Search results for: Regional Screening Method (RSM)

Authors: Taiwo O. Margaret, Olaoluwa O. Olaoluwa

Abstract:

Moraceae family has immense phytochemical constituents and significant pharmacological properties, hence have great medicinal values. The aim of this study was to screen and quantify phytochemicals as well as the antioxidant activities of the leaf and stem bark extracts and fractions (crude ethanol extracts, n-hexane, ethyl acetate and aqueous ethanol fractions) of Ficus sagittifolia. Leaf and stem bark of F. sagittifolia were extracted by maceration method using ethanol to give ethanol crude extract. The ethanol crude extract was partitioned by n-hexane and ethyl-acetate to give their respective fractions. All the extracts were screened for their phytochemicals using standard methods. The total phenolic, flavonoid, tannin, saponin contents and antioxidant activity were determined by spectrophotometric method while the alkaloid content was evaluated by titrimetric method. The amount of total phenolic in extracts and fractions were estimated in comparison to gallic acid, whereas total flavonoids, tannins and saponins were estimated corresponding to quercetin, tannic acid and saponin respectively. 2, 2-diphenylpicryl hydrazyl radical (DPPH)* and phosphomolybdate methods were used to evaluate the antioxidant activities of leaf and stem bark of F. sagittifolia. Phytochemical screening revealed the presence of flavonoids, saponins, terpenoids/steroids, alkaloids for both extracts of leaf and stem bark of F. sagittifolia. The phenolic content of F. sagittifolia was most abundant in leaf ethanol crude extract as 3.53 ± 0.03 mg/g equivalent of gallic acid. Total flavonoids and tannins content were highest in stem bark aqueous ethanol fraction of F. sagittifolia estimated as 3.41 ± 0.08 mg/g equivalent of quercetin and 1.52 ± 0.05 mg/g equivalent of tannic acid respectively. The hexane leaf fraction of F. sagittifolia had the utmost saponin and alkaloid content as 5.10 ± 0.48 mg/g equivalent of saponins and 0.171 ± 0.39 g of alkaloids. Leaf aqueous ethanol fraction of F. sagittifolia showed high antioxidant activity (IC₅₀ value of 63.092 µg/mL) and stem ethanol crude extract (227.43 ± 0.78 mg/g equivalent of ascorbic acid) for DPPH and phosphomolybdate method respectively and the least active was found to be the stem hexane fraction using both methods (313.32 µg/mL; 16.21 ± 1.30 mg/g equivalent of ascorbic acid). The presence of these phytochemicals in the leaf and stem bark of F. sagittifolia are responsible for their therapeutic importance as well as the ability to scavenge free radicals in living systems.

Keywords: Antioxidant activity, Ficus sagittifolia, Moraceae, phytochemicals.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: Shigeaki Sakurai, Youichi Kitahata, Ryohei Orihara

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This paper proposes a method that discovers sequential patterns corresponding to user-s interests from sequential data. This method expresses the interests as constraint patterns. The constraint patterns can define relationships among attributes of the items composing the data. The method recursively decomposes the constraint patterns into constraint subpatterns. The method evaluates the constraint subpatterns in order to efficiently discover sequential patterns satisfying the constraint patterns. Also, this paper applies the method to the sequential data composed of stock price indexes and verifies its effectiveness through comparing it with a method without using the constraint patterns.

Keywords: Sequential pattern mining, Constraint pattern, Attribute constraint, Stock price indexes

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Authors: T. Matsubayashi, T. Yamada

Abstract:

In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.

