We study the scattering of acoustic waves by an object composed of several adjacent parts with different material properties. For this problem we derive an integral formulation of the second kind. This formulation only involves one Dirichlet datum and one Neumann datum at each point of each interface of the object, so that our formulation can be considered to belong to the same family as the fo...

We introduce the Poincaré series for a divisorial valuation v and prove that this series is an equivalent algebraic datum to the dual graph of v. We give an explicit computation of the Poincaré series.

For a class of semilinear parabolic equations, we prove both global existence and finite-time blow-up depending on the initial datum. The proofs involve tools from the potential-well theory, from the criticalpoint theory, and from classical comparison principles.

In this paper we very preliminarily investigate the possibility of measuring the post-Newtonian general relativistic gravitoelectric and gravitomagnetic components of the acceleration of gravity on the Earth, in continuous regime, with two absolute measurements at the equator and the south pole with superconducting gravimeters. The magnitudes of such relativistic effects are 10 m s and 10 m s, ...

Homcts(π1,ét(C),Q × ` ) ∼= Hom(Pic0(k),Q` ) + (Ẑ Frobc −−−→ Q` ). where c ∈ C(Fq) is a fixed rational point. Our proof will proceed by upgrading this equality to an equivalence of geometric objects. First, we’ll interpretHomcts(π1,ét(C),Q × ` ) in terms of rank one `-adic local systems on C. Similarly, we’ll interpret the datum of Hom(Pic0(k),Q` ) + (Ẑ Frobc −−−→ Q` ) as a “character sheaf” on ...

In this paper, we address the problem of collecting data from sensor nodes using a model-aided approach. In our approach, a model is maintained by a node and a replica of the model is maintained the base station. The base station uses the replica model to estimate the actual measurement data of the sensor node in usual time, and an actual measurement datum is sent to the base station only when ...

The concept of information is still lacking a complete understanding, as witnessed by the large number of different meanings that overload the terms “data”, “knowledge”, and “information”. In this paper, a definition of information (named epistemic information) based on the knowledge states of agents is proposed. It is used to analyze, understand, and explain some puzzling phenomena, like the s...