Search results for: differential forms

Authors: Ankita Shukla, Tiratha Raj Singh

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Colorectal cancer (CRC) imposes serious mortality burden worldwide and it has been increasing for past consecutive years. Continuous efforts have been made so far to diagnose the disease condition and to identify the root cause for it. In this study, we performed the pathway level as well as the differential gene expression studies for CRC. We analyzed the gene expression profile GSE24514 from Gene Expression Omnibus (GEO) along with the gene pathways involved in the CRC. This analysis helps us to understand the behavior of the genes that have shown differential expression through their targeted pathways. Pathway analysis for the targeted genes covers the wider area which therefore decreases the possibility to miss the significant ones. This will prove to be beneficial to expose the ones that have not been given attention so far. Through this analysis, we attempt to understand the various neighboring genes that have close relationship to the targeted one and thus proved to be significantly controlling the CRC. It is anticipated that the identified hub and neighboring genes will provide new directions to look at the pathway level differently and will be crucial for the regulatory processes of the disease.

Keywords: mismatch repair, microsatellite instability, carcinogenesis, morbidity

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Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

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Authors: A. B. Disu, M. S. Dada

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This study was conducted to investigate two dimensional heat transfer of a free convective-radiative MHD (Magneto-hydrodynamics) flow with temperature dependent viscosity and heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls. The fluid viscosity is assumed to vary as an exponential function of temperature. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities were expressed in terms of complex exponential series of plane wave equation. The resultant differential equations were solved by Differential Transform Method (DTM). The numerical computations were presented graphically to show the salient features of the fluid flow and heat transfer characteristics. The skin friction and Nusselt number were also analyzed for various governing parameters.

Keywords: differential transform method, MHD free convection, porous medium, two dimensional radiation, two wavy walls

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

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For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization

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Authors: Aline M. C. Santoro, João C. Pantoja, Eduardo P. Rossetti

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While the aim of the modernist movement was to deny known typology, the creation of a new formal language also gave it new meaning, which was now related to Form. This is specifically true in the modern capital of Brazil, where Niemeyer sought to demonstrate the manner in which the new materials available, such as reinforced concrete, were able to produce innovative forms. With this study, we aim to demonstrate the relationship between Niemeyer’s forms and the topological typology known as tessellation, through the presentation of two case studies, the Monument to Caxias and the Saint George Orthodox Church. At a first glance, our purpose is to present the definition of Form, especially with relationship to the works of Niemeyer, seeking to identify in them the concepts presented by Moussavi. Afterwards, we will use a computer-based approach to study and model the forms of two of his buildings with the McNeel Rhinoceros program, where, with the aid of diagrams and renderings, we will be able to clearly and legibly represent their organic forms and further understand their structural systems. When we recognise the concept of typology as a starting point for structural form, it can be concluded that the case studies presented here are encompassed by the typology presented by Moussavi since they derive from his basic structural systems.

Keywords: form, Niemeyer, structure, typology, topology

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Authors: Mamidi Ramakrishna Rao

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Doubly-fed induction generators (DFIG) due to their advantages like speed variation and four-quadrant operation, find its application in wind turbines. DFIG besides supplying power to the grid has to support reactive power (kvar) under grid voltage variations, should contribute minimum fault current during faults, have high efficiency, minimum weight, adequate rotor protection during crow-bar-operation from +20% to -20% of rated speed.  To achieve the optimum performance, a good electromagnetic design of DFIG is required. In this paper, a simple and heuristic global optimization – Differential Evolution has been used. Variables considered are lamination details such as slot dimensions, stack diameters, air gap length, and generator stator and rotor stack length. Two operating conditions have been considered - voltage and speed variations. Constraints included were reactive power supplied to the grid and limiting fault current and torque. The optimization has been executed separately for three objective functions - maximum efficiency, weight reduction, and grid fault stator currents. Subsequent calculations led to the conclusion that designs determined through differential evolution help in determining an optimum electrical design for each objective function.

