Search results for: Polynomial roots

Authors: Ruigang Zhang, Wuyungaowa, Xingchen Ma

Abstract:

In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

Keywords: Generating functions, operators sequence group, Riordan arrays, R. G operator group, combinatorial identities.

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Authors: J. Linjikao, P. Inthima, A. Kongbangkerd

Abstract:

In vitro conservation of orchid germplasm provides an effective technique for ex situ conservation of orchid diversity. In this study, an efficient protocol for in vitro conservation of Vandopsis lissochiloides (Gaudich.) Pfitz. plantlet under slow growth conditions was investigated. Plantlets were cultured on different strength of Vacin and Went medium (½VW and ¼VW) supplemented with different concentrations of mannitol (0, 2, 4, 6 and 8%), sucrose (0 and 3%) and 50 g/L potato extract, 150 mL/L coconut water. The cultures were incubated at 25±2 °C and maintained under 20 µmol/m²s light intensity for 24 weeks without subculture. At the end of preservation period, the plantlets were subcultured to fresh medium for growth recovery. The results found that the highest leaf number per plantlet could be observed on ¼VW medium without adding sucrose and mannitol while the highest root number per plantlet was found on ½VW added with 3% sucrose without adding mannitol after 24 weeks of in vitro storage. The results showed that the maximum number of leaves (5.8 leaves) and roots (5.0 roots) of preserved plantlets were produced on ¼VW medium without adding sucrose and mannitol. Therefore, ¼VW medium without adding sucrose and mannitol was the best minimum growth conditions for medium-term storage of V. lissochiloides plantlets.

Keywords: Preservation, Vandopsis, germplasm, in vitro.

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Authors: G. Khatisashvili, M. Gordeziani, G. Adamia, E. Kvesitadze, T. Sadunishvili, G. Kvesitadze

Abstract:

The ability of agricultural and decorative plants to absorb and detoxify TNT and RDX has been studied. All tested 8 plants, grown hydroponically, were able to absorb these explosives from water solutions: Alfalfa > Soybean > Chickpea> Chikling vetch >Ryegrass > Mung bean> China bean > Maize. Differently from TNT, RDX did not exhibit negative influence on seed germination and plant growth. Moreover, some plants, exposed to RDX containing solution were increased in their biomass by 20%. Study of the fate of absorbed [1-14ðí]-TNT revealed the label distribution in low and high-molecular mass compounds, both in roots and above ground parts of plants, prevailing in the later. Content of 14ðí in lowmolecular compounds in plant roots are much higher than in above ground parts. On the contrary, high-molecular compounds are more intensively labeled in aboveground parts of soybean. Most part (up to 70%) of metabolites of TNT, formed either by enzymatic reduction or oxidation, is found in high molecular insoluble conjugates. Activation of enzymes, responsible for reduction, oxidation and conjugation of TNT, such as nitroreductase, peroxidase, phenoloxidase and glutathione S-transferase has been demonstrated. Among these enzymes, only nitroreductase was shown to be induced in alfalfa, exposed to RDX. The increase in malate dehydrogenase activities in plants, exposed to both explosives, indicates intensification of Tricarboxylic Acid Cycle, that generates reduced equivalents of NAD(P)H, necessary for functioning of the nitroreductase. The hypothetic scheme of TNT metabolism in plants is proposed.

Keywords: Higher plants, TNT, RDX, transformation.

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Authors: Y. Z. Wu, Z. Dong, S. K. You

Abstract:

Global approximation using metamodel for complex mathematical function or computer model over a large variable domain is often needed in sensibility analysis, computer simulation, optimal control, and global design optimization of complex, multiphysics systems. To overcome the limitations of the existing response surface (RS), surrogate or metamodel modeling methods for complex models over large variable domain, a new adaptive and regressive RS modeling method using quadratic functions and local area model improvement schemes is introduced. The method applies an iterative and Latin hypercube sampling based RS update process, divides the entire domain of design variables into multiple cells, identifies rougher cells with large modeling error, and further divides these cells along the roughest dimension direction. A small number of additional sampling points from the original, expensive model are added over the small and isolated rough cells to improve the RS model locally until the model accuracy criteria are satisfied. The method then combines local RS cells to regenerate the global RS model with satisfactory accuracy. An effective RS cells sorting algorithm is also introduced to improve the efficiency of model evaluation. Benchmark tests are presented and use of the new metamodeling method to replace complex hybrid electrical vehicle powertrain performance model in vehicle design optimization and optimal control are discussed.

