Loosely speaking, “homotopy theory” is a perspective which treats objects as equivalent if they have the same “shape” which, for a category theorist, occurs when there exists a certain class W of morphisms that one would like to invert, but which are not in fact isomorphisms. Model categories provide a setting in which one can do “abstract homotopy theory” in subjects far removed from the origi...

Itay Neeman found in [7] a new way of iterating proper forcing notions and extended it in [8] to א2. In [5] his construction for א1 ([7]) was generalized to semi-proper forcing notions. We apply here finite structures with pistes in order extend the construction to higher cardinals. In the final model a very weak form of SPFA will hold. 1 Basic definitions and main results The following two def...

Congruence proofs for bisimulation equivalences on higher{order process calculi tend to be signiicantly more complex than their counterparts in rst{order process algebra frameworks. The fact that higher{order synchronization invokes substitution seems to be the main problem. The reason is that it renders standard rst{order proof techniques circular in the higher{order case, and this situation i...

This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse Baum-Connes assembly map is injective; the coarse Baum-Connes assembly map is not surjective; the maximal coarse BaumConnes assembly map is an isomorphism. These res...

We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)s some functions supported on ellipsoids. In particular, we derive expression torsion function and give examples $s$-harmonic functions. As an application, infer that weak maximum principle fails in eccentric ellipsoids $s\in(1, \sqrt{3}+3/2)$ any dimension $n\geq 2$. build a coun...

Introduction Blended modeling aims at boosting the development of complex multi-domain systems by enabling seamless multi-notation modeling. The synchronization mechanisms between notations are embodied in model transformations. Manually defining transformations requires specific knowledge transformation languages, and it is a time-consuming error-prone task. Moreover, whenever any synchronized...

We characterize symmetry transformations of Lagrangian extremals generating “on shell” conservation laws. relate to Jacobi fields and study symmetries higher variations by proving that a pair given the lth variation field sth same (with s < l) is associated with an “off conserved current. The current two constructed, as case study, its expression for invariant sets Yang–Mills connections...

We consider a class of higher order nonlinear degenerate parabolic systems, whose easiest model is the parabolic p-Laplacean system ∫ ΩT ( u · φt − |Dmu|p−2Dmu ·Dmφ ) dz = ∫