background and aims. previous researches, conducted mostly on extracted teeth, have shown that efficacy of calculus removal decreases with increasing pocket depth, but there is still a lack of clinical studies concerning the correlation be-tween residual calculus and varying pocket depths. the objective of the present clinical study was to assess the efficiency of mechanical tooth depuration by...

We present an untyped linear lambda calculus with braids, the corresponding combinatory logic, and semantic models given by crossed G-sets.

Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, inc...

In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calcu...

The aim of the present work is to present a characterization of the Gentzen System G by means of a regulated grammar, according to the Formal Languages Theory. Given a proposition, which is supposed to be a tautology, a grammar will be produced and the generation of the respective language will represent a calculation in G. This language can be interpreted as either, a proof or a counter-exampl...

The two parameter quantum group G r;s is generated by ve elements, four of which form a Hopf subalgebra isomorphic to GL q (2), while the fth generator relates G r;s to GL p;q (2). We construct explicitly the dual algebra of G r;s and show that it is isomorphic to the single parameter deformation of gl(2) gl(1), with the second parameter appearing in the costructure. We also formulate a di eren...

OBJECTIVE Evaluate the effect of raw bovine cortical bone (CB) (medullary bone cross-sectioned) and marrow or epiphyseal 'spongy' bone (SB) as chew items to reduce dental calculus in adult dogs. METHODS Eight 3-year-old Beagle dogs were observed in two study periods. In the first study, the dogs each received a piece of bovine femur CB (122 ± 17 g) daily and in the second study, a piece of bo...

The homogeneous functional calculus on vector lattices is a useful tool in a variety of areas. One of the interesting application is the study of powers of Banach lattices initiated by G. Ya. Lozanovskĭı [18]. Recently G. Buskes and A. van Rooij [8] introduced the concept of squares of Archimedean vector lattices which allows to represent orthoregular bilinear operators as linear regular operat...

CONTENTS We prove two lemmata about Schubert calculus on generalized 1. Background on Schubert Problems f|ag manifolds G/B, and in the case of the ordinary flag manifold 2. The Schubert Problems Graph and Its Structure for Small GLn/B we interpret them combinatorially in terms of descents, GLn(C) and geometrically in terms of missing subspaces. One of them 3. Proofs of the Lemmata gives a symme...