Keywords: Global approximation, polynomial response surface, domain decomposition, domain combination, multiphysics modeling, hybrid powertrain optimization

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Authors: Abbas Hani, Seyed Ali Hoseini Abari

Abstract:

Soil chemical and physical properties have important roles in compartment of the environment and agricultural sustainability and human health. The objectives of this research is determination of spatial distribution patterns of Cd, Zn, K, pH, TNV, organic material and electrical conductivity (EC) in agricultural soils of Natanz region in Esfehan province. In this study geostatistic and non-geostatistic methods were used for prediction of spatial distribution of these parameters. 64 composite soils samples were taken at 0-20 cm depth. The study area is located in south of NATANZ agricultural lands with area of 21660 hectares. Spatial distribution of Cd, Zn, K, pH, TNV, organic material and electrical conductivity (EC) was determined using geostatistic and geographic information system. Results showed that Cd, pH, TNV and K data has normal distribution and Zn, OC and EC data had not normal distribution. Kriging, Inverse Distance Weighting (IDW), Local Polynomial Interpolation (LPI) and Redial Basis functions (RBF) methods were used to interpolation. Trend analysis showed that organic carbon in north-south and east to west did not have trend while K and TNV had second degree trend. We used some error measurements include, mean absolute error(MAE), mean squared error (MSE) and mean biased error(MBE). Ordinary kriging(exponential model), LPI(Local polynomial interpolation), RBF(radial basis functions) and IDW methods have been chosen as the best methods to interpolating of the soil parameters. Prediction maps by disjunctive kriging was shown that in whole study area was intensive shortage of organic matter and more than 63.4 percent of study area had shortage of K amount.

Keywords: Electrical conductivity, Geostatistics, Geographical Information System, TNV

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Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan

Abstract:

In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.

Keywords: Diophantine equation, Pell equation, quadratic form.

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Authors: Hussain Al-Qassem

Abstract:

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain Lp boundedness for these oscillatory integrals under rather weak size conditions on the kernel function.

Keywords: Fourier transform, oscillatory integrals, Orlicz spaces, Block spaces, Extrapolation, Lp boundedness.

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Authors: M.H. Ahmad Fadzil, Esa Prakasa, Hurriyatul Fitriyah, Hermawan Nugroho, Azura Mohd Affandi, S.H. Hussein

Abstract:

Psoriasis is a widespread skin disease affecting up to 2% population with plaque psoriasis accounting to about 80%. It can be identified as a red lesion and for the higher severity the lesion is usually covered with rough scale. Psoriasis Area Severity Index (PASI) scoring is the gold standard method for measuring psoriasis severity. Scaliness is one of PASI parameter that needs to be quantified in PASI scoring. Surface roughness of lesion can be used as a scaliness feature, since existing scale on lesion surface makes the lesion rougher. The dermatologist usually assesses the severity through their tactile sense, therefore direct contact between doctor and patient is required. The problem is the doctor may not assess the lesion objectively. In this paper, a digital image analysis technique is developed to objectively determine the scaliness of the psoriasis lesion and provide the PASI scaliness score. Psoriasis lesion is modelled by a rough surface. The rough surface is created by superimposing a smooth average (curve) surface with a triangular waveform. For roughness determination, a polynomial surface fitting is used to estimate average surface followed by a subtraction between rough and average surface to give elevation surface (surface deviations). Roughness index is calculated by using average roughness equation to the height map matrix. The roughness algorithm has been tested to 444 lesion models. From roughness validation result, only 6 models can not be accepted (percentage error is greater than 10%). These errors occur due the scanned image quality. Roughness algorithm is validated for roughness measurement on abrasive papers at flat surface. The Pearson-s correlation coefficient of grade value (G) of abrasive paper and Ra is -0.9488, its shows there is a strong relation between G and Ra. The algorithm needs to be improved by surface filtering, especially to overcome a problem with noisy data.

Keywords: psoriasis, roughness algorithm, polynomial surfacefitting.

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Authors: A. Pashayev, C. Ardil, R. Sadiqov

Abstract:

Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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Authors: Mohamed K. El Daou

Abstract:

We construct an exponentially weighted Legendre- Gauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to Sturm-Liouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented.

Keywords: Oscillatory functions, Sturm-Liouville problems, legendre polynomial, gauss points.

