Search results for: Euclidean-5 space
1411 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 15041410 A New Class F2 (M, 0, N)L„ p)F of The Double Difference Sequences of Fuzzy Numbers
Authors: N. Subramanian, C. Murugesan
Abstract:
The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.
Keywords: Orlicz function, solid space, metric space, completeness
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10021409 Need of National Space Legislation for Space Faring Nations
Authors: Muhammad Naveed, Yang Caixia
Abstract:
The need for national space legislation is pivotal, particularly in light of the fact that in recent years space activities have grown immensely both in volume and diversity. Countries are progressively developing capabilities in space exploration and scientific discoveries, market their capabilities to manufacture satellites, provide launch services from their facilities and are looking to privatize and commercialize their space resources. Today, nations are also seeking to comprehend the technological and financial potential of the private sector and are considering to share their financial burdens with them and to limit their exposures to risks, but they are lagging behind in legal framework in this regard. In the perspective of these emerging developments, it is therefore, felt that national space legislation should be enacted with the goal of building and implementing a vibrant and transparent legal framework at the national level to hasten investments and to ensure growth in this capital intensive - highly yield strategic sector. This study looks at (I) the international legal framework that governs space activities; (II) motivation behind making national space laws; and (III) the need for national space legislation. The paper concludes with some recommendations with regards to the conceivable future direction for national space legislation, in particular space empowered sub-areas for countries.
Keywords: International conventions, national legislation, space faring nation, space law.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11921408 New Class of Chaotic Mappings in Symbol Space
Authors: Inese Bula
Abstract:
Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.
Keywords: Infinite symbol space, prefix metric, chaotic mapping, generator function, jump mapping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15081407 Time Map
Authors: A. Peveri
Abstract:
The interaction of mass will determine the curvature of space-time, may determine that events proceed at different rates of time at each point in space, so each has a corresponding gravitational potential time. So we can find different values of gravity (g), corresponding to different times (t), thus making a "map of time in space." The space-time is curved by present mass, causing a force of attraction towards the body, but if you invest the curvature of space-time, we find that this field is repulsive: Obtaining negative gravitational forces and positive gravitational forces respectively.
Keywords: Space-time, time, positive gravitation, negative gravitation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15131406 Weighted Composition Operators Acting between Kind of Weighted Bergman-Type Spaces and the Bers-Type Space
Authors: Amnah E. Shammahy
Abstract:
In this paper, we study the boundedness and compactness of the weighted composition operator Wu,φ, which is induced by an holomorphic function u and holomorphic self-map φ, acting between the NK-space and the Bers-type space H∞α on the unit disk.
Keywords: Weighted composition operators, NK-space, Bers-type space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16251405 Analysis on the Development and Evolution of China's Territorial Spatial Planning
Authors: He YuanYan
Abstract:
In recent years, China has implemented the reform of land and space planning. As an important public policy, land and space planning plays a vital role in the construction and development of cities. Land and space planning throughout the country is in full swing, but there are still many disputes from all walks of life. The content, scope, and specific implementation process of land and space planning are also ambiguous, leading to the integration of multiple regulation problems such as unclear authority, unclear responsibilities, and poor planning results during the implementation of land and space planning. Therefore, it is necessary to sort out the development and evolution of domestic and foreign land space planning, clarify the problems and cruxes from the current situation of China's land space planning, and sort out the obstacles and countermeasures to the implementation of this policy, so as to deepen the understanding of the connotation of land space planning. It is of great practical significance for all planners to correctly understand and clarify the specific contents and methods of land space planning and to smoothly promote the implementation of land space planning at all levels.
Keywords: Territorial spatial planning, public policy, land space, overall planning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2121404 Research on Spatial Morphology and Protection of Traditional Rural Settlements Based on Space Syntax: Taking Xiazhuang Village and Shijia Village in Huzhou as Example
Authors: Shenpu Liu
Abstract:
Space syntax, a paradigm of the urban research, which manifests people’s intuitive and abstract perception of a material space with a solid mathematical way, explores how space represents its social characteristics. Taking Xiazhuang village and Shijia Village in Huzhou as an example and focusing on inward structure and street space, this article recognizes the connotative significance of the settlement with the aid of space syntax theory and quantitative analysis method from the perspective of spatial configuration to present relevant suggestions for its future planning and provides references for traditional rural settlement protection.Keywords: Shijia village, space configuration, space syntax, traditional rural settlement, Xiazhuang village.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10261403 Topological Quantum Diffeomorphisms in Field Theory and the Spectrum of the Space-Time
Authors: Francisco Bulnes
Abstract:
Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, spectrum of ring, topological quantum diffeomorphisms.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9961402 Digital Transformation as the Subject of the Knowledge Model of the Discursive Space
Authors: Rafal Maciag
Abstract:
Due to the development of the current civilization, one must create suitable models of its pervasive massive phenomena. Such a phenomenon is the digital transformation, which has a substantial number of disciplined, methodical interpretations forming the diversified reflection. This reflection could be understood pragmatically as the current temporal, a local differential state of knowledge. The model of the discursive space is proposed as a model for the analysis and description of this knowledge. Discursive space is understood as an autonomous multidimensional space where separate discourses traverse specific trajectories of what can be presented in multidimensional parallel coordinate system. Discursive space built on the world of facts preserves the complex character of that world. Digital transformation as a discursive space has a relativistic character that means that at the same time, it is created by the dynamic discourses and these discourses are molded by the shape of this space.
