Search results for: network topology

Authors: Toru Murayama, Akinori Nagano, Zhi-Wei Luo

Abstract:

In this research, we study a control method of a multivehicle system while considering the limitation of communication range for each vehicles. When we control networked vehicles with limitation of communication range, it is important to control the communication network structure of a multi-vehicle system in order to keep the network-s connectivity. From this, we especially aim to control the network structure to the target structure. We formulate the networked multi-vehicle system with some disturbance and the communication constraints as a hybrid dynamical system, and then we study the optimal control problems of the system. It is shown that the system converge to the objective network structure in finite time when the system is controlled by the receding horizon method. Additionally, the optimal control probrems are convertible into the mixed integer problems and these problems are solvable by some branch and bound algorithm.

Keywords: Hybrid system, multi-vehicle system, receding horizon control, topology control.

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Authors: T. Taufik, R. Prasetyo, D. Dolan, D. Garinto

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Today-s Voltage Regulator Modules (VRMs) face increasing design challenges as the number of transistors in microprocessors increases per Moore-s Law. These challenges have recently become even more demanding as microprocessors operate at sub voltage range at significantly high current. This paper presents a new multiphase topology with cell configuration for improved performance in low voltage and high current applications. A lab scale hardware prototype of the new topology was design and constructed. Laboratory tests were performed on the proposed converter and compared with a commercially available VRM. Results from the proposed topology exhibit improved performance compared to the commercially available counterpart.

Keywords: Voltage Regulator Modules, dc-dc converters, powerelectronics.

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Authors: Kittipong Tripetch, Nobuhiko Nakano

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Two types of floating active resistors based on a complementary regulated cascode topology with cross-coupled regulated transistors are presented in this paper. The first topology is a high swing complementary regulated cascode active resistor. The second topology is a complementary common gate with a regulated cross coupled transistor. The small-signal input resistances of the floating resistors are derived. Three graphs of the input current versus the input voltage for different aspect ratios are designed and plotted using the Cadence Spectre 0.18-µm Rohm Semiconductor process. The total harmonic distortion graphs are plotted for three different aspect ratios with different input-voltage amplitudes and different input frequencies. From the simulation results, it is observed that a resistance of approximately 8.52 MΩ can be obtained from supply voltage at  ±0.9 V.

Keywords: Complementary common gate, complementary regulated cascode, current mirror, floating active resistors.

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Authors: Carmen Navarrete, Eloy Anguiano

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In the last years, the computers have increased their capacity of calculus and networks, for the interconnection of these machines. The networks have been improved until obtaining the actual high rates of data transferring. The programs that nowadays try to take advantage of these new technologies cannot be written using the traditional techniques of programming, since most of the algorithms were designed for being executed in an only processor,in a nonconcurrent form instead of being executed concurrently ina set of processors working and communicating through a network.This paper aims to present the ongoing development of a new system for the reconfiguration of grouping of computers, taking into account these new technologies.

Keywords: Dynamic network topology, resource and task allocation, parallel computing, heterogeneous computing, dynamic reconfiguration.

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Authors: Doraid Dalalah

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A topologically oriented neural network is very efficient for real-time path planning for a mobile robot in changing environments. When using a recurrent neural network for this purpose and with the combination of the partial differential equation of heat transfer and the distributed potential concept of the network, the problem of obstacle avoidance of trajectory planning for a moving robot can be efficiently solved. The related dimensional network represents the state variables and the topology of the robot's working space. In this paper two approaches to problem solution are proposed. The first approach relies on the potential distribution of attraction distributed around the moving target, acting as a unique local extreme in the net, with the gradient of the state variables directing the current flow toward the source of the potential heat. The second approach considers two attractive and repulsive potential sources to decrease the time of potential distribution. Computer simulations have been carried out to interrogate the performance of the proposed approaches.

Keywords: Mobile robot, Path Planning, Mesh, Potential field.

