Search results for: continuous dependence

Authors: Catalin Gales, Ionel Dumitrel Ghiba

Abstract:

This paper studies questions of continuous data dependence and uniqueness for solutions of initial boundary value problems in linear micropolar thermoelastic mixtures. Logarithmic convexity arguments are used to establish results with no definiteness assumptions upon the internal energy.

Keywords: Cellular materials, continuous dependence, micro polar mixtures, uniqueness.

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Authors: Jürgen Beyer

Abstract:

In association with path dependence, researchers often talk of institutional “lock-in", thereby indicating that far-reaching path deviation or path departure are to be regarded as exceptional cases. This article submits the alleged general inclination for stability of path-dependent processes to a critical review. The different reasons for path dependence found in the literature indicate that different continuity-ensuring mechanisms are at work when people talk about path dependence (“increasing returns", complementarity, sequences etc.). As these mechanisms are susceptible to fundamental change in different ways and to different degrees, the path dependence concept alone is of only limited explanatory value. It is therefore indispensable to identify the underlying continuity-ensuring mechanism as well if a statement-s empirical value is to go beyond the trivial, always true “history matters".

Keywords: path dependence, increasing returns, historicalinstitutionalism, lock-in.

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Authors: Chatchai Pesee

Abstract:

This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

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Authors: Adrian O’Hagan, Robert McLoughlin

Abstract:

Considerable focus in the world of insurance risk quantification is placed on modeling loss values from lines of business (LOBs) that possess upper tail dependence. Copulas such as the Joe, Gumbel and Student-t copula may be used for this purpose. The copula structure imparts a desired level of tail dependence on the joint distribution of claims from the different LOBs. Alternatively, practitioners may possess historical or simulated data that already exhibit upper tail dependence, through the impact of catastrophe events such as hurricanes or earthquakes. In these circumstances, it is not desirable to induce additional upper tail dependence when modeling the joint distribution of the loss values from the individual LOBs. Instead, it is of interest to accurately assess the degree of tail dependence already present in the data. The empirical copula and its associated upper tail dependence coefficient are presented in this paper as robust, efficient means of achieving this goal.

Keywords: Empirical copula, extreme events, insurance loss reserving, upper tail dependence coefficient.

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Authors: Alexander L. Dmitriev, Sophia A. Bulgakova

Abstract:

Temperature dependence of force of gravitation is one of the fundamental problems of physics. This problem has got special value in connection with that the general theory of relativity, supposing the weakest positive influence of a body temperature on its weight, actually rejects an opportunity of measurement of negative influence of temperature on gravity in laboratory conditions. Really, the recognition of negative temperature dependence of gravitation, for example, means basic impossibility of achievement of a singularity («a black hole») at a gravitational collapse. Laboratory experiments with exact weighing the heated up metal samples, indicating negative influence temperatures of bodies on their physical weight are described. Influence of mistakes of measurements is analyzed. Calculations of distribution of temperature in volume of the bar, agreed with experimental data of time dependence of weight of samples are executed. The physical substantiation of negative temperature dependence of weight of the bodies, based on correlation of acceleration at thermal movement of micro-particles of a body and its absolute temperature, are given.

Keywords: Gravitation, temperature, weight.

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: A. Maruf Aytekin

Abstract:

We present our approach on using continuous delivery pattern for release management. One of the key practices of agile and lean teams is the continuous delivery of new features to stakeholders. The main benefits of this approach lie in the ability to release new applications rapidly which has real strategic impact on the competitive advantage of an organization. Organizations that successfully implement Continuous Delivery have the ability to evolve rapidly to support innovation, provide stable and reliable software in more efficient ways, decrease the amount of resources need for maintenance, and lower the software delivery time and costs. One of the objectives of this paper is to elaborate a case study where IT division of Central Securities Depository Institution (MKK) of Turkey apply Continuous Delivery pattern to improve release management process.

Keywords: Automation, continuous delivery, deployment, release management.

