Search results for: switching activity matrix

Authors: Azam Anaraki Firooz, Ali Reza Mahjoub, Abbas Ali Khodadadi

Abstract:

The paper reports the preparation and photocatalytic activity of ZnO/SnO2 and SnO2 nanoparticles. These nanoparticles were synthesized by hydrothermal method. The products were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM). Their grain sizes are about 50-100 nm. The photocatalytic activities of these materials were investigated for congo red removal from aqueous solution under UV light irradiation. It was shown that the use of ZnO/SnO2 as photocatalyst have better photocatalytic activity for degradation of congo red than SnO2 or TiO2 (anatase, particle size: 30nm) alone.

Keywords: ZnO/SnO2 nanoparticle, hydrothermal, photocatalysis

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Authors: Yan Yu, Wang Yu, Chen Xintong, Liu Yi, Zhang Yanzhong, Wang Yanji, Chen Xingyu, Zhang Miaocheng, Tong Yi

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Neuromorphic computing based on spiking neural networks (SNNs) has emerged as a promising avenue for building the next generation of intelligent computing systems. Owing to their high-density integration, low power, and outstanding nonlinearity, memristors have attracted emerging attention on achieving SNNs. However, fabricating a low-power and robust memristor-based spiking neuron without extra electrical components is still a challenge for brain-inspired systems. In this work, we demonstrate a TiO2-based threshold switching (TS) memristor to emulate a leaky integrate-and-fire (LIF) neuron without auxiliary circuits, used to realize single layer fully connected (FC) SNNs. Moreover, our TiO2-based resistive switching (RS) memristors realize spiking-time-dependent-plasticity (STDP), originating from the Ag diffusion-based filamentary mechanism. This work demonstrates that TiO2-based memristors may provide an efficient method to construct hardware neuromorphic computing systems.

Keywords: Leaky integrate-and-fire, memristor, spiking neural networks, spiking-time-dependent-plasticity.

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Authors: S. Angalaparameswari, T.S. Mohamed Saleem, M. Alagusundaram, S. Ramkanth, V.S. Thiruvengadarajan, K. Gnanaprakash, C. Madhusudhana Chetty, G. Pratheesh

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The present research was designed to investigate the anti-microbial activity of aristolochic acid from the root of Aristolochia bracteata. From the methanolic & ethyl extract extracts of Aristolochia bracteata aristolochic acid I was isolated and conformed through IR, NMR & MS. The percentage purity of aristolochic acid I was determined by UV & HPLC method. Antibacterial activity of extracts of Aristolochia bracteata and the isolated compound was determined by disc diffusion method. The results reveled that the isolated aristolochic acid from methanolic extract was more pure than the compound from ethyl acetate extract. The various extracts (500μg/disc) of Aristolochia bracteata showed moderate antibacterial activity with the average zone of inhibition of 7-18 mm by disc diffusion method. Among the extracts, ethyl acetate & methanol extracts were shown good anti-microbial activity and the growth of E.coli (18 mm) was strongly inhibited. Microbial assay of isolated compound (Aristolochic acid I) from ethyl acetate & methanol extracts were shown good antimicrobial activity and the zone of inhibition of both at higher concentration 50 μg/ml was similar with the standard aristolochic acid. It may be concluded that the isolated compound of aristolochic acid I has good anti-bacterial activity.

Keywords: Aristolochic acid I, Anti-microbial activity, Aristolochia bracteata, Bacillus subtilis, E.coli

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Authors: H. Afer, N. Rouag, R. Penelle

Abstract:

In the Fe-3%Si sheets, grade Hi-B, with AlN and MnS as inhibitors, the Goss grains which abnormally grow do not have a size greater than the average size of the primary matrix. In this heterogeneous microstructure, the size factor is not a required condition for the secondary recrystallization. The onset of the small Goss grain abnormal growth appears to be related to a particular behavior of their grain boundaries, to the local texture and to the distribution of the inhibitors. The presence and the evolution of oriented clusters ensure to the small Goss grains a favorable neighborhood to grow. The modified Monte-Carlo approach, which is applied, considers the local environment of each grain. The grain growth is dependent of its real spatial position; the matrix heterogeneity is then taken into account. The grain growth conditions are considered in the global matrix and in different matrixes corresponding to A component clusters. The grain growth behaviour is considered with introduction of energy only, energy and mobility, energy and mobility and precipitates.

