The eta invariant of the Dirac operator over a noncompact cofinite quotient of PSL(2,R) is defined through a regularized trace following Melrose. It reduces to the standard definition in terms of eigenvalues in the case of a totally nontrivial spin structure. When the S1-fibers are rescaled, the metric becomes of nonexact fibred-cusp type near the ends. We completely describe the continuous spe...

The Berezin transform $\widetilde{A}$ and the radius of an operator $A$ on reproducing kernel Hilbert space over some set $Q$ with normalized $k_{\eta}:=\dfrac{K_{\eta}}{\left\Vert K_{\eta}\right\Vert}$ are defined, respectively, by $\widetilde{A}(\eta)=\left\langle {A}k_{\eta},k_{\eta}\right\rangle$, $\eta\in Q$ $\mathrm{ber} (A):=\sup_{\eta\in Q}\left\vert \widetilde{A}{(\eta)}\right\vert$. A...

We present a new strong normalisation proof for a λ-calculus with interleaving strictly positive inductive types λ which avoids the use of impredicative reasoning, i.e., the theorem of Knaster-Tarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel. To achieve this we show that every strictly positive operator on types gives rise to an operator o...

The recently developed theory1 of monotone nonlinear operators T from a Banach space X to its conjugate space X* can be considered most naturally as an extension to nonvariational problems of the basic ideas of the direct method of the calculus of variations. First of all, in practice, its simplest and most basic application is to a class of nonlinear elliptic boundary value problems2 which is ...

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated...

This paper is concerned with the study of a penalization-gradient algorithm for solving variational inequalities, namely, find x ∈ C such that 〈Ax, y − x〉 ≥ 0 for all y ∈ C, where A : H → H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ : H → ∪ { ∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter ...

Mapping composition is a fundamental operation in metadata driven applications. Given a mapping over schemas σ1, σ2, and σ3, the composition problem is to find an equivalent mapping over only σ1 and σ3. We describe a new composition algorithm that targets practical applications. It incorporates view unfolding. It eliminates as many σ2 symbols as possible, even if not all can be eliminated. It c...

We prove that the principal pivot transform (also known as partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part to part. show is matrix monotone by establishing Hermitian square representations for and derivative.

In this paper, by using a resolvent operator technique of (H,η)-monotone mappings, we study the behavior and sensitivity of the solutions for a system of variational inclusions with (H,η)-monotone operators in Hilbert spaces. Mathematics Subject Classification: 49J40, 47H19, 47H10

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...