Search results for: skew polynomial rings

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: Daniel Panario, Daniel Santana de Freitas, Brett Stevens

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Almost Perfect Nonlinear (APN) permutations with optimal resistance against differential cryptanalysis can be found in several domains. The permutation used in the standard for symmetric cryptography (the AES), for example, is based on a special kind of inversion in GF(28). Although very close to APN (2-uniform), this permutation still contains one number 4 in its differential spectrum, which means that, rigorously, it must be classified as 4-uniform. This fact motivates the search for fully APN permutations in other domains of definition. The extremely high complexity associated to this kind of problem precludes an exhaustive search for an APN permutation with 256 elements to be performed without the support of a suitable mathematical structure. On the other hand, in principle, there is nothing to indicate which mathematically structured domains can effectively help the search, and it is necessary to test several domains. In this work, the search for APN permutations in rings ℤ2×ℤ2k is investigated. After a full, exhaustive search with k=2 and k=3, all possible APN permutations in those rings were recorded, together with their differential profiles. Some very promising heuristics in these cases were collected so that, when used as a basis to prune backtracking for the same search in ℤ2×ℤ8 (search space with size 16! ≅244), just a few tenths of a second were enough to produce an APN permutation in a single CPU. Those heuristics were empirically extrapolated so that they could be applied to a backtracking search for APNs over ℤ2×ℤ16 (search space with size 32! ≅2117). The best permutations found in this search were further refined through Simulated Annealing, with a definition of neighbors suitable to this domain. The best result produced with this scheme was a 3-uniform permutation over ℤ2×ℤ16 with only 24 values equal to 3 in the differential spectrum (all the other 968 values were less than or equal 2, as it should be the case for an APN permutation). Although far from being fully APN, this result is technically better than a 4-uniform permutation and demanded only a few seconds in a single CPU. This is a strong indication that the use of mathematically structured domains, like the rings described in this work, together with heuristics based on smaller cases, can lead to dramatic cuts in the computational resources involved in the complexity of the search for APN permutations in extremely large domains.

Keywords: APN permutations, heuristic searches, symmetric cryptography, S-box design

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Authors: Bernardo C. P. Albuquerque, Darym J. F. Campos

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Increasing our ability to solve complex engineering problems is directly related to the processing capacity of computers. By means of such equipments, one is able to fast and accurately run numerical algorithms. Besides the increasing interest in numerical simulations, probabilistic approaches are also of great importance. This way, statistical tools have shown their relevance to the modelling of practical engineering problems. In general, statistical approaches to such problems consider that the random variables involved follow a normal distribution. This assumption tends to provide incorrect results when skew data is present since normal distributions are symmetric about their means. Thus, in order to visualize and quantify this aspect, 9 statistical distributions (symmetric and skew) have been considered to model a hypothetical slope stability problem. The data modeled is the friction angle of a superficial soil in Brasilia, Brazil. Despite the apparent universality, the normal distribution did not qualify as the best fit. In the present effort, data obtained in consolidated-drained triaxial tests and saturated direct shear tests have been modeled and used to analytically derive the probability density function (PDF) of the safety factor of a hypothetical slope based on Mohr-Coulomb rupture criterion. Therefore, based on this analysis, it is possible to explicitly derive the failure probability considering the friction angle as a random variable. Furthermore, it is possible to compare the stability analysis when the friction angle is modelled as a Dagum distribution (distribution that presented the best fit to the histogram) and as a Normal distribution. This comparison leads to relevant differences when analyzed in light of the risk management.

Keywords: statistical slope stability analysis, skew distributions, probability of failure, functions of random variables

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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: Manoj Kumar Patel

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In this paper, we introduce and give various properties of weak* Rad-plus-supplemented and cofinitely weak* Rad-plus-supplemented modules over some special kinds of rings, in particular, artinian serial ring and semiperfect ring. Also prove that ring R is artinian serial if and only if every right and left R-module is weak* Rad-plus-supplemented. We provide the counter example which proves that weak* Rad-plus-supplemented module is the generalization of plus-supplemented and Rad-plus-supplemented modules. Furthermore, as an application of above finding results of this research article, our main focus is to characterized the semisimple ring, artinian principal ideal ring, semilocal ring, semiperfect ring, perfect ring, commutative noetherian ring and Dedekind domain in terms of weak* Rad-plus-supplemented module.