Keywords: Abnormal grain growth, grain boundary energy andmobility, neighbourhood, oriented clusters.

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Authors: M. Ghorbany

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A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

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Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Christiana Gauci-Sciberras

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The first language (L1) could be used in foreign language teaching and learning as a pedagogical tool to scaffold new knowledge in the target language (TL) upon linguistic knowledge that the learner already has. In a bilingual context, code-switching between the two languages usually occurs in classrooms. One of the reasons for code-switching is because both languages are used for scaffolding new knowledge. This research paper aims to find out why both the L1 (Maltese) and the L2 (English) are used in the classroom of Mandarin Chinese as a foreign language (CFL) in the bilingual context of Malta. This research paper also aims to find out the learners’ perceptions of the use of a bilingual medium of instruction. Two research methods were used to collect qualitative data; semi-structured interviews with adult learners of Mandarin Chinese and lesson observations. These two research methods were used so that the data collected in the interviews would be triangulated with data collected in lesson observations. The L1 (Maltese) is the language of instruction mostly used. The teacher and the learners switch to the L2 (English) or to any other foreign language according to the need at a particular instance during the lesson.

Keywords: Chinese, bilingual, pedagogical purpose of L1 and L2, CFL acquisition.

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Authors: Somenath Mukherjee, Rajdeep Ray, Raj Kumar Samanta, Mofazzal H. Khondekar, Gautam Sanyal

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In next generation wireless networks (i.e., 4G and beyond), one of the main objectives is to ensure highest level of customer satisfaction in terms of data transfer speed, decrease in cost and delay, non-rejection and no drop of calls, availability of ‘always-on’ connectivity and services, continuity of connected services, hastle-free roaming in addition to the convenience of use of network services from anywhere and anytime. To take care of these requirements effectively, internet service providers (ISPs) and network planners have to go for major capacity enhancement of network resources and at the same time these resources are to be used effectively and efficiently to reduce cost and to increase revenue. In this work, the effective bandwidth available in a Mobile Switching Center (MSC) of a wireless network providing multi-class multimedia services is analyzed. Bandwidth requirement of the users for a customized Quality of Service (QoS) is estimated. The findings of the QoS estimation are applied for the capacity planning and admission control of the multi-class traffic flows coming into the MSC.

Keywords: Next generation wireless network, mobile switching center, multi-class traffic, quality of service, admission control, effective bandwidth.

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Authors: MD Zaheer Ansari, A.K. Nirala

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In this study spatial-temporal speckle correlation techniques have been applied for the quality evaluation of three different Indian fruits namely apple, pear and tomato for the first time. The method is based on the analysis of variations of laser light scattered from biological samples. The results showed that crosscorrelation coefficients of biospeckle patterns change subject to their freshness and the storage conditions. The biospeckle activity was determined by means of the cross-correlation functions of the intensity fluctuations. Significant changes in biospeckle activity were observed during their shelf lives. From the study, it is found that the biospeckle activity decreases with the shelf-life storage time. Further it has been shown that biospeckle activity changes according to their respiration rates.

Keywords: Biospeckle, cross-correlation, respiration, shelf-life.

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Authors: Milan Hladik

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The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Mohamed Ali AlShaari, Khalid M. ElFitori

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In the field of Quran Studies known as GHAREEB AL QURAN (The study of the meanings of strange words and structures in Holy Quran), it is difficult to distinguish some pragmatic meanings from conceptual meanings. One who wants to study this subject may need to look for a common usage between any two words or more; to understand general meaning, and sometimes may need to look for common differences between them, even if there are synonyms (word sisters).

Some of the distinguished scholars of Arabic linguistics believe that there are no synonym words, they believe in varieties of meaning and multi-context usage. Based on this viewpoint, our method was designedto look for synonyms of a word, then the differences that distinct the word and their synonyms.

There are many available books that use such a method e.g. synonyms books, dictionaries, glossaries, and some books on the interpretations of strange vocabulary of the Holy Quran, but it is difficult to look up words in these written works.

