Search results for: Gram polynomials

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: R. B. Ogunrinde

Abstract:

This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: Differential equations, Numerical, Initial value problem, Polynomials.

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Authors: Reihaneh Ahmadzadeh Ghavidel, Mehdi Ghiafeh Davoodi

Abstract:

The usefulness of weaning foods to meet the nutrient needs of children is well recognized, and most of them are precooked roller dried mixtures of cereal and/or legume flours which posses a high viscosity and bulk when reconstituted. The objective of this study was to formulate composite weaning foods using cereals, malted legumes and vegetable powders and analyze them for nutrients, functional properties and sensory attributes. Selected legumes (green gram and lentil) were germinated, dried and dehulled. Roasted wheat, rice, carrot powder and skim milk powder also were used. All the ingredients were mixed in different proportions to get four formulations, made into 30% slurry and dried in roller drier. The products were analyzed for proximate principles, mineral content, functional and sensory qualities. The results of analysis showed following range of constituents per 100g of formulations on dry weight basis, protein, 18.1-18.9 g ; fat, 0.78-1.36 g ; iron, 5.09-6.53 mg; calcium, 265-310 mg. The lowest water absorption capacity was in case of wheat green gram based and the highest was in rice lentil based sample. Overall sensory qualities of all foods were graded as “good" and “very good" with no significant differences. The results confirm that formulated weaning foods were nutritionally superior, functionally appropriate and organoleptically acceptable.

Keywords: malted legumes, weaning foods, nutrition, functional properties

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Authors: R. Farkh, K. Laabidi, M. Ksouri

Abstract:

In this paper, we consider the control of time delay system by Proportional-Integral (PI) controller. By Using the Hermite- Biehler theorem, which is applicable to quasi-polynomials, we seek a stability region of the controller for first order delay systems. The essence of this work resides in the extension of this approach to second order delay system, in the determination of its stability region and the computation of the PI optimum parameters. We have used the genetic algorithms to lead the complexity of the optimization problem.

Keywords: Genetic algorithm, Hermit-Biehler theorem, optimization, PI controller, second order delay system, stability region.

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

Abstract:

The edges of low contrast images are not clearly distinguishable to 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: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Kouamana Bousson, Paulo Machado

Abstract:

The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the indirect or direct methods. The indirect methods are based on maximum principle of Pontryagin, on the other hand, in the direct methods it is necessary to transform into a nonlinear programming problem. We propose an approach based on direct methods with a pseudospectral integration scheme built on Chebyshev polynomials.

Keywords: Pseudospectral Methods, Trajectory Optimization, 4DTrajectories

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Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Said Laachir, Aziz Laaribi

Abstract:

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.

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Authors: C. S. Saini

Abstract:

The composite flour blend consisting of corn, pearl millet, black gram and wheat bran in the ratio of 80:5:10:5 was taken to prepare the extruded product and their effect on physical properties of extrudate was studied. The extrusion process was conducted in laboratory by using twin screw extruder. The physical characteristics evaluated include lateral expansion, bulk density, water absorption index, water solubility index, and rehydration ratio and moisture retention. The Central Composite Rotatable Design (CCRD) was used to decide the level of processing variables i.e. feed moisture content (%), screw speed (rpm), and barrel temperature (oC) for the experiment. The data obtained after extrusion process were analyzed by using response surface methodology. A second order polynomial model for the dependent variables was established to fit the experimental data. The numerical optimization studies resulted in 127°C of barrel temperature, 246 rpm of screw speed, and 14.5% of feed moisture as optimum variables to produce acceptable extruded product. The responses predicted by the software for the optimum process condition resulted in lateral expansion 126%, bulk density 0.28 g/cm3, water absorption index 4.10 g/g, water solubility index 39.90%, rehydration ratio 544% and moisture retention 11.90% with 75% desirability.

Keywords: Black gram, corn flour, extrusion, physical characteristics.