Keywords: design optimization, performance, DFIG, differential evolution

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Authors: Hsu-Yung Cheng, Kuo-Chang Hsu, Chi-Chang Chan, Mei-Hui Tseng, Chih-Chang Yu, Ya-Sheng Liu

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Photovoltaics modules are usually not installed horizontally to avoid water or dust accumulation. However, the measured irradiance data on tilted surfaces are rarely available since installing pyranometers with various tilt angles induces high costs. Therefore, estimating solar irradiance on tilted surfaces is an important research topic. In this work, artificial neural networks (ANN) are utilized to construct the transfer model to estimate solar irradiance on tilted surfaces. Instead of predicting tilted irradiance directly, the proposed method estimates the differences between the horizontal irradiance and the irradiance on a tilted surface. The outputs of the ANNs in the proposed design are differential values. The experimental results have shown that the proposed ANNs with differential outputs can substantially improve the estimation accuracy compared to ANNs that estimate the titled irradiance directly.

Keywords: photovoltaics, artificial neural networks, tilted irradiance, solar energy

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

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

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

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Authors: Vural Erdogan

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We created two-dimensional hexagonal cellular automata to obtain complexity by using simple rules same as Conway’s game of life. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction problems, we developed 2-states and 3-states hexagonal growing algorithms that reach large populations through random initial states. Unlike the game of life, we used six neighbourhoods cellular automata instead of eight or four neighbourhoods. First simulations explained that whether we are able to obtain sort of oscillators, blinkers, and gliders. Inspired by Wolfram's 1D cellular automata complexity and life-like structures, we simulated 2D synchronous, discrete, deterministic cellular automata to reach life-like forms with 2-states cells. The life-like formations and the oscillators have been explained how they contribute to initiating self-maintenance together with self-reproduction and self-replication. After comparing simulation results, we decided to develop the algorithm for another step. Appending a new state to the same algorithm, which we used for reaching life-like structures, led us to experiment new branching and fractal forms. All these studies tried to demonstrate that complex life forms might come from uncomplicated rules.

Keywords: hexagonal cellular automata, self-replication, self-reproduction, self- maintenance

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Authors: Naveed Ahmad, Farooq Ahmad, Abdul Aal Al-Khazaal

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Rheology can be used as a tool to examine the crystallization kinetics of polymers and polymer composites, and it provides more accurate results than the commonly used conventional techniques like differential scanning calorimetry (DSC) when the crystallization kinetics are slow. Crystallization occurs when crystalline polymers are cooled below their thermodynamic melting point temperature. At the start of this process, there is a gradual change in the mechanical response of the material from the liquid to the solid state, which is due to the change at the microstructure level of the polymer and polymer composites. This is one of the main characteristics of the rheological methodology that sets it apart from the conventional DSC method. In the present work, we used both rheological and differential scanning calorimetric techniques to perform both isothermal and non-isothermal crystallization experiments on a range of syndiotactic polypropylenes/clay composites with varying doses of clay contents in order to investigate the crystallization behavior of the materials. The objective of this work is to explore the effect of clay contents on the crystallization behavior of the syndiotactic polypropylene/clay composites and to couple the rheological methods with more conventional techniques such as Differential Scanning Calorimetry (DSC). Time sweep tests at a constant heating rate of 40°C/minutes were used to investigate the crystallization kinetics using the Atomic Rheumetric Expansion System (ARES). Crystallization behavior was found to be strongly dependent on the clay contents of syndiotactic polypropylene/clay composites. Both melting point (Tₘ) and crystallization temperatures (T𝒸) were found to increase with an increase in clay contents. Excellent agreement is found between the results obtained by both the rheological and differential scanning calorimetric (DSC) methods.

Keywords: quiescent crystallization, polymer composites, rheology, differential scanning calorimetry, syndiotactic polypropylene/clay composites

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Authors: Jayashree Aanand, Gajjam

