Search results for: polynomial adjustments

Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

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Authors: Benson Ade Eniola Afere

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Over the years, kernel density estimation has been extensively studied within the context of nonparametric density estimation. The fundamental components of kernel density estimation are the kernel function and the bandwidth. While the mathematical exploration of the kernel component has been relatively limited, its selection and development remain crucial. The Mean Integrated Squared Error (MISE), serving as a measure of discrepancy, provides a robust framework for assessing the effectiveness of any kernel function. A kernel function with a lower MISE is generally considered to perform better than one with a higher MISE. Hence, the primary aim of this article is to create kernels that exhibit significantly reduced MISE when compared to existing classical kernels. Consequently, this article introduces a cluster of hybrid polynomial kernel families. The construction of these proposed kernel functions is carried out heuristically by combining two kernels from the classical polynomial kernel family using probability axioms. We delve into the analysis of error propagation within these kernels. To assess their performance, simulation experiments, and real-life datasets are employed. The obtained results demonstrate that the proposed hybrid kernels surpass their classical kernel counterparts in terms of performance.

Keywords: classical polynomial kernels, cluster of families, global error, hybrid Kernels, Kernel density estimation, Monte Carlo simulation

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Authors: Navdeep Goel, Salvador Gabarda

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Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4x4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4*4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4*4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain.

Keywords: chirp signals, image multiplexing, image transformation, linear canonical transform, polynomial approximation

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Authors: Xue Junwei

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The rapid economic development of China has made it a critical global market. Multinational companies operating in China face evolving challenges, necessitating adjustments in their marketing strategies. This study uses SWOT analysis and qualitative research methods to explore the trends and countermeasures for adjusting the marketing strategies of multinational companies in China. The research employs the SWOT analysis, quantitative as well as qualitative research techniques to investigate the marketing strategy adjustments of multinational companies in China. The study reveals emerging trends and proposes strategic countermeasures for multinational companies to adapt their marketing strategies in the Chinese market. This research contributes to the existing literature by providing insights into the dynamic environment of multinational companies in China and offering practical recommendations for strategy adjustments. Data were collected using qualitative research methods, including interviews and case studies, and quantitative research methods, such as questionnaires to study multinational companies in China. The collected data were analyzed using SWOT analysis to identify the strengths, weaknesses, opportunities, and threats faced by multinational companies in China, guiding the formulation of effective marketing strategies. This study addresses the challenges faced by multinational companies in China, the need for strategic adjustments, and the potential approaches to enhancing marketing effectiveness in this market. The study emphasizes the significance of adapting marketing strategies to align with the changing landscape of the Chinese market. It provides actionable recommendations for multinational companies to thrive in this environment.

Keywords: multinational company, marketing strategies, Chinese market, SWOT

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Authors: Ming-Jong Tsai, T. M. Wu, R. C. Chu

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The purpose of this study is to develop an Advanced linear calibration Technique for air flow sensing by using CTA-based Hot wire Anemometry. It contains a host PC with Human Machine Interface, a wind tunnel, a wind speed controller, an automatic data acquisition module, and nonlinear calibration model. To improve the fitting error by using single fitting polynomial, this study proposes a Multiple three-order Polynomial Fitting Method (MPFM) for fitting the non-linear output of a CTA-based Hot wire Anemometry. The CTA-based anemometer with built-in fitting parameters is installed in the wind tunnel, and the wind speed is controlled by the PC-based controller. The Hot-Wire anemometer's thermistor resistance change is converted into a voltage signal or temperature differences, and then sent to the PC through a DAQ card. After completion measurements of original signal, the Multiple polynomial mathematical coefficients can be automatically calculated, and then sent into the micro-processor in the Hot-Wire anemometer. Finally, the corrected Hot-Wire anemometer is verified for the linearity, the repeatability, error percentage, and the system outputs quality control reports.

Keywords: flow rate sensing, hot wire, constant temperature anemometry (CTA), linear calibration, multiple three-order polynomial fitting method (MPFM), temperature compensation

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Authors: A. Boualouch, A. Frigui, T. Nasser, A. Essadki, A.Boukhriss

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This work deals with the vector control of the active and reactive powers of a Double-Fed Induction generator DFIG used as a wind generator by the polynomial RST controller. The control of the statoric power transfer between the machine and the grid is achieved by acting on the rotor parameters and control is provided by the polynomial controller RST. The performance and robustness of the controller are compared with PI controller and evaluated by simulation results in MATLAB/simulink.

Keywords: DFIG, RST, vector control, wind turbine

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Authors: Serge Provost, Yishan Zang

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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.

Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation

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Authors: Benson Ade Eniola Afere

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This paper introduces a family of fourth-order hybrid beta polynomial kernels developed for statistical analysis. The assessment of these kernels' performance centers on two critical metrics: asymptotic mean integrated squared error (AMISE) and kernel efficiency. Through the utilization of both simulated and real-world datasets, a comprehensive evaluation was conducted, facilitating a thorough comparison with conventional fourth-order polynomial kernels. The evaluation procedure encompassed the computation of AMISE and efficiency values for both the proposed hybrid kernels and the established classical kernels. The consistently observed trend was the superior performance of the hybrid kernels when compared to their classical counterparts. This trend persisted across diverse datasets, underscoring the resilience and efficacy of the hybrid approach. By leveraging these performance metrics and conducting evaluations on both simulated and real-world data, this study furnishes compelling evidence in favour of the superiority of the proposed hybrid beta polynomial kernels. The discernible enhancement in performance, as indicated by lower AMISE values and higher efficiency scores, strongly suggests that the proposed kernels offer heightened suitability for statistical analysis tasks when compared to traditional kernels.

Keywords: AMISE, efficiency, fourth-order Kernels, hybrid Kernels, Kernel density estimation

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Authors: Pingshan Chen, Zhiliang Dong

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In order to estimate the post-construction settlement more objectively, the power-polynomial model is proposed, which can reflect the trend of settlement development based on the observed settlement data. It was demonstrated by an actual case history of an embankment, and during the prediction. Compared with the other three prediction models, the power-polynomial model can estimate the post-construction settlement more accurately with more simple calculation.

Keywords: prediction, model, post-construction settlement, soft ground

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Authors: B. Touati, A. Saad, B. Lips, A. Abdenbi, M. Mokhtari.

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The purpose of this study is an application of experiment design method for dimensioning of a solar drying system. NIMROD software was used to build up the matrix of experiments and to analyze the results. The software has the advantages of being easy to use and consists of a forced way, with some choices about the number and range of variation of the parameters, and the desired polynomial shape. The first design of experiments performed concern the drying with constant input characteristics of the hot air in the dryer and a second design of experiments in which the drying chamber is coupled with a solar collector. The first design of experiments allows us to study the influence of various parameters and get the studied answers in a polynomial form. The correspondence between the polynomial thus determined, and the model results were good. The results of the polynomials of the second design of experiments and those of the model are worse than the results in the case of drying with constant input conditions. This is due to the strong link between all the input parameters, especially, the surface of the sensor and the drying chamber, and the mass of the product.

Keywords: solar drying, experiment design method, NIMROD, mint leaves

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Authors: L. J. de Bessa Neto, V. S. Filho, J. V. Ferreira Nunes, G. C. Bergamo

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There are many situations in which human activities have significant effects on the environment. Damage to the ozone layer is one of them. The objective of this work is to use the Least Squares Method, considering the linear, exponential, logarithmic, power and polynomial models of the second degree, to analyze through the coefficient of determination (R²), which model best fits the behavior of the chlorodifluoromethane (HCFC-142b) in parts per trillion between 1992 and 2018, as well as estimates of future concentrations between 5 and 10 periods, i.e. the concentration of this pollutant in the years 2023 and 2028 in each of the adjustments. A total of 809 observations of the concentration of HCFC-142b in one of the monitoring stations of gases precursors of the deterioration of the ozone layer during the period of time studied were selected and, using these data, the statistical software Excel was used for make the scatter plots of each of the adjustment models. With the development of the present study, it was observed that the logarithmic fit was the model that best fit the data set, since besides having a significant R² its adjusted curve was compatible with the natural trend curve of the phenomenon.

Keywords: chlorodifluoromethane (HCFC-142b), ozone, least squares method, regression models

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Authors: S. A. Gayvoronsky, T. A. Ezangina

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The robust control system objects with interval-undermined parameters is considers in this paper. Initial information about the system is its characteristic polynomial with interval coefficients. On the basis of coefficient estimations of quality indices and criterion of the maximum stability degree, the methods of synthesis of a robust regulator parametric is developed. The example of the robust stabilization system synthesis of the rope tension is given in this article.

Keywords: interval polynomial, controller synthesis, analysis of quality factors, maximum degree of stability, robust degree of stability, robust oscillation, system accuracy

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

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The edges of low contrast images are not clearly distinguishable to the human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: low contrast image, fractional order differentiator, Laplacian of Gaussian (LoG) method, chebyshev polynomial

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Authors: R. R. Hordijk, O. J. G. Somsen

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Traditionally, radar systems are the eyes and ears of a ship. However, these systems have their drawbacks and nowadays they are extended with systems that work with video and photos. Processing of data from these videos and photos is however very labour-intensive and efforts are being made to automate this process. A major problem when trying to recognize objects in water is that the 'background' is not homogeneous so that traditional image recognition technics do not work well. Main question is, can a method be developed which automate this recognition process. There are a large number of parameters involved to facilitate the identification of objects on such images. One is varying the resolution. In this research, the resolution of some images has been reduced to the extreme value of 1% of the original to reduce clutter before the polynomial fit (pre-processing). It turned out that the searched object was clearly recognizable as its grey value was well above the average. Another approach is to take two images of the same scene shortly after each other and compare the result. Because the water (waves) fluctuates much faster than an object floating in the water one can expect that the object is the only stable item in the two images. Both these methods (pre-processing and comparing two images of the same scene) delivered useful results. Though it is too early to conclude that with these methods all image problems can be solved they are certainly worthwhile for further research.

