In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefèvre’s thesis. Finally, starting from an idea of V. Lyubashenko’s, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal catego...

In families of polynomial functions one may encounter “singularity exchange at infinity” when singular points escape from the space and produce “virtual” singularities of the limit polynomial, which have themselves an influence on the topology. The total quantity of singularity involved in this phenomenon may not be conserved. Inspite of the fact that some of the ingredients do not behave well ...

We demonstrate how infinities improve the expressivity, power, readability, conciseness, and compositionality of a program logic. We prove that adding infinities to Presburger arithmetic enables these improvements without sacrificing decidability. We develop Omega++, a Coq-certified decision procedure for Presburger arithmetic with infinity and benchmark its performance. Both the program and pr...

We present the theory of the viscosity solutions of the inhomogeneous infinity Laplace equation ∂xi u∂xj u∂ 2 xixj u = f in domains in Rn. We show existence and uniqueness of a viscosity solution of the Dirichlet problem under the intrinsic condition f does not change its sign. We also discover a characteristic property, which we call the comparison with standard functions property, of the visc...

We study the fraction f of nucleotides involved in the formation of a cactuslike secondary structure of random heteropolymer RNA-like molecules. In the low-temperature limit, we study this fraction as a function of the number c of different nucleotide species. We show, that with changing c, the secondary structures of random RNAs undergo a morphological transition: f(c)→1 for c≤c(cr) as the cha...

We present results from the first fully relativistic simulations of the critical collapse of rotating radiation fluids. We observe critical scaling both in subcritical evolutions-in which case the fluid disperses to infinity and leaves behind flat space-and in supercritical evolutions, which lead to the formation of black holes. We measure the mass and angular momentum of these black holes, and...

Motivated by the “tug-of-war” game studied in [12], we consider a “non-local” version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of flipping a coin in order to decide which direction to choose and then moving of a fixed amount > 0 (as is done in the classical case), it is a s-stable Levy process which chooses at the same time bot...

The next-to-leading nonperturbative contributions to heavy quarkonium systems are calculated. The applicability of the Voloshin-Leutwyler approach to heavy quarko-nia systems for the physical cases of Bottomonium and Charmonium is investigated. We study whether the background gluon field correlation time can be considered to be infinity or not, by calculating the leading correction to this assu...

We present some multiplicity results concerning parameterized Schrödinger type equations which involve nonlinearities with sublinear growth at infinity. Some stability properties of solutions with respect to the parameters are also established in an appropriate Sobolev space.

We consider space-times which are asymptotically flat at spacelike infinity, i. It is well known that, in general, one cannot have a smooth differentiable structure at i, but have to use direction dependent structures. Instead of the oftenly used C-differentiabel structure, we suggest a weaker differential structure, a C + structure. The reason for this is that we have not seen any completions ...