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The grammatical tradition in Sanskrit literature emphasizes the importance of the correct use of Sanskrit words or linguistic units (sādhu śabda) that brings the meritorious values, denying the attribution of the same religious merit to the incorrect use of Sanskrit words (asādhu śabda) or the vernacular or corrupt forms (apa-śabda or apabhraṁśa), even though they may help in communication. The current research, the culmination of the doctoral research on sentence definition, studies the difference among the comprehension of both correct and incorrect word forms in Sanskrit and Marathi languages in India. Based on the total of 19 experiments (both web-based and classroom-controlled) on approximately 900 Indian readers, it is found that while the incorrect forms in Sanskrit are comprehended with lesser accuracy than the correct word forms, no such difference can be seen for the Marathi language. It is interpreted that the incorrect word forms in the native language or in the language which is spoken daily (such as Marathi) will pose a lesser cognitive load as compared to the language that is not spoken on a daily basis but only used for reading (such as Sanskrit). The theoretical base for the research problem is as follows: among the three main schools of Language Science in ancient India, the Vaiyākaraṇas (Grammarians) hold that the corrupt word forms do have their own expressive power since they convey meaning, while as the Mimāṁsakas (the Exegesists) and the Naiyāyikas (the Logicians) believe that the corrupt forms can only convey the meaning indirectly, by recalling their association and similarity with the correct forms. The grammarians argue that the vernaculars that are born of the speaker’s inability to speak proper Sanskrit are regarded as degenerate versions or fallen forms of the ‘divine’ Sanskrit language and speakers who could not use proper Sanskrit or the standard language were considered as Śiṣṭa (‘elite’). The different ideas of different schools strictly adhere to their textual dispositions. For the last few years, sociolinguists have agreed that no variety of language is inherently better than any other; they are all the same as long as they serve the need of people that use them. Although the standard form of a language may offer the speakers some advantages, the non-standard variety is considered the most natural style of speaking. This is visible in the results. If the incorrect word forms incur the recall of the correct word forms in the reader as the theory suggests, it would have added one extra step in the process of sentential cognition leading to more cognitive load and less accuracy. This has not been the case for the Marathi language. Although speaking and listening to the vernaculars is the common practice and reading the vernacular is not, Marathi readers have readily and accurately comprehended the incorrect word forms in the sentences, as against the Sanskrit readers. The primary reason being Sanskrit is spoken and also read in the standard form only and the vernacular forms in Sanskrit are not found in the conversational data.

Keywords: experimental sociolinguistics, grammaticality and meaningfulness, Marathi, Sanskrit

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Authors: Anuar Ishak

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The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: Hideki Yoshikawa, Masahiro Kaminaga, Arimitsu Shikoda, Toshinori Suzuki

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Round addition differential fault analysis (DFA) using operation bypassing for lightweight block ciphers with on-the-fly key schedule is presented. For 64-bit KLEIN and 64-bit LED, it is shown that only a pair of correct ciphertext and faulty ciphertext can derive the secret master key. For PRESENT, one correct ciphertext and two faulty ciphertexts are required to reconstruct the secret key.

Keywords: differential fault analysis (DFA), round addition, block cipher, on-the-fly key schedule

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Authors: M. Naveed Akhter, Jawad Aslam, Omer Gillani

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To aid and rehabilitate increasing number of patients suffering from spinal cord injury (SCI) and stroke, a lightweight, wearable, and 3D printable exoskeletal glove has been developed. Unlike previously developed metal or fabric-based exoskeletons, this research presents the development of soft exoskeletal glove made of thermoplastic polyurethane (TPU). The drive mechanism consists of a single motor-driven antagonistic tendon to perform extension or flexion of middle and index finger. The tendon-based differential drive has been incorporated to allow for grasping of irregularly shaped objects. The design features easy 3D-printability with TPU without a need for supports. The overall weight of the glove and the actuation unit is approximately 500g. Performance of the glove was tested on a custom test-bench with integrated load cells, and the grip strength was tested to be around 30N per finger while grasping objects of irregular shape.

Keywords: 3D printable, differential drive, exoskeletal glove, rehabilitation, single motor driven

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Authors: Mary Rosa Espinosa-Ochoa