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Authors: Abhishek, Seema Devi, Jyoti Ohri

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A mobile ad hoc network (MANET) represents a system of wireless mobile nodes that can self-organize freely and dynamically into arbitrary and temporary network topology. Unlike a wired network, wireless network interface has limited transmission range. Routing is the task of forwarding data packets from source to a given destination. Ad-hoc On Demand Distance Vector (AODV) routing protocol creates a path for a destination only when it required. This paper describes the implementation of AODV routing protocol using MATLAB-based Truetime simulator. In MANET's node movements are not fixed while they are random in nature. Hence intelligent techniques i.e. fuzzy and ANFIS are used to optimize the transmission range. In this paper, we compared the transmission range of AODV, fuzzy AODV and ANFIS AODV. For soft computing AODV, we have taken transmitted power and received threshold as input and transmission range as output. ANFIS gives better results as compared to fuzzy AODV.

Keywords: ANFIS, AODV, fuzzy, MANET, reactive routing protocol, routing protocol, Truetime.

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Authors: Xingyu Pan, Laure Tougne

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For recognizing coins, the graved release date is important information to identify precisely its monetary type. However, reading characters in coins meets much more obstacles than traditional character recognition tasks in the other fields, such as reading scanned documents or license plates. To address this challenging issue in a numismatic context, we propose a training-free approach dedicated to detection and recognition of the release date of the coin. In the first step, the date zone is detected by comparing histogram features; in the second step, a topology-based algorithm is introduced to recognize coin numbers with various font types represented by binary gradient map. Our method obtained a recognition rate of 92% on synthetic data and of 44% on real noised data.

Keywords: Coin, detection, character recognition, topology.

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Authors: Dulal Acharjee, Punyaban Patel

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For collecting data from all sensor nodes, some changes in Dynamic Source Routing (DSR) protocol is proposed. At each hop level, route-ranking technique is used for distributing packets to different selected routes dynamically. For calculating rank of a route, different parameters like: delay, residual energy and probability of packet loss are used. A hybrid topology of DMPR(Disjoint Multi Path Routing) and MMPR(Meshed Multi Path Routing) is formed, where braided topology is used in different faulty zones of network. For reducing energy consumption, variant transmission ranges is used instead of fixed transmission range. For reducing number of packet drop, a fuzzy logic inference scheme is used to insert different types of delays dynamically. A rule based system infers membership function strength which is used to calculate the final delay amount to be inserted into each of the node at different clusters. In braided path, a proposed 'Dual Line ACK Link'scheme is proposed for sending ACK signal from a damaged node or link to a parent node to ensure that any error in link or any node-failure message may not be lost anyway. This paper tries to design the theoretical aspects of a model which may be applied for collecting data from any large hanging iron structure with the help of wireless sensor network. But analyzing these data is the subject of material science and civil structural construction technology, that part is out of scope of this paper.

Keywords: Metallic corrosion, Multi Path Routing, DisjointMPR, Meshed MPR, braided path, dual line ACK link, route rankingand Fuzzy Logic.

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Authors: M. A. Islam, P. J. Hazell, J. P. Escobedo, M. Saadatfar

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Metallic foams have good potential for lightweight structures for impact and blast mitigation. Therefore it is important to find out the optimized foam structure (i.e. cell size, shape, relative density, and distribution) to maximise energy absorption. In this paper, quasistatic compression and microstructural characterization of closed-cell aluminium foams of different pore size and cell distributions have been carried out. We present results for two different aluminium metal foams of density 0.49-0.51 g/cc and 0.31- 0.34 g/cc respectively that have been tested in quasi-static compression. The influence of cell geometry and cell topology on quasistatic compression behaviour has been investigated using optical microscope and computed tomography (micro-CT) analysis. It is shown that the deformation is not uniform in the structure and collapse begins at the weakest point.

Keywords: Metal foams, micro-CT, cell topology, quasistatic compression.

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Authors: A. Starczewska, A. Nawrat, K. Daniec, J. Homa, K. Hołda

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Border Gateway Protocol (BGP) is the main routing protocol that enables routing establishment between all autonomous systems, which are the basic administrative units of the internet. Due to the poor protection of BGP, it is important to use additional BGP security systems. Many solutions to this problem have been proposed over the years, but none of them have been implemented on a global scale. This article describes a system capable of building images of real-time BGP network topology in order to detect BGP anomalies. Our proposal performs a detailed analysis of BGP messages that come into local network cards supplemented by information collected by remote collectors in different localizations.

