Search results for: polynomial interpolation

Authors: Hadiatullah, T. S. D. Desak Ketut, A. A. Ayu, A. N. Isna, D. P. Ririn

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Spirogyra sp. is genus of microalgae which has a high carbohydrate content that used as a best medium for bacterial fermentation to produce cellulose. This study objective to determine the effect of pulp banana in the fermented paper production process using Spirogyra sp. and characterizing of the paper product. The method includes the production of bacterial cellulose, assay of the effect fermented paper interpolating with banana pulp using Spirogyra sp., and the assay of paper characteristics include gram-mage paper, water assay absorption, thickness, power assay of tensile resistance, assay of tear resistance, density, and organoleptic assay. Experiments were carried out with completely randomized design with a variation of the concentration of sewage treatment in the fermented paper production interpolating banana pulp using Spirogyra sp. Each parameter data to be analyzed by Anova variance that continued by real difference test with an error rate of 5% using the SPSS. Nata production results indicate that different carbon sources (glucose and sugar) did not show any significant differences from cellulose parameters assay. Significantly different results only indicated for the control treatment. Although not significantly different from the addition of a carbon source, sugar showed higher potency to produce high cellulose. Based on characteristic assay of the fermented paper showed that the paper gram-mage indicated that the control treatment without interpolation of a carbon source and a banana pulp have better result than banana pulp interpolation. Results of control gram-mage is 260 gsm that show optimized by cardboard. While on paper gram-mage produced with the banana pulp interpolation is about 120-200 gsm that show optimized by magazine paper and art paper. Based on the density, weight, water absorption assays, and organoleptic assay of paper showing the highest results in the treatment of pulp banana interpolation with sugar source as carbon is 14.28 g/m2, 0.02 g and 0.041 g/cm2.minutes. The conclusion found that paper with nata material interpolating with sugar and banana pulp has the potential formulation to produce super-quality paper.

Keywords: cellulose, fermentation, grammage, paper, Spirogyra sp.

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Authors: Fariza Yunus, Jasmee Jaafar, Zamalia Mahmud, Nurul Nisa’ Khairul Azmi, Nursalleh K. Chang, Nursalleh K. Chang

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Variation of air temperature from one place to another is cause by air temperature controls. In general, the most important control of air temperature is elevation. Another significant independent variable in estimating air temperature is the location of meteorological stations. Distances to coastline and land use type are also contributed to significant variations in the air temperature. On the other hand, in homogeneous terrain direct interpolation of discrete points of air temperature work well to estimate air temperature values in un-sampled area. In this process the estimation is solely based on discrete points of air temperature. However, this study presents that air temperature controls also play significant roles in estimating air temperature over homogenous terrain of Peninsular Malaysia. An Inverse Distance Weighting (IDW) interpolation technique was adopted to generate continuous data of air temperature. This study compared two different datasets, observed mean monthly data of T, and estimation error of T–T’, where T’ estimated value from a multiple regression model. The multiple regression model considered eight independent variables of elevation, latitude, longitude, coastline, and four land use types of water bodies, forest, agriculture and build up areas, to represent the role of air temperature controls. Cross validation analysis was conducted to review accuracy of the estimation values. Final results show, estimation values of T–T’ produced lower errors for mean monthly mean air temperature over homogeneous terrain in Peninsular Malaysia.

Keywords: air temperature control, interpolation analysis, peninsular Malaysia, regression model, air temperature

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Authors: Pedro Mauricio Acosta, Carlos Andrés Caro

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This research presents the regionalization of IDF curves for the department of Boyacá, Colombia, which comprises 16 towns, including the provincial capital, Tunja. For regionalization adjustment parameters (U and alpha) of the IDF curves stations referred to in the studied area were used. Similar regionalization is used by the interpolation of intensities. In the case of regionalization by parameters found by the construction of the curves intensity, duration and frequency estimation methods using ordinary moments and maximum likelihood. Regionalization and interpolation of data were performed with the assistance of Arcgis software. Within the development of the project the best choice to provide a level of reliability such as to determine which of the options and ways to regionalize is best sought. The resulting isolines maps were made in the case of regionalization intensities, each map is associated with a different return period and duration in order to build IDF curves in the studied area. In the case of the regionalization maps parameters associated with each parameter were performed last.

