Search results for: classical polynomial kernels

Authors: O. Ahmed Apampa, Yinusa, A. Jimoh

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The aim of this study was to develop an appropriate model for predicting the compaction behavior of lateritic soils and corn cob ash (CCA) stabilized lateritic soils. This was done by first adopting an equation earlier developed for fine-grained soils and subsequent adaptation by others and extending it to modified lateritic soil through the introduction of alpha and beta parameters which are polynomial functions of the CCA binder input. The polynomial equations were determined with MATLAB R2011 curve fitting tool, while the alpha and beta parameters were determined by standard linear programming techniques using the Solver function of Microsoft Excel 2010. The model so developed was a good fit with a correlation coefficient R2 value of 0.86. The paper concludes that it is possible to determine the optimum moisture content and the maximum dry density of CCA stabilized soils from the compaction test of the unmodified soil, and recommends that this procedure is extended to other binder stabilized lateritic soils to facilitate quick decision making in roadworks.

Keywords: compaction, corn cob ash, lateritic soil, stabilization

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Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

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The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

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Authors: Saba Riaz, Syed A. Hussain

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This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

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Authors: Malika Yaici, Kamel Hariche

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In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

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Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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Authors: A. Selmi, A. Bisharat

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Using Fourier transform and based on the Mindlin's 2^nd gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.

Keywords: Eshelby tensor, Eshelby-like tensor, Green’s function, Mindlin’s 2nd gradient model, spherical inclusion

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Authors: Lu Zhao, Nadir Farhi, Yeltsin Valero, Zoi Christoforou, Nadia Haddadou

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In this paper, a long short-term memory (LSTM) neural network model is proposed to replicate simultaneously car-following and lane-changing behaviors in road networks. By combining two kinds of LSTM layers and three input designs of the neural network, six variants of the LSTM model have been created. These models were trained and tested on the NGSIM 101 dataset, and the results were evaluated in terms of longitudinal speed and lateral position, respectively. Then, we compared the LSTM model with a classical car-following model (the intelligent driving model (IDM)) in the part of speed decision. In addition, the LSTM model is compared with a model using classical neural networks. After the comparison, the LSTM model demonstrates higher accuracy than the physical model IDM in terms of car-following behavior and displays better performance with regard to both car-following and lane-changing behavior compared to the classical neural network model.

Keywords: traffic modeling, neural networks, LSTM, car-following, lane-change

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

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Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: monomial forms, rectangular surfaces, CAGD curves, monomial matrix applications

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Authors: U. Demir

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18th century which is the period of 'change' in the Ottoman Empire, affects the architecture as well, where the Classical period is left behind, architecture is differentiated in the form language. This change is especially noticeable in monumental buildings and thus manifested itself in the mosques. But, is it possible to talk about the structural context of the 'change' which has been occurred in decoration? The aim of this study is to investigate the changes and classical relations of the 18th century mosques through plan schedules and structure systems. This study focuses on the monumental mosques constructed during the reign of the three sultans who ruled in the second half of the century (Mustafa the 3rd 1757-1774, Abdülhamid the 1st 1774-1789 and Selim the 3rd). According to their construction years these are 'Ayazma, Laleli, Zeyneb Sultan, Fatih, Beylerbeyi, Şebsefa Kadın, Eyüb Sultan, Mihrişah Valide Sultan and Üsküdar-Selimiye' mosques. As a plan scheme, four mosques have a square or close to a rectangular square scheme, while the others have a rectangle scheme and showing the longitudinal development of the mihrab axis. This situation is widespread throughout the period. In addition to the longitudinal development plan, which is the general characteristic of the 18th century mosques, the use of the classical plan schemes continued in the same direction. Spatialization of the mihrab area was applied to the five mosques while other mosques were applied as niches on the wall surface. This situation is widespread in the period of the second half of the century. In the classical period, the lodges may be located at the back of the mosques interior, not interfering with the main worship area. In the period, the lodges were withdrawn from the main worship area. They are separated from the main interior with their own structural and covering systems. The plans seem to be formed as a result of the addition of lodge parts to the northern part of the Classical period mosques. The 18th century mosques are the constructions where the change of the architectural language and style can be observed easily. This change and the break from the classical period manifest themselves quickly in the structural elements, wall surface decorations, pencil work designs, small scale decor elements, motifs. The speed and intensity of change in the decor does not occur the same as in structural context. The mosque construction rules from the traditional and classical era still continues in the century. While some mosque structures have a plan which is inherited from the classical successor, some of were constructed with the same classical period rules. Nonetheless, the location and transformation of the lodges, which are affecting the interior design, are noteworthy. They provide a significant transition on the way to the new language of the mosque design that will be experienced in the next century. It is intended to draw attention to the structural evolution of the 18th century Ottoman architecture through the royal mosques within the scope of this conference.