Keywords: Border Gateway Protocol, BGP, BGP hijacking, cybersecurity, detection.

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Authors: J. Seetaram, P. Satish Kumar

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Mobile Adhoc Networks (MANETs) are infrastructure-less, dynamic network of collections of wireless mobile nodes communicating with each other without any centralized authority. A MANET is a mobile device of interconnections through wireless links, forming a dynamic topology. Routing protocols have a big role in data transmission across a network. Routing protocols, two major classifications are unipath and multipath. This study evaluates performance of an on-demand multipath routing protocol named Adhoc On-demand Multipath Distance Vector routing (AOMDV). This study proposes Energy Aware AOMDV (EAAOMDV) an extension of AOMDV which decreases energy consumed on a route.

Keywords: Mobile Adhoc Network (MANET), unipath, multipath, Adhoc On-demand Multipath Distance Vector routing (AOMDV).

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Authors: Abdi T. Abdalla, Justinian Anatory

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This paper investigates the possibility of improving throughputs of some Media Access Controls protocols such as ALOHA, slotted ALOHA and Carrier Sense Multiple Access with Collision Avoidance with the aim of increasing the performance of Powerline access networks. In this investigation, the real Powerline network topology in Tanzania located in Dar es Salaam City, Kariakoo area was used as a case study. During this investigation, Wireshark Network Protocol Analyzer was used to analyze data traffic of similar existing network for projection purpose and then the data were simulated using MATLAB. This paper proposed and analyzed three improvement techniques based on collision domain, packet length and combination of the two. From the results, it was found that the throughput of Carrier Sense Multiple Access with Collision Avoidance protocol improved noticeably while ALOHA and slotted ALOHA showed insignificant changes especially when the hybrid techniques were employed.

Keywords: Access Network, ALOHA, Broadband Powerline Communication, Slotted ALOHA, CSMA/CA and MAC Protocols.

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Authors: R. Asokan, A. M. Natarajan

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Mobile adhoc network (MANET) is a collection of mobile devices which form a communication network with no preexisting wiring or infrastructure. Multiple routing protocols have been developed for MANETs. As MANETs gain popularity, their need to support real time applications is growing as well. Such applications have stringent quality of service (QoS) requirements such as throughput, end-to-end delay, and energy. Due to dynamic topology and bandwidth constraint supporting QoS is a challenging task. QoS aware routing is an important building block for QoS support. The primary goal of the QoS aware protocol is to determine the path from source to destination that satisfies the QoS requirements. This paper proposes a new energy and delay aware protocol called energy and delay aware TORA (EDTORA) based on extension of Temporally Ordered Routing Protocol (TORA).Energy and delay verifications of query packet have been done in each node. Simulation results show that the proposed protocol has a higher performance than TORA in terms of network lifetime, packet delivery ratio and end-to-end delay.

Keywords: EDTORA, Mobile Adhoc Networks, QoS, Routing, TORA

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Authors: Alexandros Leontitsis, Archana P. Sangole

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This article presents a short discussion on optimum neighborhood size selection in a spherical selforganizing feature map (SOFM). A majority of the literature on the SOFMs have addressed the issue of selecting optimal learning parameters in the case of Cartesian topology SOFMs. However, the use of a Spherical SOFM suggested that the learning aspects of Cartesian topology SOFM are not directly translated. This article presents an approach on how to estimate the neighborhood size of a spherical SOFM based on the data. It adopts the L-curve criterion, previously suggested for choosing the regularization parameter on problems of linear equations where their right-hand-side is contaminated with noise. Simulation results are presented on two artificial 4D data sets of the coupled Hénon-Ikeda map.

Keywords: Parameter estimation, self-organizing feature maps, spherical topology.