Keywords: intensity duration, frequency curves, regionalization, hydrology

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Authors: Kittipong Tripetch, Nobuhiko Nakano

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This paper proposes one stage and two stage CMOS Complementary Regulated Cascode Distributed Amplifier (CRCDA) design based on Inductive and Transformer coupling techniques. Usually, Distributed amplifier is based on inductor coupling between gate and gate of MOSFET and between drain and drain of MOSFET. But this paper propose some new idea, by coupling with differential primary windings of transformer between gate and gate of MOSFET first stage and second stage of regulated cascade amplifier and by coupling with differential secondary windings transformer of MOSFET between drain and drain of MOSFET first stage and second stage of regulated cascade amplifier. This paper also proposes polynomial modeling of Silicon Transformer passive equivalent circuit from Nanyang Technological University which is used to extract frequency response of transformer. Cadence simulation results are used to verify validity of transformer polynomial modeling which can be used to design distributed amplifier without Cadence. 4 parameters of scattering matrix of 2 port of the propose circuit is derived as a function of 4 parameters of impedance matrix.

Keywords: CMOS regulated cascode distributed amplifier, silicon transformer modeling with polynomial, low power consumption, distribute amplification technique

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Authors: Schadrack Mwizerwa

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The characterization and prediction of landslides are crucial for assessing geological hazards and mitigating risks to infrastructure and communities. This research aims to develop a probabilistic framework for analyzing excavation-induced landslides, which is fundamental for assessing geological hazards and mitigating risks to infrastructure and communities. The study uses Hermite polynomial chaos, a non-stationary random process, to analyze the stability of a slope and characterize the failure probability of a real landslide induced by highway construction excavation. The correlation within the data is captured using the Karhunen-Loève (KL) expansion theory, and the finite element method is used to analyze the slope's stability. The research contributes to the field of landslide characterization by employing advanced random field approaches, providing valuable insights into the complex nature of landslide behavior and the effectiveness of advanced probabilistic models for risk assessment and management. The data collected from the Baiyuzui landslide, induced by highway construction, is used as an illustrative example. The findings highlight the importance of considering the probabilistic nature of landslides and provide valuable insights into the complex behavior of such hazards.

Keywords: Hermite polynomial chaos, Karhunen-Loeve, slope stability, probabilistic analysis

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Authors: Rahul Patel

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Ahmedabad, a city located in western India, is experiencing rapid growth due to urbanization and industrialization. It is projected to become a metropolitan city in the near future, resulting in various construction activities. Soil testing is necessary before construction can commence, requiring construction companies and contractors to periodically conduct soil testing. The focus of this study is on the process of creating a spatial database that is digitally formatted and integrated with geotechnical data and a Geographic Information System (GIS). Building a comprehensive geotechnical (Geo)-database involves three steps: collecting borehole data from reputable sources, verifying the accuracy and redundancy of the data, and standardizing and organizing the geotechnical information for integration into the database. Once the database is complete, it is integrated with GIS, allowing users to visualize, analyze, and interpret geotechnical information spatially. Using a Topographic to Raster interpolation process in GIS, estimated values are assigned to all locations based on sampled geotechnical data values. The study area was contoured for SPT N-Values, Soil Classification, Φ-Values, and Bearing Capacity (T/m2). Various interpolation techniques were cross-validated to ensure information accuracy. This GIS map enables the calculation of SPT N-Values, Φ-Values, and bearing capacities for different footing widths and various depths. This study highlights the potential of GIS in providing an efficient solution to complex phenomena that would otherwise be tedious to achieve through other means. Not only does GIS offer greater accuracy, but it also generates valuable information that can be used as input for correlation analysis. Furthermore, this system serves as a decision support tool for geotechnical engineers.

Keywords: ArcGIS, borehole data, geographic information system, geo-database, interpolation, SPT N-value, soil classification, Φ-Value, bearing capacity

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Authors: Tze Jin Wong, Lee Feng Koo, Pang Hung Yiu

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Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC_4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC₃ cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC_4,6 cryptosystem than LUC₃ and LUC cryptosystems. Current study concludes that LUC_4,6 cryptosystem is more secure than LUC and LUC₃ cryptosystems in sustaining against Lenstra’s attack.

