measurement of soil saturated hydraulic conductivity, ks, is normally affected by flow patterns such as macro pore; however, most current techniques do  not differentiate flow types, causing major problems in describing water and chemical flows within the soil matrix. this study compares eight models for scaling ks and predicted matrix and macro pore ks, using a database composed of 50 datasets...

various scaling methods such as relative viscosity, peclet and reynolds scaling were used to find the best scaling law. scaling and modeling of the flow curves of various model emulsions consist of tragacanth gum (tg) (0.5, 1 % wt), oleic acid (5, 10% v/v) and wpi (2, 4 % wt) were investigated and the best models were selected. as these emulsions are non-newtonian, they do not obey the usual, si...

About 50 years ago Lukasiewicz, Tarski, see 6, 4] and others studied the implicational calculus, i. e. the set PIF (pure implicational formulas) of those propositional formulas that are constructed exclusively from Boolean variables and the propositional implication ! as the only connective. Obviously this class of formulas is not able to represent all Boolean functions. While every formula in ...

We characterize computationally the functions provable in second order logic with set existence restricted to natural classes of rst order formulas. A classi cation of rst-order set-existence by implicational rank yields a natural hierarchy of complexity classes within the class of Kalmar-elementary functions: The functions over f0; 1g constructively provable using set existence for formulas of...

Closure system on a finite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of finite lattices, and the tools of economic description of a finite lattice have long existed in lattice theory. We present this approach by describing the so-called D-basis and introducing the concept of ordered direct basis of an impli...

In this note we show how any formula δ with a proof of super-polynomial size in M→ has a poly-sized proof in K→ . This fact entails that any propositional classical tautology has short proofs, i.e., NP=CoNP. 1 Every classical tautology has short proofs This article reports the results on the investigation on the existence of short proofs for every Classical Propositional Logic tautology. Firstl...

A minimal formula of a given logic L is a formula which is provable in L and is not a non-trivial substitution instance of other provable formulas in L. In [5], Y. Komori asked whether normal proofs of minimal formulas are unique in the implicational fragments of natural deduction systems for the intuitionistic logic and the logic BCK. It was already shown that the answer is positive for BCK, w...