The worst-case complexity of cut elimination in sequent calculi for first order based logics is investigated in terms of the increase in logical depth of the deduction. It is shown that given a calculus satisfying a general collection of sufficient conditions for cut elimination and given a deduction with cuts, there exists a cut free deduction with a logical depth, in the worst case, hyper-exp...

It has recently been shown that cut-free deep inference systems exhibit an exponential speed-up over cut-free sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search non-determinism induced by the deep inference methodology: the higher the depth of inference, the higher the non-determinism. In this work we improv...

In the present study, the six legged concrete (SLC) elements are placed at the bed of a flume downstream of a chute in different layouts, densities and number of longitudinal rows of SLC elements. Each test was run for different flow conditions (Froude numbers ranged 5.3 to 8.1). During each test, the water surface profile, the roller length and the jump length measured.  Applying the experimen...

Hydrological jump characteristics in a rectangular open channel flume with sluice gates at both ends are the focus of this article. Among many aspects hydraulic that have been examined analytically and experimentally are: (i) Sequent depth relation (y2y1), (ii) Length jump, (iii) Relative loss energy (ELE1), (iv) Water profile jump. There was total 15 inflow tests conducted. With values between...

The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of this equation. This equation has a direct solution only for the rectangular channels. The trial and error procedure as well as the graphical solution are the existing methods of solving hydraulic jump equations. No direct solutions are avai...

The effect of an abruptly expanding channel on the main characteristics of hydraulic jump is considered experimentally. The present study was made for supercritical flow of Froude number varying between 2 to 9 and approach to expanded channel width ratios 0.4, 0.5, 0.6 and 0.8. Physical explanations of the variation of these characteristics under varying flow conditions are discussed based on t...