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The study of overgeneralization in inflectional morphology provides evidence for understanding how a child's mind works when applying linguistic patterns in a novel way. High-frequency inflectional forms in the input cause inappropriate use in contexts related to lower-frequency forms. Children learn verbs as lexical items and new forms develop only gradually, around their second year: most of the utterances that children produce are closely related to what they have previously produced. Spanish has a complex verbal system that inflects for person, mood, and tense. Approximately 200 verbs are irregular, and bare roots always require an inflected form, which represents a challenge for the memory. The aim of this research is to investigate i) what kinds of overgeneralization errors children make in verb production, ii) to what extent these errors are related to verb forms previously produced, and iii) whether the overgeneralized verb components are also frequent in children’s linguistic inventory. It consists of a high-density longitudinal study of a middle-class girl (1;11,24-2;02,24) from Mexico City, whose utterances were recorded almost daily for three months to compile a unique corpus in the Spanish language. Of the 358 types of inflected verbs produced by the child, 9.11% are overgeneralizations. Not only are inflected forms (verbal and pronominal clitics) overgeneralized, but also verbal roots. Each of the forms can be traced to previous utterances, and they show that the child is detecting morphological patterns. Neither verbal roots nor inflected forms are associated with high frequency patterns in her own speech. For example, the child alternates the bare roots of an irregular verb, cáye-te* and cáiga-te* (“fall down”), to express the imperative of the verb cá-e-te (fall down.IMPERATIVE-PRONOMINAL.CLITIC), although cay-ó (PAST.PERF.3SG) is the most frequent form of her previous complete inventory, and the combined frequency of caer (INF), cae (PRES.INDICATIVE.3SG), and caes (PRES.INDICATIVE.2SG) is the same as that of as caiga (PRES.SUBJ.1SG and 3SG). These results provide evidence that a) two forms of the same verb compete in the child’s memory, and b) although the child uses her own inventory to create new forms, these forms are not necessarily frequent in her memory storage, which means that her mind is more sensitive to external stimuli. Language acquisition is a developing process, given the sensitivity of the human mind to linguistic interaction with the outside world.

Keywords: inflection, morphology, child language acquisition, Spanish

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Authors: Hamdi Belgacem, Fradi Aymen

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In this paper we present a low power, low cost differential logic unit (LU). The proposed LU receives dual-rail inputs and generates dual-rail outputs. The proposed circuit can be used in Arithmetic and Logic Units (ALU) of processor. It can be also dedicated for self-checking applications based on dual duplication code. Four logic functions as well as their inverses are implemented within a single Logic Unit. The hardware overhead for the implementation of the proposed LU is lower than the hardware overhead required for standard LU implemented with standard CMOS logic style. This new implementation is attractive as fewer transistors are required to implement important logic functions. The proposed differential logic unit can perform 8 Boolean logical operations by using only 16 transistors. Spice simulations using a 32 nm technology was utilized to evaluate the performance of the proposed circuit and to prove its acceptable electrical behaviour.

Keywords: differential logic unit, double pass transistor logic, low power CMOS design, low cost CMOS design

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: Shih-Hao Chen, Chi-Wai Chow

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Visible light communication combined with spread spectrum modulation is demonstrated in this study. Differential signaling method also ensures the proposed system that can support high immunity to ambient light interference. Experiment result shows the proposed system has 6 dB gain comparing with the original On-Off Keying modulation scheme.

Keywords: Visible Light Communication (VLC), Spread Spectrum Modulation (SSM), On-Off Keying, visible light communication

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Authors: Yujia Sun

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Research on nominalizations in English can be traced back to at least the 1960s and even centered in the field nowadays. At the very beginning, the discussion was about the relationship between verbs and nouns, but then it moved to the distinct senses embodied in different forms of nominals, namely, various types of nominalizations. This paper tries to address the issue that how speakers perceive different forms of verbal nouns, and what might influence their perceptions. The data are collected through a self-designed questionnaire targeted at native speakers of American English, and the employment of the Corpus of Contemporary American English (COCA). The results show that semantic differences between different forms of nominals do play a role in people’s preference to certain form than another. But it still awaits more explorations to see how the frequency of usage is interrelates to this issue.

