Abstract In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) <mm...

where a and b are arbitrary real numbers satisfying a < b, x ∈ W1,1(a,b) and f belongs to a space of functions described below. By an appropriate choice of representatives, W1,1(a,b) can be identified with the set of absolutely continuous functions x : [a,b] → R1, and henceforth we will assume that this has been done. Denote by M the set of integrands f = f (t,x, p) : R3 → R1 which satisfy the ...

1 Noncommutative Polly Cracker and preliminaries from noncommutative algebra The noncommutative Polly Cracker cryptosystems were developed by T.Rai in his Ph.D. dissertation ([1]), and rely on the fact that there are ideals of noncom-mutative algebras over finite fields that have infinite reduced Groebner bases. First let us briefly present notations that will be used further in the text. Every...

Domain Base Model checker refinements Transition system Temporal formula Spurious counterexample — > ¢¤ £¥¦ §© ̈ a « ¬ is the simplest model on which to check a formula yet achieving the same precision as does. R. Giacobazzi and I. Mastroeni:Domain Compression for Complete Abstractions – p.14/15 Future works: Geometry of Domain Transformers Compressor Compressor join−unif Obfuscator Ofuscator uc...

B. Adeva a, L. Afanasyev b, Y. Allkofer c, C. Amsler d, A. Anania e, S. Aogaki f, A. Benelli b, V. Brekhovskikh g, T. Cechak h, M. Chiba i, P. Chliapnikov g, C. Ciocarlan f, S. Constantinescu f, P. Doskarova h, D. Drijard j, A. Dudarev b, M. Duma f, D. Dumitriu f, D. Fluerasu f, A. Gorin g, O. Gorchakov b, K. Gritsay b, C. Guaraldo k, M. Gugiu f, M. Hansroul j, Z. Hons l, S. Horikawa c, Y. Iwas...

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A function or a real variable f is said to be periodic with period P if f(x+ P ) = f(x) holds for all x. Hence, if we know the values of f on an interval of length P , we know its values everywhere. If f is a function defined on an interval [a, b), we can extend f to a function defined for all x which is periodic of period b− a. We simply define f(x) to be f(x+ n(b− a)), where n is the integer ...

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that ̂ B p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), ̂ F s,q p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), if 0 < p < 1, 0 < q < 1, s ∈ R, while ̂ B p (Rn) = B s−n ( 1 p −1 ) ,q 1 (R ), ̂ F s,q p (Rn) = B s−n ( 1 p −1 ) ,1 1 (R ), if 0 < p < 1, 1 ≤ q < +∞, s ∈ R, and ̂ B p (Rn) = B p (R), ̂ F s,q p (Rn) = F s,1 p (R), if 1 ≤ p < +∞, 0 < q < 1...