Search results for: Pivot Point.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1768

Search results for: Pivot Point.

1198 Relational Framework and its Applications

Authors: Lidia Obojska

Abstract:

This paper has, as its point of departure, the foundational axiomatic theory of E. De Giorgi (1996, Scuola Normale Superiore di Pisa, Preprints di Matematica 26, 1), based on two primitive notions of quality and relation. With the introduction of a unary relation, we develop a system totally based on the sole primitive notion of relation. Such a modification enables a definition of the concept of dynamic unary relation. In this way we construct a simple language capable to express other well known theories such as Robinson-s arithmetic or a piece of a theory of concatenation. A key role in this system plays an abstract relation designated by “( )", which can be interpreted in different ways, but in this paper we will focus on the case when we can perform computations and obtain results.

Keywords: language, unary relations, arithmetic, computability

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1260
1197 Study of Single Network Adjustment Using QOCA Software in Korea

Authors: Seongchan Kang, Hongsik Yun, Hyukgil Kim, Minwoo Park

Abstract:

For this study, this researcher conducted a precision network adjustment with QOCA, the precision network adjustment software developed by Jet Propulsion Laboratory, to perform an integrated network adjustment on the Unified Control Points managed by the National Geographic Information Institute. Towards this end, 275 Unified Control Points observed in 2008 were selected before a network adjustment is performed on those 275 Unified Control Points. The RMSE on the discrepancies of coordinates as compared to the results of GLOBK was ±6.07mm along the N axis, ±2.68mm along the E axis and ±6.49mm along the U axis.

Keywords: Network adjustment, QOCA, unified control point.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1848
1196 The Application of Homotopy Method In Solving Electrical Circuit Design Problem

Authors: Talib Hashim Hasan

Abstract:

This paper describes simple implementation of homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed point methods. In homoptopy methods, an embedding parameter is used to control the convergence. The method purposed in this work utilizes a special homotopy called Newton homotopy. Numerical example solved in MATLAB is given to show the effectiveness of the purposed method

Keywords: electrical circuit homotopy, methods, MATLAB, Newton homotopy

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3029
1195 The Effect of Symmetry on the Perception of Happiness and Boredom in Design Products

Authors: Michele Sinico

Abstract:

The present research investigates the effect of symmetry on the perception of happiness and boredom in design products. Three experiments were carried out in order to verify the degree of the visual expressive value on different models of bookcases, wall clocks, and chairs. 60 participants directly indicated the degree of happiness and boredom using 7-point rating scales. The findings show that the participants acknowledged a different value of expressive quality in the different product models. Results show also that symmetry is not a significant constraint for an emotional design project.

Keywords: Product experience, emotional design, symmetry, expressive qualities.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 807
1194 A New Voting Approach to Texture Defect Detection Based on Multiresolutional Decomposition

Authors: B. B. M. Moasheri, S. Azadinia

Abstract:

Wavelets have provided the researchers with significant positive results, by entering the texture defect detection domain. The weak point of wavelets is that they are one-dimensional by nature so they are not efficient enough to describe and analyze two-dimensional functions. In this paper we present a new method to detect the defect of texture images by using curvelet transform. Simulation results of the proposed method on a set of standard texture images confirm its correctness. Comparing the obtained results indicates the ability of curvelet transform in describing discontinuity in two-dimensional functions compared to wavelet transform

Keywords: Curvelet, Defect detection, Wavelet.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1573
1193 Predictive Model of Sensor Readings for a Mobile Robot

Authors: Krzysztof Fujarewicz

Abstract:

This paper presents a predictive model of sensor readings for mobile robot. The model predicts sensor readings for given time horizon based on current sensor readings and velocities of wheels assumed for this horizon. Similar models for such anticipation have been proposed in the literature. The novelty of the model presented in the paper comes from the fact that its structure takes into account physical phenomena and is not just a black box, for example a neural network. From this point of view it may be regarded as a semi-phenomenological model. The model is developed for the Khepera robot, but after certain modifications, it may be applied for any robot with distance sensors such as infrared or ultrasonic sensors.

