Search results for: barrel principle

Authors: Tao Shun, Xiao Xiangning, HadjSaid, N.

Abstract:

In a liberalized electricity market, it is not surprising that different customers require different power quality (PQ) levels at different price. Power quality related to several power disturbances is described by many parameters, so how to define a comprehensive hierarchy evaluation system of power quality (PQCHES) has become a concerned issue. In this paper, based on four electromagnetic compatibility (EMC) levels, the numerical range of each power disturbance is divided into five grades (Grade I –Grade V), and the “barrel principle" of power quality is used for the assessment of overall PQ performance with only one grade indicator. A case study based on actual monitored data of PQ shows that the site PQ grade indicates the electromagnetic environment level and also expresses the characteristics of loads served by the site. The shortest plank principle of PQ barrel is an incentive mechanism, which can combine with the rewards/penalty mechanism (RPM) of consumed energy “on quality demand", to stimulate utilities to improve the overall PQ level and also stimulate end-user more “smart" under the infrastructure of future SmartGrid..

Keywords: Power quality, electromagnetic compatibility, SmartGrid, comprehensive evaluation, barrel principle, electricitymarket

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Authors: Shobha Sharma, Amita Dev

Abstract:

This research paper presents highly optimized barrel shifter at 22nm Hi K metal gate strained Si technology node. This barrel shifter is having a unique combination of static and dynamic body bias which gives lowest power delay product. This power delay product is compared with the same circuit at same technology node with static forward biasing at ‘supply/2’ and also with normal reverse substrate biasing and still found to be the lowest. The power delay product of this barrel sifter is .39362X10-17J and is lowered by approximately 78% to reference proposed barrel shifter at 32nm bulk CMOS technology. Power delay product of barrel shifter at 22nm Hi K Metal gate technology with normal reverse substrate bias is 2.97186933X10-17J and can be compared with this design’s PDP of .39362X10-17J. This design uses both static and dynamic substrate biasing and also has approximately 96% lower power delay product compared to only forward body biased at half of supply voltage. The NMOS model used are predictive technology models of Arizona state university and the simulations to be carried out using HSPICE simulator.

Keywords: Dynamic body biasing, highly optimized barrel shifter, PDP, Static body biasing.

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Authors: Hamed Bagheri, Seyd Javid Shariati

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The effects of type and amount of solvent on lubricant which is used in disposable medical devices are investigated in this article. Two kinds of common solvent, n-Hexane and n-Heptane, are used. The mechanical behavior of syringe has shown that n-Heptane has better mixing ratio and also more effective spray process in the barrel of syringe than n-Hexane because of similar solubility parameter to silicon oil. The results revealed that movement of plunger in the barrel increases when pure silicone is used because non-uniform film is created on the surface of barrel, and also, it seems that the form of silicon is converted from oil to gel due to sterilization process. The results showed that the convenient mixing ratio of solvent/lubricant oil is 80/20.

Keywords: Disposable medical devices, lubricant oil, solvent effect, solubility parameter.

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Authors: YaoAn Lu, QingZhen Bi, BaoRui Du, ShuLin Chen, LiMin Zhu, Kai Huang

Abstract:

Taking the design tolerance into account, this paper presents a novel efficient approach to generate iso-scallop tool path for five-axis strip machining with a barrel cutter. The cutter location is first determined on the scallop surface instead of the design surface, and then the cutter is adjusted to locate the optimal tool position based on the differential rotation of the tool axis and satisfies the design tolerance simultaneously. The machining strip width and error are calculated with the aid of the grazing curve of the cutter. Based on the proposed tool positioning algorithm, the tool paths are generated by keeping the scallop height formed by adjacent tool paths constant. An example is conducted to confirm the validity of the proposed method.

Keywords: Strip machining, barrel cutter, iso-scallop tool path, sculptured surfaces, differential motion.

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Authors: Arnab Majumdar, Sanjoy Sadhukhan

Abstract:

Although gun barrel steels are an important variety from defense view point, available literatures are very limited. In the present work, an IF grade Ni-Cr-Mo-V high strength low alloy steel is produced in Electric Earth Furnace-ESR Route. Ingot was hot forged to desired dimension with a reduction ratio of 70-75% followed by homogenization, hardening and tempering treatment. Sample chemistry, NMIR, macro and micro structural analyses were done. Mechanical properties which include tensile, impact, and fracture toughness were studied. Ultrasonic testing was done to identify internal flaws. The existing high strength low alloy Ni-Cr-Mo-V steel shows improved properties in modified processing route and heat treatment schedule in comparison to properties noted earlier for manufacturing of gun barrels. The improvement in properties seems to withstand higher explosive loads with the same amount of steel in gun barrel application.