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Authors: Maryam Hsaini, Mostafa Nouri-Baygi

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A critical problem in wireless sensor networks is limited battery and memory of nodes. Therefore, each node in the network could maintain only a subset of its neighbors to communicate with. This will increase the battery usage in the network because each packet should take more hops to reach its destination. In order to tackle these problems, spanner graphs are defined. Since each node has a small degree in a spanner graph and the distance in the graph is not much greater than its actual geographical distance, spanner graphs are suitable candidates to be used for the topology of a wireless sensor network. In this paper, we study Yao graphs and their behavior for a randomly selected set of points. We generate several random point sets and compare the properties of their Yao graphs with the complete graph. Based on our data sets, we obtain several charts demonstrating how Yao graphs behave for a set of randomly chosen point set. As the results show, the stretch factor of a Yao graph follows a normal distribution. Furthermore, the stretch factor is in average far less than the worst case stretch factor proved for Yao graphs in previous results. Furthermore, we use Yao graph for a realistic point set and study its stretch factor in real world.

Keywords: Wireless sensor network, spanner graph, Yao Graph.

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Authors: A. Krishna Veni, R.Geetha

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Wireless Sensor Networks (WSNs) are suitable for many scenarios in the real world. The retrieval of data is made efficient by the data aggregation techniques. Many techniques for the data aggregation are offered and most of the existing schemes are not energy efficient and secure. However, the existing techniques use the traditional clustering approach where there is a delay during the packet transmission since there is no proper scheduling. The presented system uses the Velocity Energy-efficient and Link-aware Cluster-Tree (VELCT) scheme in which there is a Data Collection Tree (DCT) which improves the lifetime of the network. The VELCT scheme and the construction of DCT reduce the delay and traffic. The network lifetime can be increased by avoiding the frequent change in cluster topology. Secure and Efficient Transmission of Aggregated data (SETA) improves the security of the data transmission via the trust value of the nodes prior the aggregation of data. Since SETA considers the data only from the trustworthy nodes for aggregation, it is more secure in transmitting the data thereby improving the accuracy of aggregated data.

Keywords: Aggregation, lifetime, network security, wireless sensor network.

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Authors: N. R. Harris, J. Curry

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This paper describes the construction and operation of an experimental LoRaWAN network surrounding the University of Southampton in the United Kingdom. Following successful installation, an experimental node design is built and characterised, with particular emphasis on radio range. Several configurations are investigated, including different data rates, and varying heights of node. It is concluded that although range can be great (over 8 km in this case), environmental topology is critical. However, shorter range implementations, up to about 2 km in an urban environment, are relatively insensitive although care is still needed. The example node and the relatively simple base station reported demonstrate that LoraWan can be a very low cost and practical solution to Internet of Things type applications for distributed monitoring systems with sensors spread over distances of several km.

Keywords: Wireless sensor network, LoRa, internet of things, propagation.

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Authors: Y. Harold Robinson, M. Rajaram

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Wireless mesh networking is rapidly gaining in popularity with a variety of users: from municipalities to enterprises, from telecom service providers to public safety and military organizations. This increasing popularity is based on two basic facts: ease of deployment and increase in network capacity expressed in bandwidth per footage; WMNs do not rely on any fixed infrastructure. Many efforts have been used to maximizing throughput of the network in a multi-channel multi-radio wireless mesh network. Current approaches are purely based on either static or dynamic channel allocation approaches. In this paper, we use a hybrid multichannel multi radio wireless mesh networking architecture, where static and dynamic interfaces are built in the nodes. Dynamic Adaptive Channel Allocation protocol (DACA), it considers optimization for both throughput and delay in the channel allocation. The assignment of the channel has been allocated to be codependent with the routing problem in the wireless mesh network and that should be based on passage flow on every link. Temporal and spatial relationship rises to re compute the channel assignment every time when the pattern changes in mesh network, channel assignment algorithms assign channels in network. In this paper a computing path which captures the available path bandwidth is the proposed information and the proficient routing protocol based on the new path which provides both static and dynamic links. The consistency property guarantees that each node makes an appropriate packet forwarding decision and balancing the control usage of the network, so that a data packet will traverse through the right path.

Keywords: Wireless mesh network, spatial time division multiple access, hybrid topology, timeslot allocation.