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Authors: Awais Adnan, Muhammad Ali, Amir Hanif Dar

Abstract:

Image Searching was always a problem specially when these images are not properly managed or these are distributed over different locations. Currently different techniques are used for image search. On one end, more features of the image are captured and stored to get better results. Storing and management of such features is itself a time consuming job. While on the other extreme if fewer features are stored the accuracy rate is not satisfactory. Same image stored with different visual properties can further reduce the rate of accuracy. In this paper we present a new concept of using polynomials of sorted histogram of the image. This approach need less overhead and can cope with the difference in visual features of image.

Keywords: Sorted Histogram, Polynomial Curves, feature pointsof images, Grayscale, visual properties of image.

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Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wavebeam both in elevation and azimuth. In this paper a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: N. M. Kamoh, D. G. Gyemang, M. C. Soomiyol

Abstract:

This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.

Keywords: Collocation shifted Legendre polynomials, Simpson’s rule and Volterra integro-differential equations.

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Authors: M. Naimi, M. B. Khaled

Abstract:

The aim of the present work was to test in vitro inhibition of food pathogens and spoilage bacteria by crude bacteriocins from autochthonous lactic acid bacteria. Thirty autochthonous lactic acid bacteria isolated previously, belonging to the genera: Lactobacillus, Carnobacterium, Lactococcus, Vagococcus, Streptococcus, and Pediococcus, have been screened by an agar spot test and a well diffusion assay against Gram-positive and Gram-negative harmful bacteria: Bacillus cereus, Bacillus subtilis ATCC 6633, Escherichia coli ATCC 8739, Salmonella typhimurium ATCC 14028, Staphylococcus aureus ATCC 6538, and Pseudomonas aeruginosa under conditions means to reduce lactic acid and hydrogen peroxide effect to select bacteria with high bacteriocinogenic potential. Furthermore, crude bacteriocins semiquantification and heat sensitivity to different temperatures (80, 95, 110°C, and 121°C) were performed. Another exploratory test concerning the response of St. aureus ATCC 6538 to the presence of crude bacteriocins was realized. It has been observed by the agar spot test that fifteen candidates were active toward Gram-positive targets strains. The secondary screening demonstrated an antagonistic activity oriented only against St. aureus ATCC 6538, leading to the selection of five isolates: L_m14, L_m21, L_m23, L_m24, and L_m25 with a larger inhibition zone compared to the others. The ANOVA statistical analysis reveals a small variation of repeatability: L_m21: 0.56%, L_m23: 0%, L_m25: 1.67%, L_m14: 1.88%, L_m24: 2.14%. Conversely, slight variation was reported in terms of inhibition diameters: 9.58± 0.40, 9.83± 0.46 and 10.16± 0.24 8.5 ± 0.40 10 mm for, L_m21, L_m23, L_m25, L_m14and L_m24, indicating that the observed potential showed a heterogeneous distribution (BMS = 0.383, WMS = 0.117). The repeatability coefficient calculated displayed 7.35%. As for the bacteriocins semiquantification, the five samples exhibited production amounts about 4.16 for L_m21, L_m23, L_m25 and 2.08 AU/ml for L_m14, L_m24. Concerning the sensitivity the crude bacteriocins were fully insensitive to heat inactivation, until 121°C, they preserved the same inhibition diameter. As to, kinetic of growth , the µmax showed reductions in pathogens load for L_m21, L_m23, L_m25, L_m14, L_m24 of about 42.92%, 84.12%, 88.55%, 54.95%, 29.97% in the second trails. Inversely, this pathogen growth after five hours displayed differences of 79.45%, 12.64%, 11.82%, 87.88%, 85.66% in the second trails, compared to the control. This study showed potential inhibition to the growth of this food pathogen, suggesting the possibility to improve the hygienic food quality.

Keywords: Exploratory test, lactic acid bacteria, crude bacteriocins, spoilage, pathogens.

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Authors: M. A. Koroma, Z. Chuangyi, A. F., Kamara, A. M. H. Conteh

Abstract:

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

Keywords: Modified Laplace decomposition algorithm, Boundary layer equation, Padé approximant, Numerical solution.