Keywords: Gun barrel steels, IF grade, physical properties, thermal and mechanical processing, mechanical properties, ultrasonic testing.

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Authors: C. I. Omohimi, O. P. Sobukola, K. O. Sarafadeen, L.O. Sanni

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Flour from Mucuna beans (Mucuna pruriens) were used in producing texturized meat analogue using a single screw extruder to monitor modifications on the proximate composition and the functional properties at high moisture level. Response surface methodology based on Box Behnken design at three levels of barrel temperature (110, 120, 130°C), screw speed (100,120,140rpm) and feed moisture (44, 47, 50%) were used in 17 runs. Regression models describing the effect of variables on the product responses were obtained. Descriptive profile analyses and consumer acceptability test were carried out on optimized flavoured extruded meat analogue. Responses were mostly affected by barrel temperature and moisture level and to a lesser extent by screw speed. Optimization results based on desirability concept indicated that a barrel temperature of 120.15°C, feed moisture of 47% and screw speed of 119.19 rpm would produce meat analogue of preferable proximate composition, functional and sensory properties which reveals consumers` likeness for the product.

Keywords: Functional properties, mucuna bean flour, optimization, proximate composition, texturized meat analogue.

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Authors: C. M. van der Bank, Marjoné van der Bank

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International and domestic environmental law has evolved quite rapidly in the last few decades. At the international level the Stockholm and Rio Declarations paved the way for a broad based consensus of the international community on environmental issues and principles. At the Domestic level also many states have incorporated environmental protection in their constitutions and even more states are doing the same at least in their domestic legislations. In this process of evolution environmental law has unleashed a number of novel principles such as; the participatory principle, the polluter pays principle, the precautionary principle, the intergenerational and intra-generational principles, the prevention principle, the sustainable development principle and so on.

Keywords: Environment, human rights, international, protection.

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Authors: M. Michael Gromiha, Y. Yabuki, K. Imai, P. Horton, K. Fukui

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We have developed a database for membrane protein functions, which has more than 3000 experimental data on functionally important amino acid residues in membrane proteins along with sequence, structure and literature information. Further, we have proposed different methods for identifying membrane proteins based on their functions: (i) discrimination of membrane transport proteins from other globular and membrane proteins and classifying them into channels/pores, electrochemical and active transporters, and (ii) β-signal for the insertion of mitochondrial β-barrel outer membrane proteins and potential targets. Our method showed an accuracy of 82% in discriminating transport proteins and 68% to classify them into three different transporters. In addition, we have identified a motif for targeting β-signal and potential candidates for mitochondrial β-barrel membrane proteins. Our methods can be used as effective tools for genome-wide annotations.

Keywords: Membrane proteins, database, transporters, discrimination, β-signal.

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Authors: Roshayani Arshad, Normah Omar, Siti Fatimah Awang

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The move from cash accounting to accrual accounting, or rule-based to principle-based accounting, by many governments is part of an ongoing efforts in promoting a more business-like and performance-focused public sector. Using questionnaire responses from preparers of financial statements of public universities in Malaysia, this study examines the implementation challenges and benefits of principle-based accounting. Results from these responses suggest that most respondents perceived significant costs would be incurred in relation to staff training and recruitment of staffs with relevant technical knowledge. In addition, most respondents also perceived that there will be significant changes in the current accounting system and structure in order to comply with the principle-based accounting requirements. However, most respondents perceived that these changes might not result in significant benefits for management purposes, for example, financial management, budgeting and allocation of resources. Nevertheless, most respondents perceived that principle-based accounting information would facilitate the monitoring function of the board. The general perception is that adoption of principle-based accounting information is not significantly useful than rule-based accounting information is expected to change over time as preparers of the financial statements gradually understand and appreciate the benefits of principle-based accounting information. This infers that the perceived usefulness of different accounting system is a function of familiarity by the preparers.

Keywords: Accrual accounting, principle-based accounting, public sector, rule-based accounting.

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Authors: Reza Gheisari, Paulo J. Bartolo, Nicholas Goddard

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Polymeric micro-cantilevers (Cs) are rapidly becoming popular for MEMS applications such as chemo- and biosensing as well as purely electromechanical applications such as microrelays. Polymer materials present suitable physical and chemical properties combined with low-cost mass production. Hence, micro-cantilevers made of polymers indicate much more biocompatibility and adaptability of rapid prototyping along with mechanical properties. This research studies the effects of three process and one size factors on the filling behaviour in micro cavity, and the role of each in the replication of micro parts using different polymer materials i.e. polypropylene (PP) SABIC 56M10 and acrylonitrile butadiene styrene (ABS) Magnum 8434 . In particular, the following factors are considered: barrel temperature, mould temperature, injection speed and the thickness of micro features. The study revealed that the barrel temperature and the injection speed are the key factors affecting the flow length of micro features replicated in PP and ABS. For both materials, an increase of feature sizes improves the melt flow. However, the melt fill of micro features does not increase linearly with the increase of their thickness.