Keywords: Knowledge, digital transformation, discourse, discursive space, complexity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6381401 A Proposal for U-City (Smart City) Service Method Using Real-Time Digital Map
Authors: SangWon Han, MuWook Pyeon, Sujung Moon, DaeKyo Seo
Abstract:
Recently, technologies based on three-dimensional (3D) space information are being developed and quality of life is improving as a result. Research on real-time digital map (RDM) is being conducted now to provide 3D space information. RDM is a service that creates and supplies 3D space information in real time based on location/shape detection. Research subjects on RDM include the construction of 3D space information with matching image data, complementing the weaknesses of image acquisition using multi-source data, and data collection methods using big data. Using RDM will be effective for space analysis using 3D space information in a U-City and for other space information utilization technologies.
Keywords: RDM, multi-source data, big data, U-City.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8011400 Fundamental Groups in Chaotic Flat Space and Its Retractions
Authors: A. E. El-Ahmady, M. Abu-Saleem
Abstract:
The purpose of this paper is to give a combinatorial characterization and construct representations of the chaotic fundamental groups of the chaotic submanifolds of chaotic flat space by using some geometrical transformations. The chaotic homotopy groups of the limit folding for chaotic flat space are presented. The chaotic fundamental groups of some types of chaotic geodesics in chaotic flat space are deduced.
Keywords: Chaotic flat space, Chaotic folding, Chaotic retractions, Chaotic fundamental groups.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15241399 The Consumer Private Space: What is and How it can be Approached without Affecting the Consumer's Privacy
Authors: Calin Veghes
Abstract:
The concept of privacy, seen in connection to the consumer's private space and personalization, has recently gained a higher importance as a consequence of the increasing marketing efforts of the organizations based on the capturing, processing and usage of consumer-s personal data.Paper intends to provide a definition of the consumer-s private space based on the types of personal data the consumer is willing to disclose, to assess the attitude toward personalization and to identify the means preferred by consumers to control their personal data and defend their private space. Several implications generated through the definition of the consumer-s private space are identified and weighted from both the consumers- and organizations- perspectives.
Keywords: Consumer private space, personalization, privacy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15571398 IFS on the Multi-Fuzzy Fractal Space
Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed
Abstract:
The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19661397 Gravitational and Centrifugal Forces in the Nut-Kerr-Newman Space-Time
Authors: Atikur Rahman Baizid, Md. Elias Uddin Biswas, Ahsan Habib
Abstract:
Nayak et al have discussed in detail the inertial forces such as Gravitational, Coriolis-Lense-Thirring and Centrifugal forces in the Kerr-Newman Space-time in the Kerr-Newman Space-time. The main theme of this paper is to study the Gravitational and Centrifugal forces in the NUT-Kerr-Newman Space-time.Keywords: Gravitational Forces, Centrifugal Forces, Nut-Kerr-Newman, Space time.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12801396 Hybrid Color-Texture Space for Image Classification
Authors: Hassan El Maia, Ahmed Hammouch, Driss Aboutajdine
Abstract:
This work presents an approach for the construction of a hybrid color-texture space by using mutual information. Feature extraction is done by the Laws filter with SVM (Support Vectors Machine) as a classifier. The classification is applied on the VisTex database and a SPOT HRV (XS) image representing two forest areas in the region of Rabat in Morocco. The result of classification obtained in the hybrid space is compared with the one obtained in the RGB color space.
Keywords: Color, texture, laws filter, mutual information, SVM, hybrid space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18171395 Identification of Configuration Space Singularities with Local Real Algebraic Geometry
Authors: Marc Diesse, Hochschule Heilbronn
Abstract:
We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.Keywords: Linkages, configuration space singularities, real algebraic geometry, analytic geometry, computer algebra.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5041394 Research on the Transformation of Bottom Space in the Teaching Area of Zijingang Campus, Zhejiang University
Authors: Jia Xu
Abstract:
There is a lot of bottom space in the teaching area of Zijingang Campus of Zhejiang University, which benefits to the ventilation, heat dissipation, circulation, partition of quiet and noisy areas and diversification of spaces. Hangzhou is hot in summer but cold in winter, so teachers and students spend much less time in the bottom space of buildings in winter than in summer. Recently, depending on the teachers and students’ proposals, the school transformed the bottom space in the teaching area to provide space for relaxing, chatting and staying in winter. Surveying and analyzing the existing ways to transform, the paper researches deeply on the transformation projects of bottom space in the teaching buildings. It is believed that this paper can be a salutary lesson to make the bottom space in the teaching areas of universities richer and bring more diverse activities for teachers and students.