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Authors: Alexander Efremov

Abstract:

A system for market identification (SMI) is presented. The resulting representations are multivariable dynamic demand models. The market specifics are analyzed. Appropriate models and identification techniques are chosen. Multivariate static and dynamic models are used to represent the market behavior. The steps of the first stage of SMI, named data preprocessing, are mentioned. Next, the second stage, which is the model estimation, is considered in more details. Stepwise linear regression (SWR) is used to determine the significant cross-effects and the orders of the model polynomials. The estimates of the model parameters are obtained by a numerically stable estimator. Real market data is used to analyze SMI performance. The main conclusion is related to the applicability of multivariate dynamic models for representation of market systems.

Keywords: market identification, dynamic models, stepwise regression.

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Authors: Radhika Jain, Sangeeta Goomer

Abstract:

In the present study an attempt has been made to re-engineer traditional wadi into wholesome ready-to-use cereal-pulse-based chunks rich in protein quality and fibre content. Chunks were made using extrusion-dehydration combination. Two formulations i.e., whole green gram dhal with instant oats and washed green gram dhal with whole oats were formulated. These chunks are versatile in nature as they can be easily incorporated in day-to-day home-made preparations such as pulao, potato curry and kadhi. Cereal-pulse ratio was calculated using NDpCal%. Limiting amino acids such as lysine, tryptophan, methionine, cysteine and threonine were calculated for maximum amino acid profile in cereal-pulse combination. Time-temperature combination for extrusion at 130^oC and dehydration at 65^oC for 7 hours and 15 minutes were standardized to obtain maximum protein and fibre content. Proximate analysis such as moisture, fat and ash content were analyzed. Protein content of formulation was 62.10% and 68.50% respectively. Fibre content of formulations was 2.99% and 2.45%, respectively. Using a 5-point hedonic scale, consumer preference trials of 102 consumers were conducted and analyzed. Evaluation of chunks prepared in potato curry, kadi and pulao showed preferences for colour 82%, 87%, 86%, texture and consistency 80%, 81%, 88%, flavour and aroma 74%, 82%, 86%, after taste 70%, 75%, 86% and overall acceptability 77%, 75%, 88% respectively. High temperature inactivates antinutritional compounds such as trypsin inhibitors, lectins, saponins etc. Hence, availability of protein content was increased. Developed products were palatable and easy to prepare.

Keywords: Extrusion, NDpCal%, protein quality, wadi.

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear control design for nonlinear systems by using two-stage formal linearization and twotype LQ controls. The ordinary LQ control is designed on almost linear region around the steady state point. On the other region, another control is derived as follows. This derivation is based on coordinate transformation twice with respect to linearization functions which are defined by polynomials. The linearized systems can be made up by using Taylor expansion considered up to the higher order. To the resulting formal linear system, the LQ control theory is applied to obtain another LQ control. Finally these two-type LQ controls are smoothly united to form a single nonlinear control. Numerical experiments indicate that this control show remarkable performances for a nonlinear system.

Keywords: Formal Linearization, LQ Control, Nonlinear Control, Taylor Expansion, Zero Function.

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Authors: Abdullah A. AlShaher

Abstract:

In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2^nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.

Keywords: Shape recognition, Arabic handwritten characters, regression curves, expectation maximization algorithm.

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Authors: Panos D. Kotsas, Tony Dodd

Abstract:

The purpose of this work is to present a method for rigid registration of medical images using 1D binary projections when a part of one of the two images is missing. We use 1D binary projections and we adjust the projection limits according to the reduced image in order to perform accurate registration. We use the variance of the weighted ratio as a registration function which we have shown is able to register 2D and 3D images more accurately and robustly than mutual information methods. The function is computed explicitly for n=5 Chebyshev points in a [-9,+9] interval and it is approximated using Chebyshev polynomials for all other points. The images used are MR scans of the head. We find that the method is able to register the two images with average accuracy 0.3degrees for rotations and 0.2 pixels for translations for a y dimension of 156 with initial dimension 256. For y dimension 128/256 the accuracy decreases to 0.7 degrees for rotations and 0.6 pixels for translations.