For that reason, we proposed a logical entity, which we called Differences Matrix (DM).

DM groups the synonyms words to extract the relations between them and to know the general meaning, which defines the skeleton of all word synonyms; this meaning is expressed by a word of its sisters.

In Differences Matrix, we used  the sisters(words) as titles for rows and columns, and in the obtained  cells we tried to define the row title (word) by using column title (her sister), so the relations between sisters appear, the expected result is well defined groups of sisters for each word. We represented the obtained results formally, and used the defined groups as a base for building the ontology of the Holy Quran synonyms.

Keywords: Quran, synonyms, Differences Matrix, ontology

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Authors: Biao Qin, Jin Huang

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In this paper, together with some improved Lyapunov-Krasovskii functional and effective mathematical techniques, several sufficient conditions are derived to guarantee the error system is globally asymptotically stable with H∞ performance, in which both the time-delay and its time variation can be fully considered. In order to get less conservative results of the state estimation condition, zero equalities and reciprocally convex approach are employed. The estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities. A numerical example is provided to illustrate the usefulness and effectiveness of the obtained results.

Keywords: H∞ performance, Neural networks, State estimation.

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Authors: Shazia Javed, Noor Atinah Ahmad

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In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

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Authors: Reem I. Altamimi, Geoff D. Skinner

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Extended periods engaged in sedentary behavior increases the risk of becoming overweight and/or obese which is linked to other health problems. Adding technology to the term ‘active living’ permits its inclusion in promoting and facilitating habitual physical activity. Technology can either act as a barrier to, or facilitate this lifestyle, depending on the chosen technology. Physical Activity Monitoring Technologies (PAMTs) are a popular example of such technologies. Different contemporary PAMTs have been evaluated based on customer reviews; however, there is a lack of published experimental research into the efficacy of PAMTs. This research aims to investigate the reliability of four PAMTs: two wristbands (Fitbit Flex and Jawbone UP), a waist-clip (Fitbit One), and a mobile application (iPhone Health Application) for recording a specific distance walked on a treadmill (1.5km) at constant speed. Physical activity tracking technologies are varied in their recordings, even while performing the same activity. This research demonstrates that Jawbone UP band recorded the most accurate distance compared to Fitbit One, Fitbit Flex, and iPhone Health Application.

Keywords: Fitbit, Jawbone UP, mobile tracking applications, physical activity tracking technologies.

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Authors: Young-Seok Choi

Abstract:

It has been known that a characteristic Burst-Suppression (BS) pattern appears in EEG during the early recovery period following Cardiac Arrest (CA). Here, to explore the relationship between cortical and subcortical neural activities underlying BS, extracellular activity in the parietal cortex and the centromedian nucleus of the thalamus and extradural EEG were recorded in a rodent CA model. During the BS, the cortical firing rate is extraordinarily high, and that bursts in EEG correlate to dense spikes in cortical neurons. Newly observed phenomena are that 1) thalamic activity reemerges earlier than cortical activity following CA, and 2) the correlation coefficient of cortical and thalamic activities rises during BS period. These results would help elucidate the underlying mechanism of brain recovery after CA injury.

Keywords: Cortex, thalamus, cardiac arrest, burst-suppression.

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Authors: Sahil, Rajeev Saha, Sanjeev Kumar

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Material selection is one of the key issues for the production of reliable and quality products in industries. A number of materials are available for a single product due to which material selection become a difficult task. The aim of this paper is to select appropriate material for gear used in fuel pump by using Graph Theory and Matrix Approach (GTMA). GTMA is a logical and systematic approach that can be used to model and analyze various engineering systems. In present work, four alternative material and their seven attributes are used to identify the best material for given product.

Keywords: Material, GTMA, MADM, digraph, decision making.

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Authors: C. B. Vishwakarma

Abstract:

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.

Keywords: Model Order Reduction, Stability, Hankel Matrix, Time-Domain, Integral Square Error.

