We can assume that all components of x, y, u, v are nonzero. To see why this is so, suppose that the result was proven for this case and we were given four arbitrary nonzero vectors x, y, u, and v. We could transform them via a single nonsingular transformation T such that each component of T x, T y, T u, T v was nonzero (Lemma 2.2). Then for all Hermitian matrices P we would have (T x) T P (T ...

a series of novel indeno[1, 2-b]quinoxalin-11-ylidenamines 2-9 have been synthesized via condensation of indane[1, 2-b]quinoxalin-11-one (1) with various primary aromatic amines in presence of acoh for 3 h. compound 1 was synthesized by condensation of indane-1,2,3-trione with benzene-1,2-diamine in presence of acoh. the synthesized compounds were characterized by ir, 1h-nmr, mass spectra and e...

For simplicity, we adopt the following rules: x denotes a set, r, s denote real numbers, n denotes a natural number, V denotes a real linear space, v, u, w, p denote vectors of V , A, B denote subsets of V , A1 denotes a finite subset of V , I denotes an affinely-independent subset of V , I1 denotes a finite affinelyindependent subset of V , F denotes a family of subsets of V , and L1, L2 denot...

1. I n t r o d u c t i o n ~ ]e concep t o f fuzzy s e t s d e f i n e d by Zadeh 1 ) g i v e s an i m p o r t a n t m a t h e m a t i c a l c l u e f o r an approach to s t u d i e s o f sys tems w i th no sha rp b o u n d a r i e s . L a t e l y , t h e fuzzy i n t e g r a l 2 ) b a s e d on t h e fuzzy s e t t h e o r y has been proposed and a p p l i e d t o t he measurement o f fuzzy o b j...

in this report, synthesis, characterization and application of silica perchloric acid nanosphere as a novel and heterogeneous catalyst is described. these nanospheres have been characterized by xrd, ft-ir, bet and tga spectra and also by sem and tem images. the results show that it has a spherical shape and the particles size are between 75 and 100 nm. the catalytic activity has been investigat...

The background to t h i s work is the s i m u l a t i o n of a p lanne r who o p e r a t e s in a dynamic e n v i r o n m e n t , by r e c o g n i s i n g the p l ans o f o t h e r s and p r e d i c t i n g f u t u r e e v e n t s . The domain is t h a t of a d r i v e r who must n e g o t i a t e a r o u t e , obey ing t r a f f i c r e g u l a t i o n s , and t a k i n g account o f and a v o...

while most tinnitus cases have some degree of hearing impairment, a small percent of the patients admitted to ear, nose and throat clinics or hearing evaluation centers are those who complain of tinnitus despite having normal hearing thresholds. present study was performed in order to better understanding of the probable causes of tinnitus and to investigate possible changes in the cochlear and...

B r e c k B a l d w i n T h o m a s S. M o r t o n A m i t B a g g a I n s t i t u t e f o r R e s e a r c h D e p a r t m e n t o f C o m p u t e r D e p a r t m e n t o f C o m p u t e r i n C o g n i t i v e S c i e n c e a n d I n f o r m a t i o n S c i e n c e S c i e n c e U n i v e r s i t y o f P e n n s y l v a n i a U n i v e r s i t y o f P e n n s y l v a n i a D u k e U n i v e r ...

In this article we write algorithms and MATLAB programs to find the total energy of Cycle some related graphs. The concept matrix a graph G is introduced by K.Palani&M.Lalithakumari in [9]. Let G=(V, E) be (p, q) simple graph. V (G) = {νi/i 1,2, ... p} E {ei/i q}. T T(G) square order p + q whose (i, j)-entry defined as: