Search results for: positive almost periodic solution

Authors: M. K. Hasan, Y. H. Ng, J. Sulaiman

Abstract:

This paper present the implementation of a new ordering strategy on Successive Overrelaxation scheme on two dimensional boundary value problems. The strategy involve two directions alternatingly; from top and bottom of the solution domain. The method shows to significantly reduce the iteration number to converge. Four numerical experiments were carried out to examine the performance of the new strategy.

Keywords: Two dimensional boundary value problems, Successive Overrelaxation scheme, Alternating Top-Bottom strategy, fast convergence

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Authors: Ilia Marchevsky, Victoriya Moreva

Abstract:

The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

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Authors: A. B. Khoshnevis, F. Zeydabadi, F. Sokhanvar

Abstract:

The data measurement of mean velocity has been taken for the wake of single circular cylinder with three different diameters for two different velocities. The effects of change in diameter and in velocity are studied in self-similar coordinate system. The spatial variations of velocity defect and that of the half-width have been investigated. The results are compared with those published by H.Schlichting. In the normalized coordinates, it is also observed that all cases except for the first station are self-similar. By attention to self-similarity profiles of mean velocity, it is observed for all the cases at the each station curves tend to zero at a same point.

Keywords: Self-similarity, wake of single circular cylinder

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Authors: Sami Hidouri, Taoufik Aguili

Abstract:

We consider fast and accurate solutions of scattering problems by large perfectly conducting objects (PEC) formulated by an optimization of the Method of Auxiliary Sources (MAS). We present various techniques used to reduce the total computational cost of the scattering problem. The first technique is based on replacing the object by an array of finite number of small (PEC) object with the same shape. The second solution reduces the problem on considering only the half of the object.These t

Keywords: Method of Auxiliary Sources, Scattering, large object, RCS, computational resources.

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Authors: Mohanapriya Subramanian, V. Raj

Abstract:

Direct methanol fuel cells (DMFCs) are considered to be one of the most promising candidates for portable and stationary applications in the view of their advantages such as high energy density, easy manipulation, high efficiency and they operate with liquid fuel which could be used without requiring any fuel-processing units. Electrolyte membrane of DMFC plays a key role as a proton conductor as well as a separator between electrodes. Increasing concern over environmental protection, biopolymers gain tremendous interest owing to their eco-friendly bio-degradable nature. Pectin is a natural anionic polysaccharide which plays an essential part in regulating mechanical behavior of plant cell wall and it is extracted from outer cells of most of the plants. The aim of this study is to develop and demonstrate pectin based polymer composite membranes as methanol impermeable polymer electrolyte membranes for DMFCs. Pectin based nanocomposites membranes are prepared by solution-casting technique wherein pectin is blended with chitosan followed by the addition of optimal amount of sulphonic acid modified Titanium dioxide nanoparticle (S-TiO2). Nanocomposite membranes are characterized by Fourier Transform-Infra Red spectroscopy, Scanning electron microscopy, and Energy dispersive spectroscopy analyses. Proton conductivity and methanol permeability are determined into order to evaluate their suitability for DMFC application. Pectin-chitosan blends endow with a flexible polymeric network which is appropriate to disperse rigid S-TiO2 nanoparticles. Resulting nanocomposite membranes possess adequate thermo-mechanical stabilities as well as high charge-density per unit volume. Pectin-chitosan natural polymeric nanocomposite comprising optimal S-TiO2 exhibits good electrochemical selectivity and therefore desirable for DMFC application.

Keywords: Biopolymers, fuel cells, nanocomposite, methanol crossover.

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Authors: Sangita Pokhrel, Nalinda Somasiri, Rebecca Jeyavadhanam, Swathi Ganesan

Abstract:

Tourism is a booming industry with huge future potential for global wealth and employment. There are countless data generated over social media sites every day, creating numerous opportunities to bring more insights to decision-makers. The integration of big data technology into the tourism industry will allow companies to conclude where their customers have been and what they like. This information can then be used by businesses, such as those in charge of managing visitor centres or hotels, etc., and the tourist can get a clear idea of places before visiting. The technical perspective of natural language is processed by analysing the sentiment features of online reviews from tourists, and we then supply an enhanced long short-term memory (LSTM) framework for sentiment feature extraction of travel reviews. We have constructed a web review database using a crawler and web scraping technique for experimental validation to evaluate the effectiveness of our methodology. The text form of sentences was first classified through VADER and RoBERTa model to get the polarity of the reviews. In this paper, we have conducted study methods for feature extraction, such as Count Vectorization and Term Frequency – Inverse Document Frequency (TFIDF) Vectorization and implemented Convolutional Neural Network (CNN) classifier algorithm for the sentiment analysis to decide if the tourist’s attitude towards the destinations is positive, negative, or simply neutral based on the review text that they posted online. The results demonstrated that from the CNN algorithm, after pre-processing and cleaning the dataset, we received an accuracy of 96.12% for the positive and negative sentiment analysis.

Keywords: Counter vectorization, Convolutional Neural Network, Crawler, data technology, Long Short-Term Memory, LSTM, Web Scraping, sentiment analysis.

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Hölder continuity condition, Fréchet derivative, fifth order convergence, recurrence relations.

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Authors: Asadollah Aghajani, Yaghoub Jalilian

Abstract:

Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

Keywords: Functional integral equation, fixed-point, measure of noncompactness, attractive solution, asymptotic stability.

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Authors: Roberto Gaudino, Antonino Nespola, Dario Zeolla, Stefano Straullu, Vittorio Curri, Gabriella Bosco, Roberto Cigliutti, Stefano Capriata, Paolo Solina.

Abstract:

We demonstrate a 40Gbps downstream PON transmission based on PM-QPSK modulation using commercial DFB lasers without optical amplifier in the ODN, obtaining 40dB power budget. We discuss this solution within NG-PON2 architectures.

Keywords: DFB lasers, Optical Coherent Receiver, Passive Optical Networks.

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Authors: Zenon Chaczko, Essam Rahali, Rizwan Tariq

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This paper introduces a process for the module level integration of computer based systems. It is based on the Six Sigma Process Improvement Model, where the goal of the process is to improve the overall quality of the system under development. We also present a conceptual framework that shows how this process can be implemented as an integration solution. Finally, we provide a partial implementation of key components in the conceptual framework.

Keywords: Software Quality, Six Sigma, System Integration, 3SI Process, 3SI Conceptual Framework.

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Authors: Wanida Wonsawat

Abstract:

This research describes a voltammetric approach to determine amounts of vitamin C (Ascorbic acid) in orange juice sample, using three screen printed electrode. The anodic currents of vitamin C were proportional to vitamin C concentration in the range of 0 – 10.0 mM with the limit of detection of 1.36 mM. The method was successfully employed with 2 µL of the working solution dropped on the electrode surface. The proposed method was applied for the analysis of vitamin C in packed orange juice without sample purification or complexion of sample preparation step.

Keywords: Ascorbic acid, Vitamin C, Juice, Voltammetry

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.

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Authors: Anis Gharbi, Mohamed Haouari, Talel Ladhari, Mohamed Ali Rakrouki

Abstract:

We address a complex scheduling problem arising in the wood panel industry with the objective of minimizing a quadratic function of job tardiness. The proposed solution strategy, which is based on an effective genetic algorithm, has been coded and implemented within a major Tunisian company, leader in the wood panel manufacturing. Preliminary experimental results indicate significant decrease of delivery times.

Keywords: Genetic algorithm, heuristic, hybrid flowshop, total weighted squared tardiness.

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Authors: Eduardo da Silva, Tânia Caetano, Jessica B. Lopes

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Emotion dysregulation has been linked to psychopathology in general and, in particular, to substance abuse and other addiction-related disorders, such as eating disorders, impulsive disorder, and gambling. It has been proposed that a lessening of the difficulties in emotion regulation can have a significant positive impact on the treatment of these disorders. The present study explores the association between the progress in the Change & Grow^® therapeutic model (5 stages of treatment), and the decrease in the difficulties related to emotion regulation. The Change & Grow^® model has five stages of treatment according to the model’s five principles (Truth, Acceptance, Gratitude, Love and Responsibility) and incorporates different therapeutic approaches such as positive psychology, cognitive and behavioral therapy and third generation therapies. The main objective is to understand the impact of the presented therapeutic model on difficulties in emotion regulation in patients with addiction-related disorders. The exploratory study has a cross-sectional design. Participants were 44 (15 women and 29 men) Portuguese patients in the residential Villa Ramadas International Treatment Centre. The instrument used was the Portuguese version of the Difficulties in Emotion Regulation Scale (DERS), which measures six dimensions of emotion regulation (Strategies, Non-acceptance, Awareness, Impulse, Goals, and Clarity). The mean rank scores for both the DERS total score and the Impulse subscale showed statistically significant differences according to Stage of Treatment/Principles. Furthermore, Stage of Treatment/Principles held a negative correlation with the scores of the Non-acceptance and Impulse subscales, as well as the DERS total score. The results indicate that the Change & Grow^® model seems to have an impact in lessening the patient’s difficulties in emotion regulation. The Impulse dimension suffered the greater impact, which supports the well-known relevance of impulse control, or related difficulties, in addiction-related disorders.