Keywords: binary projections, image registration, reduceddimension images.

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Authors: Mohamed Othmani, Yassine Khlifi

Abstract:

This paper presents a technique for compact three dimensional (3D) object model reconstruction using wavelet networks. It consists to transform an input surface vertices into signals,and uses wavelet network parameters for signal approximations. To prove this, we use a wavelet network architecture founded on several mother wavelet families. POLYnomials WindOwed with Gaussians (POLYWOG) wavelet families are used to maximize the probability to select the best wavelets which ensure the good generalization of the network. To achieve a better reconstruction, the network is trained several iterations to optimize the wavelet network parameters until the error criterion is small enough. Experimental results will shown that our proposed technique can effectively reconstruct an irregular 3D object models when using the optimized wavelet network parameters. We will prove that an accurateness reconstruction depends on the best choice of the mother wavelets.

Keywords: 3D object, optimization, parametrization, Polywog wavelets, reconstruction, wavelet networks.

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Authors: E. Srinivasan, D. Ebenezer

Abstract:

Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.

Keywords: Image filtering, detail preservation, median filters, nonlinear filters, order statistics filtering, Rank order filtering.

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

Abstract:

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: Suttijit Sriwatcharakul

Abstract:

The bioactivity studies from the weed ethanolic crude extracts from leaf, stem, pod and root of wild spider flower; Cleoma viscosa Linn. were analyzed for the growth inhibition of 6 bacterial species; Salmonella typhimurium TISTR 5562, Pseudomonas aeruginosa ATCC 27853, Staphylococcus aureus TISTR 1466, Streptococcus epidermidis ATCC 1228, Escherichia coli DMST 4212 and Bacillus subtilis ATCC 6633 with initial concentration crude extract of 50 mg/ml. The agar well diffusion results found that the extracts inhibit only gram positive bacteria species; S. aureus, S. epidermidis and B. subtilis. The minimum inhibition concentration study with gram positive strains revealed that leaf crude extract give the best result of the lowest concentration compared with other plant parts to inhibit the growth of S. aureus, S. epidermidis and B. subtilis at 0.78, 0.39 and lower than 0.39 mg/ml, respectively. The determination of total phenolic compounds in the crude extracts exhibited the highest phenolic content was 10.41 mg GAE/g dry weight in leaf crude extract. Analyzed the efficacy of free radical scavenging by using DPPH radical scavenging assay with all crude extracts showed value of IC50 of leaf, stem, pod and root crude extracts were 8.32, 12.26, 21.62 and 35.99 mg/ml, respectively. Studied cytotoxicity of crude extracts on human breast adenocarcinoma cell line by MTT assay found that pod extract had the most cytotoxicity CC50 value, 32.41 µg/ml. Antioxidant activity and cytotoxicity of crude extracts exhibited that the more increase of extract concentration, the more activities indicated. According to the bioactivities results, the leaf crude extract of Cleoma viscosa Linn. is the most interesting plant part for further work to search the beneficial of this weed.

Keywords: Antimicrobial, antioxidant activity, Cleoma viscosa Linn., cytotoxicity test, total phenolic compound.

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Authors: Sudipta Majumdar

Abstract:

This paper presents a method for identification of a linear time invariant (LTI) autonomous all pole system using singular value decomposition. The novelty of this paper is two fold: First, MUSIC algorithm for estimating complex frequencies from real measurements is proposed. Secondly, using the proposed algorithm, we can identify the coefficients of differential equation that determines the LTI system by switching off our input signal. For this purpose, we need only to switch off the input, apply our complex MUSIC algorithm and determine the coefficients as symmetric polynomials in the complex frequencies. This method can be applied to unstable system and has higher resolution as compared to time series solution when, noisy data are used. The classical performance bound, Cramer Rao bound (CRB), has been used as a basis for performance comparison of the proposed method for multiple poles estimation in noisy exponential signal.

