AIM To compare the anticalculus efficacy of an experimental dentifrice (0.454% stabilized stannous fluoride/sodium hexametaphosphate) with a negative control. METHODS AND MATERIALS This was a randomized, examiner-blind, parallel group study. After a three-month run-in, qualifying subjects were randomized to the experimental or control dentifrice to use twice a day for six months. Volpe-Manhol...

In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.

BACKGROUND Dental implants require regular maintenance. It is crucial that the instrument used for maintenance be able to remove plaque and calculus from the implant surface effectively and efficiently, while causing minimal damage to its circumference. Some ultrasonic scalers may be useful for implant maintenance; however, no clinical study has examined this. This study evaluated the treatment...

The Calculus of Constructions is a higher-order formalism for writing constructive proofs in a natural deduction style, inspired from work of de Bruijn [2, 3], Girard [12], Martin-Löf [14] and Scott [18]. The calculus and its syntactic theory were presented in Coquand’s thesis [7], and an implementation by the author was used to mechanically verify a substantial number of proofs demonstrating t...

The search for a full treatment of wrapping in type logical grammar has been a task of long-standing. In this paper we present a calculus for discontinuity addressing this challenge, ω-DL. The calculus allows an unbounded number of points of discontinuity (hence the prefix ω-) and includes both deterministic and nondeterministic discontinuous connectives. We believe that it constitutes a genera...

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in Sobolev spaces. Our provides feasible extension classical Caputo Riemann–Liouville within spaces orders, including negative ones. approach enables unified treatment for calculus equations. We formulate initial value problems ordinary equations boundary partial to pr...

A special function is a that typically entitled after an early scientist who studied its features and has specific application in mathematical physics or another area of mathematics. There are few significant examples, including the hypergeometric unique species. These types functions generalized by fractional calculus, fractal, q-calculus, (q,p)-calculus k-calculus. By engaging notion q-fracti...