Keywords: Mobile robot, sensors, prediction, anticipation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1448
1192 The Effect of Catastrophic Losses on Insurance Cycle: Case of Croatia

Authors: D. Jakovčević, M. Mihelja Žaja

Abstract:

This paper provides an analysis of the insurance cycle in the Republic of Croatia and whether they are affected by catastrophic losses on a global level. In general, it is considered that insurance cycles are particularly pronounced in periods of financial crisis, but are also affected by the growing number of catastrophic losses. They cause the change of insurance cycle and premium growth and intensification and narrowing of the coverage conditions, so these variables move in the same direction and these phenomena point to a new cycle. The main goal of this paper is to determine the existence of insurance cycle in the Republic of Croatia and investigate whether catastrophic losses have an influence on insurance cycles.

Keywords: Catastrophic loss, insurance cycle, premium, Republic of Croatia.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2106
1191 Approximating Fixed Points by a Two-Step Iterative Algorithm

Authors: Safeer Hussain Khan

Abstract:

In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: Contractive-like operator, iterative algorithm, fixed point, strong convergence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2022
1190 Improvement of New Government R&D Program Plans through Preliminary Feasibility Studies

Authors: Hyun-Kyu Kang

Abstract:

As a part of an evaluation system for R&D programs, the Korean Government has applied the preliminary feasibility study to new government R&D program plans. Basically, the fundamental purpose of the preliminary feasibility study is to decide that the government will either do or do not invest in a new R&D Program. Additionally, the preliminary feasibility study can contribute to the improvement of R&D program plans. For example, 2 cases of new R&D program plans applied to the study are explained in this paper and there are expectations that these R&D programs would yield better performance than without the study. It is thought that the important point of the preliminary feasibility study is not only the effective decision making process of R&D program but also the opportunity to improve R&D program plan actually.

Keywords: Preliminary feasibility study, Government R&D program.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1304
1189 Adaptive Nonparametric Approach for Guaranteed Real-Time Detection of Targeted Signals in Multichannel Monitoring Systems

Authors: Andrey V. Timofeev

Abstract:

An adaptive nonparametric method is proposed for stable real-time detection of seismoacoustic sources in multichannel C-OTDR systems with a significant number of channels. This method guarantees given upper boundaries for probabilities of Type I and Type II errors. Properties of the proposed method are rigorously proved. The results of practical applications of the proposed method in a real C-OTDR-system are presented in this report.

Keywords: Adaptive detection, change point, interval estimation, guaranteed detection, multichannel monitoring systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1884
1188 Transferring Route Plan over Time

Authors: Barıs Kocer, Ahmet Arslan

Abstract:

Travelling salesman problem (TSP) is a combinational optimization problem and solution approaches have been applied many real world problems. Pure TSP assumes the cities to visit are fixed in time and thus solutions are created to find shortest path according to these point. But some of the points are canceled to visit in time. If the problem is not time crucial it is not important to determine new routing plan but if the points are changing rapidly and time is necessary do decide a new route plan a new approach should be applied in such cases. We developed a route plan transfer method based on transfer learning and we achieved high performance against determining a new model from scratch in every change.

Keywords: genetic algorithms, transfer learning, travellingsalesman problem

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1271
1187 Surface Topography Measurement by Confocal Spectral Interferometry

Authors: A. Manallah, C. Meier

Abstract:

Confocal spectral interferometry (CSI) is an innovative optical method for determining microtopography of surfaces and thickness of transparent layers, based on the combination of two optical principles: confocal imaging, and spectral interferometry. Confocal optical system images at each instant a single point of the sample. The whole surface is reconstructed by plan scanning. The interference signal generated by mixing two white-light beams is analyzed using a spectrometer. In this work, five ‘rugotests’ of known standard roughnesses are investigated. The topography is then measured and illustrated, and the equivalent roughness is determined and compared with the standard values.