Keywords: mosque structure, Ottoman architecture, structural evolution, 18th century architecture

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Authors: Ajmal Hussain

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In Indian music parlance, Rasa denotes a distinct aesthetic experience that builds up in the mind of the listeners while listening to a piece of Indian classical music. The distinction of the experience is rooted in the concept that it gives rise to an enhanced awareness about the Self or God and creates a mental state detached from mundane issues of everyday life. The theory of Rasa was initially proposed in the context of theatre but became a part of Indian musicological discourse roughly two thousand years ago, however, to this day, it remains shrouded in mystery due to its religious associations and connotations. This paper attempts to demystify the theory of Rasa in the light of available scientific knowledge fund particularly in Brain and Mind sciences. The paper initially describes the religious context of the theory of Rasa and then discusses its classical formulations by Bharata and Abhinavagupta including the steps and stages laid down by the latter to explain the creation of musical experience. The classical formulations are then interpreted with reference to the scientific knowledge fund about the human mind and mechanics of perception. The study uses the model of human mind as proposed by Portuguese-American neuroscientist Antonio Damasio in his theory ‘A Nesting Principle’. On the basis of the findings by Damasio, the paper interprets the experience of Rasa from a scientific perspective and clarifies the sequence of steps and stages involved in the making of musical experience. The study concludes that although the classical formulations of Rasa identify key aspects of musical experience, the association of Rasa with religion is misleading. The association with religion does not depend upon musical stimulus but the intellectual orientation of the listener. It further establishes that the function of Rasa is more profound as, from an evolutionary perspective, it can be seen as a catalyst for higher consciousness.

Keywords: aesthetic, consciousness, music, Rasa

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Authors: Hanan Moawad, Naglaa M. Abd EL-Rahman

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Erwinia carotovora var. carotovora is the main cause of soft rot in potatoes. Hyphaene thebaica was studied for biocontrol of E. carotovora which inhibited growth of E. carotovora on solid medium, a comparative study of classical and ultrasound-assisted extractions of Hyphaene thebaica fruit. The use of ultrasound decreased significant the total time of treatment and increase the total amount of crude extract. The crude extract was subjected to determine the in vitro, by a bioassay technique revealed that the treatment of paper disks with ultrasound extraction of Hyphaene thebaica reduced the growth of pathogen and produced inhibition zones up to 38mm in diameter. The antioxidant activity of ultrasound-ethanolic extract of Doum fruits (Hyphaene thebaica) was determined. Data obtained showed that the extract contains the secondary metabolites such as Tannins, Saponin, Flavonoids, Phenols, Steroids, Terpenoids, Glycosides and Alkaloids.

