indonesia Memory Sports Council (IMSC) is an institution which is engaged in the performance of the brain and the development of effective learning methods by using several techniques that can be used in considering the lessons and knowledge to grasp well, including: loci method, substitution method, and chain method. This study aims to determine the techniques and benefits of using the method given in learning and memorization by applying memory techniques taught by Indonesia Memory Sports Council (IMSC) to students and the difference if not using this method. This research uses quantitative research with survey method addressed to students of Indonesian Memory Sports Council (IMSC). The results of this study indicate that learn, understand and remember the lesson using the techniques of memory which is taught in Indonesia Memory Sport Council is very effective and faster to absorb the lesson than learning without using the techniques of memory, and this affects the academic achievement of students in each educational institution.

Keywords: chain method, Indonesia memory sports council, loci method, substitution method

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Authors: T. Kritsana, P. Sawitri, P. Teeratas

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This article aims to study the effect of pressure on rocket motor case by Finite Element Method simulation to select optimal material in rocket motor manufacturing process. In this study, cylindrical tubes with outside diameter of 122 mm and thickness of 3 mm are used for simulation. Defined rocket motor case materials are AISI4130, AISI1026, AISI1045, AL2024 and AL7075. Internal pressure used for the simulation is 22 MPa. The result from Finite Element Method shows that at a pressure of 22 MPa rocket motor case produced by AISI4130, AISI1045 and AL7075 can be used. A comparison of the result between AISI4130, AISI1045 and AL7075 shows that AISI4130 has minimum principal stress and confirm the results of Finite Element Method by the used of calculation method found that, the results from Finite Element Method has good reliability.

Keywords: rocket motor case, finite element method, principal stress, simulation

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Authors: Mohammad Ghandehari Motlagh

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Purpose: Comparing anterior chamber depth (ACD) measured with Orbscan II and Pentacam HR compared with the Smith method results. Methods: Smith method (1979) is a reliable method of measuring ACD only with help of slit lamp. In this study 102 phakic eyes as PRK candidates were imaged with both OrbScan and Pentacam and finally ACD was measured thru Smith method with slit lamp. ACD measured with Smith method was presumed as the gold standard and was compared with ACD of the 2 imaging devices. Contraindication cases for PRK and pseudophakic eyes have been excluded from the study. Results: Mean age of the patients was 35.2 ±14.8 yrs/old including 56 M(54.9%)and 46 F(45.09%).Acceptable correlation of ACD measured thru Smith method with Orbscan and Pentacam are R=0.958 and R=0.942 respectively and so Orbscan results can be used in procedures relying on ACD. Conclusion: ACDs measured with OrbScan is more precise than Pentacam and so can be more useful in some surgery procedures relying ACD results such as phakic IOLs and in cycloplegia contraindications.

Keywords: orbscan, pentacam, anterior chamber depth, slit lamp

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Authors: Tharntip Tawnie Chutikulrungsee, Oliver Kisalay Burmeister, Maumita Bhattacharya, Dragana Calic

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Sharing on social network sites (SNSs) has rapidly emerged as a new social norm and has become a global phenomenon. Billions of users reveal not only their own information (self disclosure) but also information about others (other-generated disclosure), resulting in a risk and a serious threat to either personal or informational privacy. Self-disclosure (SD) has been extensively researched in the literature, particularly regarding control of individual and existing privacy management. However, far too little attention has been paid to other-generated disclosure (OGD), especially by insiders. OGD has a strong influence on self-presentation, self-image, and electronic word of mouth (eWOM). Moreover, OGD is more credible and less likely manipulated than SD, but lacks privacy control and legal protection to some extent. This article examines OGD in depth, ranging from motivation to both online and offline impacts, based upon lived experiences from both ‘the disclosed’ and ‘the discloser’. Using purposive sampling, this phenomenological study involves an online survey and in-depth interviews. The findings report the influence of peer disclosure as well as users’ strategies to mitigate privacy issues. This article also calls attention to the challenge of OGD privacy and inadequacies in the law related to privacy protection in the digital domain.

Keywords: facebook, online privacy, other-generated disclosure, social networks sites (SNSs)

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: temporal differencing, video summarization, histogram differencing, sum conditional variance

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Tohru Kawabe

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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: sliding mode control, model predictive control, integral action, electric vehicle, slip suppression

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Authors: Jodie Hughes

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Endometriosis affects 1 in 10 individuals that were born female globally. Endometriosis incidence rates peak between 30-40 year of age, in young women and adolescents it is a rarely suspected and often ill-diagnosed. The average cost of endometriosis is €9,579 per woman. More than 75% of women have reported being absent from work due to endometriosis, with 40% of women becoming unemployed due to the disease. 46% of patients with endometriosis need to have appointments with upward of five doctors to gain a correct diagnosis. Quantitative data were collected by way of an online PSS-10 survey that included demographic questions from two sample groups of females, group 1 was females with endometriosis, group 2 were healthy women. The data were scored using Cohens scoring system, overall scores were input to SPSS. A non-parametric Mann-Whitney U test and ANOVA was used to ascertain any differences between the PSS-10 scores of the two groups. A significance level of P<0.05 was adopted. Four women were invited to take part in a semi structured interview that was recorded, transcribed and coded using interpretive phenomenological analysis (IPA) using NVivo 12. Results showed that the PSS-10 scores were significantly higher in women with endometriosis compared to healthy women with a p=<0.005. Endometriosis affects all aspects of a patient’s life, to adequately diagnose and treat the condition and improve HRQoL there needs to be better understanding of the clinical symptoms and how they impact the lives of patients.