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Authors: Daniel Stamate

Abstract:

We introduce a logic-based framework for database updating under constraints. In our framework, the constraints are represented as an instantiated extended logic program. When performing an update, database consistency may be violated. We provide an approach of maintaining database consistency, and study the conditions under which the maintenance process is deterministic. We show that the complexity of the computations and decision problems presented in our framework is in each case polynomial time.

Keywords: Databases, knowledge bases, constraints, updates, minimal change, consistency.

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Authors: S. Demiray, M. E. Pintado, P. M. L. Castro

Abstract:

There is a growing interest in the food industry and in preventive health care for the development and evaluation of natural antioxidants from medicinal plant materials. In the present work, extracts of three medicinal plants (Tilia argentea, Crataegi folium leaves and Polygonum bistorta roots) used in Turkish phytotheraphy were screened for their phenolic profiles and antioxidant properties. Crude extracts were obtained from different parts of plants, by solidliquid extraction with pure water, 70% acetone and 70% methanol aqueous solvents. The antioxidant activity of the extracts was determined by ABTS.+ radical cation scavenging activity. The Folin Ciocalteu procedure was used to assess the total phenolic concentrations of the extracts as gallic acid equivalents. A modified liquid chromatography-electro spray ionization-mass spectrometry (LC-ESI-MS) was used to obtain chromatographic profiles of the phenolic compounds in the medicinal plants. The predominant phenolic compounds detected in different extracts of the plants were catechin, protocatechuic and chlorogenic acids. The highest phenolic contents were obtained by using 70% acetone as aqueous solvent, whereas the lowest phenolic contents were obtained by water extraction due to Folin Ciocalteu results. The results indicate that acetone extracts of Tilia argentea had the highest antioxidant capacity as free ABTS radical scavengers. The lowest phenolic contents and antioxidant capacities were obtained from Polygonum bistorta root extracts.

Keywords: Medicinal plants, antioxidant activity, totalphenolics, LC-ESI-MS.

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Authors: T. Punjansing, M. Nakkuntod, S. Homchan, P. Inthima, A. Kongbangkerd

Abstract:

The influence of organic supplements on growth and multiplication efficiency of Phaius tankervilleae var. alba seedlings was investigated. 12 week-old seedlings were cultured on half-strength semi-solid Murashige and Skoog (MS) medium supplemented with 30 g/L sucrose, 8 g/L agar and various concentrations of coconut water (0, 50, 100, 150 and 200 mL/L) combined with potato extract (0, 25 and 50 g/L) and the pH was adjusted to 5.8 prior to autoclaving. The cultures were then kept under constant photoperiod (16 h light: 8 h dark) at 25 ± 2 °C for 12 weeks. The highest number of shoots (3.0 shoots/explant) was obtained when cultured on the medium added with 50 ml/L coconut water and 50 g/L potato extract whereas the highest number of leaves (5.9 leaves/explant) and roots (6.1 roots/explant) could receive on the medium supplemented with 150 ml/L coconut water and 50 g/L potato extract. with 150 ml/L coconut water and 50 g/L potato extract. Additionally, plantlets of P. tankervilleae var. alba were transferred to grow into seven different substrates i.e. soil, sand, coconut husk chip, soil-sand mix (1: 1), soil-coconut husk chip mix (1: 1), sand-coconut husk chip mix (1: 1) and soil-sand-coconut husk chip mix (1: 1: 1) for four weeks. The results found that acclimatized plants showed 100% of survivals when sand, coconut husk chip and sand-coconut husk chip mix are used as substrates. The number of leaves induced by sand-coconut husk chip mix was significantly higher than that planted in other substrates (P > 0.05). Meanwhile, no significant difference in new shoot formation among these substrates was observed (P < 0.05). This precursory developing protocol was likely to be applied for more large scale of plant production as well as conservation of germplasm of this orchid species.

Keywords: Acclimatization, coconut water, orchid, Phaius tankervilleae var. alba., potato extract.

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Authors: Violina R. Angelova

Abstract:

Comparative research has been conducted to allow us to determine the content of macro and microelements in the vegetative and reproductive organs of grass pea and the quality of grass pea seeds, as well as to identify the possibility of grass pea growth on soils contaminated by heavy metals. The experiment was conducted on an agricultural field subjected to contamination from the Non-Ferrous-Metal Works (MFMW) near Plovdiv, Bulgaria. The experimental plots were situated at different distances of 0.5 km and 8 km, respectively, from the source of pollution. On reaching commercial ripeness the grass pea plants were gathered. The composition of the macro and microelements in plant materials (roots, stems, leaves, seeds), and the dry matter content, sugars, proteins, fats and ash contained in the grass pea seeds were determined. Translocation factors (TF) and bioaccumulation factor (BCF) were also determined. The quantitative measurements were carried out through inductively-coupled plasma (ICP). The grass pea plant can successfully be grown on soils contaminated by heavy metals. Soil pollution with heavy metals does not affect the quality of the grass pea seeds. The seeds of the grass pea contain significant amounts of nutrients (K, P, Cu, Fe Mn, Zn) and protein (23.18-29.54%). The distribution of heavy metals in the organs of the grass pea has a selective character, which reduces in the following order: leaves > roots > stems > seeds. BCF and TF values were greater than one suggesting efficient accumulation in the above ground parts of grass pea plant. Grass pea is a plant that is tolerant to heavy metals and can be referred to the accumulator plants. The results provide valuable information about the chemical and nutritional composition of the seeds of the grass pea grown on contaminated soils in Bulgaria. The high content of macro and microelements and the low concentrations of toxic elements in the grass pea grown in contaminated soil make it possible to use the seeds of the grass pea as animal feed.

Keywords: Grass pea, heavy metals, micro and macroelements, polluted soils, quality.

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Authors: Nkem Angela Udeani

Abstract:

Despite the wide spread use of synthetic dyes, natural dyes are still exploited and used to enhance its inherent aesthetic qualities as a major material for beautification of the body. Centuries before the discovery of synthetic dyes, natural dyes were the only source of dye open to mankind. Dyes are extracted from plant - leaves, roots and barks, insect secretions, and minerals. However, research findings have made it clear that of all, plants- leaves, roots, barks or flowers are the most explored and exploited in which henna (Lawsonia innermis L.) is one of those plants. Experiment has also shown that henna is used in body painting in conjunction with an alkaline (Ammonium Sulphate) as a fixing agent. This of course gives a clue that if colour derived from henna is properly investigated, it may not only be used for body decoration but possibly, may have affinity to fiber substrate. This paper investigates the dyeing potentials – dye ability and fastness qualities of henna dye extracts on cotton and linen fibers using mordants like ammonium sulphate and other alkalis (hydrosulphate and caustic soda, potash, common salt, potassium alum). Hot and cold water and ethanol solvent were used in the extraction of the dye to investigate the most effective method, dye ability, and fastness qualities of these extracts under room temperature. The results of the experiment show that cotton have a high rate of dye intake than other fiber. On a similar note, the colours obtained depend most on the solvent used. In conclusion, hot water extraction appears more effective. While the colours obtained from ethanol and both cold hot methods of extraction range from light to dark yellow, light green to army green and to some extent shades of brown hues.

Keywords: Dye, fabrics, henna leaves, potential.

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Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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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: José Maria A. Pangilinan, Gerrit K. Janssens

Abstract:

This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution. The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions. Results show that the evolutionary algorithm can find diverse solutions to the MSPP in polynomial time (based on several network instances) and can be an alternative when other methods are trapped by the tractability problem.

Keywords: Multiobjective evolutionary optimization, geneticalgorithms, shortest paths.

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Authors: Daniel Stamate

Abstract:

The paper presents an approach for handling uncertain information in deductive databases using multivalued logics. Uncertainty means that database facts may be assigned logical values other than the conventional ones - true and false. The logical values represent various degrees of truth, which may be combined and propagated by applying the database rules. A corresponding multivalued database semantics is defined. We show that it extends successful conventional semantics as the well-founded semantics, and has a polynomial time data complexity.

Keywords: Reasoning under uncertainty, multivalued logics, deductive databases, logic programs, multivalued semantics.

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Authors: Rajneesh Rani, Renu Dhir, G. S. Lehal

Abstract:

Script identification is one of the challenging steps in the development of optical character recognition system for bilingual or multilingual documents. In this paper an attempt is made for identification of English numerals at word level from Punjabi documents by using Gabor features. The support vector machine (SVM) classifier with five fold cross validation is used to classify the word images. The results obtained are quite encouraging. Average accuracy with RBF kernel, Polynomial and Linear Kernel functions comes out to be greater than 99%.

Keywords: Script identification, gabor features, support vector machines.