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Authors: M. Esmaeilzadeh, H. Roohbakhsh, A. Ghaedzadeh

Abstract:

In this paper, the absorption and fluorescence emission spectra of Yb:Y3Al5O12 (YAG)(25 at%) crystal as a disk laser medium are measured at high temperature (300-450K). The absorption and emission cross sections of Yb:YAG crystal are determined using Reciprocity method. Temperature dependence of 941nm absorption cross section and 1031nm emission cross section is extracted in the range of 300-450K. According to our experimental results, an exponential temperature dependence between 300K and 450K is acquired for the 1031nm peak emission cross section and also for 941nm peak absorption cross section of Yb:YAG crystal. These results could be used for simulation and design of high power highly doped Yb:YAG thin disk lasers.

Keywords: Yb:YAG crystal, Emission cross section, Absorption coefficient, Temperature dependence, Reciprocity method.

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Authors: C. M. M. Paschoal, D. do N. Souza, L. A. P. Santos

Abstract:

In this study three commercial semiconductor devices were characterized in the laboratory for computed tomography dosimetry: one photodiode and two phototransistors. It was evaluated four responses to the irradiation: dose linearity, energy dependence, angular dependence and loss of sensitivity after X ray exposure. The results showed that the three devices have proportional response with the air kerma; the energy dependence displayed for each device suggests that some calibration factors would be applied for each one; the angular dependence showed a similar pattern among the three electronic components. In respect to the fourth parameter analyzed, one phototransistor has the highest sensitivity however it also showed the greatest loss of sensitivity with the accumulated dose. The photodiode was the device with the smaller sensitivity to radiation, on the other hand, the loss of sensitivity after irradiation is negligible. Since high accuracy is a desired feature for a dosimeter, the photodiode can be the most suitable of the three devices for dosimetry in tomography. The phototransistors can also be used for CT dosimetry, however it would be necessary a correction factor due to loss of sensitivity with accumulated dose.

Keywords: Dosimetry, computed tomography, phototransistor, photodiode

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Authors: Ritu Shitak

Abstract:

Humans are social mammals, of the primate order. Our biology, our behaviour and our pathologies are unique to us. In our desire to understand, reduce solitary confinement one source of information is the many reports of social isolation of other social mammals, especially primates. A behavioural study was conducted in the department of pharmacology at Indira Gandhi Medical College, Shimla in Himachalpradesh province in India using white albino mice. Different behavioural parameters were observed by using open field, tail suspension, tests for aggressive behaviour and social interactions and the effect of isolation was studied. The results were evaluated and the standard statistics were applied. The said study was done to establish facts that isolation itself impairs social behaviour and can lead to alcohol dependence as well as related drug dependence.

Keywords: Albino Mice, Drug Dependence, Social isolation.

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Authors: Shumin Hou, Yourong Li, Sanxing Zhao

Abstract:

Much time series data is generally from continuous dynamic system. Firstly, this paper studies the detection of the nonlinearity of time series from continuous dynamics systems by applying the Phase-randomized surrogate algorithm. Then, the Delay Vector Variance (DVV) method is introduced into nonlinearity test. The results show that under the different sampling conditions, the opposite detection of nonlinearity is obtained via using traditional test statistics methods, which include the third-order autocovariance and the asymmetry due to time reversal. Whereas the DVV method can perform well on determining nonlinear of Lorenz signal. It indicates that the proposed method can describe the continuous dynamics signal effectively.

Keywords: Nonlinearity, Time series, continuous dynamics system, DVV method

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Authors: T. Hashimoto, N. Miki, H. Maki

Abstract:

We report the size dependence of 1D superconductivity in ultrathin (10-130 nm) nanowires produced by coating suspended carbon nanotubes with a superconducting NbN thin film. The resistance-temperature characteristic curves for samples with ≧25 nm wire width show the superconducting transition. On the other hand, for the samples with 10-nm width, the superconducting transition is not exhibited owing to the quantum size effect. The differential resistance vs. current density characteristic curves show some peak, indicating that Josephson junctions are formed in nanowires. The presence of the Josephson junctions is well explained by the measurement of the magnetic field dependence of the critical current. These understanding allow for the further expansion of the potential application of NbN, which is utilized for single photon detectors and so on.