Keywords: Flow length, micro-cantilevers, micro injection moulding, microfabrication.

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Authors: Han Xiao, Xiaoyan Zhu

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Margin-Based Principle has been proposed for a long time, it has been proved that this principle could reduce the structural risk and improve the performance in both theoretical and practical aspects. Meanwhile, feed-forward neural network is a traditional classifier, which is very hot at present with a deeper architecture. However, the training algorithm of feed-forward neural network is developed and generated from Widrow-Hoff Principle that means to minimize the squared error. In this paper, we propose a new training algorithm for feed-forward neural networks based on Margin-Based Principle, which could effectively promote the accuracy and generalization ability of neural network classifiers with less labelled samples and flexible network. We have conducted experiments on four UCI open datasets and achieved good results as expected. In conclusion, our model could handle more sparse labelled and more high-dimension dataset in a high accuracy while modification from old ANN method to our method is easy and almost free of work.

Keywords: Max-Margin Principle, Feed-Forward Neural Network, Classifier.

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Authors: Yingchun Jiang, Yan Tang

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In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces Hs(Rd) and H-s(Rd).

Keywords: Nonstationary, dual frames, dual Sobolev spaces, extension principle.

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Authors: C. S. Saini

Abstract:

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

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

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Authors: Manouchehr Amiri

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This article presents a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary Data Matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principle is investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Bekenstein, and mass-energy equivalence are derived.

Keywords: Physical theory of information, binary data matrix model, Shannon information theory, bit information principle.

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Authors: Tomáš Urbanec

Abstract:

Paper presents simple sixport principle and its frequency bandwidth. The novel multisixport approach is presented with its possibilities, typical parameters and frequency bandwidth. Practical implementation is shown with its measurement parameters and calibration. The bandwidth circa 1:100 is obtained.

Keywords: microwave measurement, sixport, VNA, wideband.

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Authors: Georgi Yordanov Georgiev, Michael Daly, Erin Gombos, Amrit Vinod, Gajinder Hoonjan

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Measures of complexity and entropy have not converged to a single quantitative description of levels of organization of complex systems. The need for such a measure is increasingly necessary in all disciplines studying complex systems. To address this problem, starting from the most fundamental principle in Physics, here a new measure for quantity of organization and rate of self-organization in complex systems based on the principle of least (stationary) action is applied to a model system - the central processing unit (CPU) of computers. The quantity of organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has a fine, S-shaped structure, revealing some of the mechanisms of self-organization. The principle of least action helps to explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self organization to improve their quality. It can be applied to other complex systems from Physics, Chemistry, Biology, Ecology, Economics, Cities, network theory and others where complex systems are present.

Keywords: Organization, self-organization, complex system, complexification, quantitative measure, principle of least action, principle of stationary action, attractor, progressive development, acceleration, stochastic.

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

Abstract:

This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: Online data updates, covariance matrix, online principle component analysis (OPCA), matrix perturbation.

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Authors: B. Sudhakar, K. A. Ponnusamy

Abstract:

In India cotton was the major commercial crop and cultivating all the states. In recent years, area of cotton declined due to pest and disease attack, drought, lower price for the produces etc. The first reason as pest and disease attack will be the challenges and it is of utmost importance that in future the insect problems would have to be tackled through Integrated Pest Management (IPM). The present study deals with principle knowledge of IPM adopting cotton cultivators in irrigated and rainfed conditions. Under irrigated conditions, among cultural practices, all respondents had principle knowledge about growing high yielding and pest resistant hybrids, sowing quality and certified seeds and avoiding cotton ratoon cropping. Regarding mechanical practices all respondents had principle knowledge about collecting and destroying egg, larvae and pupae of pests and removing and destroying pest and disease infected cotton squares, flowers and other shed materials. With regard to biological practices, 93% of them had principle knowledge about spraying neem oil, followed by 82% about tying Trichogramma eggcard. Among chemical practices, more than 90% of the respondents had principle knowledge about of spraying herbicide (96%), identifying ETL (Economic Threshold Level) for cotton pests (94%), and applying safe insecticides (90%). Under rainfed condition, among cultural practices, all respondents had principle knowledge about sowing quality and certified seeds and growing high yielding and pest resistant hybrids seeds. Regarding mechanical practices hundred percentage of the respondents had principle knowledge on the mechanical practices viz., collecting and destroying egg, larvae and pupae of pests and removing and destroying pest and disease infected cotton squares, flowers and other shed materials. With regard to biological practices, 96% of the respondents had correct in principle knowledge about spraying neem oil, followed by 89% about tying Trichogramma eggcard. With regard to chemical practices, more than 90% of the respondents had principle knowledge of applying safe insecticides (95%), avoiding repeated use of the same insecticides (95%), identifying ETL for cotton pests (94%) and applying granular insecticides (90%).

