In this survey, we review fundamental properties of coalgebras and their representation theory. Following J.A. Green we present the block theory of coalgebras using indecomposable injectives comodules. Using the cohom and cotensor functors we state Takeuchi-Morita equivalence and use it to sketch the proof of existence of “basic” coalgebras, due to the author and S. Montgomery. This leads to a ...

Abstract. The approach, referred to as ”monodromy transform”, provides some general base for solution of all known integrable space time symmetry reductions of Einstein equations for the case of pure vacuum gravitational fields, in the presence of gravitationally interacting massless fields, as well as for some string theory induced gravity models. In this communication we present the key point...

We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations...

The paper presents an introduction to the theory of hyperbolic virtual polytopes from the viewpoint of combinatorial rigidity theory. Namely, we give a shortcut for a reader who is acquainted with the notions of Laman graphs, 3D liftings and pointed tilings. From this viewpoint, a hyperbolic virtual polytope is a stressed pointed graph embedded in the sphere S. The advantage of such a presentat...

In this paper, I analyze a general equilibrium on-the-job search model with endogenous search intensity and heterogenous workers and firms. Wages are set through bargaining as in Cahuc, Postel-Vinay, and Robin (2006). I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient search on and off the job, I provide proof that the equilibrium firm productivity ...

In one stream of development, one partner in the project had just achieved an interpretation of group cohomology or Lie-algebra cohomology in terms of higher-dimensional central extensions, as developed by Rodelo–Van der Linden [14, 15]. It extends the classical interpretation of the second group cohomology in terms of equivalence classes of short exact sequences with central kernel. This devel...

Flows over time provide a natural and convenient description for the dynamics of a continuous stream of particles traveling from a source to a sink in a network, allowing to track the progress of each infinitesimal particle along time. A basic model for the propagation of flow is the so-called fluid queue model in which the time to traverse an edge is composed of a flow-dependent waiting time i...

We give a rigorous proof of existence for solitary waves of a peridynamics model in one space dimension recently investigated by Silling (J. Mech. Phys. Solids 96:121–132, 2016). We adapt the variational framework developed by Friesecke and Wattis (Comm. Math Phys. 161:391–418, 1994) for the FermiPasta-Ulam-Tsingou lattice equations to treat a truncated problem which cuts off short-range intera...

We present a semantical proof of existence of normal forms for system F including -equality. A reduction-free normalisation function can be obtained from this. The proof uses the method of glueing (a variant of) the term model along the global sections functor, carried out in the internal language of a category of presheaves. As a by-product we obtain an semantical explanation of higherorder ab...

We have seen that the proof of existence of inverses for elements of Ext(X) can be based on a lifting theorem for (completely) positive maps of C(X) into a quotient C∗-algebra of the form E/K, where E ⊆ B(H) is a C∗-algebra containing the compact operators K. That argument works equally well for arbitrary C∗-algebras in place of C(X) whenever a completely positive lifting exists. Thus we are le...