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Authors: Nilima Gajbhiye

Abstract:

The acid rain causes change in pH level of soil it is directly influence on root and leaf growth. Yield of the crop was reduced if acidity of soil is more. Acid rain seeps into the earth and poisons plants and trees by dissolving toxic substances in the soil, such as aluminum, which get absorbed by the roots. In present investigation, effect of acid rain on crop Vigna radiata was studied. The effect of acid rain on change in soil fertility was detected in which pH of control sample was 6.5 and pH of 1% H2SO4 and 1% HNO3 were 3.5. Nitrogen nitrate in soil was high in 1% HNO3 treated soil & Control sample. Ammonium nitrogen in soil was low in 1% HNO3 & H2SO4 treated soil. Ammonium nitrogen was medium in control and other samples. The effect of acid rain on seed germination on 3rd day of germination control sample growth was 6.1cm with plumule 0.001% HNO3 & 0.001% H2SO4 was 5.5cm with plumule and 8cm with plumule. On 10th day fungal growth was observed in 1% and 0.1% H2SO4 concentrations when all plants were dead. The effect of acid rain on crop productivity was investigated on 3rd day roots were developed in plants. On 12th day Vigna radiata showed more growth in 0.1% HNO3 and 0.1% H2SO4 treated plants as compare to control plants. On 20th day development of discoloration of plant pigments were observed on acid treated plants leaves. On 34th day Vigna radiata showed flower in 0.1% HNO3, 0.01% HNO3 and 0.01% H2SO4treated plants and no flowers were observed on control plants. On 42th day 0.1% HNO3, 0.01% HNO and 0.01% H2SO4 treated Vigna radiata variety and control plants were showed seeds on plants. In Vigna radiate variety 0.1%, 0.01% HNO3, 0.01% H2SO4treated plants were dead on 46th day and fungal growth was observed. The toxicological study was carried out on Vigna radiata plants exposed to 1% HNO3 cells were damaged more than 1% H2SO4. Leaf sections exposed to 0.001% HNO3 & H2SO4 showed less damaged of cells and pigmentation observed in entire slide when compare with control plant.

Keywords: Acid rain, pH, Vigna radiate, HNO3 & H2SO4.

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Authors: Hassan E. A. Ibrahim, Mohamed F. Serag

Abstract:

In this paper, Novel method, Particle Swarm Optimization (PSO) algorithm, based technique is proposed to estimate and analyze the steady state performance of self-excited induction generator (SEIG). In this novel method the tedious job of deriving the complex coefficients of a polynomial equation and solving it, as in previous methods, is not required. By comparing the simulation results obtained by the proposed method with those obtained by the well known mathematical methods, a good agreement between these results is obtained. The comparison validates the effectiveness of the proposed technique.

Keywords: Evolution theory, MATLAB, optimization, PSO, SEIG.

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Authors: Martin Bader

Abstract:

During the last years, the genomes of more and more species have been sequenced, providing data for phylogenetic recon- struction based on genome rearrangement measures. A main task in all phylogenetic reconstruction algorithms is to solve the median of three problem. Although this problem is NP-hard even for the sim- plest distance measures, there are exact algorithms for the breakpoint median and the reversal median that are fast enough for practical use. In this paper, this approach is extended to the transposition median as well as to the weighted reversal and transposition median. Although there is no exact polynomial algorithm known even for the pairwise distances, we will show that it is in most cases possible to solve these problems exactly within reasonable time by using a branch and bound algorithm.

Keywords: Comparative genomics, genome rearrangements, me-dian, reversals, transpositions.

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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: Young Hee Geum

Abstract:

We propose the numerical method defined by

xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N,

and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: Asymptotic error constant, iterative method , multiple root, root-finding.

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Authors: Panos Kotsas

Abstract:

This paper presents the application of a signal intensity independent registration criterion for non-rigid body registration of medical images. The criterion is defined as the weighted ratio image of two images. The ratio is computed on a voxel per voxel basis and weighting is performed by setting the ratios between signal and background voxels to a standard high value. The mean squared value of the weighted ratio is computed over the union of the signal areas of the two images and it is minimized using the Chebyshev polynomial approximation. The geometric transformation model adopted is a local cubic B-splines based model.

Keywords: Medical image, non-rigid, registration.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented. The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm implementation for the control of a seven link (7 degrees of freedom, 7DOF) manipulator are given.

Keywords: Manipulator, trajectory planning, unknown obstacles

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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Authors: Larissa Roots

Abstract:

Vibrations of circular cylindrical shells made of layered composite materials are considered. The shells are weakened by circumferential cracks. The influence of circumferential cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility coupled with the coefficient of the stress intensity known in the linear elastic fracture mechanics. Numerical results are presented for the case of the shell with one circular crack.

Keywords: Layered shell, axisymmetric vibration, crack.

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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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