Keywords: NbN nanowire, carbon nanotube, quantum size effect, Josephson junction

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Authors: S. Raja Ratna, R. Ravi

Abstract:

Securing the confidential data transferred via wireless network remains a challenging problem. It is paramount to ensure that data are accessible only by the legitimate users rather than by the attackers. One of the most serious threats to organization is jamming, which disrupts the communication between any two pairs of nodes. Therefore, designing an attack-defending scheme without any packet loss in data transmission is an important challenge. In this paper, Dependence based Malicious Route Defending DMRD Scheme has been proposed in multi path routing environment to prevent jamming attack. The key idea is to defend the malicious route to ensure perspicuous transmission. This scheme develops a two layered architecture and it operates in two different steps. In the first step, possible routes are captured and their agent dependence values are marked using triple agents. In the second step, the dependence values are compared by performing comparator filtering to detect malicious route as well as to identify a reliable route for secured data transmission. By simulation studies, it is observed that the proposed scheme significantly identifies malicious route by attaining lower delay time and route discovery time; it also achieves higher throughput.

Keywords: Attacker, Dependence, Jamming, Malicious.

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Authors: Shiwei Deng, Yang Bao

Abstract:

In this paper, we present a model-based regression test suite reducing approach that uses EFSM model dependence analysis and probability-driven greedy algorithm to reduce software regression test suites. The approach automatically identifies the difference between the original model and the modified model as a set of elementary model modifications. The EFSM dependence analysis is performed for each elementary modification to reduce the regression test suite, and then the probability-driven greedy algorithm is adopted to select the minimum set of test cases from the reduced regression test suite that cover all interaction patterns. Our initial experience shows that the approach may significantly reduce the size of regression test suites.

Keywords: Dependence analysis, EFSM model, greedy algorithm, regression test.

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Authors: M. Asato, C. Liu, N. Fujima, T. Hoshino, Y. Chen, T. Mohri

Abstract:

We study the temperature dependence of the interaction energies (IEs) of X (=Ru, Rh) impurities in Pd, due to the Fermi-Dirac (FD) distribution and the thermal vibration effect by the Debye-Grüneisen model. The n-body (n=2~4) IEs among X impurities in Pd, being used to calculate the internal energies in the free energies of the Pd-rich PdX alloys, are determined uniquely and successively from the lower-order to higher-order, by the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR), combined with the generalized gradient approximation in the density functional theory. We found that the temperature dependence of IEs due to the FD distribution, being usually neglected, is very important to reproduce the X-concentration dependence of the observed solvus temperatures of the Pd-rich PdX (X=Ru, Rh) alloys.

Keywords: Full-potential KKR-Green’s function method, Fermi-Dirac distribution, GGA, phase diagram of Pd-rich PdX (X=Ru, Rh) alloys, thermal vibration effect.

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Authors: Subir Kundu, Sukhendra Singh, Sumedha Ojha, Kanika Kundu

Abstract:

The continuous decline of petroleum and natural gas reserves and non linear rise of oil price has brought about a realisation of the need for a change in our perpetual dependence on the fossil fuel. A day to day increased consumption of crude and petroleum products has made a considerable impact on our foreign exchange reserves. Hence, an alternate resource for the conversion of energy (both liquid and gas) is essential for the substitution of conventional fuels. Biomass is the alternate solution for the present scenario. Biomass can be converted into both liquid as well as gaseous fuels and other feedstocks for the industries.

Keywords: Bioenergy, Biomass conversion, Biorefining, Efficient utilisation of night soil.