Keywords: Lucas sequence, Dickson polynomial, faulty signature, corresponding signature, congruence

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: Derkaoui Orkia, Lehireche Ahmed

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The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

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The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: eigenvalues/eigenvectors, latent values/vectors, matrix fraction description, state space description

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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: 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: 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: Alsaidi M. Altaher, Mohd Tahir Ismail

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Wavelet thresholding has been a power tool in curve estimation and data analysis. In the presence of outliers this non parametric estimator can not suppress the outliers involved. This study proposes a new two-stage combined method based on the use of the median filter as primary step before applying wavelet thresholding. After suppressing the outliers in a signal through the median filter, the classical wavelet thresholding is then applied for removing the remaining noise. We use automatic boundary corrections; using a low order polynomial model or local polynomial model as a more realistic rule to correct the bias at the boundary region; instead of using the classical assumptions such periodic or symmetric. A simulation experiment has been conducted to evaluate the numerical performance of the proposed method. Results show strong evidences that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating outlier’s sensitivity.

Keywords: boundary correction, median filter, simulation, wavelet thresholding

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Authors: Betsy Ng, Seng Chee Tan, Choon Lang Quek, Peter Looker, Jaime Koh

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The purpose of the present study was to determine the particular scale rating that stands out for an instrument. The instrument was designed to assess student perceptions of various learning environments, namely face-to-face, online and blended. The original instrument had a 5-point Likert items (1 = strongly disagree and 5 = strongly agree). Alternate versions were modified with a 6-point Likert scale and a bar scale rating. Participants consisted of undergraduates in a local university were involved in the usability testing of the instrument in an electronic setting. They were presented with the 5-point, 6-point and percentage-bar (100-point) scale ratings, in response to their perceptions of learning environments. The 5-point and 6-point Likert scales were presented in the form of radio button controls for each number, while the percentage-bar scale was presented with a sliding selection. Among these responses, 6-point Likert scale emerged to be the best overall. When participants were confronted with the 5-point items, they either chose 3 or 4, suggesting that data loss could occur due to the insensitivity of instrument. The insensitivity of instrument could be due to the discreet options, as evidenced by response interpolation. To avoid the constraint of discreet options, the percentage-bar scale rating was tested, but the participant responses were not well-interpolated. The bar scale might have provided a variety of responses without a constraint of a set of categorical options, but it seemed to reflect a lack of perceived and objective accuracy. The 6-point Likert scale was more likely to reflect a respondent’s perceived and objective accuracy as well as higher sensitivity. This finding supported the conclusion that 6-point Likert items provided a more accurate measure of the participant’s evaluation. The 5-point and bar scale ratings might not be accurately measuring the participants’ responses. This study highlighted the importance of the respondent’s perception of accuracy, respondent’s true evaluation, and the scale’s ease of use. Implications and limitations of this study were also discussed.

Keywords: usability, interpolation, sensitivity, Likert scales, accuracy

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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: Imdat Taymaz, Erman Aslan, Kemal Cakir

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The Lattice Boltzmann Method (LBM) is performed to computationally investigate the laminar flow and heat transfer of an incompressible fluid with constant material properties in a 2D channel with a built-in triangular prism. Both momentum and energy transport is modelled by the LBM. A uniform lattice structure with a single time relaxation rule is used. Interpolation methods are applied for obtaining a higher flexibility on the computational grid, where the information is transferred from the lattice structure to the computational grid by Lagrange interpolation. The flow is researched on for different Reynolds number, while Prandtl number is keeping constant as a 0.7. The results show how the presence of a triangular prism effects the flow and heat transfer patterns for the steady-state and unsteady-periodic flow regimes. As an evaluation of the accuracy of the developed LBM code, the results are compared with those obtained by a commercial CFD code. It is observed that the present LBM code produces results that have similar accuracy with the well-established CFD code, as an additionally, LBM needs much smaller CPU time for the prediction of the unsteady phonema.

Keywords: laminar forced convection, lbm, triangular prism

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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: 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: Kiana Zeighami, Morteza Ozlati Moghadam

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Designing a high accuracy and high precision motion controller is one of the important issues in today’s industry. There are effective solutions available in the industry but the real-time performance, smoothness and accuracy of the movement can be further improved. This paper discusses a complete solution to carry out the movement of three stepper motors in three dimensions. The objective is to provide a method to design a fully integrated System-on-Chip (SOC)-based motion controller to reduce the cost and complexity of production by incorporating Field Programmable Gate Array (FPGA) into the design. In the proposed method the FPGA receives its commands from a host computer via wireless internet communication and calculates the motion trajectory for three axes. A profile generator module is designed to realize the interpolation algorithm by translating the position data to the real-time pulses. This paper discusses an approach to implement the linear interpolation algorithm, since it is one of the fundamentals of robots’ movements and it is highly applicable in motion control industries. Along with full profile trajectory, the triangular drive is implemented to eliminate the existence of error at small distances. To integrate the parallelism and real-time performance of FPGA with the power of Central Processing Unit (CPU) in executing complex and sequential algorithms, the NIOS II soft-core processor was added into the design. This paper presents different operating modes such as absolute, relative positioning, reset and velocity modes to fulfill the user requirements. The proposed approach was evaluated by designing a custom-made FPGA board along with a mechanical structure. As a result, a precise and smooth movement of stepper motors was observed which proved the effectiveness of this approach.