Keywords: Confocal spectral interferometry, Nondestructive testing, Optical metrology, Surface topography, Roughness.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 974
1186 Robust Probabilistic Online Change Detection Algorithm Based On the Continuous Wavelet Transform

Authors: Sergei Yendiyarov, Sergei Petrushenko

Abstract:

In this article we present a change point detection algorithm based on the continuous wavelet transform. At the beginning of the article we describe a necessary transformation of a signal which has to be made for the purpose of change detection. Then case study related to iron ore sinter production which can be solved using our proposed technique is discussed. After that we describe a probabilistic algorithm which can be used to find changes using our transformed signal. It is shown that our algorithm works well with the presence of some noise and abnormal random bursts.

Keywords: Change detection, sinter production, wavelet transform.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1459
1185 Validation Testing for Temporal Neural Networks for RBF Recognition

Authors: Khaled E. A. Negm

Abstract:

A neuron can emit spikes in an irregular time basis and by averaging over a certain time window one would ignore a lot of information. It is known that in the context of fast information processing there is no sufficient time to sample an average firing rate of the spiking neurons. The present work shows that the spiking neurons are capable of computing the radial basis functions by storing the relevant information in the neurons' delays. One of the fundamental findings of the this research also is that when using overlapping receptive fields to encode the data patterns it increases the network-s clustering capacity. The clustering algorithm that is discussed here is interesting from computer science and neuroscience point of view as well as from a perspective.

Keywords: Temporal Neurons, RBF Recognition, Perturbation, On Line Recognition.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1492
1184 The Democratization of 3D Capturing: An Application Investigating Google Tango Potentials

Authors: Carlo Bianchini, Lorenzo Catena

Abstract:

The appearance of 3D scanners and then, more recently, of image-based systems that generate point clouds directly from common digital images have deeply affected the survey process in terms of both capturing and 2D/3D modelling. In this context, low cost and mobile systems are increasingly playing a key role and actually paving the way to the democratization of what in the past was the realm of few specialized technicians and expensive equipment. The application of Google Tango on the ancient church of Santa Maria delle Vigne in Pratica di Mare – Rome presented in this paper is one of these examples.

Keywords: Architectural survey, augmented/mixed/virtual reality, Google Tango project, image-based 3D capturing.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 711
1183 Evaluating Sinusoidal Functions by a Low Complexity Cubic Spline Interpolator with Error Optimization

Authors: Abhijit Mitra, Harpreet Singh Dhillon

Abstract:

We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.

Keywords: Arithmetic, spline interpolator, hardware design, erroranalysis, optimization methods.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2057
1182 A Simple Adaptive Algorithm for Norm-Constrained Optimization

Authors: Hyun-Chool Shin

Abstract:

In this paper we propose a simple adaptive algorithm iteratively solving the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates scalar normalization which is computationally much simpler. The analysis of stationary point is presented to show that the proposed algorithm indeed solves the constrained optimization problem. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.

Keywords: constrained optimization, unit-norm, LMS, principle component analysis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2128
1181 Input-Output Analysis in Laptop Computer Manufacturing

Authors: H. Z. Ulukan, E. Demircioğlu, M. Erol Genevois

Abstract:

The scope of this paper and the aim of proposed model were to apply monetary Input –Output (I-O) analysis to point out the importance of reusing know-how and other requirements in order to reduce the production costs in a manufacturing process for a laptop computer. I-O approach using the monetary input-output model is employed to demonstrate the impacts of different factors in a manufacturing process. A sensitivity analysis showing the correlation between these different factors is also presented. It is expected that the recommended model would have an advantageous effect in the cost minimization process.