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Authors: X. Mamaqi, J.Miguel, P. Olave

Abstract:

The aim of this paper is to provide an empirical evidence about the effects that the management of continuous training have on employability (or employment stability) in the Spanish labour market. With this purpose a binary logit model with interaction effect is been used. The dependent variable includes two situations of the active workers: continuous and discontinuous employability. To distinguish between them an Employability Index Stability (ESI) was calculated taking into account two factors: time worked and job security. Various aspects of the continuous training and personal workers data are used as independent variables. The data obtained from a survey of a sample of 918 employed have revealed a relationship between the likelihood of continuous employability and continuous training received. The empirical results support the positive and significant relationship between various aspects of the training provided by firms and employability likelihood of the workers, postulate alike from a theoretical point of view.

Keywords: training management, employability/employmentstability, binary logit model, interaction effect, Spanish marketlabour.

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Authors: Taher Omran Ahmed, Abdullatif Mihdi Buras

Abstract:

Decision support systems are usually based on multidimensional structures which use the concept of hypercube. Dimensions are the axes on which facts are analyzed and form a space where a fact is located by a set of coordinates at the intersections of members of dimensions. Conventional multidimensional structures deal with discrete facts linked to discrete dimensions. However, when dealing with natural continuous phenomena the discrete representation is not adequate. There is a need to integrate spatiotemporal continuity within multidimensional structures to enable analysis and exploration of continuous field data. Research issues that lead to the integration of spatiotemporal continuity in multidimensional structures are numerous. In this paper, we discuss research issues related to the integration of continuity in multidimensional structures, present briefly a multidimensional model for continuous field data. We also define new aggregation operations. The model and the associated operations and measures are validated by a prototype.

Keywords: Continuous Data, Data warehousing, DecisionSupport, SOLAP

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Authors: Subir Kundu, Sukhendra Singh, Sumedha Ojha, Kanika Kundu

Abstract:

The continuous decline of petroleum and natural gas reserves and non linear rise of oil price has brought about a realisation of the need for a change in our perpetual dependence on the fossil fuel. A day to day increased consumption of crude and petroleum products has made a considerable impact on our foreign exchange reserves. Hence, an alternate resource for the conversion of energy (both liquid and gas) is essential for the substitution of conventional fuels. Biomass is the alternate solution for the present scenario. Biomass can be converted into both liquid as well as gaseous fuels and other feedstocks for the industries.

Keywords: Bioenergy, Biomass conversion, Biorefining, Efficient utilisation of night soil.

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Authors: E. Farshidi, N. Ahmadpoor

Abstract:

In this paper, a alternative structure method for continuous time sigma delta modulator is presented. In this modulator for implementation of integrators in loop filter second generation current conveyors are employed. The modulator is designed in CMOS technology and features low power consumption (<2.8mW), low supply voltage (±1.65), wide dynamic range (>65db), and with 180khZ bandwidth. Simulation results confirm that this design is suitable for data converters.

Keywords: Current Conveyor, continuous, sigma delta, MOS, modulator

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Authors: Hiba Basim Alwan, Ku Ruhana Ku-Mahamud

Abstract:

A direction for ACO is to optimize continuous and mixed (discrete and continuous) variables in solving problems with various types of data. Support Vector Machine (SVM), which originates from the statistical approach, is a present day classification technique. The main problems of SVM are selecting feature subset and tuning the parameters. Discretizing the continuous value of the parameters is the most common approach in tuning SVM parameters. This process will result in loss of information which affects the classification accuracy. This paper presents two algorithms that can simultaneously tune SVM parameters and select the feature subset. The first algorithm, ACO_R-SVM, will tune SVM parameters, while the second IACO_MV-R-SVM algorithm will simultaneously tune SVM parameters and select the feature subset. Three benchmark UCI datasets were used in the experiments to validate the performance of the proposed algorithms. The results show that the proposed algorithms have good performances as compared to other approaches.

Keywords: Continuous ant colony optimization, incremental continuous ant colony, simultaneous optimization, support vector machine.