Keywords: 3-axis linear interpolation, FPGA, motion controller, micro-stepping

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Authors: Thanh Van Hoang, Tien Yin Chou, Yao Min Fang, Yi Min Huang, Xuan Linh Nguyen

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Reliable information on the spatial distribution of annual rainfall and temperature is essential in research projects relating to urban and regional planning. This research presents results of a classification of temperature and rainfall in the Red River Delta of northern Vietnam based on measurements from seven meteorological stations (Ha Nam, Hung Yen, Lang, Nam Dinh, Ninh Binh, Phu Lien, Thai Binh) in the river basin over a thirty-years period from 1982-2011. The average accumulated rainfall trends in the delta are analysed and form the basis of research essential to weather and climate forecasting. This study employs interpolation based on the Kriging Method for daily rainfall (min and max) and daily temperature (min and max) in order to improve the understanding of sources of variation and uncertainly in these important meteorological parameters. To the Kriging method, the results will show the different models and the different parameters based on the various precipitation series. The results provide a useful reference to assist decision makers in developing smart agriculture strategies for the Red River Delta in Vietnam.

Keywords: spatial interpolation method, ArcGIS, temperature variability, rainfall variability, Red River Delta, Vietnam

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Authors: Peter Joseph Basil Morris, Chhabi Nigam, S. Ramakrishnan, P. Radhakrishna

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This paper brings out the analysis of the airborne Synthetic Aperture Radar (SAR) data using the Range Migration Algorithm (RMA) for the spotlight mode of operation. Unlike in polar format algorithm (PFA), space-variant defocusing and geometric distortion effects are mitigated in RMA since it does not assume that the illuminating wave-fronts are planar. This facilitates the use of RMA for imaging scenarios involving severe differential range curvatures enabling the imaging of larger scenes at fine resolution and at shorter ranges with low center frequencies. The RMA algorithm for the spotlight mode of SAR is analyzed in this paper using the airborne data. Pre-processing operations viz: - range de-skew and motion compensation to a line are performed on the raw data before being fed to the RMA component. Various stages of the RMA viz:- 2D Matched Filtering, Along Track Fourier Transform and Slot Interpolation are analyzed to find the performance limits and the dependence of the imaging geometry on the resolution of the final image. The ability of RMA to compensate for severe differential range curvatures in the two-dimensional spatial frequency domain are also illustrated in this paper.

Keywords: range migration algorithm, spotlight SAR, synthetic aperture radar, matched filtering, slot interpolation

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Authors: Shouji Yujiro, Memei Dukovic, Mist Yakubu

Abstract:

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: Jaehyug Lee, Tae-Ho Song

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Vacuum insulation panel (VIP) can achieve very low thermal conductivity by evacuating its inner space. Heat transfer in the core materials of highly-evacuated VIP occurs by conduction through the solid structure and radiation through the pore. The effect of various scattering modes in combined conduction-radiation in VIP is investigated through numerical analysis. The discrete ordinates interpolation method (DOIM) incorporated with the commercial code FLUENT® is employed. It is found that backward scattering is more effective in reducing the total heat transfer while isotropic scattering is almost identical with pure absorbing/emitting case of the same optical thickness. For a purely scattering medium, the results agree well with additive solution with diffusion approximation, while a modified term is added in the effect of optical thickness to backward scattering is employed. For other scattering phase functions, it is also confirmed that backwardly scattering phase function gives a lower effective thermal conductivity. Thus, the materials with backward scattering properties, with radiation shields are desirable to lower the thermal conductivity of VIPs.

Keywords: combined conduction and radiation, discrete ordinates interpolation method, scattering phase function, vacuum insulation panel

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

Abstract:

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: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

Abstract:

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds is not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: structural healthcare monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation

Procedia PDF Downloads 407

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

Procedia PDF Downloads 129