We propose inference systems for binary relations with composition laws of the form S o T ~ U in the context of resolution-type theorem proving. Particulary interesting examples include transitivity, partial orderings, equality and the combination of equality with other transitive relations. Our inference mechanisms are based on standard techniques from term rewriting and represent a refinement...

There is a well known connection between three problems related to Optimal Stopping of Markov Chain and the equality of three corresponding indices: the classical Gittins index in the Ratio Maximization Problem, the Kathehakis-Veinot index in a Restart Problem, and Whittle index in a family of Retirement Problems. In [13] these three problems and these three indices were generalized in such a w...

We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of N species the universal gravitational cutoff is Λ = MPlanck/ √ N , as opposed to MPlanck. We demonstrate consistency of our solution by showing the equality of the two entropies in explicit examples in which the relat...

The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma...

We analyze the time reversal of waves in a turbulent medium using the parabolic Markovian model. We prove that the time reversal resolution can be a nonlinear function of the wavelength and independent of the aperture. We establish a duality relation between the turbulence-induced wave spread and the time-reversal resolution which can be viewed as an uncertainty inequality for random media. The...

The purpose of this paper is to introduce a natural multidimensional generalization (MMRM) of the one dimensional multifractal random measures (MRM) introduced by Bacry and Muzy in [1]. The measures M we introduce are different from zero, homogeneous in space, isotropic and satisfy the following exact scale invariance relation: if T denotes some given cutoff parameter then the following equalit...

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. We show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of ...

We derive analogs of the Jarzynski equality and Crooks relation to characterize the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponen...

We introduce a concept of behavioural implementation for algebraic specifications which is based on an indistinguishability relation (called behavioural equality). The central objective of this work is the investigation of proof rules that first allow us to establish the correctness of behavioural implementations in a modular way and moreover are practicable enough to induce proof obligations t...

We prove that in Solovay model every OD equivalence E on reals either admits an OD reduction to the equality on the set of all countable (of length < ω1 ) binary sequences, or continuously embeds E0, the Vitali equivalence. If E is a Σ1 1 (resp. Σ 1 2 ) relation then the reduction in the “either” part can be chosen in the class of all ∆1 (resp. ∆2 ) functions. The proofs are based on a topology...