We study the adiabatic limit of the eta invariant of the Dirac operator over cofinite quotient of PSL(2,R), which is a noncompact manifold with a nonexact fibred-cusp metric near the ends.

and Applied Analysis 3 called cofinite if the recession function f0 of f satisfies f0 y ∞, for all y / 0 see 15, page 116 . Then f is cofinite if and only if dom f∗ R by means of 15, Corollary 13.3.1 . The terminology “cofinite” is renewed as “coercive” in 16, 3.26 Theorem . Now we take a look at Atteia and Raı̈ssouli 11, Proposition 4.4 with a refined proof. Proposition 2.1 See Atteia and Raı̈ss...

We study a boundary value problem in subsonic aeroelasticity and introduce the cofinite Hilbert transform as a tool in solving an auxiliary linear integral equation on the complement of a finite interval on the real line R.

Given an impartial combinatorial game G, we create a class of related games (CISG) by specifying a finite set of positions in G and forbidding players from moving to those positions (leaving all other game rules unchanged). Such modifications amount to taking cofinite induced subgraphs (CIS) of the original game graph. Some recent numerical/heuristic work has suggested that the underlying struc...

Let $A$ be a commutative noetherian ring, $\mathfrak{a}$ an ideal of $A$, and $m,n$ non-negative integers. $M$ $A$-module such that $\operatorname{Ext}^i\_A(A/\mathfrak{a},M)$ is finitely generated for all $i\leq m+n$. We define class $\mathcal{S}n(\mathfrak{a})$ modules we assume $H{\mathfrak{a}}^s(M)\in\mathcal{S}{n}(\mathfrak{a})$ $s\leq m$. show $H{\mathfrak{a}}^s(M)$ $\mathfrak{a}$-cofinit...

We study the syntactic complexity of finite/cofinite, definite and reverse definite languages. The syntactic complexity of a class of languages is defined as the maximal size of syntactic semigroups of languages from the class, taken as a function of the state complexity n of the languages. We prove that (n − 1)! is a tight upper bound for finite/cofinite languages and that it can be reached on...

Let S1(Γ,Γ) be the statement: For each sequence of point-cofinite open covers, one can pick one element from each cover and obtain a point-cofinite cover. b is the minimal cardinality of a set of reals not satisfying S1(Γ,Γ). We prove the following assertions: (1) If there is an unbounded tower, then there are sets of reals of cardinality b, satisfying S1(Γ,Γ). (2) It is consistent that all set...