Keywords: endometriosis, HRQoL, perceived stress, women

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Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

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Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R-colour component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: feature extraction, remote sensing, image retrieval, chromaticity, water index, spectral library, integrated method

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Authors: Emma Whewell, Lee Waters, Mark Wall

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This paper is a mixed methods investigation into the perceived barriers to attainment and progression. Initially entry level data was analysed to identify some of the key characteristics of the student cohort- for example entry route, age and ethnic background. Secondly, a phenomenological case study of the lived experiences of 15 level 5 sport and exercise students was conducted. It aimed to understand the complexities of success in higher education, far beyond entry qualifications, indices of deprivation and POLAR characteristics, to offer a first-hand account of student perceptions and interpretations of the barriers they face in progression, retention and completion on their programme. Using focus groups and interviews with students from a range of indices we offer a set of rich case studies exploring the interpretations of our students’ lived experiences and challenges. Findings demonstrate a complex set of circumstances that centre on managing workload, use of support services and aspirations of students that conflict with university priorities. Conclusions centre on the role of academic and pastoral support, assumptions about priorities of students and practical interventions to support achievement.

Keywords: access and participation, higher education, progression and retention, barriers

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: F. Boufera, F. Debbat

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This paper deals with an approach based on limit-cycles method for the problem of obstacle avoidance of mobile robots in unknown environments for any form of obstacles. The purpose of this approach is the improvement of limit-cycles method in order to obtain safe and flexible navigation. The proposed algorithm has been successfully tested in different configuration on simulation.

Keywords: mobile robot, navigation, avoidance of obstacles, limit-cycles method

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Authors: B. Harman, E. Gringart, C. Harms

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There is evidence that increasing numbers of adults of child-bearing age in Australia do not have children. While there has been research into the life experiences of non-parents, one of the issues is that the differences between people who choose not to have children – the childfree – and people who cannot have children – the childless – are not clearly defined. The qualitative research reported here adopted an interpretative phenomenological approach to examine the life experiences of non-parents. Potential participants from Australia were invited to complete an online survey describing their experiences of life without children. An examination of the data from 229 participants (188 female, 41 male) revealed that they defined their non-parent status as either childfree or childless. There are, however, five sub-categories of child freedom identified by the participants, whereas previous research has not recognized such distinctions. The variance in the definition of child freedom is important because it may be related to the life journey as a non-parent. The current paper will firstly discuss the different groups of childfree and childless people. Secondly, it will examine the life experiences and journeys of non-parents in light of how the participants defined themselves. From a social psychological perspective, the current research is important as it highlights the socially held stereotypes and the stigma experienced by non-parents in Australia.

Keywords: Australia, childfree, childless, non-parents, qualitative, social psychology

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Rahman Dashti, Ehsan Gord

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In this paper, an improved impedance based fault location method is proposed. In this method, online fault locating is performed using voltage and current information at the beginning of the feeder. Determining precise fault location in a short time increases reliability and efficiency of the system. The proposed method utilizes information about main component of voltage and current at the beginning of the feeder and distributed generation unit (DGU) in order to precisely locate different faults in acceptable time. To evaluate precision and accuracy of the proposed method, a 13-node is simulated and tested using MATLAB.

Keywords: distribution network, fault section determination, distributed generation units, distribution protection equipment

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Authors: W. S. Lawal, T. Akande

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Abstract— Four (4) difference methods were employed to detoxify Jatropha carcas, they were physical method (it include soaking and sun drying) Chemical (the use of methylated sprit, hexane and methane). Biological (the use of Aspergillus niger and then sundry for 7days and then Bacillus lichiformis) and Combined method (the combination of chemical and biological methods). Phobol esther analysis was carried out after the detoxification methods and it was found that the combined method is better off (P<0.05). Detoxified Jatropha from each of this methods was sundry and grinded for easy inclusion into poultry feed, detoxified jatropha was included at 0%, 0.5%, 1%, 2%, 3%, 4%, and 5% but the combined method was increased up to 7% because the birds were able to tolerate it, the 0% was the control experiment. 405 day old broiler chicks was used to test the effect of detoxified Jatropha carcas on their performance, there are 5birds per treatment and there are 3 replicates, the experiment lasted for 8weeks,highest number of mortality was obtained in physical method, birds in chemical method tolerated up to 3% Jatropha carcas, biological method is better, as birds there were comfortable at 5% but the best of them is combined method the birds did very well at 7% as there were less mortality and highest weight gain was achieved here (P<0.05) and it was recommended.

Keywords: phobol esther, inclusion level, tolerance level, Jatropha carcas

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Authors: Dianah Kitiabi

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This study examines the experiences of graduate international students in Study Abroad (SA) in order to understand the evolution of their second language (L2) skills during the period of their sojourn abroad. The study documents students’ perspectives through analysis of interview data situated within the context of their overall SA experience. Based on a phenomenological approach, the study focuses on a sample of nine graduate students with at least one year of SA experience. Gass & Mackey’s (2007) interaction approach and Vygotsky’s (1962) sociocultural theory help frame the study within the discourse of second language acquisition (SLA) in SA, such as to highlight the effects of SA on L2 skills of advanced-level learners. The findings of the study are first presented as individual case vignettes where students’ interpretations of their personal experiences are described in entirety, followed by an analysis across the cases that highlight emergent themes. The results of this study show that the linguistic outcomes of international students studying abroad are highly individualized. Although students reported to have improved some of their L2 skills, they also reported a lack of improvement in other L2 skills, most of which differed by case. What emerges is that besides contextual factors, students’ pre-program exposure to L2, interactions with NSs, frequency of L2 use in context, and personal beliefs contribute to their linguistic gains in SA.

Keywords: context, interaction, second language acquisition, study abroad

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Authors: Hadi Farhadian, Homayoon Katibeh

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In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above-mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm the high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occurred in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m.

Keywords: water Seepage, Amirkabir Tunnel, analytical method, DEM, SGR

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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