Search results for: topological analysis

Authors: Weijian Rong

Abstract:

Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft first-countable spaces, soft second-countable spaces and soft separable spaces, and some basic properties of these concepts are explored.

Keywords: soft sets, soft first-countable spaces, soft second countable spaces, soft separable spaces, soft Lindelöf.

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Authors: David Sherwell, Vivien Visaya

Abstract:

We consider the topological entropy of maps that in general, cannot be described by one-dimensional dynamics. In particular, we show that for a multivalued map F generated by singlevalued maps, the topological entropy of any of the single-value map bounds the topological entropy of F from below.

Keywords: Multivalued maps, Topological entropy, Selectors

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Authors: Fucai Lin

Abstract:

Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft closed mapping, soft open mappings, soft connected spaces and soft paracompact spaces. We also redefine the concept of soft points such that it is reasonable in soft topological spaces. Moreover, some basic properties of these concepts are explored.

Keywords: soft sets, soft open mappings, soft closed mappings, soft connected spaces, soft paracompact spaces.

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Authors: Maatoug Hassine, Mourad Hrizi

Abstract:

In this paper, we consider a geometric inverse source problem for the heat equation with Dirichlet and Neumann boundary data. We will reconstruct the exact form of the unknown source term from additional boundary conditions. Our motivation is to detect the location, the size and the shape of source support. We present a one-shot algorithm based on the Kohn-Vogelius formulation and the topological gradient method. The geometric inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a source function. Then, we present a non-iterative numerical method for the geometric reconstruction of the source term with unknown support using a level curve of the topological gradient. Finally, we give several examples to show the viability of our presented method.

Keywords: Geometric inverse source problem, heat equation, topological sensitivity, topological optimization, Kohn-Vogelius formulation.

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Authors: Mohamed Abdelwahed

Abstract:

The aeration process via injectors is used to combat the lack of oxygen in lakes due to eutrophication. A 3D numerical simulation of the resulting flow using a simplified model is presented. In order to generate the best dynamic in the fluid with respect to the aeration purpose, the optimization of the injectors location is considered. We propose to adapt to this problem the topological sensitivity analysis method which gives the variation of a criterion with respect to the creation of a small hole in the domain. The main idea is to derive the topological sensitivity analysis of the physical model with respect to the insertion of an injector in the fluid flow domain. We propose in this work a topological optimization algorithm based on the studied asymptotic expansion. Finally we present some numerical results, showing the efficiency of our approach

Keywords: Quasi Stokes equations, Numerical simulation, topological optimization, sensitivity analysis.

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Authors: Shiping Wang, Peiyong Zhu, William Zhu

Abstract:

Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.

Keywords: Covering, poset, down-set, lattice, topological space, topological base.

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Authors: Hongzhi Wang, Jianzhong Li, Jizhou Luo

Abstract:

In many applications, data is in graph structure, which can be naturally represented as graph-structured XML. Existing queries defined on tree-structured and graph-structured XML data mainly focus on subgraph matching, which can not cover all the requirements of querying on graph. In this paper, a new kind of queries, topological query on graph-structured XML is presented. This kind of queries consider not only the structure of subgraph but also the topological relationship between subgraphs. With existing subgraph query processing algorithms, efficient algorithms for topological query processing are designed. Experimental results show the efficiency of implementation algorithms.

Keywords: XML, Graph Structure, Topological query.

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Authors: Yasmeen A. S. Essawy, Khaled Nassar

Abstract:

With the rapid increase of complexity in the building industry, professionals in the A/E/C industry were forced to adopt Building Information Modeling (BIM) in order to enhance the communication between the different project stakeholders throughout the project life cycle and create a semantic object-oriented building model that can support geometric-topological analysis of building elements during design and construction. This paper presents a model that extracts topological relationships and geometrical properties of building elements from an existing fully designed BIM, and maps this information into a directed acyclic Elemental Graph Data Model (EGDM). The model incorporates BIM-based search algorithms for automatic deduction of geometrical data and topological relationships for each building element type. Using graph search algorithms, such as Depth First Search (DFS) and topological sortings, all possible construction sequences can be generated and compared against production and construction rules to generate an optimized construction sequence and its associated schedule. The model is implemented in a C# platform.

Keywords: Building information modeling, elemental graph data model, geometric and topological data models, and graph theory.

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Authors: Fahad Alsharari, Mohd Salmi Md Noorani

Abstract:

A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron- Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift, x will be in the Motzkin subshift M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, a new direct method of calculating the topological entropy of the Motzkin shift is given without any measure theoretical discussion.

Keywords: Motzkin shift, topological entropy.