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Authors: Ibrahim Gomaa, Hoda M. O. Mokhtar

Abstract:

Although most of the existing skyline queries algorithms focused basically on querying static points through static databases; with the expanding number of sensors, wireless communications and mobile applications, the demand for continuous skyline queries has increased. Unlike traditional skyline queries which only consider static attributes, continuous skyline queries include dynamic attributes, as well as the static ones. However, as skyline queries computation is based on checking the domination of skyline points over all dimensions, considering both the static and dynamic attributes without separation is required. In this paper, we present an efficient algorithm for computing continuous skyline queries without discriminating between static and dynamic attributes. Our algorithm in brief proceeds as follows: First, it excludes the points which will not be in the initial skyline result; this pruning phase reduces the required number of comparisons. Second, the association between the spatial positions of data points is examined; this phase gives an idea of where changes in the result might occur and consequently enables us to efficiently update the skyline result (continuous update) rather than computing the skyline from scratch. Finally, experimental evaluation is provided which demonstrates the accuracy, performance and efficiency of our algorithm over other existing approaches.

Keywords: Continuous query processing, dynamic database, moving object, skyline queries.

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Authors: Guangpu Chen

Abstract:

When the failure function is monotone, some monotonic reliability methods are used to gratefully simplify and facilitate the reliability computations. However, these methods often work in a transformed iso-probabilistic space. To this end, a monotonic simulator or transformation is needed in order that the transformed failure function is still monotone. This note proves at first that the output distribution of failure function is invariant under the transformation. And then it presents some conditions under which the transformed function is still monotone in the newly obtained space. These concern the copulas and the dependence concepts. In many engineering applications, the Gaussian copulas are often used to approximate the real word copulas while the available information on the random variables is limited to the set of marginal distributions and the covariances. So this note catches an importance on the conditional monotonicity of the often used transformation from an independent random vector into a dependent random vector with Gaussian copulas.

Keywords: Monotonic, Rosenblatt, Nataf transformation, dependence concepts, completely positive matrices, Gaussiancopulas

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Authors: K. Daud, A. F. Abidin, N. Hamzah, H. S. Nagindar Singh

Abstract:

This paper produces a new approach for power quality analysis using a windowing technique based on Continuous S-transform (CST). This half-cycle window technique approach can detect almost correctly for initial detection of disturbances i.e. voltage sags, swells, and transients. Samples in half cycle window has been analyzed based continuous S-transform for entire disturbance waveform. The modified parameter has been produced by MATLAB programming m-file based on continuous s-transform. CST has better time frequency and localization property than traditional and also has ability to detect the disturbance under noisy condition correctly. The excellent time-frequency resolution characteristic of the CST makes it the most an attractive candidate for analysis of power system disturbances signals.

Keywords: Power quality disturbances, initial detection, half cycle windowing, continuous S-transform.

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Authors: Ioannis P. Panapakidis, Marios N. Moschakis

Abstract:

With the continuous increment of smart meter installations across the globe, the need for processing of the load data is evident. Clustering-based load profiling is built upon the utilization of unsupervised machine learning tools for the purpose of formulating the typical load curves or load profiles. The most commonly used algorithm in the load profiling literature is the K-means. While the algorithm has been successfully tested in a variety of applications, its drawback is the strong dependence in the initialization phase. This paper proposes a novel modified form of the K-means that addresses the aforementioned problem. Simulation results indicate the superiority of the proposed algorithm compared to the K-means.

Keywords: Clustering, load profiling, load modeling, machine learning, energy efficiency and quality.