Keywords: visualization, graph drawing, Internet Map

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Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

Abstract:

Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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Authors: Mohsen Keyvanfard

Abstract:

A new, simple and highly sensitive kinetic spectrophotometric method was developed for the determination of trace amounts of Ru(III) in the range of 0.06-20 ng/ml .The method is based on the inhibitory effect of ruthenium(III) on the oxidation of Rhodamine B by bromate in acidic and micellar medium. The reaction was monitored spectrophotometrically by measuring the decreasing in absorbance of Rhodamine B at 554 nm with a fixedtime method..The limit of detection is 0.04 ng/ml Ru(III).The relative standard deviation of 5 and 10 ng/ml Ru(III) was 2.3 and 2.7 %, respectively. The method was applied to the determination of ruthenium in real water samples

Keywords: Ruthenium ;Inhibitory; Rhodamine B; bromate

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: Exponential smoothing method, open data, operation estimation, train schedule.

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Authors: J. A. Michline Rupa, S. Ganesh

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This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

Keywords: Backward/Forward sweep method, Distribution system, Load flow analysis.

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Authors: M.Suganthi, M.Madheswaran

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This paper presents a novel approach to finding a priori interesting regions in mammograms. In order to delineate those regions of interest (ROI-s) in mammograms, which appear to be prominent, a topographic representation called the iso-level contour map consisting of iso-level contours at multiple intensity levels and region segmentation based-thresholding have been proposed. The simulation results indicate that the computed boundary gives the detection rate of 99.5% accuracy.

Keywords: Breast Cancer, Mammogram, and Segmentation.

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: A. Nikkar, M. Mighani

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In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: Natasha Hussain, Maleeha Aslam, Robina Farooq

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Hepatitis B and hepatitis C are among the most significant hepatic infections all around the world that may lead to hepatocellular carcinoma. This study is first time performed at the blood transfussion centre of Omar hospital, Lahore. It aims to determine the sero-prevalence of these diseases by screening the apparently healthy blood donors who might be the carriers of HBV or HCV and pose a high risk in the transmission. It also aims the comparison between the sensitivity of two diagnostic tests; chromatographic immunoassay – one step test device and Enzyme Linked Immuno Sorbant Assay (ELISA). Blood serum of 855 apparently healthy blood donors was screened for Hepatitis B surface antigen (HBsAg) and for anti HCV antibodies. SPSS version 12.0 and X2 (Chi-square) test were used for statistical analysis. The seroprevalence of HCV was 8.07% by the device method and by ELISA 9.12% and that of HBV was 5.6% by the device and 6.43% by ELISA. The unavailability of vaccination against HCV makes it more prevalent. Comparing the two diagnostic methods, ELISA proved to be more sensitive.

Keywords: ELISA, Sensitivity comparison of diagnostic tests, seroprevalence of Hepatitis B and C

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Authors: Li Jiang, Baoguang Tian

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In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: K. Thu, Yin Y. Mon, Tin A. Khaing, Ohn M. Tun

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The aim of the study was to investigate phytochemical properties, antimicrobial activity and cytotoxicity of Aloe vera. The phytochemical screening of the extracts of leaves of A. vera revealed the presence of bioactive compounds such as alkaloids, tannins, flavonoids phenolic compounds, and etc. with absence of cyanogenic glycosides. Three different solvents such as methanol, ethanol and Di-Methyl sulfoxide were used to screen the antimicrobial activity of A. vera leaves against four human clinical pathogens by agar well diffusion method. The maximum antibacterial activities were observed in methanol extract followed by ethanol and Di-Methyl sulfoxide. It was also found that remarkable antibacterial activities with methanolic and ethanolic extracts of A. vera compared with the standard antibiotic, tetracycline that was not active against E. coli and S. boydii and supported the view that A. vera is a potent antimicrobial agent compared with the conventional antibiotic. Moreover, the brine shrimps (Artemia salina) toxicity test exhibited LC50 value was 569.52 ppm. The resulting data indicated that the A. vera plant have less toxic effects on brine shrimp. Hence, it is signified that Aloe vera plant extract is safe to be used as an antimicrobial agent.

Keywords: Aloe vera L., antimicrobial activity, brine shrimp, cytotoxicity, phytochemical properties.