Keywords: Addiction, Change & Grow®, emotion regulation, psychopathology.

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Authors: Suttijit Sriwatcharakul

Abstract:

The bioactivity studies from the weed ethanolic crude extracts from leaf, stem, pod and root of wild spider flower; Cleoma viscosa Linn. were analyzed for the growth inhibition of 6 bacterial species; Salmonella typhimurium TISTR 5562, Pseudomonas aeruginosa ATCC 27853, Staphylococcus aureus TISTR 1466, Streptococcus epidermidis ATCC 1228, Escherichia coli DMST 4212 and Bacillus subtilis ATCC 6633 with initial concentration crude extract of 50 mg/ml. The agar well diffusion results found that the extracts inhibit only gram positive bacteria species; S. aureus, S. epidermidis and B. subtilis. The minimum inhibition concentration study with gram positive strains revealed that leaf crude extract give the best result of the lowest concentration compared with other plant parts to inhibit the growth of S. aureus, S. epidermidis and B. subtilis at 0.78, 0.39 and lower than 0.39 mg/ml, respectively. The determination of total phenolic compounds in the crude extracts exhibited the highest phenolic content was 10.41 mg GAE/g dry weight in leaf crude extract. Analyzed the efficacy of free radical scavenging by using DPPH radical scavenging assay with all crude extracts showed value of IC50 of leaf, stem, pod and root crude extracts were 8.32, 12.26, 21.62 and 35.99 mg/ml, respectively. Studied cytotoxicity of crude extracts on human breast adenocarcinoma cell line by MTT assay found that pod extract had the most cytotoxicity CC50 value, 32.41 µg/ml. Antioxidant activity and cytotoxicity of crude extracts exhibited that the more increase of extract concentration, the more activities indicated. According to the bioactivities results, the leaf crude extract of Cleoma viscosa Linn. is the most interesting plant part for further work to search the beneficial of this weed.

Keywords: Antimicrobial, antioxidant activity, Cleoma viscosa Linn., cytotoxicity test, total phenolic compound.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

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In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

Keywords: Homotopy perturbation method, Exact solution, Cauchy problem, inhomogeneous wave equation

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Authors: A. Siam, R. Maamri, Z. Sahnoun

Abstract:

The development of adaptive user interfaces (UI) presents for a long time an important research area in which researcher attempt to call upon the full resources and skills of several disciplines, The adaptive UI community holds a thorough knowledge regarding the adaptation of UIs with users and with contexts of use. Several solutions, models, formalisms, techniques and mechanisms were proposed to develop adaptive UI. In this paper, we propose an approach based on the fuzzy set theory for modeling the concept of the appropriateness of different solutions of UI adaptation with different situations for which interactive systems have to adapt their UIs.

Keywords: Adaptive user interfaces, adaptation solution’s appropriateness, fuzzy sets.

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Authors: Tomáš Bublík, Miroslav Virius

Abstract:

This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and subgraph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

Keywords: AST, Java, tree matching, Scripthon, source code recognition

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Authors: Hassan Haghighi, Seyedeh Zahra Hosseini, Seyedeh Elahe Jalambadani

Abstract:

ERP systems are often supposed to be implemented and deployed in multi-national companies. On the other hand, an ERP developer may plan to market and sale its product in various countries. Therefore, an EPR system should have the ability to communicate with its users, who usually have different languages and cultures, in a suitable way. EPR support of Multilanguage capability is a solution to achieve this objective. In this paper, an agent oriented architecture including several independent but cooperative agents has been suggested that helps to implement Multilanguage EPR systems.

Keywords: enterprise resource planning, Multilanguage, software architecture, agent oriented architecture, intelligence, learning, translation.