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Authors: Luis Arias, Jorge E. Pezoa, Daniel Sbárbaro

Abstract:

In this paper, an automated algorithm to estimate and remove the continuous baseline from measured spectra containing both continuous and discontinuous bands is proposed. The algorithm uses previous information contained in a Continuous Database Spectra (CDBS) to obtain a linear basis, with minimum number of sampled vectors, capable of representing a continuous baseline. The proposed algorithm was tested by using a CDBS of flame spectra where Principal Components Analysis and Non-negative Matrix Factorization were used to obtain linear bases. Thus, the radical emissions of natural gas, oil and bio-oil flames spectra at different combustion conditions were obtained. In order to validate the performance in the baseline estimation process, the Goodness-of-fit Coefficient and the Root Mean-squared Error quality metrics were evaluated between the estimated and the real spectra in absence of discontinuous emission. The achieved results make the proposed method a key element in the development of automatic monitoring processes strategies involving discontinuous spectral bands.

Keywords: Flame spectra, removing baseline, recovering spectrum.

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Authors: Ch. Nerl, M. Wimmer, P. Hofer, E. Kaschnitz

Abstract:

The present article deals with a composite casting process that allows to produce bilayer AlSn6-Al strips based on the technique of horizontal continuous casting. In the first part experimental investigations on the production of a single layer AlSn6 strip are described. Afterwards essential results of basic compound casting trials using simple test specimen are presented to define the thermal conditions required for a metallurgical compound between the alloy AlSn6 and pure aluminium. Subsequently, numerical analyses are described. A finite element model was used to examine a continuous composite casting process. As a result of the simulations the main influencing parameters concerning the thermal conditions within the composite casting region could be pointed out. Finally, basic guidance is given for the design of an appropriate composite mould system.

Keywords: Aluminium alloys, composite casting, compound casting, continuous casting, numerical simulation

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Authors: Noboru Wakamoto, Kiyotaka Obunai, Kazuya Okubo, Toru Fujii

Abstract:

The aim of this study is to moderate the dependence of counter frictional coefficient on temperature between counter surfaces and to reduce the wear of C/C composites at low temperature. To modify the C/C composites, Silica (SiO₂) powders were added into phenolic resin for carbon precursor. The preform plate of the precursor of C/C composites was prepared by conventional filament winding method. The C/C composites plates were obtained by carbonizing preform plate at 2200 °C under an argon atmosphere. At that time, the silicon carbides (SiC) were synthesized around the surfaces and the internal vacancies of the C/C composites. The frictional coefficient on the counter surfaces and specific wear volumes of the C/C composites were measured by our developed frictional test machine like pin-on disk type. The XRD indicated that SiC was synthesized in the body of C/C composite fabricated by current method. The results of friction test showed that coefficient of friction of unmodified C/C composites have temperature dependence when the test condition was changed. In contrast, frictional coefficient of the C/C composite modified with SiO₂ powders was almost constant at about 0.27 when the temperature condition was changed from Room Temperature (RT) to 300 °C. The specific wear rate decreased from 25×10^-6 mm²/N to 0.1×10^-6 mm²/N. The observations of the surfaces after friction tests showed that the frictional surface of the modified C/C composites was covered with a film produced by the friction. This study found that synthesizing SiC around surface and internal vacancies of C/C composites was effective to moderate the dependence on the frictional coefficient and reduce to the abrasion of C/C composites.

Keywords: C/C composites, frictional coefficient, SiC, wear.

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Authors: V. Arbabi , I. Ebrahimzadeh, H. Ghanbari, M.M. Kaykha

Abstract:

Horizontal continuous casting is widely used to produce semi-finished non-Ferrous products. Homogeneity in the metallurgical characteristics and mechanical properties for this product is vital for industrial application. In the present work, the microstructure and mechanical properties of a horizontal continuous cast two-phase brass billet have been studied. Impact strength and hardness variations were examined and the phase composition and porosity studied with image analysis software. Distinct differences in mechanical properties were observed between the upper, middle and lower parts of the billet, which are explained in terms of the morphology and size of the phase in the microstructure. Hardness variation in the length of billet is higher in upper area but impact strength is higher in lower areas.

Keywords: Horizontal Continuous Casting, Two-phase brasses, CuZn40Al1 alloy, Microstructure, Impact Strength.

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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