... U ) , where ( T , + ) is a group and U is a set of T - subgroups such that UV = { 0 } , TU + V for any distinct U , V EU and to any u ET \ { 0 } there is exactly one U EU with u Є U. ( 3.1 ) Definition ( Bacon spread ) Let ( T , + ) be a ...

... u * = u * μοφ u * transforms as a vector field in any transition region when the opens covering of M overlap . It allows to write : ( df ∈ F ) ( u * ( f ) ∈ F ) * εν . Definition 43 Metric induced on V * by the metric g on V ...

... Definition 2 Definition 4.12 The inner product on C ... 9 Consider two row vectors in Ch . Suppose u = ( U1 , U2 , un ) and v = ( V1 , V2 , U¿ , Vi Є C. We now define the inner product , written as ( u , v ) , to be n * ( u , v ) = u ...

... u ' is u ⇒ v ′ ( u ' hası v ′ ^ v ′ isr v ) ) 2. For axioms 2 ~ 5 , soundness are similarly proved . 3. For axiom 6 , soundness is shown by the restriction of an object term in definition 4 and lemma 9 . For any a , b , b ' ЄŌ U Ō ...

... definition of generalized rough sets by employing the concept of σ - algebra and discussed the relationships with ... U be a universe of discourse and R an equivalence relation on U. For any X ⊆ U , its corresponding element ...

... definition 13 ) . From a class of all plausible world models M for W , a subset , which satisfies exactly all applicable defaults is found . Such a set is named the IDL model U ... DEFINITION 31 [ MOD ( W ) ] : MOD ( W ) is the set of ...

... definition , 81 ( x ) = B ( y ) + Image d = 0. This means that ( y ) e Image By . Thus , B ( y ) = B ( ) ( u ) ) for some u € E. Hence y − y ( u ) is a member of Ker B = Image a . Suppose that y – 7 ( u ) = a ( u ) , where v € D ...

William S. Massey. the chain u the subset | u | = | ēt , i where the union is over all cells et such that the corresponding coefficient g ; 0. If u = 0 , we define [ u ] = Ø . The set [ u ] is called the support of u . It has the ...

... U and F = n { X , X ,, ... X } be a classification of U. We extend the five basic types of classifications in- troduced in ( Grzymala Busse , 1988 ) as follows : Definition 15 : We say that F is strongly R + S { R * S respectively } ...

... Definition 3.1 . We define VP and VP by the transfinite induction on ordinals a as follows : VP = 0 , ᏙᏢ VP + 1 = { uu is a function with dom ( u ) CVP and ran ( u ) = Factp } , VP = Ua < VP where A is a limit ordinal . VP VP ...