In this paper we shall prove two theorems (Stability Theorem, Local Torelli Theorem) for symplectic varieties. Let us recall the notion of a symplectic singularity. Let X be a good representative of a normal singularity. Then the singularity is symplectic if the regular locus U of X admits an everywhere non-degenerate holomorphic closed 2-form ω where ω extends to a regular form on Y for a reso...

To a given language L, we associate the sets ins(L) (resp. &l(L)) consisting of words with the following property: their insertion into (deletion from) any word of L yields words which also belong to L. Properties of these sets and of languages which are insertion (deletion) closed are obtained. Of special interest is the case when the language is ins-closed (del-closed) and finitely generated....

We prove that in the category of achimedean lattice-ordered groups with weak unit there is no homomorphism-closed monoreflection strictly between the strongest essential monoreflection (the so-called “closure under countable composition”) and the strongest monoreflection (the epicompletion). It follows that in the category of regular σframes, the only non-trivial monoreflective subcategory that...

Nagata conjectured that everyM -space is homeomorphic to a closed subspace of the product of a countably compact space and a metric space. This conjecture was refuted by Burke and van Douwen, and A. Kato, independently. However, we can show that there is a c.c.c. poset P of size 2 such that in V P Nagata’s conjecture holds for each first countable regular space from the ground model (i.e. if a ...

Families of Languages AFL thm if F is closed under substitution with λ-free regular sets, morphism, union with regular sets [easy for cfg] & intersection with regular sets, then F is closed under inverse morphism Figure 26: closure properties of CF II 12 intersection with regular languages a;A/α a a;A/α λ;A/α λ;A/α { } } { ⇒ ⇒ { anbn | n ≥ 1 }∗ ∩ { w ∈ {a, b}∗ |#ax even } r1 p1 q1 r0 p0 q0 r p ...

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

The (bounded) hairpin completion and its iterated versions are operations on formal languages which have been inspired by the hairpin formation in DNA-biochemistry. The paper answers two questions asked in the literature about the iterated hairpin completion. The first question is whether the class of regular languages is closed under iterated bounded hairpin completion. Here we show that this ...