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Authors: Defne Akay, Bekir S. Kandemir

Abstract:

In this paper, we investigate the low-lying energy levels of the two-dimensional parabolic graphene quantum dots (GQDs) in the presence of topological defects with long range Coulomb impurity and subjected to an external uniform magnetic field. The low-lying energy levels of the system are obtained within the framework of the perturbation theory. We theoretically demonstrate that a valley splitting can be controlled by geometrical parameters of the graphene quantum dots and/or by tuning a uniform magnetic field, as well as topological defects. It is found that, for parabolic graphene dots, the valley splitting occurs due to the introduction of spatial confinement. The corresponding splitting is enhanced by the introduction of a uniform magnetic field and it increases by increasing the angle of the cone in subcritical regime.

Keywords: Coulomb impurity, graphene cones, graphene quantum dots, topological defects.

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Authors: Fei Hao, Hai Wang

Abstract:

One of research issues in social network analysis is to evaluate the position/importance of users in social networks. As the information diffusion in social network is evolving, it seems difficult to evaluate the importance of users using traditional approaches. In this paper, we propose an evaluation approach for user importance with fractal view in social networks. In this approach, the global importance (Fractal Importance) and the local importance (Topological Importance) of nodes are considered. The basic idea is that the bigger the product of fractal importance and topological importance of a node is, the more important of the node is. We devise the algorithm called TFRank corresponding to the proposed approach. Finally, we evaluate TFRank by experiments. Experimental results demonstrate our TFRank has the high correlations with PageRank algorithm and potential ranking algorithm, and it shows the effectiveness and advantages of our approach.

Keywords: TFRank, Fractal Importance, Topological Importance, Social Network

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Authors: M. Vatsa, R. Singh, A. Noore

Abstract:

This paper presents a novel iris recognition system using 1D log polar Gabor wavelet and Euler numbers. 1D log polar Gabor wavelet is used to extract the textural features, and Euler numbers are used to extract topological features of the iris. The proposed decision strategy uses these features to authenticate an individual-s identity while maintaining a low false rejection rate. The algorithm was tested on CASIA iris image database and found to perform better than existing approaches with an overall accuracy of 99.93%.

Keywords: Iris recognition, textural features, topological features.

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Authors: Jaedo Kim, Youngjoon Han, Hernsoo Hahn

Abstract:

This paper propose the robust character segmentation method for license plate with topological transform such as twist,rotation. The first step of the proposed method is to find a candidate region for character and license plate. The character or license plate must be appeared as closed loop in the edge image. In the case of detecting candidate for character region, the evaluation of detected region is using topological relationship between each character. When this method decides license plate candidate region, character features in the region with binarization are used. After binarization for the detected candidate region, each character region is decided again. In this step, each character region is fitted more than previous step. In the next step, the method checks other character regions with different scale near the detected character regions, because most license plates have license numbers with some meaningful characters around them. The method uses perspective projection for geometrical normalization. If there is topological distortion in the character region, the method projects the region on a template which is defined as standard license plate using perspective projection. In this step, the method is able to separate each number region and small meaningful characters. The evaluation results are tested with a number of test images.

Keywords: License Plate Detection, Character Segmentation, Perspective Projection, Topological Transform.

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Authors: Kairat T. Mynbaev, Elena N. Lomakina

Abstract:

We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.

Keywords: Approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space.

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Authors: Ahmet Z. Ozcelik, Serkan Narli

Abstract:

In this study, a minimal submaximal element of LIT(X) (the lattice of all intuitionistic topologies for X, ordered by inclusion) is determined. Afterwards, a new contractive property, intuitionistic mega-connectedness, is defined. We show that the submaximality and mega-connectedness are not complementary intuitionistic topological invariants by identifying those members of LIT(X) which are intuitionistic mega-connected.

Keywords: Intuitionistic set; intuitionistic topology;intuitionistic submaximality and mega-connectedness.

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Authors: Muniyasamy Kalanchiam, Baskar Mannai

Abstract:

Topology Optimization is a defined as the method of determining optimal distribution of material for the assumed design space with functionality, loads and boundary conditions [1]. Topology optimization can be used to optimize shape for the purposes of weight reduction, minimizing material requirements or selecting cost effective materials [2]. Topology optimization has been implemented through the use of finite element methods for the analysis, and optimization techniques based on the method of moving asymptotes, genetic algorithms, optimality criteria method, level sets and topological derivatives. Case study of Typical “Fuselage design" is considered for this paper to explain the benefits of Topology Optimization in the design cycle. A cylindrical shell is assumed as the design space and aerospace standard pay loads were applied on the fuselage with wing attachments as constraints. Then topological optimization is done using Finite Element (FE) based software. This optimization results in the structural concept design which satisfies all the design constraints using minimum material.