Keywords: MUSIC algorithm, Cramer Rao bound, frequency estimation.

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Authors: Santosh Kumar, Anand Prakash, Kanak Sinha, Anita K Verma

Abstract:

Vernonia divergens Benth., commonly known as “Insulin Plant” (Fam: Asteraceae) is a potent sugar killer. Locally the leaves of the plant, boiled in water are successfully administered to a large number of diabetic patients. The present study evaluates the putative anti-diabetic ingredients, isolated from the in vivo and in vitro grown plantlets of V. divergens for their antimicrobial and anticancer activities. Sterilized explants of nodal segments were cultured on MS (Musashige and Skoog, 1962) medium in presence of different combinations of hormones. Multiple shoots along with bunch of roots were regenerated at 1mg l-1 BAP and 0.5 mg l-1 NAA. Micro-plantlets were separated and sub-cultured on the double strength (2X) of the above combination of hormones leading to increased length of roots and shoots. These plantlets were successfully transferred to soil and survived well in nature. The ethanol extract of plantlets from both in vivo & in vitro sources were prepared in soxhlet extractor and then concentrated to dryness under reduced pressure in rotary evaporator. Thus obtainedconcentrated extracts showed significant inhibitory activity against gram negative bacteria like Escherichia coli and Pseudomonas aeruginosa but no inhibition was found against gram positive bacteria. Further, these ethanol extracts were screened for in vitro percentage cytotoxicity at different time periods (24 h, 48 h and 72 h) of different dilutions. The in vivo plant extract inhibited the growth of EAC mouse cell lines in the range of 65, 66, 78, and 88% at 100, 50, 25 & 12.5μg mL-1 but at 72 h of treatment. In case of the extract of in vitro origin, the inhibition was found against EAC cell lines even at 48h. During spectrophotometric scanning, the extracts exhibited different maxima (ʎ) - four peaks in in vitro extracts as against single in in vivo preparation suggesting the possible change in the nature of ingredients during micropropagation through tissue culture techniques.

Keywords: Anti-cancer, Anti-microbial, EAC mouse cell, Tissue culture, Vernonia divergens.

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Authors: Prakash G L, Thejaswini M, S H Manjula, K R Venugopal, L M Patnaik

Abstract:

Wireless sensor network can be applied to both abominable and military environments. A primary goal in the design of wireless sensor networks is lifetime maximization, constrained by the energy capacity of batteries. One well-known method to reduce energy consumption in such networks is data aggregation. Providing efcient data aggregation while preserving data privacy is a challenging problem in wireless sensor networks research. In this paper, we present privacy-preserving data aggregation scheme for additive aggregation functions. The Cluster-based Private Data Aggregation (CPDA)leverages clustering protocol and algebraic properties of polynomials. It has the advantage of incurring less communication overhead. The goal of our work is to bridge the gap between collaborative data collection by wireless sensor networks and data privacy. We present simulation results of our schemes and compare their performance to a typical data aggregation scheme TAG, where no data privacy protection is provided. Results show the efficacy and efficiency of our schemes.

Keywords: Aggregation, Clustering, Query Processing.

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Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.

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Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

Abstract:

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: Cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol.

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Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

The problem of N cracks interaction in an isotropic elastic solid is decomposed into a subproblem of a homogeneous solid without crack and N subproblems with each having a single crack subjected to unknown tractions on the two crack faces. The unknown tractions, namely pseudo tractions on each crack are expanded into polynomials with unknown coefficients, which have to be determined by the consistency condition, i.e. by the equivalence of the original multiple cracks interaction problem and the superposition of the N+1 subproblems. In this paper, Kachanov-s approach of average tractions is extended into the method of moments to approximately impose the consistence condition. Hence Kachanov-s method can be viewed as the zero-order method of moments. Numerical results of the stress intensity factors are presented for interactions of two collinear cracks, three collinear cracks, two parallel cracks, and three parallel cracks. As the order of moment increases, the accuracy of the method of moments improves.

Keywords: Crack interaction, stress intensity factor, multiplecracks, method of moments.

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