Keywords: cofinitely weak* Rad-plus-supplemented module , Dedekind domain, Rad-plus-supplemented module, semiperfect ring

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Authors: P. Kazymbet, G. Abildinova, K.Makhambetov, M. Bakhtin, D. Rybalkina, K. Zhumadilov

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Conducted cytogenetic research in workers Stepnogorsk Mining-Chemical Combine (Akmola region) with the study of 26341 chromosomal metaphase. Using a regression analysis with program DataFit, version 5.0, dependence between exposure dose and the following cytogenetic exponents has been studied: frequency of aberrant cells, frequency of chromosomal aberrations, frequency of the amounts of dicentric chromosomes, and centric rings. Experimental data on calibration curves "dose-effect" enabled the development of a mathematical model, allowing on data of the frequency of aberrant cells, chromosome aberrations, the amounts of dicentric chromosomes and centric rings calculate the absorbed dose at the time of the study. In the dose range of 0.1 Gy to 5.0 Gy dependence cytogenetic parameters on the dose had the following equation: Y = 0,0067е^0,3307х (R2 = 0,8206) – for frequency of chromosomal aberrations; Y = 0,0057е^0,3161х (R2 = 0,8832) –for frequency of cells with chromosomal aberrations; Y =5 Е-0,5е^0,6383 (R2 = 0,6321) – or frequency of the amounts of dicentric chromosomes and centric rings on cells. On the basis of cytogenetic parameters and regression equations calculated absorbed dose in workers of uranium production at the time of the study did not exceed 0.3 Gy.

Keywords: Stepnogorsk, mathematical modeling, cytogenetic, dicentric chromosomes

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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: 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: Akila Tayeb-Benmachiche, Saber-Mustapha Zendaoui, Salah-Eddine Bouaoud, Bachir Zouchoune

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The variation of the metal coordination site in π-coordinated polycyclic aromatic hydrocarbons (PAH) corresponds to the haptotropic rearrangement or haptotropic migration in which the metal fragment MLn is considered as the moveable moiety that is shifted between two rings of polycyclic or heteropolycyclic ligands. These structural characteristics and dynamical properties give to this category of transition metal complexes a considerable interest. We have investigated the coordination and the haptotropic shifts of (CO)3Ti and CpV moieties over the phenanthridine aromatic system and according to the metal atom nature. The optimization of (CO)3Ti(PHND) and CpV(PHND), using the Amsterdam Density Functional (ADF) program, without a symmetrical restriction of geometry gives an η6 coordination mode of the C6 and C5N rings, which in turn give rise to a six low-lying deficient 16-MVE of each (CO)3Ti(PHND) and CpV(PHND) structure (three singlet and three triplet state structures for Ti complexes and three triplet and three quintet state structures for V complexes). Thus, the η6–η6 haptotropic migration of the metal fragment MLn from the terminal C6 ring to the central C5N ring has been achieved by a loss of energy. However, its η6–η6 haptotropic migration from central C5N ring to the terminal C6 rings has been accomplished by a gain of energy. These results show the capability of the phenanthridine ligand to adapt itself to the electronic demand of the metal in agreement with the nature of the metal–ligand bonding and demonstrate that this theoretical study can also be applied to large fused π-systems.

Keywords: electronic structure, bonding analysis, density functional theory, coordination chemistry haptotropic migration

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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: 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: Reza Samsami

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The aim of the study was to degradation of polycyclic aromatic hydrocarbons (PAHs) by proxy-acid method. The amounts of PAHs were determined in a silty-clay soil sample of an aged oil refinery field in Abadan, Iran. Proxy-acid treatment method was investigated. The results have shown that the proxy-acid system is an effective method for degradation of PAHs. The results also demonstrated that the number of fused aromatic rings have not significant effects on PAH removal by proxy-acid method. The results also demonstrated that the number of fused aromatic rings have not significant effects on PAH removal by proxy-acid method.

Keywords: proxy-acid treatment, silty-clay soil, PAHs, degradation

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Authors: Farzad Shirzad, Bohlol Alijani, Mehry Akbary, Mohammad Saligheh

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Climate change and global warming are very important issues today. The process of climate change, especially changes in temperature and precipitation, is the most important issue in the environmental sciences. Climate change means changing the averages in the long run. Iran is located in arid and semi-arid regions due to its proximity to the equator and its location in the subtropical high pressure zone. In this respect, the Hyrcanian forest is a green necklace between the Caspian Sea and the south of the Alborz mountain range. In the forty-third session of UNESCO, it was registered as the second natural heritage of Iran. Beech is one of the most important tree species and the most industrial species of Hyrcanian forests. In this research, using dendroclimatology, the width of the tree ring, and climatic data of temperature and precipitation from Shanderman meteorological station located in the study area, And non-parametric Mann-Kendall statistical method to investigate the trend of climate change over a time series of 202 years of growth ringsAnd Pearson statistical method was used to correlate the growth of "ring" growth rings of beech trees with climatic variables in the region. The results obtained from the time series of beech growth rings showed that the changes in beech growth rings had a downward and negative trend and were significant at the level of 5% and climate change occurred. The average minimum, medium, and maximum temperatures and evaporation in the growing season had an increasing trend, and the annual precipitation had a decreasing trend. Using Pearson method during fitting the correlation of diameter of growth rings with temperature, for the average in July, August, and September, the correlation is negative, and the average temperature in July, August, and September is negative, and for the average The average maximum temperature in February was correlation-positive and at the level of 95% was significant, and with precipitation, in June the correlation was at the level of 95% positive and significant.