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

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In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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Authors: Mehrnoosh Omati, Mahmod Reza Sahebi

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The information on land use/land cover changing plays an essential role for environmental assessment, planning and management in regional development. Remotely sensed imagery is widely used for providing information in many change detection applications. Polarimetric Synthetic aperture radar (PolSAR) image, with the discrimination capability between different scattering mechanisms, is a powerful tool for environmental monitoring applications. This paper proposes a new boundary-based segmentation algorithm as a fundamental step for land cover change detection. In this method, first, two PolSAR images are segmented using integration of marker-controlled watershed algorithm and coupled Markov random field (MRF). Then, object-based classification is performed to determine changed/no changed image objects. Compared with pixel-based support vector machine (SVM) classifier, this novel segmentation algorithm significantly reduces the speckle effect in PolSAR images and improves the accuracy of binary classification in object-based level. The experimental results on Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) polarimetric images show a 3% and 6% improvement in overall accuracy and kappa coefficient, respectively. Also, the proposed method can correctly distinguish homogeneous image parcels.

Keywords: Coupled Markov random field, environment, object-based analysis, Polarimetric SAR images.

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Authors: Nicolay Zarutskiy, Roman Bulkin

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The paper deals with the existing methods of force-torque sensor calibration with a number of components from one to six, analyzed their advantages and disadvantages, the necessity of introduction of a calibration method. Calibration method and its constructive realization are also described here. A calibration method allows performing automated force-torque sensor calibration both with selected components of the main vector of forces and moments and with complex loading. Thus, two main advantages of the proposed calibration method are achieved: the automation of the calibration process and universality.

Keywords: Automation, calibration, calibration device, calibration method, force-torque sensors.

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Authors: S. A. Eftekhari

Abstract:

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Keywords: Dam-reservoir system, Differential quadrature method, Fluid-structure interaction, Galerkin method, Integral quadrature method.

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Authors: Xijian Wang

Abstract:

This paper is concerned with the numerical minimization of energy functionals in BV ( ) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.

Keywords: finite element method, discontinuous Galerkin method, total variation minimization, inpainting

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Authors: Ali Gholami

Abstract:

In this research the Preparation of Land use map of scanner LISS III satellite data, belonging to the IRS in the Aghche region in Isfahan province, is studied carefully. For this purpose, the IRS satellite images of August 2008 and various land preparation uses in region including rangelands, irrigation farming, dry farming, gardens and urban areas were separated and identified. Therefore, the GPS and Erdas Imaging software were used and three methods of Maximum Likelihood, Mahalanobis Distance and Minimum Distance were analyzed. In each of these methods, matrix error and Kappa index were calculated and accuracy of each method, based on percentages: 53.13, 56.64 and 48.44, were obtained respectively. Considering the low accuracy of these methods in separation of land preparation use, the visual interpretation of the map was used. Finally, regional visits of 150 points were noted at random and no error was observed. It shows that the map prepared by visual interpretation is in high accuracy. Although the probable errors due to visual interpretation and geometric correction might happen but the desired accuracy of the map which is more than 85 percent is reliable.

Keywords: Land use map, Aghche Region, Erdas Imagine, satellite images

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Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

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In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

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This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: Fluid-structure coupling, inverse methods, naval, vibrations.

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Authors: Elżbieta Antczak

Abstract:

Cities offer important opportunities for economic development and for expanding access to basic services, including health care and education, for large numbers of people. Moreover, green areas (as an integral part of sustainable urban development) present a major opportunity for improving urban environments, quality of lives and livelihoods. This paper examines, using spatial concentration and spatial taxonomic measures, regional diversification of greenery in the cities of Poland. The analysis includes location quotients, Lorenz curve, Locational Gini Index, and the synthetic index of greenery and spatial statistics tools: (1) To verify the occurrence of strong concentration or dispersion of the phenomenon in time and space depending on the variable category, and, (2) To study if the level of greenery depends on the spatial autocorrelation. The data includes the greatest Polish cities, categories of the urban greenery (parks, lawns, street greenery, and green areas on housing estates, cemeteries, and forests) and the time span 2004-2015. According to the obtained estimations, most of cites in Poland are already taking measures to become greener. However, in the country there are still many barriers to well-balanced urban greenery development (e.g. uncontrolled urban sprawl, poor management as well as lack of spatial urban planning systems).

