Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
Shiva panchākshara stotraThe hymn is composed by the great advaita philosopher ādi shankara Bhagavadpāda.This hymn is comprised of six shlokas, the first five shlokas praising lord Shiva and the sixth shloka describing the benefit of chanting the hymn.The first letter of each of the five shlokas starts with each of the five syllables of the great Shiva panchākshara.Shiva Shadakshara StotraIt has six shlokas praising the glory of the lord Shiva and his six syllable mantra. The six syllable mantra is the famous five syllable mantra preceded by OmThere is no difference between the mantra and the deity worshipped through it.The starting letters of each shloka when arranged horizontally the mantra Om namah shivāya is revealed.Each shloka has many occurrences of the syllable which is praised through the shloka.
It is a well-established fact that since Vedic astrology has its basis in Vedic knowledge, it is as old as human creation and has been used from time immemorial to dispel the unfounded horrors and prejudices of the human mind. Rahu and Ketu, the two nodal points of the Moon, constitute the core of Vedic astrology. Ancient Indian seers visualised the north and the south nodes of the Moon as the most interesting and mysterious planetary influences. However, Rahu and Ketu have either been ignored or misunderstood in studies of Vedic astrology. This book is an attempt to dispel the darkness that surrounds Rahu and Ketu so that they can be better understood and their importance in Vedic astrology appreciated. By no means the final word on Rahu and Ketu, this book attempts to provide readers with a practical understanding of these two nodes so that they can be placed in perspective. The book also provides other insights into Vedic astrology. The use of horoscopes of some prominent persons makes an understanding of Rahu and Ketu easier both for astrology enthusiasts and for other readers.
Wireless communication is one of the fastest growing industry segments today. Many types of wireless networks are now being used for applications such as personal communication, entertainment, rural and urban healthcare, smart home building, inventory control, and surveillance. This book introduces the basic concepts of wireless networks and mobile
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.
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