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

[04.1] Comparing L spaces. Let 1 ≤ p, p′ < ∞. When is L[a, b] ⊂ Lp [a, b] for finite intervals [a, b] and Lebesgue measure? When is L(R) ⊂ Lp(R)? When is ` ⊂ `p? Discussion: Take p < p′. We claim that L[a, b] ⊃ Lp [a, b], with proper containment. The function f that is (x − a) 1 p′ on (a, b] and 0 off that interval is not in L ′ , but is in L. Given f ∈ Lp [a, b], let E be the set of x ∈ [a, b]...

Abstract A generating set for a finite group G is minimal if no proper subset generates , and $m(G)$ denotes the maximal size of . We prove conjecture Lucchini, Moscatiello Spiga by showing that there exist $a,b&gt; 0$ such any satisfies $m(G) \leqslant \cdot \delta (G)^b$ $\delta (G) = \sum _{p \text { prime}} m(G_p)$ where $G_p$ Sylow p -subgroup To do this, we first bound all almost simple g...

The articles [8], [19], [2], [10], [12], [18], [20], [1], [15], [5], [21], [11], [3], [9], [7], [6], [17], [4], [16], [14], and [13] provide the terminology and notation for this paper. For simplicity, we adopt the following convention: Ω, I are non empty sets, F is a σ-field of subsets of Ω, P is a probability on F , D, E, F are families of subsets of Ω, A, B, s are non empty subsets of F , b ...

s i n c e t h e l a t e 1960s, s e v e r a l c o n s t i t u t i v e m o d e l s h a v e b e e n d e v e l o p e d f o r s a n d s d e s c r i b i n g t h e i r s t r e s s-s t r a i n e h a v i o r. m o s t o f t h e s e m o d e l s w e r e e s t a b l i s h e d b a s e d o n a m e a s u r e o f t h e p l a s t i c w o r k a n d s o m e y i e l d c r i t e r i a, a m o n g t h e m b e i n g t ...

Proof. Suppose the first condition holds. Let B ⊇ C and let a be any realization of p|B. For γ ∈ Γ(Ba), we can write γ as f(a) for some B-definable function. Then γ |= f∗p|B. Also, p is B-invariant and f is B-definable, so the type f∗p is B-invariant. Since it is constant, it must contain the formula x = γ0 for some γ0, and γ0 must be B-definable. Therefore the formula x = γ0 is in f∗p|B, and s...

Abstract We study the behavior of Haar coefficients in Besov and Triebel–Lizorkin spaces on $${\mathbb R}$$ R , for a parameter range which system is not an unconditional basis. First, we obtain parameters, extending up to smoothness $$s&lt;1$$ s &lt; 1</mm...

Numerical study of various processes leads to the need for clarification (extensions) limits applicability computational constructs and modeling tools. In this article, we differentiability in space Lebesgue integrable functions consistency concept with fundamental constructions such as Taylor expansion finite differences is considered. The function $f$ from $L_1 [a; b]$ called $(k,L)$-differen...