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Authors: Joshi Manohar. V., Sujatha. P., Anjaneyulu K. S. R

Abstract:

The range of the output power is a very important and evident limitation of two-level inverters. In order to overcome this disadvantage, multilevel inverters are introduced. Recently, Cascade H-Bridge inverters have emerged as one of the popular converter topologies used in numerous industrial applications. The modulation switching strategies such as phase shifted carrier based Pulse Width Modulation (PWM) technique and Stair case modulation with Selective Harmonic Elimination (SHE) PWM technique are generally used. NR method is used to solve highly non linear transcendental equations which are formed by SHEPWM method. Generally NR method has a drawback of requiring good initial guess but in this paper a new approach is implemented for NR method with any random initial guess. A three phase CHB 11-level inverter is chosen for analysis. MATLAB/SIMULINK programming environment and harmonic profiles are compared. Finally this paper presents a method at fundamental switching frequency with least % THDV.

Keywords: Cascade H-bridge 11- level Inverter, NR method, Phase shifted carrier based pulse width modulation (PSCPWM), Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Total Harmonic Distortion (%THDv).

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Authors: Lianglin Xiong, Xiuyong Ding, Shouming Zhong

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In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Keywords: Asymptotical stability, neutral system, nonlinear perturbation, delay-dependent, linear matrix inequality (LMI).

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Authors: Yue Du, Sahan C. B. Herath, Qing-Guo Wang, Harry Asada, Peter C. Y. Chen

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Mechanical interaction between endothelial cells (ECs) and the extracellular matrix (or collagen gel) is known to influence the sprouting response of endothelial cells during angiogenesis. This influence is believed to impact on the capability of endothelial cells to sense soluble chemical cues. Quantitative analysis of endothelial-cell-mediated displacement of the collagen gel provides a means to explore this mechanical interaction. Existing analysis in this context is generally limited to 2D settings. In this paper, we investigate the mechanical interaction between endothelial cells and the extracellular matrix in terms of the endothelial-cellmediated displacement of the collagen gel in both 2D and 3D. Digital image correlation and Digital volume correlation are applied on confocal reflectance image stacks to analyze cell-mediated displacement of the gel. The skeleton of the sprout is extracted from phase contrast images and superimposed on the displacement field to further investigate the link between the development of the sprout and the displacement of the gel.

Keywords: Angiogenesis, digital image correlation, digital volume correlation, interaction between ECs and ECM.

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

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In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: Multi-agent, Linear Matrix Inequalities (LMIs), Kronecker Product, Sampled-Data, Lyapunov method.

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Authors: Minghui Wang

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Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.

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Authors: Mustafa Erat

Abstract:

Glutathione S-transferase was purified from human erythrocytes and effects of some polyphenols were investigated on the enzyme activity. The purification procedure was performed on Glutathione-Agarose affinity chromatography after preparation of erythrocytes hemolysate with a yield of 81%. The purified enzyme showed a single band on the SDS-PAGE. The effects of some poliphenolic compounds such as catechin, dopa, dopamine, progallol and catechol were examined on the in vitro GST activity. Catechin was determined to be inhibitor for the enzyme, but others were not effective on the enzyme as inhibitors or activators. IC50 value -the concentration of inhibitor which reduces enzyme activity by 50%- was estimated to be 10 mM. Ki constants were also calculated as 6.38 ± 0,70 mM with GSH substrate, and 3.86 ± 0,78 mM with CDNB substrate using the equations of graphs for the inhibitor, and its inhibition type was determined as non-competitive.

Keywords: Drug resistance, Glutathione S-transferase, Inhibition.

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Authors: Renee P. Baang, Romeo M. Del Rosario, Nenita D. Palmes

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The crude methanol extracts of five indigenous vegetables namely, Amarathus tricolor, Basella rubra L., Chochurus olitorius L., Ipomea batatas, and Momordica chuchinensis L., were examined for their phytochemical profile and antioxidant activity using 1,1-diphenyl-2-picrylhydrazyl (DPPH) free radical. The values for DPPH radical scavenging activity ranged from 7.6-89.53% with B. rubra and I. batatas having the lowest and highest values, respectively. The total flavonoid content of all five indigenous vegetables ranged from 74.65-277.3 mg quercetin equivalent per gram of dried vegetable material while the total phenolic content ranged from 1.93-6.15 mg gallic acid equivalent per gram dried material. Phytochemical screening revealed the presence of steroids, flavonoids, saponins, tannins, carbohydrates and reducing sugars, which may also be associated with the antioxidant activity shown by these indigenous vegetables.