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Authors: Mohamed Fawzi Mahboub, Mourad Djebli

Abstract:

The expansion mechanism of a partially ionized plasma produced by laser interaction with solid target (copper) is studied. For this purpose we use a hydrodynamical model which includes a source term combined with Saha's equation. The obtained self-similar solution in the limit of quasi-neutrality shows that the expansion, at the earlier stage, is driven by the combination of thermal pressure and electrostatic potential. They are of the same magnitude. The initial ionized fraction and the temperature are the leading parameters of the expanding profiles,

Keywords: expansion, quasi-neutral, laser-ablated plasma, self- similar.

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Authors: Moustafa Osman Mohammed

Abstract:

Integration sustainability outcomes give attention to construction ecology in the design review of urban environments to comply with Earth’s System that is composed of integral parts of the (i.e., physical, chemical and biological components). Naturally, exchange patterns of industrial ecology have consistent and periodic cycles to preserve energy flows and materials in Earth’s System. When engineering topology is affecting internal and external processes in system networks, it postulated the valence of the first-level spatial outcome (i.e., project compatibility success). These instrumentalities are dependent on relating the second-level outcome (i.e., participant security satisfaction). The construction ecology-based topology (i.e., as feedback energy system) flows from biotic and abiotic resources in the entire Earth’s ecosystems. These spatial outcomes are providing an innovation, as entails a wide range of interactions to state, regulate and feedback “topology” to flow as “interdisciplinary equilibrium” of ecosystems. The interrelation dynamics of ecosystems are performing a process in a certain location within an appropriate time for characterizing their unique structure in “equilibrium patterns”, such as biosphere and collecting a composite structure of many distributed feedback flows. These interdisciplinary systems regulate their dynamics within complex structures. These dynamic mechanisms of the ecosystem regulate physical and chemical properties to enable a gradual and prolonged incremental pattern to develop a stable structure. The engineering topology of construction ecology for integration sustainability outcomes offers an interesting tool for ecologists and engineers in the simulation paradigm as an initial form of development structure within compatible computer software. This approach argues from ecology, resource savings, static load design, financial other pragmatic reasons, while an artistic/architectural perspective, these are not decisive. The paper described an attempt to unify analytic and analogical spatial modeling in developing urban environments as a relational setting, using optimization software and applied as an example of integrated industrial ecology where the construction process is based on a topology optimization approach.

Keywords: Construction ecology, industrial ecology, urban topology, environmental planning.

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Authors: Fariba Tadayon, Elmira Hassanlou, Hasan Bagheri, Mostafa Jafarian

Abstract:

Heavy metals are released into water, plants, soil, and food by natural and human activities. Lead has toxic roles in the human body and may cause serious problems even in low concentrations, since it may have several adverse effects on human. Therefore, determination of lead in different samples is an important procedure in the studies of environmental pollution. In this work, an ultrasonic assisted-ionic liquid based-liquid-liquid microextraction (UA-IL-DLLME) procedure for the determination of lead in zucchini, pomegranate, and lettuce has been established and developed by using flame atomic absorption spectrometer (FAAS). For UA-IL-DLLME procedure, 10 mL of the sample solution containing Pb2+ was adjusted to pH=5 in a glass test tube with a conical bottom; then, 120 μL of 1-Hexyl-3-methylimidazolium hexafluoro phosphate (CMIM)(PF6) was rapidly injected into the sample solution with a microsyringe. After that, the resulting cloudy mixture was treated by ultrasonic for 5 min, then the separation of two phases was obtained by centrifugation for 5 min at 3000 rpm and IL-phase diluted with 1 cc ethanol, and the analytes were determined by FAAS. The effect of different experimental parameters in the extraction step including: ionic liquid volume, sonication time and pH was studied and optimized simultaneously by using Response Surface Methodology (RSM) employing a central composite design (CCD). The optimal conditions were determined to be an ionic liquid volume of 120 μL, sonication time of 5 min, and pH=5. The linear ranges of the calibration curve for the determination by FAAS of lead were 0.1-4 ppm with R2=0.992. Under optimized conditions, the limit of detection (LOD) for lead was 0.062 μg.mL-1, the enrichment factor (EF) was 93, and the relative standard deviation (RSD) for lead was calculated as 2.29%. The levels of lead for pomegranate, zucchini, and lettuce were calculated as 2.88 μg.g-1, 1.54 μg.g-1, 2.18 μg.g-1, respectively. Therefore, this method has been successfully applied for the analysis of the content of lead in different food samples by FAAS.

Keywords: Dispersive liquid-liquid microextraction, Central composite design, Food samples, Flame atomic absorption spectrometry.

