The paper investigates the way in which the property of a language operation ⋄ ”to be invertible” helps in solving language equations of the type L⋄Y = R. In the beginning, the simple case where ⋄ denotes catenation is studied, but the results are then generalized for various invertible insertion and deletion operations. For most of the considered operations ⋄, the problem ”Does there exist a s...

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u0 ∈H3/4 + (R) whose restriction belongs to H l((b,∞)) for some l ∈ Z+ and b ∈ R we prove that the restriction of the corresponding solution u(·, t) belongs to H l((β ,∞)) for any β ∈ R and any t ∈ (0,T ). Thus, this type of regularity propagates with ...

The current paper proves the results announced in [6]. We isolate a new large cardinal concept, “remarkability.” Consistencywise, remarkable cardinals are between ineffable and ω-Erdös cardinals. They are characterized by the existence of “0-like” embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(R) absoluteness for...

Denote by γ the Gauss measure on R and by L the Ornstein– Uhlenbeck operator. In this paper we introduce a Hardy space h(γ) of Goldberg type and show that for each u in R\{0} and r > 0 the operator (rI+L) is unbounded from h(γ) to L(γ). This result is in sharp contrast both with the fact that (rI+L) is bounded from H(γ) to L(γ), where H(γ) denotes the Hardy type space introduced in [MM], and wi...

We examined Zl+l− and Zbb̄ couplings in the minimal supersymmetric model (MSSM) with explicit R-parity violating interactions. We found the top quark L-violating couplings λi3k and B-violating couplings λ ′′ 3j3 could give significant contributions through the top quark loops. To accomadate the latest Rl data, λ ′ i3k are suject to stringent bounds, some of which can be much stronger than the cu...

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