Keywords: Antioxidant, DPPH radical scavenging activity, Philippine indigenous vegetables, phytochemical screening.

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Authors: M. Rodionov, Z. Dedovets

Abstract:

This article discusses ways to implement a differentiated approach to developing academic motivation for mathematical studies which relies on defining the primary structural characteristics of motivation. The following characteristics are considered: features of realization of cognitive activity, meaningmaking characteristics, level of generalization and consistency of knowledge acquired by personal experience. The assessment of the present level of individual student understanding of each component of academic motivation is the basis for defining the relevant educational strategy for its further development.

Keywords: Learning activity, mathematics, motivation, student.

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Authors: Faizal A. Samman, Thomas Hollstein, Manfred Glesner

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A synchronous network-on-chip using wormhole packet switching and supporting guaranteed-completion best-effort with low-priority (LP) and high-priority (HP) wormhole packet delivery service is presented in this paper. Both our proposed LP and HP message services deliver a good quality of service in term of lossless packet completion and in-order message data delivery. However, the LP message service does not guarantee minimal completion bound. The HP packets will absolutely use 100% bandwidth of their reserved links if the HP packets are injected from the source node with maximum injection. Hence, the service are suitable for small size messages (less than hundred bytes). Otherwise the other HP and LP messages, which require also the links, will experience relatively high latency depending on the size of the HP message. The LP packets are routed using a minimal adaptive routing, while the HP packets are routed using a non-minimal adaptive routing algorithm. Therefore, an additional 3-bit field, identifying the packet type, is introduced in their packet headers to classify and to determine the type of service committed to the packet. Our NoC prototypes have been also synthesized using a 180-nm CMOS standard-cell technology to evaluate the cost of implementing the combination of both services.

Keywords: Network-on-Chip, Parallel Pipeline Router Architecture, Wormhole Switching, Two-Level Priority Service.

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Authors: M.Meskinfam, M. S. Sadjadi, H.Jazdarreh

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In this study, we report the synthesis and characterization of nanohydroxyapatite (nHAp) in gelatin-starch matrix via biomimetic method. Characterization of the samples was performed using X-ray diffraction (XRD) and Fourier Transform infrared spectroscopy (FT-IR). The Size and morphology of the nHAp samples were determined using scanning and transmission electron microscopy (SEM and TEM). The results reveal that the shape and morphology of nHAp is influenced by presence of biopolymers as template. Carbonyl and amino groups from gelatin and hydroxyl from starch play crucial roles in HAp formation on the surface of gelatin-starch.

Keywords: Biocomposite, Biomimetic , Nano Hydroxyapatite , Template.

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Authors: M. M. Mon, S. S. Maw, Z. K. Oo

Abstract:

Antioxidant activities of ethanolic extracts of Ardisia japonica Blume., Ageartum conyzoides Linn., and Cocculus hirsutus Linn Diels. leaves was determined qualitatively and quantitatively in this research. 1, 1-diphenyl-2-picrylhydrazyl (DPPH) free radical solution was used to investigate free radical scavenging activity of these leaves extracts. Ascorbic acid (Vitamin C) was used as the standard. In the present investigation, it is found that all of these extracts have remarkable antioxidant activities. The EC50 values of these ethanolic extracts were 12.72 μg/ml for A. japonica, 15.19 μg/ml for A. conyzoides, 10.68 μg/ml for C. hirsutus respectively. Among these Myanmar medicinal plants, C. hirsutus showed higher antioxidant activities as well as free radical scavenging activity than black tea (Camellia sinensis), the famous antioxidant, and A. japonica and A. conyzoides showed a rather lower antioxidant activity than tea extracts. According to results from bioassay with carrot discs infected with Agrobacterium tumefaciens, all extracts showed anti-tumor activity after 3 weeks of incubation. No gall was detected in carrot disks treated with C. hirsutus and A. japonica extracts in the dose of 100ppm and in carrot discs treated with A. conyzoides extract in the dose of 1000 ppm. Therefore, the research clearly indicates that these weedy plants of dry farm land are exceptionally advantageous for human health.

Keywords: Antioxidant, Anti-tumor activity, Carrot-discbioassay, DPPH

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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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