Keywords: ultrasound, classical extract, biological control, Erwinia carotovora, Hyphaene thebaica

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Authors: Oloyede John Adebayo

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This paper tested a variant of the monetary model of exchange rate determination, called Frankel’s Capital Account Monetary Model (CAAM) based on Real Interest Rate Differential, on the floating exchange rate experiences of three developing countries of Africa; viz: Ghana, Nigeria and the Gambia. The study adopted the Auto regressive Instrumental Package (AIV) and Almon Polynomial Lag Procedure of regression analysis based on the assumption that the coefficients follow a third-order Polynomial with zero-end constraint. The results found some support for the CAAM hypothesis that exchange rate responds proportionately to changes in money supply, inversely to income and positively to interest rates and expected inflation differentials. On this basis, the study points the attention of monetary authorities and researchers to the relevance and usefulness of CAAM as appropriate tool and useful benchmark for analyzing the exchange rate behaviour of most developing countries.

Keywords: exchange rate, monetary model, interest differentials, capital account

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Authors: Surinder Deswal, Mahesh Pal

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The paper investigates the potential of support vector machines based regression approach to model the mass transfer capacity of multiple plunging jets, both vertical (θ = 90°) and inclined (θ = 60°). The data set used in this study consists of four input parameters with a total of eighty eight cases. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 (root mean square error values of 0.0025 and 0.0020) were achieved by using polynomial and radial basis kernel functions based support vector regression respectively. Results suggest an improved performance by radial basis function in comparison to polynomial kernel based support vector machines. The estimated overall mass transfer coefficient, by both the kernel functions, is in good agreement with actual experimental values (within a scatter of ±15 %); thereby suggesting the utility of support vector machines based regression approach.

Keywords: mass transfer, multiple plunging jets, support vector machines, ecological sciences

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Authors: Paulo Cesar Pereira Junior, Alexandre Monteiro, Rafael da Luz Ribeiro, Antonio Carlos Sobieranski, Aldo von Wangenheim

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In this paper, we present a comparison between convolutional neural networks and classical computer vision approaches, for the specific precision agriculture problem of weed mapping on sugarcane fields aerial images. A systematic literature review was conducted to find which computer vision methods are being used on this specific problem. The most cited methods were implemented, as well as four models of convolutional neural networks. All implemented approaches were tested using the same dataset, and their results were quantitatively and qualitatively analyzed. The obtained results were compared to a human expert made ground truth for validation. The results indicate that the convolutional neural networks present better precision and generalize better than the classical models.

Keywords: convolutional neural networks, deep learning, digital image processing, precision agriculture, semantic segmentation, unmanned aerial vehicles

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: Ankita Sharma

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The study proposes to review the perception of women in the Classical Age (500-336 BC) when Greek Philosophy was in bloom. It was observed that women had very few rights and were still under the control of men. One of the possible reasons for this exclusion was woman’s biology that had a huge influence on her being seen as inferior to men. The text ‘Hippocratic Corpus’ focuses on the biological construct of the female body in classical Greek science that perpetuated the idea of women as second-class citizens and were considered inherently weaker than men. The research highlights the significance of the text that was used to encourage women of that time to get married and produce children and how till today the perception remains the same. The Greek belief of need for confinement and control of 'wandering uterus' has led to superior understanding of men. The pivotal emphasis of this research is to women and their bodies that are depicted in a misogynistic way which paved the way for Hippocratic writers to influence the society’s attitude towards women in their writings. It is intended to draw attention to the prevailing cultural assumptions and preconceived notions about female anatomy that had a pervasive influence in the following centuries with its roots being in ancient science.

Keywords: classical Greek theory, women, wandering womb, modern ideology

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Authors: S. O. Oyamakin, A. U. Chukwu,

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We proposed a Hyperbolic Gompertz Growth Model (HGGM), which was developed by introducing a stabilizing parameter called θ using hyperbolic sine function into the classical gompertz growth equation. The resulting integral solution obtained deterministically was reprogrammed into a statistical model and used in modeling the height and diameter of Pines (Pinus caribaea). Its ability in model prediction was compared with the classical gompertz growth model, an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while using testing the independence of the error term using the runs test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic gompertz growth models better than the source model (classical gompertz growth model) while the results of R2, Adj. R2, MSE, and AIC confirmed the predictive power of the Hyperbolic Monomolecular growth models over its source model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, gompertz