Keywords: Input-Output Analysis, Monetary Input-Output Model, Manufacturing Process, Laptop Computer.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4627
1180 A Fast and Robust Protocol for Reconstruction and Re-Enactment of Historical Sites

Authors: S. I. Abu Alasal, M. M. Esbeih, E. R. Fayyad, R. S. Gharaibeh, M. Z. Ali, A. A. Freewan, M. M. Jamhawi

Abstract:

This research proposes a novel reconstruction protocol for restoring missing surfaces and low-quality edges and shapes in photos of artifacts at historical sites. The protocol starts with the extraction of a cloud of points. This extraction process is based on four subordinate algorithms, which differ in the robustness and amount of resultant. Moreover, they use different -but complementary- accuracy to some related features and to the way they build a quality mesh. The performance of our proposed protocol is compared with other state-of-the-art algorithms and toolkits. The statistical analysis shows that our algorithm significantly outperforms its rivals in the resultant quality of its object files used to reconstruct the desired model.

Keywords: Meshes, Point Clouds, Surface Reconstruction Protocols, 3D Reconstruction.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2003
1179 A New Type Safety-Door for Earthquake Disaster Prevention - Part I

Authors: Daniel Y. Abebe, Jaehyouk Choi

Abstract:

From the past earthquake events, many people get hurt at the exit while they are trying to go out of the buildings because of the exit doors are unable to be opened. The door is not opened because it deviates from its the original position. The aim of this research is to develop and evaluate a new type safety door that keeps the door frame in its original position or keeps its edge angles perpendicular during and post-earthquake. The proposed door is composed of three components: outer frame joined to the wall, inner frame (door frame) and circular hollow section connected to the inner and outer frame which is used as seismic energy dissipating device.

Keywords: Earthquake disaster, FE analysis, Low yield point steel, Safety-doors.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2281
1178 The Different Ways to Describe Regular Languages by Using Finite Automata and the Changing Algorithm Implementation

Authors: Abdulmajid Mukhtar Afat

Abstract:

This paper aims at introducing finite automata theory, the different ways to describe regular languages and create a program to implement the subset construction algorithms to convert nondeterministic finite automata (NFA) to deterministic finite automata (DFA). This program is written in c++ programming language. The program reads FA 5tuples from text file and then classifies it into either DFA or NFA. For DFA, the program will read the string w and decide whether it is acceptable or not. If accepted, the program will save the tracking path and point it out. On the other hand, when the automation is NFA, the program will change the Automation to DFA so that it is easy to track and it can decide whether the w exists in the regular language or not.

Keywords: Finite Automata, subset construction DFA, NFA.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1986
1177 Distributed Self-Healing Protocol for Unattended Wireless Sensor Network

Authors: E. Golden Julie, E. Sahaya Rose Vigita, S. Tamil Selvi

Abstract:

Wireless sensor network is vulnerable to a wide range of attacks. Recover secrecy after compromise, to develop technique that can detect intrusions and able to resilient networks that isolates the point(s) of intrusion while maintaining network connectivity for other legitimate users. To define new security metrics to evaluate collaborative intrusion resilience protocol, by leveraging the sensor mobility that allows compromised sensors to recover secure state after compromise. This is obtained with very low overhead and in a fully distributed fashion using extensive simulations support our findings.

Keywords: WSN security, intrusion resilience, compromised sensors, mobility.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1757
1176 Existence and Stability Analysis of Discrete-time Fuzzy BAM Neural Networks with Delays and Impulses

Authors: Chao Wang, Yongkun Li

Abstract:

In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.

Keywords: Discrete-time fuzzy BAM neural networks, ımpulses, global exponential stability, global asymptotical stability, equilibrium point.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1508
1175 Modelling Peer Group Dieting Behaviour

Authors: M. J. Cunha

Abstract:

The aim of this paper is to understand how peers can influence adolescent girls- dieting behaviour and their body image. Departing from imitation and social learning theories, we study whether adolescent girls tend to model their peer group dieting behaviours, thus influencing their body image construction. Our study was conducted through an enquiry applied to a cluster sample of 466 adolescent high school girls in Lisbon city public schools. Our main findings point to an association between girls- and peers- dieting behaviours, thus reinforcing the modelling hypothesis.