Keywords: Bottom space, teaching area, transformation, Zijingang Campus of Zhejiang University.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7241393 Optimal Straight Line Trajectory Generation in 3D Space using Deviation Algorithm
Authors: T. C. Manjunath, C. Ardil
Abstract:
This paper presents an efficient method of obtaining a straight-line motion in the tool configuration space using an articulated robot between two specified points. The simulation results & the implementation results show the effectiveness of the method.Keywords: Bounded deviation algorithm, Straight line motion, Tool configuration space, Joint space, TCV.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26121392 Localization for Indoor Service Robot Using Natural Landmark on the Ceiling
Authors: Seung-Hun Kim, Changwoo Park
Abstract:
In this paper, we present a localization of a mobile robot with localization modules which have two ceiling-view cameras in indoor environments. We propose two kinds of localization method. The one is the localization in the local space; we use the line feature and the corner feature between the ceiling and wall. The other is the localization in the large space; we use the natural features such as bulbs, structures on the ceiling. These methods are installed on the embedded module able to mount on the robot. The embedded module has two cameras to be able to localize in both the local space and the large spaces. The experiment is practiced in our indoor test-bed and a government office. The proposed method is proved by the experimental results.
Keywords: Robot, Localization, Indoor, Ceiling vision, Local space, Large space, Complex space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21711391 Deployment of a Biocompatible International Space Station into Geostationary Orbit
Authors: Tim Falk, Chris Chatwin
Abstract:
This study explores the possibility of a space station that will occupy a geostationary equatorial orbit (GEO) and create artificial gravity using centripetal acceleration. The concept of the station is to create a habitable, safe environment that can increase the possibility of space tourism by reducing the wide variation of hazards associated with space exploration. The ability to control the intensity of artificial gravity through Hall-effect thrusters will allow experiments to be carried out at different levels of artificial gravity. A feasible prototype model was built to convey the concept and to enable cost estimation. The SpaceX Falcon Heavy rocket with a 26,700 kg payload to GEO was selected to take the 675 tonne spacecraft into orbit; space station construction will require up to 30 launches, this would be reduced to 5 launches when the SpaceX BFR becomes available. The estimated total cost of implementing the Sussex Biocompatible International Space Station (BISS) is approximately $47.039 billion, which is very attractive when compared to the cost of the International Space Station, which cost $150 billion.
Keywords: Artificial gravity, biocompatible, geostationary orbit, space station.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5551390 On the Differential Geometry of the Curves in Minkowski Space-Time II
Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut
Abstract:
In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.Keywords: Frenet Apparatus, Time-like Curves, MinkowskiSpace-time.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16541389 Moving From Problem Space to Solution Space
Authors: Bilal Saeed Raja, M. Ali Iqbal, Imran Ihsan
Abstract:
Extracting and elaborating software requirements and transforming them into viable software architecture are still an intricate task. This paper defines a solution architecture which is based on the blurred amalgamation of problem space and solution space. The dependencies between domain constraints, requirements and architecture and their importance are described that are to be considered collectively while evolving from problem space to solution space. This paper proposes a revised version of Twin Peaks Model named Win Peaks Model that reconciles software requirements and architecture in more consistent and adaptable manner. Further the conflict between stakeholders- win-requirements is resolved by proposed Voting methodology that is simple adaptation of win-win requirements negotiation model and QARCC.Keywords: Functional Requirements, Non Functional Requirements, Twin Peaks Model, QARCC.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18551388 Urban Life on the Go: Urban Transformation of Public Space
Authors: E. Zippelius
Abstract:
Urban design aims to provide a stage for public life that, when once brought to life, is right away subject to subtle but continuous transformation. This paper explores such transformations and searches for ways how public life can be reinforced in the case of a housing settlement for the displaced in Nicosia, Cyprus. First, a sound basis of theoretical knowledge is established through literature review, notably the theory of the Production of Space by Henri Lefebvre, exploring its potential and defining key criteria for the following empirical analysis. The analysis is pinpointing the differences between spatial practice, representation of space and spaces of representation as well as their interaction, alliance, or even conflict. In doing so uncertainties, chances and challenges are unraveled that will be consequently linked to practice and action and lead to the formulation of a design strategy. A strategy, though, that does not long for achieving an absolute, finite certainty but understands the three dimensions of space formulated by Lefebvre as equal and space as continuously produced, hence, unfinished.Keywords: Production of space, public space, urban life, urban transformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5721387 Real-time Detection of Space Manipulator Self-collision