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: algorithm, determinant, computation, eigenvalue, time complexity

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Authors: Khaled I. Nawafleh

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In this work, we apply the method of Hamilton-Jacobi to obtain solutions of Hamiltonian systems in classical mechanics with two certain structures: the first structure plays a central role in the theory of time-dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians, including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. Then, another expression of geometry of the Hamilton Jacobi equation is retrieved for Hamiltonians with time-dependent and frictional terms. Both approaches shall be applied to many physical examples.

Keywords: Hamilton-Jacobi, time dependent lagrangians, dissipative systems, variational principle

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Authors: Farina Riaz, Shahab Abdulla, Srinjoy Ganguly, Hajime Suzuki, Ravinesh C. Deo, Susan Hopkins

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Recently, quantum machine learning has received significant attention. For various types of data, including text and images, numerous quantum machine learning (QML) models have been created and are being tested. Images are exceedingly complex data components that demand more processing power. Despite being mature, classical machine learning still has difficulties with big data applications. Furthermore, quantum technology has revolutionized how machine learning is thought of, by employing quantum features to address optimization issues. Since quantum hardware is currently extremely noisy, it is not practicable to run machine learning algorithms on it without risking the production of inaccurate results. To discover the advantages of quantum versus classical approaches, this research has concentrated on colored image data. Deep learning classification models are currently being created on Quantum platforms, but they are still in a very early stage. Black and white benchmark image datasets like MNIST and Fashion MINIST have been used in recent research. MNIST and CIFAR-10 were compared for binary classification, but the comparison showed that MNIST performed more accurately than colored CIFAR-10. This research will evaluate the performance of the QML algorithm on the colored benchmark dataset CIFAR-10 to advance QML's real-time applicability. However, deep learning classification models have not been developed to compare colored images like Quantum Convolutional Neural Network (QCNN) to determine how much it is better to classical. Only a few models, such as quantum variational circuits, take colored images. The methodology adopted in this research is a hybrid approach by using penny lane as a simulator. To process the 10 classes of CIFAR-10, the image data has been translated into grey scale and the 28 × 28-pixel image containing 10,000 test and 50,000 training images were used. The objective of this work is to determine how much the quantum approach can outperform a classical approach for a comprehensive dataset of color images. After pre-processing 50,000 images from a classical computer, the QCNN model adopted a hybrid method and encoded the images into a quantum simulator for feature extraction using quantum gate rotations. The measurements were carried out on the classical computer after the rotations were applied. According to the results, we note that the QCNN approach is ~12% more effective than the traditional classical CNN approaches and it is possible that applying data augmentation may increase the accuracy. This study has demonstrated that quantum machine and deep learning models can be relatively superior to the classical machine learning approaches in terms of their processing speed and accuracy when used to perform classification on colored classes.

Keywords: CIFAR-10, quantum convolutional neural networks, quantum deep learning, quantum machine learning

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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: Sanjay Singh, Sushil Kumar, Rashmi Jain

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Quantum registering is another pattern in computational hypothesis and a quantum mechanical framework has a few helpful properties like Entanglement. We plan to store data concerning the structure and substance of a basic picture in a quantum framework. Consider a variety of n qubits which we propose to use as our memory stockpiling. In recent years classical processing is switched to quantum image processing. Quantum image processing is an elegant approach to overcome the problems of its classical counter parts. Image storage, retrieval and its processing on quantum machines is an emerging area. Although quantum machines do not exist in physical reality but theoretical algorithms developed based on quantum entangled states gives new insights to process the classical images in quantum domain. Here in the present work, we give the brief overview, such that how entangled states can be useful for quantum image storage and retrieval. We discuss the properties of tripartite Greenberger-Horne-Zeilinger and W states and their usefulness to store the shapes which may consist three vertices. We also propose the techniques to store shapes having more than three vertices.