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Authors: Hsuan-Ku Liu

Abstract:

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: Grigorios N. Beligiannis, Georgios A. Tsirogiannis, Panayotis E. Pintelas

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In this contribution, the use of a new genetic operator is proposed. The main advantage of using this operator is that it is able to assist the evolution procedure to converge faster towards the optimal solution of a problem. This new genetic operator is called ''intuition'' operator. Generally speaking, one can claim that this operator is a way to include any heuristic or any other local knowledge, concerning the problem, that cannot be embedded in the fitness function. Simulation results show that the use of this operator increases significantly the performance of the classic Genetic Algorithm by increasing the convergence speed of its population.

Keywords: Genetic algorithms, intuition operator, reasonable genomes, complex search space, nonlinear fitness functions

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Authors: E. Al Daoud

Abstract:

In many cases, theoretical treatments are available for models for which there is no perfect physical realization. In this situation, the only possible test for an approximate theoretical solution is to compare with data generated from a computer simulation. In this paper, Monte Carlo tools are used to study and compare the elementary particles models. All the experiments are implemented using 10000 events, and the simulated energy is 13 TeV. The mean and the curves of several variables are calculated for each model using MadAnalysis 5. Anomalies in the results can be seen in the muons masses of the minimal supersymmetric standard model and the two Higgs doublet model.

Keywords: Feynman rules, hadrons, Lagrangian, Monte Carlo, simulation.

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Authors: Zia Amjad, Salem S. Alghamdi

Abstract:

The study was conducted at the student educational farm at the College of Food and Agriculture in the Kingdom of Saudi Arabia. The aim of study was to characterize 154 Vicia faba L. accessions using agro-morphological traits based on The International Union for the Protection of New Varieties of Plants (UPOV) and The International Board for Plant Genetic Resources (IBPGR) descriptors. This research is significant as it contributes to the understanding of the genetic diversity and potential yield of V. faba in Saudi Arabia. In the study, 24 agro-morphological characters including 11 quantitative and 13 qualitative were observed for genetic variation. All the results were analyzed using multivariate analysis i.e., principal component analysis (PCA). First, six principal components (PC) had eigenvalues greater than one; accounted for 72% of available V. faba genetic diversity. However, first three components revealed more than 10% of genetic diversity each i.e., 22.36%, 15.86% and 10.89% respectively. PCA distributed the V. faba accessions into different groups based on their performance for the characters under observation. PC-1, which represented 22.36% of the genetic diversity, was positively associated with stipule spot pigmentation, intensity of streaks, pod degree of curvature and to some extent with 100 seed weight. PC-2 covered 15.86 of the genetic diversity and showed positive association for average seed weight per plant, pod length, number of seeds per plant, 100 seed weight, stipule spot pigmentation, intensity of streaks (same as in PC-1) and to some extent for pod degree of curvature and number of pods per plant. PC-3 revealed 10.89% of genetic diversity and expressed positive association for number of pods per plant and number of leaflets per plant. This study contributes to the understanding of the genetic diversity and potential yield of V. faba in the Kingdom of Saudi Arabia. By establishing a core collection of V. faba, the research provides a valuable resource for future conservation and utilization of this crop worldwide.

Keywords: Agro-morphological characterization, genetic diversity, core collection, PCA, Vicia faba L.

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Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.

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Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

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Authors: A. Faro, D. Giordano, M. Pennisi, G. Scarciofalo, C. Spampinato, F. Tramontana

Abstract:

The paper proposes a methodology to process the signals coming from the Transcranial Magnetic Stimulation (TMS) in order to identify the pathology and evaluate the therapy to treat the patients affected by demency diseases. In particular, a fuzzy model is developed to identify the demency of the patients affected by Subcortical Ischemic Vascular Dementia and to measure the positive effect, if any, of a repetitive TMS on their motor performances. A tool is also presented to support the mentioned analysis.

Keywords: TMS, SIVD, Electromiography , Fuzzy Logic.

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Authors: Hamid Reza Pakzad

Abstract:

Ion-acoustic solitary waves in a plasma with nonthermal electrons, thermal positrons and warm ions are investigated using Sagdeev-s pseudopotential technique. We study the effects of non-thermal electrons and ion temperature on solitons and show both negative and positive potential waves are possible.

Keywords: Ion acoustic waves, Solitons, Nonlinear phenomena, Sagdeev potential

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