Keywords: Greenery, urban areas, regional spatial diversification and concentration, spatial taxonomic measure.

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Authors: Anton A. Larenkov, Alesya Ya Maruk

Abstract:

In the present study, highly effective iTLC single strip method for the determination of radiochemical purity (RCP) of ⁶⁸Ga-BCA-peptides was developed (with no double-developing, changing of eluents or other additional manipulation). In this method iTLC-SG strips and commonly used eluent TFA_aq. (3-5 % (v/v)) are used. The method allows determining each of the key radiochemical forms of ⁶⁸Ga (colloidal, bound, ionic) separately with the peaks separation being no less than 4 σ. Rf = 0.0-0.1 for ⁶⁸Ga-colloid; Rf = 0.5-0.6 for ⁶⁸Ga-BCA-peptides; Rf = 0.9-1.0 for ionic ⁶⁸Ga. The method is simple and fast: For developing length of 75 mm only 4-6 min is required (versus 18-20 min for pharmacopoeial method). The method has been tested on various compounds (including ⁶⁸Ga-DOTA-TOC, ⁶⁸Ga-DOTA-TATE, ⁶⁸Ga-NODAGA-RGD₂ etc.). The cross-validation work for every specific form of ⁶⁸Ga showed good correlation between method developed and control (pharmacopoeial) methods. The method can become convenient and much more informative replacement for pharmacopoeial methods, including HPLC.

Keywords: DOTA-TATE, 68Ga, quality control, radiochemical purity, radiopharmaceuticals, iTLC.

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Authors: A. Kistaubayeva, I. Savitskaya, D. Ibrayeva, M. Abdulzhanova, N. Voronova

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36 strains of sulfur-oxidizing bacteria were isolated in Southern Kazakhstan soda-saline soils and identified. Screening of strains according bio-oxidation (destruction thiosulfate to sulfate) and enzymatic (Thiosulfate dehydrogenises and thiosulfate reductase) activity was conducted. There were selected modes of aeration and culture conditions (pH, temperature), which provide optimum harvest cells. These strains can be used in bio-melioration technology.

Keywords: Elemental sulfur, oxidation activity, Тhiobacilli, fertilizers, heterotrophic S-oxidizers.

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Authors: Xiaohui Han, Yuhan Wang, Jing Shi

Abstract:

This paper proposed a stiffness analysis method for a 3-PRS mechanism for welding thick aluminum plate using FSW technology. In the molding process, elastic deformation of lead-screws and links are taken into account. This method is based on the virtual work principle. Through a survey of the commonly used stiffness performance indices, the minimum and maximum eigenvalues of the stiffness matrix are used to evaluate the stiffness of the 3-PRS mechanism. Furthermore, A FEA model has been constructed to verify the method. Finally, we redefined the workspace using the stiffness analysis method.

Keywords: 3-PRS, parallel mechanism, stiffness analysis, workspace.

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Authors: Abdolali Basiri

Abstract:

In this paper we present an efficient method for inverting an ideal in the ideal class group of a Cab curve by extending the method which is presented in [3]. More precisely we introduce a useful generator for the inverse ideal as a K[X]-module.

Keywords: Cab Curves, Ideal Class Group

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Authors: Jamal Amani Rad, Kourosh Parand

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In this paper, we have applied the homotopy perturbation method (HPM) for obtaining the analytical solution of unsteady flow of gas through a porous medium and we have also compared the findings of this research with some other analytical results. Results showed a very good agreement between results of HPM and the numerical solutions of the problem rather than other analytical solutions which have previously been applied. The results of homotopy perturbation method are of high accuracy and the method is very effective and succinct.

Keywords: Unsteady gas equation, Homotopy perturbation method(HPM), Porous medium, Nonlinear ODE

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