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Authors: Chiang Tzu-Chiang, Chang Jia-Lin, Tsai Yue-Fu, Li Sha-Pai

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With the advantage of wireless network technology, there are a variety of mobile applications which make the issue of wireless sensor networks as a popular research area in recent years. As the wireless sensor network nodes move arbitrarily with the topology fast change feature, mobile nodes are often confronted with the void issue which will initiate packet losing, retransmitting, rerouting, additional transmission cost and power consumption. When transmitting packets, we would not predict void problem occurring in advance. Thus, how to improve geographic routing with void avoidance in wireless networks becomes an important issue. In this paper, we proposed a greedy geographical void routing algorithm to solve the void problem for wireless sensor networks. We use the information of source node and void area to draw two tangents to form a fan range of the existence void which can announce voidavoiding message. Then we use source and destination nodes to draw a line with an angle of the fan range to select the next forwarding neighbor node for routing. In a dynamic wireless sensor network environment, the proposed greedy void avoiding algorithm can be more time-saving and more efficient to forward packets, and improve current geographical void problem of wireless sensor networks.

Keywords: Wireless sensor network, internet routing, wireless network, greedy void avoiding algorithm, bypassing void.

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Authors: Afif Saleh Abugharsa

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The IEEE 802.15.4 standard is designed for low-rate wireless personal area networks (LR-WPAN) with focus on enabling wireless sensor networks. It aims to give a low data rate, low power consumption, and low cost wireless networking on the device-level communication. The objective of this study is to investigate the performance of IEEE 802.15.4 based networks using simulation tool. In this project the network simulator 2 NS2 was used to several performance measures of wireless sensor networks. Three scenarios were considered, multi hop network with a single coordinator, star topology, and an ad hoc on demand distance vector AODV. Results such as packet delivery ratio, hop delay, and number of collisions are obtained from these scenarios.

Keywords: ZigBee, wireless sensor networks, IEEE 802.15.4, low power, low data rate

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Authors: Marko A. Rodriguez

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There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a topological feature of the directed network. Also, there exists an injective function that maps a directed network to an undirected network (i.e. an undirected unlabeled network). The edge directionality in the directed network is represented as a topological feature of the undirected network. Through function composition, there exists an injective function that maps a semantic network to an undirected network. Thus, aside from space constraints, the semantic network construct does not have any modeling functionality that is not possible with either a directed or undirected network representation. Two proofs of this idea will be presented. The first is a proof of the aforementioned function composition concept. The second is a simpler proof involving an undirected binary encoding of a semantic network.

Keywords: general-modeling, multi-relational networks, semantic networks

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Authors: Weng Ming Chu

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When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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Authors: H. El Fadili, K. Zenkouar, H. Qjidaa

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This paper proposes a neural network weights and topology optimization using genetic evolution and the backpropagation training algorithm. The proposed crossover and mutation operators aims to adapt the networks architectures and weights during the evolution process. Through a specific inheritance procedure, the weights are transmitted from the parents to their offsprings, which allows re-exploitation of the already trained networks and hence the acceleration of the global convergence of the algorithm. In the preprocessing phase, a new feature extraction method is proposed based on Legendre moments with the Maximum entropy principle MEP as a selection criterion. This allows a global search space reduction in the design of the networks. The proposed method has been applied and tested on the well known MNIST database of handwritten digits.

Keywords: Genetic algorithm, Legendre Moments, MEP, Neural Network.

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Authors: Mohammad J. Almalkawi

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A broadband wire monopole antenna loaded by inhomogeneous stack of annular dielectric ring resonators (DRRs) is proposed. The proposed antenna exhibits a broad impedance bandwidth from 3 to 30 GHz. This is achieved by adding an external step matching network at the antenna feed point. The matching network is comprised of three annular DRRs possessing different permittivity values and sharing the same axial over a finite ground plane. The antenna performance is characterized using full-wave EM simulation. Compared to previous-reported wire antennas with improved bandwidth achieved by DRRs, the proposed topology provides relatively compact realization and superior broadband performance.

Keywords: Broadband, dielectric ring resonator, wire monopole antenna.

