Theorem 1 Assume that μ is not an even integer. Then there exists f ∈ D(R) such that |f | / ∈ B p,q (R), for every q <∞. Remark. If μ is an even integer, then t 7→ |t| is a C∞ function. Such functions are known to act on B p,q(R) ∩ L∞(Rn) (cf. [6, thm. 5.3.6(1), p. 336]). Theorem 2 Let μ > 1. Assume that s < n/p or that s = n/p and q > 1. Then there exists a positive unbounded function f such t...

v a g u e p r o p e r t i e s o f ' h o m o t o p i c a l e x a c t n e s s ' , a p p e a r i n g f o r i n s t a n c e i n t h e f i b r e o r c o f i b r e s e q u e n c e o f a m a p . S u c h n o t i o n s o f e x a c t n e s s c a n b e g i v e n f o r v e r y g e n e r a l ' c a t e g o r i e s w i t h h o m o t o p i e s ' h a v i n g h o m o t o p y k e r n e l s a n d c o k e r n e l s...

(ii) F is a family of subsets of Ω which has the structure of a σ-field: a) ∅ ∈ F b) If A ∈ F , then its complement A also belongs to F c) A1, A2, . . . ∈ F =⇒ ∪i=1Ai ∈ F (iii) P is a function which associates a number P (A) to each set A ∈ F with the following properties: a) 0 ≤ P (A) ≤ 1, b) P (Ω) = 1 c) For any sequence A1, A2, . . . of disjoints sets in F (that is, Ai∩Aj = ∅ if i 6= j), P (...

We investigate the complexity of Boolean clone membership problem (CMP): given a set functions $F$ and function $f$, determine if $f$ is in generated by $F$, i.e., it can be expressed circuit with $F$-gates. Here, elements are as circuits or formulas over usual De Morgan basis. B\"ohler Schnoor (2007) proved that for any fixed coNP-complete, few exceptions where P. Vollmer (2009) incorrectly cl...

1 3 4 E a rn e st M o n e y D e p o si t (E M D ): A n E M D o f R s. 5 ,0 0 ,0 0 0 ( R u p e e s F iv e L a k h O n ly ) in t h e f o rm o f a d e m a n d d ra ft /p a y o rd e r d ra w n i n f a v o u r o f In d ia P o st P a y m e n ts B a n k L im it e d s h o u ld b e s u b m it te d a lo n g w it h t h e t e ch n ic a l B id . R e q u e s b a n k t o a cc e p t B a n k G u a ra n te e a s...

Let 〈P,≤〉 be a partially ordered set. We define the poset Boolean algebra of P , and denote it by F (P ). The set of generators of F (P ) is {xp : p ∈ P}, and the set of relations is {xp ·xq = xp : p ≤ q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and 〈G,≤G〉 is well-founded. A wellgenerated algebra is superatomic. Theorem 1 Let 〈P,≤〉 be a...

The NA57 Collaboration: F Antinori, P Bacon, A Badalà, R Barbera, A Belogianni, A Bhasin, I J Bloodworth, M Bombara, G E Bruno †, S A Bull, R Caliandro, M Campbell, W Carena, N Carrer, R F Clarke, A Dainese, A P de Haas, P C de Rijke, D Di Bari, S Di Liberto, R Divià, D Elia, D Evans, G A Feofilov, R A Fini, P Ganoti, B Ghidini, G Grella, H Helstrup, K F Hetland, A K Holme, A Jacholkowski, G T ...

where C+F(R9 p) denotes the singular chains of F(R , p), and Zp{q) denotes the Ip-module Zp with 2P-action a • x = ( l) x for xeZp and a e Zp ( ( 1) S(<T) is the sign of a). Since the Enaction on F(R, p) is proper, we may identify H*(HomEp(C^F(« , p) ; Zp(2g))) with H*(B(R ,p); Zp) [5]. By abuse of notation we denote H*(Hom2 ( Q F ^ p ) ; Zp(g))) by H*(B(R\p);Zp(q)). The interest in H*(B(R, p) ...