Keywords: Fuselage, Topology optimization, payloads, designoptimization, Finite Element Analysis.

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Authors: E. Arsuaga Uriarte, F. Díaz Martín

Abstract:

The SOM has several beneficial features which make it a useful method for data mining. One of the most important features is the ability to preserve the topology in the projection. There are several measures that can be used to quantify the goodness of the map in order to obtain the optimal projection, including the average quantization error and many topological errors. Many researches have studied how the topology preservation should be measured. One option consists of using the topographic error which considers the ratio of data vectors for which the first and second best BMUs are not adjacent. In this work we present a study of the behaviour of the topographic error in different kinds of maps. We have found that this error devaluates the rectangular maps and we have studied the reasons why this happens. Finally, we suggest a new topological error to improve the deficiency of the topographic error.

Keywords: Map lattice, Self-Organizing Map, topographic error, topology preservation.

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Authors: Yilun Shang

Abstract:

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: Algebras over integral domains, Alexandroff topology, valuation domains, integral domains.

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Authors: Yasuomi D. Sato, Yasutaka Kuriya

Abstract:

We here propose improved version of elastic graph matching (EGM) as a face detector, called the multi-scale EGM (MS-EGM). In this improvement, Gabor wavelet-based pyramid reduces computational complexity for the feature representation often used in the conventional EGM, but preserving a critical amount of information about an image. The MS-EGM gives us higher detection performance than Viola-Jones object detection algorithm of the AdaBoost Haar-like feature cascade. We also show rapid detection speeds of the MS-EGM, comparable to the Viola-Jones method. We find fruitful benefits in the MS-EGM, in terms of topological feature representation for a face.

Keywords: Face detection, Gabor wavelet based pyramid, elastic graph matching, topological preservation, redundancy of computational complexity.

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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.

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Authors: Timothee G. Leleu

Abstract:

A new technique of topological multi-scale analysis is introduced. By performing a clustering recursively to build a hierarchy, and analyzing the co-scale and intra-scale similarities, an Iterated Function System can be extracted from any data set. The study of fractals shows that this method is efficient to extract self-similarities, and can find elegant solutions the inverse problem of building fractals. The theoretical aspects and practical implementations are discussed, together with examples of analyses of simple fractals.

Keywords: hierarchical clustering, multi-scale analysis, Similarity hashing.

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Authors: Marko A. Rodriguez

Abstract:

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: Ahmet Z. Ozcelik, Serkan Narli

Abstract:

In this study, two new classes of generalized homeomorphisms are introduced and shown that one of these classes has a group structure. Moreover, some properties of these two homeomorphisms are obtained.

Keywords: Generalized closed set, homeomorphism, gsghomeomorphism, sgs-homeomorphism.

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Authors: Zelmina Lubovac, Björn Olsson, Jonas Gamalielsson

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This paper describes a novel approach for deriving modules from protein-protein interaction networks, which combines functional information with topological properties of the network. This approach is based on weighted clustering coefficient, which uses weights representing the functional similarities between the proteins. These weights are calculated according to the semantic similarity between the proteins, which is based on their Gene Ontology terms. We recently proposed an algorithm for identification of functional modules, called SWEMODE (Semantic WEights for MODule Elucidation), that identifies dense sub-graphs containing functionally similar proteins. The rational underlying this approach is that each module can be reduced to a set of triangles (protein triplets connected to each other). Here, we propose considering semantic similarity weights of all triangle-forming edges between proteins. We also apply varying semantic similarity thresholds between neighbours of each node that are not neighbours to each other (and hereby do not form a triangle), to derive new potential triangles to include in module-defining procedure. The results show an improvement of pure topological approach, in terms of number of predicted modules that match known complexes.

Keywords: Modules, systems biology, protein interactionnetworks, yeast.