Keywords: Modelling, Diet, Body image, Adolescent girls, Peer group.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1774
1174 The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations

Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1318
1173 Monitoring and Prediction of Intra-Crosstalk in All-Optical Network

Authors: Ahmed Jedidi, Mesfer Mohammed Alshamrani, Alwi Mohammad A. Bamhdi

Abstract:

Optical performance monitoring and optical network management are essential in building a reliable, high-capacity, and service-differentiation enabled all-optical network. One of the serious problems in this network is the fact that optical crosstalk is additive, and thus the aggregate effect of crosstalk over a whole AON may be more nefarious than a single point of crosstalk. As results, we note a huge degradation of the Quality of Service (QoS) in our network. For that, it is necessary to identify and monitor the impairments in whole network. In this way, this paper presents new system to identify and monitor crosstalk in AONs in real-time fashion. particular, it proposes a new technique to manage intra-crosstalk in objective to relax QoS of the network.

Keywords: All-optical networks, optical crosstalk, optical cross-connect, crosstalk, monitoring crosstalk.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1718
1172 The Correlation between Peer Aggression and Peer Victimization: Are Aggressors Victims Too?

Authors: Glenn M. Calaguas

Abstract:

To investigate the possible correlation between peer aggression and peer victimization, 148 sixth-graders were asked to respond to the Reduced Aggression and Victimization Scales (RAVS). RAVS measures the frequency of reporting aggressive behaviors or of being victimized during the previous week prior to the survey. The scales are composed of six items each. Each point represents one instance of aggression or victimization. Specifically, the Pearson Product-Moment Correlation Coefficient (PMCC) was used to determine the correlations between the scores of the sixthgraders in the two scales, both in individual items and total scores. Positive correlations were established and correlations were significant at the 0.01 levels.

Keywords: correlation, peer aggression, peer victimization, sixth-graders.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2445
1171 Evaluation of the Elastic Mechanical Properties of a Hybrid Adhesive Material

Authors: Moudar H. A. Zgoul, Amin Al Zamer

Abstract:

Adhesive materials and adhesion have been the focal point of multiple research works related to numerous applications, particularly, aerospace, and aviation industries. To enhance the properties of conventional adhesive materials, additives have been introduced to the mix in order to enhance their mechanical and physical properties by creating a hybrid adhesive material. The evaluation of the mechanical properties of such hybrid adhesive materials is thus of an essential requirement for the purpose of properly modeling their behavior accurately. This paper presents an approach/tool to simulate the behavior such hybrid adhesives in a way that will allow researchers to better understand their behavior while in service.

Keywords: Adhesive materials, analysis, hybrid adhesives, mechanical properties, simulation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1114
1170 High Capacity Data Hiding based on Predictor and Histogram Modification

Authors: Hui-Yu Huang, Shih-Hsu Chang

Abstract:

In this paper, we propose a high capacity image hiding technology based on pixel prediction and the difference of modified histogram. This approach is used the pixel prediction and the difference of modified histogram to calculate the best embedding point. This approach can improve the predictive accuracy and increase the pixel difference to advance the hiding capacity. We also use the histogram modification to prevent the overflow and underflow. Experimental results demonstrate that our proposed method within the same average hiding capacity can still keep high quality of image and low distortion

Keywords: data hiding, predictor

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1886
1169 PIL Theory

Authors: A. Peveri

Abstract:

The curvature space-time by the presence of material, this deformation must present a pattern of deformation, not random. Space is uniform, elastic and any modification that occurs in one part, causes a change in another.

This deformation exists, must be a constant value and is independent of the observer, and relates the amount of matter, the force caused by the curvature of space and surface space. This unit of space is defined in this study as PIL and represents a constant area of space, deformable in the direction and sense of the center of mass of the body. The PIL is curved and connected to the center of mass of the Earth, to get to that point, through all matter, thus forming part of any place between particles at atomic and subatomic levels. At these levels the space between each particle is flat, unlike the macro where the space curves.

Keywords: Space flat, Space curved, Unit of space, Deformation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1516