We consider the theory (ACFp)P of pairs F < K of algebraically closed fields of a given characteristic p. We exhibit a collection of additional sorts in which this theory has geometric elimination of imaginaries. The sorts are essentially of the form ∪a∈B(F )Va(K)/Ga(F ), where G, V,B are varieties over the prime field G a group scheme over B and V is a scheme over B (both with irreducible fibr...

T h i s pape r p r e s e n t s a n o v e r v i e w o f a n a l g o r i t h m f o r r i b d e t e c t i o n i n c h e s t x r a y s . The g o a l o f t h e a l g o r i t h m i s t o r e t u r n t h e l o c a t i o n o f t h e b o r d e r s o f t h e r i b s t o a s c r e e n i n g sys tem t o e n a b l e i n t e r c o s t a l spaces t o b e e x t r a c t e d and a n a l y s e d . The d e t e c t...

The b l a c k b o a r d a r c h i t e c t u r e i s a p o w e r f u l e x p e r t systems a r c h i t e c t u r e . I t s main advantages a r e f l e x i b i l i t y o f c o n t r o l and i n t e g r a t i o n o f d i f f e r e n t k i n d s o f knowledge r e p r e s e n t a t i o n s and i n f e r e n c i n g t e c h n i q u e s . At our L a b o r a t o r i e s we b u i l t a b l a c k b o a r...

let g be a graph with p vertices and q edges and a = {0, 1, 2, . . . , [q/2]}. a vertex labeling f : v (g) → a induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv. for a ∈ a, let vf (a) be the number of vertices v with f(v) = a. a graph g is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in a, |vf (a) − vf (b)| ≤ 1 and the in...

Let K=Q(θ) be an algebraic number field with θ a root of irreducible trinomial f(x)=x6+ax+b belonging to Z[x]. In this paper, for each prime p we compute the highest power dividing discriminant K in terms powers a, b and f(x). An explicit p-integral basis is also given method described obtain integral from these bases which illustrated examples.

Let Vn be a vectorspace of complex-valued functions defined on R of dimension n + 1 over C. We say that Vn is shift invariant (on R) if f ∈ Vn implies that fa ∈ Vn for every a ∈ R, where fa(x) := f(x− a) on R. In this note we prove the following. Theorem. Let Vn ⊂ C[a, b] be a shift invariant vectorspace of complex-valued functions defined on R of dimension n+ 1 over C. Let p ∈ (0, 2]. Then ‖f‖...

u n d o u b t e d l y, i n t h e l a s t d e c a d e s, t h e a s s e t p r i c i n g m o d e l i so n e o f m o s t i m p o r t a n t a n d, a t t h e s a m e t i m e, a t t r a c t i v e, f i n a n c e a r e a s. c a p m h a s b e e n t h e d o m i n a n t m o d e l i n t h i s s e c t i o n f o r m o r e t h a n 40 y e a r s. o n e r e a s o n i s i t s s t r o n g b a s e, w h i c h h a s b...

Assume that u; v : [a; b] ! R are monotonic nondecreasing on the interval [a; b] : For p; q > 1 with 1 p + 1 q = 1; we say that the complex-valued function h : [a; b] ! C is (p; q)-H-dominated by the pair (u; v) if jh (y) h (x)j [u (y) u (x)] 1=p [v (y) v (x)] 1=q for any x; y 2 [a; b] with y x: In this paper we show amongst other that Z b a f dh Z b a jf j du 1=p Z b a jf j dv 1=q ; and Z b a ...

We give some simple examples of applying the well-known elementary probability theory inequalities and properties in field logical argumentation. A probabilistic version hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, B→C have probabilities a, b, c, r, s, respectively, then for p A→C, we f(a,b,c,r,s)≤p≤g(a,b,c,r,s), functions f g given parameters. In this pape...