Keywords: Greenberger-Horne-Zeilinger, image storage and retrieval, quantum entanglement, W states

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Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

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Fields are important objects of study in algebra since they provide a useful generalization of many number systems, such as the rational numbers, real numbers, and complex numbers. In particular, the usual rules of associativity, commutativity and distributivity hold. Fields also appear in many other areas of mathematics; see the examples below. When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a commutative field or a rational domain. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a division ring ordivision algebra or sometimes a skew field. Also non-commutative field is still widely used. In French, fields are called corps (literally, body), generally regardless of their commutativity. When necessary, a (commutative) field is called corps commutative and a skew field-corps gauche. The German word for body is Körper and this word is used to denote fields; hence the use of the blackboard bold to denote a field. The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher. An extension of a field k is just a field K containing k as a subfield. One distinguishes between extensions having various qualities. For example, an extension K of a field k is called algebraic, if every element of K is a root of some polynomial with coefficients in k. Otherwise, the extension is called transcendental. The aim of Galois Theory is the study of algebraic extensions of a field. Given a field k, various kinds of closures of k may be introduced. For example, the algebraic closure, the separable closure, the cyclic closure et cetera. The idea is always the same: If P is a property of fields, then a P-closure of k is a field K containing k, having property, and which is minimal in the sense that no proper subfield of K that contains k has property P. For example if we take P (K) to be the property ‘every non-constant polynomial f in K[t] has a root in K’, then a P-closure of k is just an algebraic closure of k. In general, if P-closures exist for some property P and field k, they are all isomorphic. However, there is in general no preferable isomorphism between two closures.

Keywords: field theory, mechanic maths, supertech, rolltech

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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Authors: Jayakrishnan Narayanan, Sengamalam Periyasamy Dhanavel

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Indian classical (Karnatik) music videos across various media platforms have followed an audio-visual pattern that conforms to its socio-cultural and quasi-religious identity. The present paper analyzes the semiotic variations between ‘pure Karnatik music videos’ and ‘independent/contemporary-collaborative music videos’ posted on social media by young professional Karnatik musicians. The paper analyzes these media texts by comparing their various structural sememes namely, the title, artists, music, narrative schemata, visuals, lighting, sound, and costumes. The paper argues that the pure Karnatik music videos are marked by the presence of certain recurring mythological or third level signifiers and that these signifiers and codes are marked by their conspicuous absence in the independent music videos produced by the same musicians. While the music and the musical instruments used in both these sets of music videos remain similar, the meaning that is abducted by the beholder in each case is entirely different. The paper also attempts to study the identity conflicts that are projected through these music videos and the extent to which the cultural connotations of Karnatik music govern the production of its music videos.

Keywords: abduction, identity, media semiotics, music video

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Authors: Lydia Wahid, Mona F. Ahmed, Nevin Darwish

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The vehicle routing problem (VRP) consists of a group of customers that needs to be served. Each customer has a certain demand of goods. A central depot having a fleet of vehicles is responsible for supplying the customers with their demands. The problem is composed of two subproblems: The first subproblem is an assignment problem where the number of vehicles that will be used as well as the customers assigned to each vehicle are determined. The second subproblem is the routing problem in which for each vehicle having a number of customers assigned to it, the order of visits of the customers is determined. Optimal number of vehicles, as well as optimal total distance, should be achieved. In this paper, an approach for solving the first subproblem (the assignment problem) is presented. In the approach, a clustering algorithm is proposed for finding the optimal number of vehicles by grouping the customers into clusters where each cluster is visited by one vehicle. Finding the optimal number of clusters is NP-hard. This work presents a polynomial time clustering algorithm for finding the optimal number of clusters and solving the assignment problem.

