Consider a ring K, a topological space X and a sheaf A on X of K[[~]]-algebras. Assuming that A is ~-complete and without ~torsion, we first show how to deduce a coherency theorem for complexes of A -modules from a corresponding property for complexes of A /~A -modules. We apply this result to prove that, under a natural properness condition, the convolution of two coherent kernels over deforma...

We study the numerical solution of the problem minX≥0 ‖BX−c‖2, where X ∈ Sm is a symmetric square matrix, and B : Sm → R is a linear operator, such that B∗B is invertible. With ρ the desired fractional duality gap, we prove O( √ m log ρ−1) iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints, however not d...

For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra we construct a canonical K-homology class, which induces a Poincaré duality map K∗(C(∂Γ)⋊Γ) → K (C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case of Γ = F2 the free group on two generators. We point out a direct connection between our constructions and the ...

We introduce the notion of rigid embedding in a grid surface, a new kind of plane drawing for simple triconnected planar graphs. Rigid embeddings provide methods to (1) find well-structured (cellular, here) minimal free resolutions for arbitrary monomial ideals in three variables; (2) strengthen the Brightwell–Trotter bound on the order dimension of triconnected planar maps by giving a geometri...

The symbiotic branching model describes the evolution of two interacting populations and if started with complementary Heaviside functions, the interface where both populations are present remains compact. In this paper, we show tightness of the diffusively rescaled solutions and thus provide a first step towards a scaling limit for the interface. The crucial estimate involves a mixed fourth mo...

Adaptive finite element methods for optimization problems for second order linear elliptic partial differential equations subject to pointwise constraints on the `-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overc...

this study historically analyzes the scientific output of mathematics to describe its structure, notions and scientific origin using the historiographical method. the research data consisted of scientific outputs of mathematics in isi database, science citation index (sci) and social science citation index (ssci) during 8 years (1990 to 2007). the data collection tool was the search engine and ...

Let X be a complex Banach space and let J : X → X∗ be a duality section on X (i.e. 〈x, J(x)〉 = ‖J(x)‖‖x‖ = ‖J(x)‖2 = ‖x‖2). For any unit vector x and any (C0) contraction semigroup T = {e tA : t ≥ 0}, Goldstein proved that if X is a Hilbert space and if |〈T (t)x, J(x)〉| → 1 as t → ∞, then x is an eigenvector of A corresponding to a purely imaginary eigenvalue. In this article, we prove the simi...

In this note we introduce and study algebras ( L , V, A, 1, 0,l) of type (2,2,1,1,1) such that ( L , V, A, 0 , l ) is a bounded distributive lattice and -,is an operator that satisfies the conditions -,(a V b ) = -,a A -,b and -0 = 1. We develop the topological duality between these algebras and Priestley spaces with a relation. In addition, we characterize the congruences and the subalgebras o...