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Authors: S.M. Sarwarul Islam Rizvi, Zinat Sultana, Bo Sun, Md. Washiqul Islam

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In a very simple form a Mobile Agent is an independent piece of code that has mobility and autonomy behavior. One of the main advantages of using Mobile Agent in a network is - it reduces network traffic load. In an, ad hoc network Mobile Agent can be used to protect the network by using agent based IDS or IPS. Besides, to deploy dynamic software in the network or to retrieve information from network nodes Mobile Agent can be useful. But in an ad hoc network the Mobile Agent itself needs some security. Security services should be guaranteed both for Mobile Agent and for Agent Server. In this paper to protect the Mobile Agent and Agent Server in an ad hoc network we have proposed a solution which is based on Threshold Cryptography, a new vibe in the cryptographic world where trust is distributed among multiple nodes in the network.

Keywords: Ad hoc network, Mobile Agent, Security, Threats, Threshold Cryptography.

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Authors: Khodamorad Nabaki, Jianhu Shen, Xiaodong Huang

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This paper develops a method for considering the critical fatigue stress as a constraint in the Bi-directional Evolutionary Structural Optimization (BESO) method. Our aim is to reach an optimal design in which high cycle fatigue failure does not occur for a specific life time. The critical fatigue stress is calculated based on modified Goodman criteria and used as a stress constraint in our topology optimization problem. Since fatigue generally does not occur for compressive stresses, we use the p-norm approach of the stress measurement that considers the highest tensile principal stress in each point as stress measure to calculate the sensitivity numbers. The BESO method has been extended to minimize volume an object subjected to the critical fatigue stress constraint. The optimization results are compared with the results from the compliance minimization problem which shows clearly the merits of our newly developed approach.

Keywords: Topology optimization, BESO method, p-norm, fatigue constraint.

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Authors: Eric Filiol, Edouard Franc, Alessandro Gubbioli, Benoit Moquet, Guillaume Roblot

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Worm propagation profiles have significantly changed since 2003-2004: sudden world outbreaks like Blaster or Slammer have progressively disappeared and slower but stealthier worms appeared since, most of them for botnets dissemination. Decreased worm virulence results in more difficult detection. In this paper, we describe a stealth worm propagation model which has been extensively simulated and analysed on a huge virtual network. The main features of this model is its ability to infect any Internet-like network in a few seconds, whatever may be its size while greatly limiting the reinfection attempt overhead of already infected hosts. The main simulation results shows that the combinatorial topology of routing may have a huge impact on the worm propagation and thus some servers play a more essential and significant role than others. The real-time capability to identify them may be essential to greatly hinder worm propagation.

Keywords: Combinatorial worm, worm spreading, worm virulence, stealth worm, spreading simulation, vertex cover, networktopology, WAST simulator, SuWAST simulator.

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Authors: P.S. Prakash, S. Selvan

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Quality of Service (QoS) Routing aims to find path between source and destination satisfying the QoS requirements which efficiently using the network resources and underlying routing algorithm and to fmd low-cost paths that satisfy given QoS constraints. One of the key issues in providing end-to-end QoS guarantees in packet networks is determining feasible path that satisfies a number of QoS constraints. We present a Optimized Multi- Constrained Routing (OMCR) algorithm for the computation of constrained paths for QoS routing in computer networks. OMCR applies distance vector to construct a shortest path for each destination with reference to a given optimization metric, from which a set of feasible paths are derived at each node. OMCR is able to fmd feasible paths as well as optimize the utilization of network resources. OMCR operates with the hop-by-hop, connectionless routing model in IP Internet and does not create any loops while fmding the feasible paths. Nodes running OMCR not necessarily maintaining global view of network state such as topology, resource information and routing updates are sent only to neighboring nodes whereas its counterpart link-state routing method depend on complete network state for constrained path computation and that incurs excessive communication overhead.

Keywords: QoS Routing, Optimization, feasible path, multiple constraints.

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Authors: Karamitsos Ioannis, Orfanidis Konstantinos

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In this paper an analysis of blackouts in electric power transmission systems is implemented using a model and studied in simple networks with a regular topology. The proposed model describes load demand and network improvements evolving on a slow timescale as well as the fast dynamics of cascading overloads and outages.

Keywords: Blackout, Generator, Load, Power Load.

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Authors: K. V. Geetha, N. R. Mangalambal

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Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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