Given free modules $M\subseteq L$ of finite rank $f\geq 1$ over a principal ideal domain $R$, we give procedure to construct basis $L$ from $M$ assuming the invariant factors or elementary divisors $L/M$ are known. matrix $A\in M_{m,n}(R)$ $r$, its nullspace in $R^n$ is $R$-module $f=n-r$. We submodule $f$ naturally associated with $A$ and whose easily computable, determine quotient module then...

A t ranspor t theory is deve l oped f o r mixtures o f d i lute gases consist ing o f linear ro ta t ing d i a m a g n e t i c molecules in an external h o m o g e n e o u s magnet i c field. Th i s f o r m a l i s m is a d e q u a t e f o r a t r ea tment o f the Senf t leben-Beenakker ef fects f o r gas mixtures . Start ing po int is the s y s t e m o f l inearized W a l d m a n n S n i d e r...

A f r a m e w o r k f o r m o d e l i n g a n d r e c o g n i t i o n o f t e m p o r a l a c t i v i t i e s is proposed . T h e m o d e l i n g o f s e t s o f e x e m p l a r a c t i v i t i e s is ach ieved by p a r a m e t e r i z i n g t h e i r r e p r e s e n t a t i o n in t h e f o r m o f p r i n c i p a l c o m p o n e n t s . R e c o g n i t i o n o f s p a t i o t e m p o r a l v ...

A (D; g)-cage is a graph having the minimum number of vertices, with degree set D and girth g. Denote by f(D; g) the number of vertices in a (D; g)-cage. In this paper it is shown that f({r; m}; 6)¿ 2(rm−m+ 1) for any 26 r ¡m, and f({r; m}; 6) = 2(rm−m+ 1) if either (i) 26 r6 5 and r ¡m or (ii) m − 1 is a prime power and 26 r ¡m. Upon these results, it is conjectured that f({r; m}; 6) = 2(rm− m...

An i n f l u e n c e o f d e p a r t u r e f r o m r o t a t i o n a l e q u i l i b r i u m on t h e f l o w s t r u c t u r e n e a r a s p h e r e o f r a d i u s R = 0 . 3 m c a n be e x p e c t e d f o r f l i g h t a t a l t i t u d e s 9 0 1 2 0 km [ 1 ] . I n t h e e x p e r i m e n t a l s i m u l a t i o n o f t h e s e f l o w r e g i m e s i n w i n d t u n n e l s , t h e n o n e q...