...tp://PublishingOnline.com Peer reviewers: Dr. Sukanto Bhattacharya, Alaska Pacific University, Anchorage, AK 99508, Alaska, USA. Dr. Lariss... ...0). If V is a finite dimensional the birank of T is the dimension of the range of T and the binullity of T is the dimension of the null bispace o... ... 2 ). i.e., a linear Bitransformation is called a linear bioperator if the range bispace and the domain bispace are one and the same. Now we proce... ...(T 1 ∪ T 2 ) ( β) i.e., T ( α) = T ( β) ⇔ α = β. T is on to, that is if range of T is all of W = W 1 ∪ W 2 . It is left as an exercise for the... ...a glance at the bimatrix D = D 1 ∪ D 2 . We could describe explicitly the range and null bispace of T. Since [ ] 12 B( B, B) T = = D = D 1 ∪ D ... ...d 118 222 22 2 2i ii TC α= α , i = 1, 2,…, n, i 2 = 1, 2, …, m. The range would be a subbivector space spanned by α k ’s for which C k ’s ar...

..., M. Viteazu College, Bailesti, jud. Dolj, Romania. Dr. Sukanto Bhattacharya, Alaska Pacific University, Anchorage, AK 99508, Alaska, USA. ... ... patient and so on. Thus for us to define a FRM we need a domain space and a range space which are disjoint in the sense of concepts. We further as... ...e no intermediate relation exists within the domain elements or node and the range spaces elements. The number of elements in the range space need ... ...ain space are taken from the real vector space of dimension n and that of the range space are real vectors from the vector space of dimension m (m i... ...need not be equal to n). We denote by R the set of nodes R 1 ,…, R m of the range space, where R = {(x 1 ,…, x m ) ⏐x j = 0 or 1 } for j = 1, 2,…... ... nodes of the domain space D of an FRM and R 1 , …, R m be the nodes of the range space R of an FRM. Let the matrix E be defined as E = (e ij ) w...

...ania. 2) Dr. Sukanto Bhattacharya, Department of Business Administration, Alaska Pacific University, U.S.A. 3) Dr. M. Khoshnevisan, School of Accou... ... cases are mutually disjoint as p 1 r p 2 is unique for a given r, which ranges from 0 to α, which is exhaustive. Therefore, 21 ... ... F’ ** (N) = Σ F’ * (d r ) d r |N where d r ranges over all the divisors of N. If N is a square-free number with n ... ... where F’ * (N) = Σ F’(d r ) d r |N and d r ranges over all the divisors of N. Theorem: F’(Np 1 p 2 ) = F...

... 2005 1 Sukanto Bhattacharya Department of Business Administration Alaska Pacific University, U.S.A. Utility, Rationality and Beyon... ...the volatility process over time have coefficients of determination in the range say between 50%-70%, then we can say that t varies in the set T (50%... ... current excursions in implied volatility on short-term options lie in the range say 35 between 40%-60%, then f varies in the set F (40% - 60%). Th... ...at the possibility to lend or borrow money at a risk-free rate widens the range of investment options for an individual investor. The inclusion of th... ... greater utilty of empowerment to an individual investor due to the wider range of decision options. Of course, according to the Black-Schole... ...r utility from expected excess equity. 105 B. Extrapolating the ranges of investor’s risk aversion within each probability space: F...

...osophy 4th EDITION Sam Vaknin, Ph.D. Editing and Design: Lidija Rangelovska Lidija Rangelovska A Narcissus Publications... ... Not for Sale! Non-commercial edition. © 2004-7 Copyright Lidija Rangelovska. All rights reserved. This book, or any part thereof... ...ay not be used or reproduced in any manner without written permission from: Lidija Rangelovska – write to: palma@unet.com.mk or to samvaknin@gmai... ...ree anthologies here: http://samvak.tripod.com/freebooks.html Created by: LIDIJA RANGELOVSKA REPUBLIC OF MACEDONIA C O N T E N T S I. A I... ...rs of a plane-wrecked rugby team, stranded on an inaccessible, snow-piled, mountain range resort to eating each other in order to survive, we turn a... ...ughters and old relatives is socially condoned - though illegal - in India, China, Alaska, and parts of Africa. Genocide may have been legally sanc...