On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

Spatio-Temporal Changes in the Wetland Ecosystem of Cochin City using Remote Sensing and GIS

Urban developments have exerted immense pressure on wetlands. Urban areas are normally centers of commercial activity and continue to attract migrants in large numbers in search of employment from different areas. As a result, habitations keep coming up in the natural areas / flood plains. This is happening in various Indian cities and towns and large habitations are coming up in low-lying areas, often encroaching even over drainage channels. In some cases, houses are constructed even on top of nallahs and drains. In the case of Kochi the situation is even worse as the base of the urban development itself stands on a completely reclaimed island. Also the topography and geology demanded more reclamation of land when the city developed as an agglomerative cluster. Cochin is a coastal settlement interspersed with a large backwater system and fringed on the eastern side by laterite-capped low hills from which a number of streams drain into the backwater system. The ridge line of the eastern low hills provides a welldefined watershed delimiting Cochin basin which help to confine the environmental parameters within a physical limit. This leads to an obvious conclusion that if physiography alone is considered, the western flatland is ideal for urban development. However it will result in serious environmental deterioration, as it comprises mainly of wetland and for availability of land there has to be large scale filling up of these wetlands which includes shallow mangrove-fringed water sheets, paddy fields, Pokkali fields, estuary etc.Chapter 1 School 4 of Environmental Studies The urban boundaries of Cochin are expanding fast with a consequent over-stretching of the existing fabric of basic amenities and services. Urbanisation leads to the transformation of agricultural land into built-up areas with the concomitant problems regarding water supply, drainage, garbage and sewage disposal etc. Many of the environmental problems of Cochin are hydrologic in origin; like water-logging / floods, sedimentation and pollution in the water bodies as well as shoreline erosion

Speech Recognition of Malayalam Numbers

Digit speech recognition is important in many applications such as automatic data entry, PIN entry, voice dialing telephone, automated banking system, etc. This paper presents speaker independent speech recognition system for Malayalam digits. The system employs Mel frequency cepstrum coefficient (MFCC) as feature for signal processing and Hidden Markov model (HMM) for recognition. The system is trained with 21 male and female voices in the age group of 20 to 40 years and there was 98.5% word recognition accuracy (94.8% sentence recognition accuracy) on a test set of continuous digit recognition task.

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Economic Impact of Identity Theft in India: Lessons from Western Countries

In this computerized, globalised and internet world our computer collects various types of information’s about every human being and stores them in files secreted deep on its hard drive. Files like cache, browser history and other temporary Internet files can be used to store sensitive information like logins and passwords, names addresses, and even credit card numbers. Now, a hacker can get at this information by wrong means and share with someone else or can install some nasty software on your computer that will extract your sensitive and secret information. Identity Theft posses a very serious problem to everyone today. If you have a driver’s license, a bank account, a computer, ration card number, PAN card number, ATM card or simply a social security number you are more than at risk, you are a target. Whether you are new to the idea of ID Theft, or you have some unanswered questions, we’ve compiled a quick refresher list below that should bring you up to speed. Identity theft is a term used to refer to fraud that involves pretending to be someone else in order to steal money or get other benefits. Identity theft is a serious crime, which is increasing at tremendous rate all over the world after the Internet evolution. There is widespread agreement that identity theft causes financial damage to consumers, lending institutions, retail establishments, and the economy as a whole. Surprisingly, there is little good public information available about the scope of the crime and the actual damages it inflicts. Accounts of identity theft in recent mass media and in film or literature have centered on the exploits of 'hackers' - variously lauded or reviled - who are depicted as cleverly subverting corporate firewalls or other data protection defenses to gain unauthorized access to credit card details, personnel records and other information. Reality is more complicated, with electronic identity fraud taking a range of forms. The impact of those forms is not necessarily quantifiable as a financial loss; it can involve intangible damage to reputation, time spent dealing with disinformation and exclusion from particular services because a stolen name has been used improperly. Overall we can consider electronic networks as an enabler for identity theft, with the thief for example gaining information online for action offline and the basis for theft or other injury online. As Fisher pointed out "These new forms of hightech identity and securities fraud pose serious risks to investors and brokerage firms across the globe," I am a victim of identity theft. Being a victim of identity theft I felt the need for creating an awareness among the computer and internet users particularly youngsters in India. Nearly 70 per cent of Indian‘s population are living in villages. Government of India already started providing computer and internet facilities even to the remote villages through various rural development and rural upliftment programmes. Highly educated people, established companies, world famous financial institutions are becoming victim of identity theft. The question here is how vulnerable the illiterate and innocent rural people are if they suddenly exposed to a new device through which some one can extract and exploit their personal data without their knowledge? In this research work an attempt has been made to bring out the real problems associated with Identity theft in developed countries from an economist point of view.