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Author

H.S. Dhami

Bio: H.S. Dhami is an academic researcher. The author has contributed to research in topics: Matrix (mathematics) & Confluent hypergeometric function. The author has an hindex of 5, co-authored 19 publications receiving 78 citations.

Papers
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01 Jul 2001
TL;DR: In this paper, the authors have studied a number of hypergeometric functions of several matrix arguments by using Mathai's matrix transform technique, including the ten Lauricella-Saran functions, the Srivastava functions H A, HB,HC, the Exton's twenty-one quadruple hypergeometic functions, and the generalized Horn's functions.
Abstract: Through this introductory paper we announce to the mathematical world our studies of some new hypergeometric functions of several matrix arguments by using Mathai’s matrix transform technique. We have attempted the ten Lauricella-Saran functions; the Srivastava functions H A, HB ,HC; the Exton’s twenty-one quadruple hypergeometic functions; the Exton’s ) n D E ) k ( ) 2 ( , ) n ( D E ) k ( ) 1 ( and ) n ( C E ) k ( ) 1 ( functions; the generalized Horn’s functions ) n ( 3 H ) k ( and ) n 4 H ) k ( and the generalized Srivastava ) n B H and ) n ( C H functions. A number of reducibility cases of these functions and transformation relations have been deduced, wherever possible. Out of these only a limited number of results are being presented here owing to the space constraints. All the matrices appearing in this paper are (p x p) real symmetric positive definite matrices.

17 citations

Journal ArticleDOI
TL;DR: An attempt has been made to discuss the applicability of language model as an approach to calculate the relevance of the document by utilizing user-supplied information of those documents that are relevant to the query items.
Abstract: In the present work an attempt has been made to discuss the applicability of language model as an approach to calculate the relevance of the document by utilizing user-supplied information of those documents that are relevant to the query items. This method shall have the advantage of improving retrieval performance as we have utilized user-supplied information of those documents that are relevant to the query in question. The design and implementation of information retrieval systems is concerned with methods for storing, organizing and retrieving information from a collection of documents. The quality of a system is measured by how useful it is to the typical users of the system. In this approach, a query shall be considered generated from an “ideal” document that shall satisfy the information need. The system‟s job has been to calculate the frequency of the word in the given document and rank them accordingly. Keywords:

16 citations

01 Jul 2001
TL;DR: In this paper, the Exton's 11 K and 6 K, 3 K quadruple hypergeometric functions, the Chandel's and Horn's functions, and the generalized Srivastava's functions of matrix arguments are defined.
Abstract: In continuation of our previous studies [6], here we propose to define the Exton's 11 K and 6 K , 3 K quadruple hypergeometric functions, the Exton's (n) D E (k) (1) and the Chandel's ) n ( C E ) k ( ) 1 ( functions, the generalized Horn's ) n ( 4 H ) k ( function and the generalized Srivastava ) n ( B H and ) n ( C H functions of matrix arguments.

9 citations

01 May 2002
TL;DR: In this paper, the Mathai's definitions for Humbert's functions of matrix arguments have been studied and the relevant results for establishing the results have been obtained from Mathai.
Abstract: INTRODUCTION In this paper we continue our study of Humbert’s functions of matrix arguments. The Mathai’s definitions for these functions have already been given in our previous papers [10, 11, 12], from where we shall draw upon the relevant results necessary for establishing the results here. Besides we have also given two results in the first section below, from Mathai [4], which shall be needed in deducing the transformation relations for the functions

5 citations

Journal Article
TL;DR: In this article, the generalized Horn's functions (k)H3(n) and (kH4(n)) of matrix arguments have been defined and four results have been established.
Abstract: In this paper we have defined the generalized Horn's functions (k)H3(n) and (k)H4(n) of matrix arguments Four results have been established here-three for the function (k)H3(n) and one for the function (k)H4(n) of matrix arguments along with two special cases

5 citations


Cited by
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Journal ArticleDOI
01 Jul 1960-Nature
TL;DR: In this paper, the Confluent Hypergeometric Functions (CGF) are used to express the hypergeometric functions of a given hypergeometrical function in the form of a convex polygon.
Abstract: Confluent Hypergeometric Functions By Dr L J Slater Pp ix + 247 (Cambridge: At the University Press, 1960) 65s net

194 citations

Book
01 Jan 2003
TL;DR: This book develops the mathematical foundations of present day linguistics from a mathematical point of view starting with ideas already contained in Montague's work and equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial grammar, HPSG and GB.
Abstract: This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already contained in Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certain mathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses on abstract mathematical structures and their computational properties, but plenty of examples from different natural languages are provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory, languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using the principle of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

187 citations

Journal ArticleDOI
TL;DR: This survey investigates the recent advancement in the field of text analysis and covers two basic approaches of text mining, such as classification and clustering that are widely used for the exploration of the unstructured text available on the Web.
Abstract: In this survey, we review different text mining techniques to discover various textual patterns from the social networking sites. Social network applications create opportunities to establish interaction among people leading to mutual learning and sharing of valuable knowledge, such as chat, comments, and discussion boards. Data in social networking websites is inherently unstructured and fuzzy in nature. In everyday life conversations, people do not care about the spellings and accurate grammatical construction of a sentence that may lead to different types of ambiguities, such as lexical, syntactic, and semantic. Therefore, analyzing and extracting information patterns from such data sets are more complex. Several surveys have been conducted to analyze different methods for the information extraction. Most of the surveys emphasized on the application of different text mining techniques for unstructured data sets reside in the form of text documents, but do not specifically target the data sets in social networking website. This survey attempts to provide a thorough understanding of different text mining techniques as well as the application of these techniques in the social networking websites. This survey investigates the recent advancement in the field of text analysis and covers two basic approaches of text mining, such as classification and clustering that are widely used for the exploration of the unstructured text available on the Web.

100 citations

Proceedings ArticleDOI
24 Oct 2016
TL;DR: This work introduces a novel retrieval model by viewing the matching between queries and documents as a non-linear word transportation (NWT) problem, and defines the capacity and profit of a transportation model designed for the IR task.
Abstract: A common limitation of many information retrieval (IR) models is that relevance scores are solely based on exact (i.e., syntactic) matching of words in queries and documents under the simple Bag-of-Words (BoW) representation. This not only leads to the well-known vocabulary mismatch problem, but also does not allow semantically related words to contribute to the relevance score. Recent advances in word embedding have shown that semantic representations for words can be efficiently learned by distributional models. A natural generalization is then to represent both queries and documents as Bag-of-Word-Embeddings (BoWE), which provides a better foundation for semantic matching than BoW. Based on this representation, we introduce a novel retrieval model by viewing the matching between queries and documents as a non-linear word transportation (NWT) problem. With this formulation, we define the capacity and profit of a transportation model designed for the IR task. We show that this transportation problem can be efficiently solved via pruning and indexing strategies. Experimental results on several representative benchmark datasets show that our model can outperform many state-of-the-art retrieval models as well as recently introduced word embedding-based models. We also conducted extensive experiments to analyze the effect of different settings on our semantic matching model.

70 citations