Authors: Zhang Xiaodong, Tang Zixin, Liu Xin
Abstract:
In order to avoid self-collision of space manipulators during operation process, a real-time detection method is proposed in this paper. The manipulator is fitted into a cylinder-enveloping surface, and then, a kind of detection algorithm of collision between cylinders is analyzed. The collision model of space manipulator self-links can be detected by using this algorithm in real-time detection during the operation process. To ensure security of the operation, a safety threshold is designed. The simulation and experiment results verify the effectiveness of the proposed algorithm for a 7-DOF space manipulator.Keywords: Space manipulator, Collision detection, Self-collision, the real-time collision detection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20281386 Influence of IMV on Space Station
Authors: Fu Shiming, Pei Yifei
Abstract:
To study the impact of the inter-module ventilation (IMV) on the space station, the Computational Fluid Dynamic (CFD) model under the influence of IMV, the mathematical model, boundary conditions and calculation method are established and determined to analyze the influence of IMV on cabin air flow characteristics and velocity distribution firstly; and then an integrated overall thermal mathematical model of the space station is used to consider the impact of IMV on thermal management. The results show that: the IMV has a significant influence on the cabin air flow, the flowrate of IMV within a certain range can effectively improve the air velocity distribution in cabin, if too much may lead to its deterioration; IMV can affect the heat deployment of the different modules in space station, thus affecting its thermal management, the use of IMV can effectively maintain the temperature levels of the different modules and help the space station to dissipate the waste heat.
Keywords: CFD, Environment control and life support, Space station, Thermal management, Thermal mathematical model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20471385 Optimizing of Gas Consumption in Gas-burner Space Heater
Authors: Saead Negahdari, Davood Jalali Vahid
Abstract:
Nowadays, the importance of energy saving is clearance to everyone. By attention to increasing price of fuels and also the problems of environment pollutions, there are the most efforts for using fuels littler and more optimum in everywhere. This essay studies optimizing of gas consumption in gas-burner space heaters. In oven of each gas-burner space heaters there is two snags to prevent the hot air (the result of combustion of natural gas) to go out of oven of the gas-burner space heaters directly without delivering its heat to the space of favorite environment like a room. These snags cause a excess circulating that helps hot air deliver its heat to the space of favorite environment. It means the exhaust air temperature will be decreased then when there are no snags. This is the aim of this essay to use maximum potential energy of the natural gas to make heat. In this study, by the help of a finite volume software (FLUENT) consumption of the gas-burner space heaters is simulated and optimized. At the end of this writing, by comparing the results of software and experimental results, it will be proved the authenticity of this method.
Keywords: FLUENT, Heat transfer, Oven of Gas-burner spaceheaters, Simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18021384 Translation Surfaces in Euclidean 3-Space
Authors: Muhammed Çetin, Yılmaz Tunçer, Nejat Ekmekçi
Abstract:
In this paper, the translation surfaces in 3-dimensional Euclidean space generated by two space curves have been investigated. It has been indicated that Scherk surface is not only minimal translation surface.Keywords: Minimal surface, Surface of Scherk, Translationsurface
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18811383 Robust Control of a High-Speed Manipulator in State Space
Authors: M. M. Fateh, A. Izadbakhsh
Abstract:
A robust control approach is proposed for a high speed manipulator using a hybrid computed torque control approach in the state space. The high-speed manipulator is driven by permanent magnet dc motors to track a trajectory in the joint space in the presence of disturbances. Tracking problem is analyzed in the state space where the completed models are considered for actuators. The proposed control approach can guarantee the stability and a satisfactory tracking performance. A two-link elbow manipulator driven by electrical actuators is simulated and results are shown to satisfy conditions under technical specifications.
Keywords: Computed torque, manipulator, robust control, state space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23281382 Module and Comodule Structures on Path Space
Abstract:
On path space kQ, there is a trivial kQa-module structure determined by the multiplication of path algebra kQa and a trivial kQc-comodule structure determined by the comultiplication of path coalgebra kQc. In this paper, on path space kQ, a nontrivial kQa-module structure is defined, and it is proved that this nontrivial left kQa-module structure is isomorphic to the dual module structure of trivial right kQc-comodule. Dually, on path space kQ, a nontrivial kQc-comodule structure is defined, and it is proved that this nontrivial right kQc-comodule structure is isomorphic to the dual comodule structure of trivial left kQa-module. Finally, the trivial and nontrivial module structures on path space are compared from the aspect of submodule, and the trivial and nontrivial comodule structures on path space are compared from the aspect of subcomodule.Keywords: Quiver, path space, module, comodule, dual.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 848