Keywords: vehicle routing problems, clustering algorithms, Clarke and Wright Saving Method, agglomerative hierarchical clustering

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Authors: Hanwei Gao, Louis Jezequel, Eric Cabrol, Bernard Vitry

Abstract:

The chassis system is composed of complex elements that take up all the loads from the tire-ground contact area and thus it plays an important role in numerous specifications such as durability, comfort, crash, etc. During the development of new vehicle projects in Renault, durability validation is always the main focus while deployment of comfort comes later in the project. Therefore, sometimes design choices have to be reconsidered because of the natural incompatibility between these two specifications. Besides, robustness is also an important point of concern as it is related to manufacturing costs as well as the performance after the ageing of components like shock absorbers. In this paper an approach is proposed aiming to realize a multi-objective optimization between chassis endurance and comfort while taking the random factors into consideration. The adaptive-sparse polynomial chaos expansion method (PCE) with Chebyshev polynomial series has been applied to predict responses’ uncertainty intervals of a system according to its uncertain-but-bounded parameters. The approach can be divided into three steps. First an initial design of experiments is realized to build the response surfaces which represent statistically a black-box system. Secondly within several iterations an optimum set is proposed and validated which will form a Pareto front. At the same time the robustness of each response, served as additional objectives, is calculated from the pre-defined parameter intervals and the response surfaces obtained in the first step. Finally an inverse strategy is carried out to determine the parameters’ tolerance combination with a maximally acceptable degradation of the responses in terms of manufacturing costs. A quarter car model has been tested as an example by applying the road excitations from the actual road measurements for both endurance and comfort calculations. One indicator based on the Basquin’s law is defined to compare the global chassis durability of different parameter settings. Another indicator related to comfort is obtained from the vertical acceleration of the sprung mass. An optimum set with best robustness has been finally obtained and the reference tests prove a good robustness prediction of Chebyshev PCE method. This example demonstrates the effectiveness and reliability of the approach, in particular its ability to save computational costs for a complex system.

Keywords: chassis durability, Chebyshev polynomials, multi-objective optimization, polynomial chaos expansion, ride comfort, robust design

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Authors: Jorge Lopez

Abstract:

In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods.

Keywords: coupled oscillators, fractional calculus, fractional oscillator, structural dynamics

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Authors: Lamiche Chaabane

Abstract:

In this study, a new method for solving sequence alignment problem is proposed, which is named ITS (Improved Tabu Search). This algorithm is based on the classical Tabu Search (TS). ITS is implemented in order to obtain results of multiple sequence alignment. Several ideas concerning neighbourhood generation, move selection mechanisms and intensification/diversification strategies for our proposed ITS is investigated. ITS have generated high-quality results in terms of measure of scores in comparison with the classical TS and simple iterative search algorithm.

Keywords: multiple sequence alignment, tabu search, improved tabu search, neighbourhood generation, selection mechanisms

Procedia PDF Downloads 271

Authors: M. Ndeley

Abstract:

The performance of global manufacturing supply chains depends on the interaction of production and transport processes. Currently, the scheduling of these processes is done separately without considering mutual requirements, which leads to no optimal solutions. An integrated scheduling of both processes enables the improvement of supply chain performance. The integrated production and transport scheduling problem (PTSP) is NP-hard, so that heuristic methods are necessary to efficiently solve large problem instances as in the case of global manufacturing supply chains. This paper presents a heuristic scheduling approach which handles the integration of flexible production processes with intermodal transport, incorporating flexible land transport. The method is based on a graph that allows a reformulation of the PTSP as a shortest path problem for each job, which can be solved in polynomial time. The proposed method is applied to a supply chain scenario with a manufacturing facility in South Africa and shipments of finished product to customers within the Country. The obtained results show that the approach is suitable for the scheduling of large-scale problems and can be flexibly adapted to different scenarios.

Keywords: production and transport scheduling problem, graph based scheduling, integrated scheduling

Procedia PDF Downloads 450