Keywords: Biological practices, chemical practices, cultural practices, mechanical practices, integrated pest management.

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: All-or-none, computational modelling, mathematical model, transmembrane voltage, action potential.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

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Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

Keywords: Fractional Fourier Transform, uncertainty principle, Fractional Fourier Span, amplitude, phase.

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Authors: M.R. Isvandzibaei, M.R. Alinaghizadeh, A.H. Zaman

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In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions

Keywords: Vibration, FGM, cylindrical shell, Hamilton's principle, clamped supported.

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Authors: Meng Hu, Lili Wang

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This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form:  Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.

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Authors: A. Benzian

Abstract:

The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.

Keywords: Inertia, principle of equivalence, tensors, Riemannian geometry.

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Authors: S. El Safty, A. El-Zonkoly

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The ability to detect and classify the type of fault plays a great role in the protection of power system. This procedure is required to be precise with no time consumption. In this paper detection of fault type has been implemented using wavelet analysis together with wavelet entropy principle. The simulation of power system is carried out using PSCAD/EMTDC. Different types of faults were studied obtaining various current waveforms. These current waveforms were decomposed using wavelet analysis into different approximation and details. The wavelet entropy of such decompositions is analyzed reaching a successful methodology for fault classification. The suggested approach is tested using different fault types and proven successful identification for the type of fault.

Keywords: Fault classification, wavelet transform, waveletentropy.

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Authors: H. Farkisch, A.I. Che-Ani, V. Ahmadi, M. Surat

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The role of neighborhood center as semi public (the balance space) is disappeared in bonding between private and public in new urbanism. In this way, a hierarchical principle in the traditional neighborhood center appears to create or develop the conditions for residents` relationships and belonging. This paper evaluates significant of hierarchical principles of the neighborhood center in residents` territoriality and its factors. In this way Miandeh neighborhood center from Boshrooyeh city was determined as a case study area. Results indicated that a hierarchical principle is the best instrument to improve the territoriality as the subcomponent of place belonging in residents. The findings help the urban designer to revitalization the neighborhoods and proceedings in organization of physical space.

Keywords: Belonging, Neighborhood center, Revitalization, Territoriality

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: Gravity gradient, accelerometer, gravity gradient sensor, single-axis rotation modulation.

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Authors: Paiboon Chuwatthanakij

Abstract:

In reference to the legal state in the Thai legal system, most people understand the minor principles of the legal state form, which are the principles that can be explained and understood easily and the results can be seen clearly, especially in the legitimacy of administrative acts. Therefore, there is no awareness of justice, which is the fundamental value of Thai law. The legitimacy of administrative acts requires the administration to adhere to the constitution and legislative laws in enforcement of the laws. If it appears that the administrative acts are illegitimate, the administrative court, as the court of justice, will revoke those acts as if they had never been set in the legal system, this will affect people’s trust as they are unaware as to whether the administrative acts that appoint their lives are legitimate or not. Regarding the revocation of administrative orders by the administrative court as if those orders had never existed, the common individual surely cannot be expected to comprehend the security of their juristic position. Therefore, the legal state does not require a revocation of the government’s acts to terminate its legal results merely because those acts are illegitimate, but there should be considerations and realizations regarding the “The Principle of the Protection of Legitimate Expectation,” which is a minor principle in the legal state’s content that focuses on supporting and protecting legitimate expectations of the juristic position of an individual and maintaining justice, which is the fundamental value of Thai law.

Keywords: Legal state, Rule of law, Protection of legitimate.

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Authors: Jose William Porras Ferreira

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This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: Shilpa N. Kulkarni, Sujata R. Patrikar

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In the present work, an attempt is made to understand electromagnetic field confinement in a subwavelength waveguide structure using concepts of quantum mechanics. Evanescent field in the waveguide is looked as inability of the photon to get confined in the waveguide core and uncertainty of position is assigned to it. The momentum uncertainty is calculated from position uncertainty. Schrödinger wave equation for the photon is written by incorporating position-momentum uncertainty. The equation is solved and field distribution in the waveguide is obtained. The field distribution and power confinement is compared with conventional waveguide theory. They were found in good agreement with each other.

Keywords: photon localization in waveguide, photon tunneling, quantum confinement of light, Schrödinger wave equation, uncertainty principle.

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