Keywords: climate change, dendroclimatology, hyrcanian forest, beech

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Authors: Kuen-Ming Shu, Jyun-Wei Chen

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Encapsulated O-rings are specifically designed to address the problem of sealing the most hostile chemicals and extreme temperature applications. Ultrasonic vibration hot embossing and ultrasonic welding techniques provide a fast and reliable method to fabricate encapsulated O-ring. This paper performs the design and analysis method of the acoustic horns with double extrusion to process tube double side flange simultaneously. The paper deals with study through Finite Element Method (FEM) of ultrasonic stepped horn used to process a capsulated O-ring, the theoretical dimensions of horns, and their natural frequencies and amplitudes are obtained through the simulations of COMOSOL software. Furthermore, real horns were fabricated, tested and verified to proof the practical utility of these horns.

Keywords: encapsulated O-rings, ultrasonic vibration hot embossing, flange making, acoustic horn, finite element analysis

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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: Sheetla Prasad

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The objective of this study is ‘discovering the real psyche of human beings for prediction of mode, direction and strength of the potential of actions of the individual. The human face was taken as a source of central point to search for the route of real psyche. Analysis of the face architecture (shape and salient features of face) was done by three directional photographs ( 600 left and right and camera facing) of human beings. The shapes and features of the human face were scaled in 177 units on the basis of face–features locations (FFL). The mathematical analysis was done of FFLs by self developed and standardized formula. At this phase, 800 samples were taken from the population of students, teachers, advocates, administrative officers, and common persons. The finding shows that real psyche has two external rings (ER). These ER are itself generator of two independent psyches (manifested and manipulated). Prima-facie, it was proved that micro differences in FFLs have potential to predict the state of art of the human psyche. The potential of psyches was determined by the saving and distribution of mental energy. It was also mathematically proved.

Keywords: face architecture, psyche, potential, face functional ratio, external rings

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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: Yungtai Lo

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Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a continuous right-skewed distribution for positive values. We review methods proposed in the literature for analyzing data with excess zeros. A two-part logit-log-normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.

Keywords: two-part model, semi-continuous variable, truncated normal, gamma regression, skew normal, Pearson residual, receiver operating characteristic curve

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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: Daihui Zhang, Marie J. Dumont

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A derivative of 5-hydroxymethylfurfural (HMF) was synthesized for the thiol-Michael addition reaction. The efficiency of the catalysts (base and nucleophiles) and side reactions during the thiol-Michael addition were investigated. Dimethylphenylphosphine efficiently initiated the thiol-Michael addition polymerization for synthesizing a series of bio-based furan polymers with different structure and properties. The benzene rings or hydroxyl groups present in the polymer chains increased the glass transition temperature (Tg) of poly (β-thioether ester). Additionally, copolymers with various compositions were obtained via adding different ratio of 1,6-hexanedithiols to 1,4-benzenedithiols. 1H NMR analysis revealed that experimental ratios of two dithiols monomers matched well with theoretical ratios. The occurrence of a reversible Diels-Alder reaction between furan rings and maleimide groups allowed poly (β-thioether ester) to be dynamically crosslinked. These polymers offer the potentials to produce materials from biomass that have both practical mechanical properties and reprocessing ability.

Keywords: copolymers, Diels-Alder reaction, hydroxymethylfurfural, Thiol-Michael addition

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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: Jorge Martinez-Garcia, Ingrid Stelzner, Joerg Stelzner, Damian Gwerder, Philipp Schuetz

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Tree-ring analysis is an important part of the quality assessment and the dating of (archaeological) wood samples. It provides quantitative data about the whole anatomical ring structure, which can be used, for example, to measure the impact of the fluctuating environment on the tree growth, for the dendrochronological analysis of archaeological wooden artefacts and to estimate the wood mechanical properties. Despite advances in computer vision and edge recognition algorithms, detection and counting of annual rings are still limited to 2D datasets and performed in most cases manually, which is a time consuming, tedious task and depends strongly on the operator’s experience. This work presents an image processing approach to detect the whole 3D tree-ring structure directly from X-ray computed tomography imaging data. The approach relies on a modified Canny edge detection algorithm, which captures fully connected tree-ring edges throughout the measured image stack and is validated on X-ray computed tomography data taken from six wood species.

Keywords: ring recognition, edge detection, X-ray computed tomography, dendrochronology

Procedia PDF Downloads 180