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Authors: Moustafa Osman Mohammed

Abstract:

This paper introduces topological order in descried social systems starting with the original concept of autopoiesis by biologists and scientists, including the modification of general systems based on socialized medicine. Topological order is important in describing the physical systems for exploiting optical systems and improving photonic devices. The stats of topologically order have some interesting properties of topological degeneracy and fractional statistics that reveal the entanglement origin of topological order, etc. Topological ideas in photonics form exciting developments in solid-state materials, that being; insulating in the bulk, conducting electricity on their surface without dissipation or back-scattering, even in the presence of large impurities. A specific type of autopoiesis system is interrelated to the main categories amongst existing groups of the ecological phenomena interaction social and medical sciences. The hypothesis, nevertheless, has a nonlinear interaction with its natural environment ‘interactional cycle’ for exchange photon energy with molecules without changes in topology (i.e., chemical transformation into products do not propagate any changes or variation in the network topology of physical configuration). The engineering topology of a biosensor is based on the excitation boundary of surface electromagnetic waves in photonic band gap multilayer films. The device operation is similar to surface Plasmonic biosensors in which a photonic band gap film replaces metal film as the medium when surface electromagnetic waves are excited. The use of photonic band gap film offers sharper surface wave resonance leading to the potential of greatly enhanced sensitivity. So, the properties of the photonic band gap material are engineered to operate a sensor at any wavelength and conduct a surface wave resonance that ranges up to 470 nm. The wavelength is not generally accessible with surface Plasmon sensing. Lastly, the photonic band gap films have robust mechanical functions that offer new substrates for surface chemistry to understand the molecular design structure, and create sensing chips surface with different concentrations of DNA sequences in the solution to observe and track the surface mode resonance under the influences of processes that take place in the spectroscopic environment. These processes led to the development of several advanced analytical technologies, which are automated, real-time, reliable, reproducible and cost-effective. This results in faster and more accurate monitoring and detection of biomolecules on refractive index sensing, antibody–antigen reactions with a DNA or protein binding. Ultimately, the controversial aspect of molecular frictional properties is adjusted to each other in order to form unique spatial structure and dynamics of biological molecules for providing the environment mutual contribution in investigation of changes due the pathogenic archival architecture of cell clusters.

Keywords: autopoiesis, engineering topology, photonic system molecular structure, biosensor

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Authors: Guojian Cheng, Tianshi Liu, Jiaxin Han, Zheng Wang

Abstract:

The competitive learning is an adaptive process in which the neurons in a neural network gradually become sensitive to different input pattern clusters. The basic idea behind the Kohonen-s Self-Organizing Feature Maps (SOFM) is competitive learning. SOFM can generate mappings from high-dimensional signal spaces to lower dimensional topological structures. The main features of this kind of mappings are topology preserving, feature mappings and probability distribution approximation of input patterns. To overcome some limitations of SOFM, e.g., a fixed number of neural units and a topology of fixed dimensionality, Growing Self-Organizing Neural Network (GSONN) can be used. GSONN can change its topological structure during learning. It grows by learning and shrinks by forgetting. To speed up the training and convergence, a new variant of GSONN, twin growing cell structures (TGCS) is presented here. This paper first gives an introduction to competitive learning, SOFM and its variants. Then, we discuss some GSONN with fixed dimensionality, which include growing cell structures, its variants and the author-s model: TGCS. It is ended with some testing results comparison and conclusions.

Keywords: Artificial neural networks, Competitive learning, Growing cell structures, Self-organizing feature maps.

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Authors: Razvan Bocu, Sabin Tabirca

Abstract:

The study of proteomics reached unexpected levels of interest, as a direct consequence of its discovered influence over some complex biological phenomena, such as problematic diseases like cancer. This paper presents a new technique that allows for an accurate analysis of the human interactome network. It is basically a two-step analysis process that involves, at first, the detection of each protein-s absolute importance through the betweenness centrality computation. Then, the second step determines the functionallyrelated communities of proteins. For this purpose, we use a community detection technique that is based on the edge betweenness calculation. The new technique was thoroughly tested on real biological data and the results prove some interesting properties of those proteins that are involved in the carcinogenesis process. Apart from its experimental usefulness, the novel technique is also computationally effective in terms of execution times. Based on the analysis- results, some topological features of cancer mutated proteins are presented and a possible optimization solution for cancer drugs design is suggested.

Keywords: Betweenness centrality, interactome networks, proteinprotein interactions, protein communities, cancer.

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Authors: Hiroto Nakashima, Toshihiro Morita, Koichiro Ohgushi

Abstract:

Laser Profiler (LP) data from aerial laser surveys have been increasingly used as topographical inputs to numerical simulations of flooding and inundation in river basins. LP data has great potential for reproducing topography, but its effective usage has not yet been fully established. In this study, flooding and inundation are simulated numerically using LP data for the Jobaru River basin of Japan’s Saga Plain. The analysis shows that the topography is reproduced satisfactorily in the computational domain with urban and agricultural areas requiring different grid sizes. A 2-D numerical simulation shows that flood flow behavior changes as grid size is varied.

Keywords: LP data, numerical simulation, topological analysis, mesh size.

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

Abstract:

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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