A Strong Completeness Theorem for the Gentzen systems associated with finite algebras
ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems.
Small perturbations in a hyperbolic stochastic partial differential equation
We study the existence and properties of the density for the law of the solution to a nonlinear hyperbolic stochastic partial differential equation, driven by a two-parameter white noise. We also analyze the asymptotic behavior of the density for the law of the solution to the equation obtained by perturbing the noise. Under unrestricted Hormander's-type conditions on the coefficients, we establish Varadhan's estimates.
Design of reinforced concrete lining in pressure tunnels, considering thermal effects and jointed rockmass
Abstract Jaeger's theory (Jaeger, Rock Mechanics and Rock Engineering , Cambridge University Press, 1972) of the design of the lining for a pressure tunnel applies to a tunnel located in an isotropic, homogeneous and elastic medium. The theory is derived from the elasticity equations for the plane stress condition. In this paper, Jaeger's theory is extended to a plane strain situation. Also included is a discussion of the effects of a uniform increase (or decrease) in the lining temperature, jointed rockmass, cracking of the tunnel lining, and cracking of the rockmass around the opening. Tables are presented for the modulus of subgrade reaction for various rockmass conditions and for rock sharing pressures for various lining conditions. The reduction factor to include the effect of joints in rockmass is derived by the analysis of a numerical model of the lined tunnel by the finite-infinite-interface element method.