# NCMMSC -2014-National Conference ON MATHEMATICAL MODELLING & SOFT COMPUTING

"NCMMSC -2014 Conference Papers "

Numerical methodologies for higher index Differential-Algebraic Equations[ ]

This paper focuses mainly on the numerical methodologies for solving Differential-Algebraic Equations (abbreviated as DAEs). An overview for the existing numerical techniques is presented.

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Frame of a Closed Subspace of L^2 (R)?L^2 (R) Generated by Translation of a F[ ]

The concept of MRA in wavelet analaysis, MRA wavelets in the superspace and Frame MRA in are now well known. In this paper we discuss frame MRA in and frame of a closed subspace of generated by translation of a function.

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Homomorphisms of Hesitant Fuzzy Subgroups[ ]

Hesitant fuzzy subgroup defined on a group G generalizes the idea of fuzzy subgroups. It mainly focuses on the multiplicity of values encountered when dealing with hesitant fuzzy sets. In this paper we introduce the notions of a homomorphism and isomorphism between two hesitant fuzzy subgroups and study their effects on hesitant fuzzy subgroups. Some results regarding the homomorphisms between some quotient subgroups are also discussed.

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On Multi-fuzzy rough sets[ ]

Rough sets have been invented to cope with uncertainty and to deal with intelligent systems characterized by incomplete information. This paper introduces the concept of relation based multi-fuzzy rough approximation operators. Multi-fuzzy sets are approximated by a multi-fuzzy relation and hence the concept of multi-fuzzy rough sets is defined. The basic set theoretic operations such as union, intersection etc. are defined in the context of multi-fuzzy rough sets. The basic rough set properties are then explored.

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Sequences in a weighted graph and characterization of partial trees[ ]

In a weighted graph, the arcs are mainly classified into a, ß and d. In this article, some sequences in weighted graphs are introduced. These concepts are based on the above classification. Characterizations of partial trees and some necessary conditions are obtained. It is shown that ß sequence of a partial tree is a zero sequence.

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The b-chromatic number of mycielskian of cycles[ ]

A b-coloring of a graph G is a proper coloring of the vertices of G such that there exist a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph G, denoted by j(G), is the maximal integer k such that G may have a b-coloring with k colors. The Mycielskian or Mycielski graph m(H) of a graph H with vertex set fv1; v2;:::; vng is a graph G obtained from H by adding n + 1 new vertices fu; u1; u2;:::; ung, joining u to each vertex ui(1 i n) and joining ui to each neighbour of vi in H. In this paper we obtained the b-chromatic number of the mycielskian of cycles.

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Web Mining for Multimedia Data-A Soft Computing Framework[ ]

The World Wide Web (WWW) is a system of interlinked hypertext documents that are accessed through the Internet. Web browsers provide easy access to numerous sources of text and multimedia very easily. Today billions of pages are indexed by search engines and finding the desired information is not so simple. This has prompted the need for developing automatic mining techniques on the WWW, by the new term “Web mining”. In web mining data can be collected at the server side, client side, proxy servers or obtained from the organization’s database. Depending on the source of data, the type may vary. Now most of the mining techniques used are text centric and the algorithms are oriented towards text mining framework. But in the present scenario, web is gaining a multimedia character with pages containing images, audios, videos etc. Web mining algorithms for multimedia data are developed recently, but it has a long way to go. This paper gives an overview of the existing techniques used for web mining of multimedia data and a better solution using soft computing for web mining of multimedia data.

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On the Metric Dimension of Joins of Two Graphs[ ]

For an ordered set of vertices and a vertex v in a connected graph G, the (metric) representation of v with respect to W is the k-vector r(v/W) = (d(v, w1), d(v, w2), …, d(v, wk)), where d(x, y)representsthe distance between the vertices x and y. A resolving set of minimum cardinality is called a minimum resolving set or abasis and the cardinality of a basis for G is its dimension dimG. For the graph G1 = (V1, E1) and G2 = (V2, E2) their joinis denoted by G1 +G2 is the graph whose vertex set is V1?V2 and the edge set is . In this paper, we determine the metric dimension of join of paths, paths and cycles, path and stars, complete graphs,complete graphs and paths.

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Aggregation Operations on Multiple Sets[ ]

As a new approach towards the vagueness, multiple sets are introduced. Then it is noticed that multiple sets are generalization of fuzzy sets, fuzzy multisets, multi fuzzy sets and multisets. Standard set operations subset, complement, union, intersection are defined on multiple sets. Aggregation operations on multiple sets are defined and their properties are explored.

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Study on Memory Hierarchy Optimizations[ ]

Cache is an important factor that affects total system performance of computer architecture. Due to the ever increasing performance gap between the processor and the main memory, it becomes crucial to bridge the gap by designing an efficient memory hierarchy capable of reducing the average memory access time. Many of the recent studies in improving performance of cache have focused on minimizing the cache miss rates. Cache miss rate can be reduced by optimizing data or instruction cache. Data is too large to be kept in cache so optimization of data cache is necessary since it has to be moved between memory and cache frequently. A way to decrease data cache miss is to restructure the code. This paper explains various restructuring techniques and analyzing of cache miss rates using valgrind tool.

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Fuzzy Graph Documet Model Representation of Document Summaries Using Eigen Vector Approach[ ]

Automatic document summarization is the process of reducing a text document into a summary that retains the points highlighting the original document. Ranking sentences according to their importance of being part in the summary is the main task in summarization. This paper proposes an effective approach for document summarization by sentence ranking. Sentence ranking is done by vector space modeling and Eigen analysis methods. Vector space model is used for representing sentences as vectors in an n-dimensional space assigning tf-idf weighting system. The principal eigen vectors of the characteristic equation will rank the sentences according to their relevance. Experimental result using standard test collections of DUC2001 corpus and Rouge Evaluation system shows that the proposed sentence ranking based on eigen analysis scheme improves conventional Tf-Idf language model based schemes.

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Numerical Implementation of BDF2 via Method of Lines for Time Dependent Nonlinear Burgers’ Equation[ ]

In this paper an efficient unconditionally stable numerical scheme is proposed for solving one dimensional quasi linear Burgers’ equation. The proposed scheme comprises of semi discretization via method of lines for the space variable and backward differentiation formula of order two (BDF2) for the time variable. The method of lines reduces the quasi linear partial differential equation in to nonlinear ordinary differential equations at each node point. The resulting nonlinear system is solved by an efficient stiff solver known as BDF2. BDF2 is an implicit solver which leads to nonlinear algebraic system and the resulting nonlinear algebraic system is linearized via Taylor series. This linearization technique is easy to implement and the accuracy of the method will remain unchanged. The linearized system of algebraic equations is solved using MATLAB 8.0. The proposed scheme is implemented on test examples and it has been observed that the numerical solution lies very close to the exact solution. Various numerical experiments have been carried out to demonstrate the performance of the method.

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Fuzzy Lattice Ordered Group[ ]

In this paper, the definition of Fuzzy l- group with respect to Fuzzy partial order relation is introduced. Some properties on Fuzzy l-groups is derived. The relation between Fuzzy l-group, DRL- group and Browerian Algebra are established..

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