Within the framework of quantum mechanics over a quadratic extension non-Archimedean field p-adic numbers, we provide definition state relying on general algebraic approach and model probability theory. As in standard complex case, distinguished set physical states are related to notion trace for certain class bounded operators and, fact, show that one can define suitable space setting, as well...

In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination suitable bootstrap-type arguments and detailed analysis nonlinearity in equation.

Formal methods have proved their usefulness for analyzing the security of protocols. Most existingresults focus on trace properties like secrecy or authentication. There are however several securityproperties, which cannot be defined (or cannot be naturally defined) as trace properties and requirea notion of behavioural equivalence. Typical examples are anonymity, privacy related pr...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

We introduce the characteristic class of an l-adic étale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz-Verdier trace formula, its trace computes the Euler-Poincaré characteristic of the sheaf. We compare the characteristic class to two other invariants arising from ramification theory. One is the Swan class of Kato-Saito [16] and the other is the 0...

We construct an analogue of Kontsevich and Vishik’s canonical trace for a class of pseudodifferential boundary value problems in Boutet de Monvel’s calculus on compact manifolds with boundary. For an operator A in the calculus (of class zero), and an auxiliary operator B, formed of the Dirichlet realization of a strongly elliptic second-order differential operator and an elliptic operator on th...

This paper makes certain observations regarding some conjectures of Milnor and Ramakrishnan in hyperbolic geometry and algebraic K-theory. As a consequence of our observations, we obtain new results and conjectures regarding the rationality and irrationality of Chern-Simons invariants of hyperbolic 3-manifolds. In this paper, by a hyperbolic 3-manifold, we shall mean a complete, oriented hyperb...

We describe a gap in Java's security model that allows a pure Java library to infer information to which it should not have access. The security violation exploits two pieces of public information: 1. The stack trace: Every Java exception object contains a string representation of the stack trace that is usually used for debugging purposes. Access to this stack trace is public. 2. The class les...

We discuss the Witten index in terms of Krein's spectral shift function, and prove invariance of the Witten index under suitable relative trace class hypotheses.

This paper makes certain observations regarding some conjectures of Milnor and Ramakrishnan in hyperbolic geometry and algebraic K-theory. As a consequence of our observations, we obtain new results and conjectures regarding the rationality and irrationality of Chern-Simons invariants of hyperbolic 3-manifolds. In this paper, by a hyperbolic 3-manifold, we shall mean a complete, oriented hyperb...