Keywords: corpus of contemporary American English, derived nominalization, frequency of usage, ing-formed nominalization

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Authors: S. Srednyak

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We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: Sim Nee Ting, Lan Eng Ng

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Standard forms of contract in Malaysia are pre-written, printed contractual documents drafted by recognised authoritative bodies in order to describe the rights and obligations of the contracting parties in all construction projects in Malaysia. Studies and form revisions are usually conducted in a relatively random and qualitative manner, but the search of contractual documents idealization remains. It is not clear how these qualitative findings could be helpful for contractual documents improvements and re-drafting. This study aims to quantitatively and systematically analyse and evaluate the rights and obligations of the contracting parties as stated in the standard forms of contract. The Institution of Engineers Malaysia (IEM) published a new standard form of contract in 2012 with a total of 63 classes but the improvements and changes in the newly revised form that are yet to be analysed. IEM form will be used as the case study for this study. Every clause in this said form were interpreted and analysed according to the involved parties including contractor, engineer and employer. Modified from Matrix Method and Likert Scale, the result analysis were conducted based on a scale from 0 to 1 with five ratings namely “Very Unbalance”, “Unbalance”, “Balance”, “Good Balance” and “Very Good Balance”. It is hoped that quantitative method of form study can be used for future form revisions and any new forms drafting so to reduce on any subjectivity in standard forms of contract studies.

Keywords: contracting parties, Malaysia, obligations, quantitative measurement, rights, standard form of contract

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Agbor Ekama Prisca Anne

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Current data on the prevalence and psychosocial correlates of sexual violence in the Cameroon is lacking, with the most recent sexual abuse and violence survey dating back to 2001. The current study sought to identify what proportion of University students have experienced sexual violence, if there are sex differences in exposure to different forms of sexual violence, and to what extent different forms of sexual violence are associated with adverse psychosocial outcomes. A nationally representative sample of University students (N = 1,020) completed self-report measures of history of sexual violence and mental health. Approximately one-in-three (34.4%) students experienced some form of sexual violence, including 14.8% who were sexually assaulted (raped) and 31.1% who were sexually harassed. Female students were significantly more likely than men to have experienced all forms of sexual violence (ps < .001), with the exception of sexual assault by teachers or guardian. All forms of sexual violence were associated with an increased likelihood of serious mental health problems, with sexual assault by a teacher associated with several other psychosocial outcomes in life, including education achievement, and behavior disorder. Sexual violence is a common experience in the general population and female students are disproportionately affected (1-in-2 girls versus 1-in-5 boys). Additional resources to increase mental health care among survivors of sexual violence is urgently needed.

Keywords: psychosocial, effects sexual, violence, females, students

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Adamu S. Salawu, Ibrahim O. Isah

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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Dave Kenneth Tayao Cayado, Carlo P. Magno

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The most common source of bias detected are those of gender and socioeconomic status. The present study investigated the Differential Item Functioning (DIF) or item bias between public and private school students in a vocabulary test. Studies on DIF were expanded by using the type of school as a source of bias. There were 200 participants in this study. 100 came from a public secondary school and 100 came from a private secondary school. The vocabulary skills of students were measured using a standardized vocabulary test for grade 7 students. Using DIF, specifically the Rasch-Welch approach, it was found that out of 24 items, 12 were biased for a specific group. The vocabulary skills on the use of slang, idiomatic expression, personification, collocations, and partitive relations were biased for private schools while the use of slang and homonymous words were biased for public school students. The analysis debunked the trend that private school students are outperforming public school students in terms of academic achievement. It was revealed that there are some competencies that private school students are having difficulty and vice versa.

Keywords: differential item functioning, item bias, public school students, private school students, vocabulary

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Authors: Elio El Kahi, Michel Khouri, Olivier Deck, Pierre Rahme, Rasool Mehdizadeh

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Recent developments in civil engineering create multiple interaction problems between the soil and the structure. One of the major problems is the impact of ground movements on buildings. Consequently, managing risks associated with these movements, requires a determination of the different influencing factors and a specific knowledge of their variability/uncertainty. The main purpose of this research is to study the behavior of structures submitted to differential settlement, in order to assess their vulnerability, taking into consideration the different sources of uncertainties. Analytical approach is applied to investigate on one hand the influence of these uncertainties that are related to the soil, and on the other hand the structure stiffness variation with the presence of openings and the movement transmitted between them as related to the origin and shape of the free-field movement. Results reveal the effect of taking these uncertainties into consideration, and specify the dominant and most significant parameters that control the ground movement associated with the Soil-Structure Interaction (SSI) phenomenon.

Keywords: analytical approach, building, damage, differential settlement, soil-structure interaction, uncertainties

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