Keywords: image processing, image recognition, polynomial fit, water

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Authors: Chiou-Yng Lee, Wen-Yo Lee, Chieh-Tsai Wu, Cheng-Chen Yang

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Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit-level and digit-level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba schemes, and used that to derive a novel scalable multiplier architecture. Analytical results show that the proposed multiplier provides a trade-off between space and time complexities. Our proposed multiplier is modular, regular, and suitable for very-large-scale integration (VLSI) implementations. It involves less area complexity compared to the multipliers based on traditional decomposition methods. It is therefore, more suitable for efficient hardware implementation of pairing based cryptography and elliptic curve cryptography (ECC) in constraint driven applications.

Keywords: digit-serial systolic multiplier, elliptic curve cryptography (ECC), Karatsuba algorithm (KA), shifted polynomial basis (SPB), pairing computation

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Authors: Bartelsen-Raemy Annabelle, Gerber Andrea

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Objectives: The adoption of the UN Convention on the Rights of Persons with Disabilities has the effect that higher education institutions in Switzerland are called upon to promote inclusive university education. In this context, our School of Social Work aims to provide fair participation and the removal of barriers in our study programmes at bachelor’s and master’s levels. In 2015 we developed a concept of reasonable adjustments for students with disabilities and chronic illness as an instrument to provide equal opportunities for those students. We reviewed the implementation of this concept as part of our quality management process. Using a qualitative research design, we explored how affected students and lecturers experience the processes and measures taken and which barriers they still perceive. Methods: We captured subjective perspectives and experience of measures by conducting 15 problem-centred interviews with affected students and three experimental focus groups with lecturers. The data was processed using structured qualitative content analysis and summarised as key categories. Results: All respondents evaluated the concept of reasonable adjustment very positively and emphasised its importance for equal opportunities. Our analysis revealed differences in the usage and perception of both groups and showed that the students interviewed were a heterogeneous group with different needs. Overall, the students described the adjustments, in particular in relation to examinations and other assignments, as a great relief. The lecturers expressed high standards for their own teaching and supervision of students and, at the same time, wished for more support from the university. However, despite the positive evaluation by the lecturers, the limits of reasonable adjustment became evident. It is necessary to consider the limits of reasonable adjustments in terms of professional skills. Conclusion: Reasonable adjustments should, therefore, be seen as an element of an inclusive university culture that must be complemented by further measures. Taking this into account, we have planned further research as a basis for the development of a diversity and inclusion policy.

Keywords: opportunities and limits, reasonable adjustment, social work education, students with disabilities

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Authors: Marinka K. Baghdasaryan, Siranush M. Muradyan, Avgen A. Gasparyan

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Based on the experimental data, the impact of resistance and reactance of the winding, as well as the magnetic permeability of the magnetic circuit steel material on the value of the electromotive force of the induction converter is investigated. The obtained results allow to estimate the main technological spreads and determine the maximum level of the electromotive force change. By the method of experiment planning, the expression of a polynomial for the electromotive force which can be used to estimate the adequacy of mathematical models to be used at the investigation and design of induction converters is obtained.

Keywords: induction converter, electromotive force, expectation, technological spread, deviation, planning an experiment, polynomial, confidence level

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Authors: Abdul Rahiman Kannam Kulam

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Reflecting the concepts of the development of the whole child, it is claimed that, purposeful engagement in physical activities or exercise involved ritual dances has the potential to engender in young people, the purpose of the present study was to analyze school children and their personal adjustment based on Ritual dance participation. For the purpose, two thousand and three hundred school children of Kerala were analyzed. AISS manual of A.K.P Sinha and R.P Singh was used to collect the data for adjustments. The adjustment qualities classifies as excellent, good, average, unsatisfactory and very unsatisfactory. The total performance denotes the state of adjustment based on the classifications. Findings of the study were subjected to percentages and ‘t’ ratio. The study enlightened that, the emotional, social and overall adjustments are better than non-athletes. But the study elucidated that, there is no difference in educational adjustment of school athletes and non athletes among school children.

Keywords: ritual dances, emotional adjustment, Poorakkali, Kolkkali, Margamkali

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: asymptotics, continuous spectrum, difference equations, eigenvalues, jost functions, spectral singularities

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Authors: Rami A. Maher, Ibraheem K. Ibraheem

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This work presents a comparison study between the state-space and polynomial methods for the design of the robust governor for load frequency control of steam turbine power systems. The robust governor is synthesized using the two approaches and the comparison is extended to include time and frequency domains performance, controller order, and uncertainty representation, weighting filters, optimality and sub-optimality. The obtained results are represented through tables and curves with reasons of similarities and dissimilarities.

Keywords: robust control, load frequency control, steam turbine, H∞-norm, system uncertainty, load disturbance

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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: 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: 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: 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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