For a field F, let R(n,m) be the ring of invariant polynomials for the action of SL(n,F) × SL(n,F) on tuples of matrices – (A,C) ∈ SL(n,F)× SL(n,F) sends (B1, . . . , Bm) ∈ M(n,F) to (AB1C , . . . , ABmC ). In this paper we call R(n,m) the ring of matrix semi-invariants. Let β(R(n,m)) be the smallest D s.t. matrix semi-invariants of degree ≤ D generate R(n,m). Guided by the Procesi-Razmyslov-Fo...

In [9] it is proved that there are subsets M of the complex plane such that for any two entire functions f and g if f [M ] = g[M ] then f = g. In [3] it was shown that the continuum hypothesis (CH) implies the existence of a similar set M ⊂ R for the class Cn(R) of continuous nowhere constant functions from R to R, while it follows from the results in [5] and [7] that the existence of such a se...

T h e e x a c t M a x w e l l f B o l t z m a n n ( M B ) , B o s e f E i n s t e i n ( B E ) a n d F e r m i f D i r a c ( F D ) e n t r o p i e s a n d p r o b a b i l i s t i c d i s t r i b u t i o n s a r e d e r i v e d b y t h e c o m b i n a t o r i a l m e t h o d o f B o l t z m a n n , w i t h o u t S t i r l i n g ’ s a p p r o x i m a t i o n . T h e n e w e n t r o p y m e a s u r...

T h e G P G P / T Æ M S d o m a i n i n d e p e n d e n t c o o r d i n a t i o n f r a m e w o r k f o r s m a l l a g e n t g r o u p s w a s f i r s t d e s c r i b e d a l m o s t t e n y e a r s a g o a n d t h e n m o r e f u l l y d e t a i l e d i n a n I C M A S 9 5 p a p e r . I n t h i s p a p e r , w e d i s c u s s t h e e v o l u t i o n o f t h i s f r a m e w o r k o v e r t h e...

One of the r e c u r r e n t d r e a m s in e l e m e n t a r y p a r t i c l e s phys ics i s that of a poss ib le fundamenta l synthes is between e l e c t r o m a g n e t i s m and weak in te rac t ions [1]. The idea has i t s or ig in in the fol lowing shared c h a r a c t e r i s t i c s : 1) Both f o r c e s affect equal ly a l l f o r m s of m a t t e r leptons as wel l as hadrons. 2) Bo...

For the ring R of integers of a ramified extension of the field of p-adic numbers and a cyclic group G of prime order p we study the extensions of the additive groups of R-representations modules of G by the group G. Let T be the field of fractions of a principal ideal domain R, F a field which contains R, let G be a finite group and Γ a matrix R-representation of G. Let M be an RG-module, whic...

"̂T^ H A T P O T E N T I A L F O R T E 1 E E N R I C H M E N T O F I s c i e n c e is w h a t B a r r o w h a s se t o u t t o e x p l o r e _JL i n Impossibility. A p r o f e s s o r o f a s t r o n o m y a t t h e U n i v e r s i t y o f S u s s e x i n E n g l a n d , B a r r o w w r i t e s w i t h g r e a t s c h o l a r s h i p , e l e g a n c e a n d w i t . H e classif ies t h e l i m i ...

c l a s s e s t ak e n f o r t h e s t u d y a r e C o n v e r s a t i o na l t r a f f i c , I n t e r a c t i ve t r a f f i c a n d b a c k g r o u nd t r a f f i c w h i c h a r e w i t h va r i e d Q o S p a r a m e t e r s. Th e p a pe r a l s o p r e s e n t s t h e a n a l yt i c a l m o d e l f o r t h e C A C. T h e pa p e r c o m p ar e s t h e c a l l b l o c k i n g pr ob a b i l i...