using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

The purpose of the study was to assess the relative base designs of three different maxillary molar stainless steel brackets with reference to the shear bond strength of three different adhesive resins. The molar brackets used were Victory series (3M Unitek), Upper Molar (GAC) and Optimesh XRT (Ormco). The adhesives used were Transbond XT (3M Unitek), Enlight (Ormco) and Sure Ortho Light Bond (...

We determine an explicit formula for a Rankin-Cohen bracket for Siegel modular forms of degree n on a certain subgroup of the symplectic group. Moreover, we lift that bracket via a Poincaré series to a Siegel cusp form on the full symplectic group.

The slots of five upper left central incisor brackets from 11 commercially available bracket systems (3M Unitek, Monrovia, Calif: Twin Torque Roth, Clarity MBT, and Victory Series MBT; Dentarum, Pforzheim, Germany: Discovery Roth (0.56 mm) and Elegance Plastic Roth; Forestadent, Pforzheim, Germany: Mini Mono MBT; TP LaPorte, Indiana: Nu-Edge Roth and Mxi Advant-Edge Roth; Ormco Corp., Orange, C...

3 Stochastic Taylor expansions 5 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Brownian Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Exponential of a vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Li...

background and aims: to obtain maximum advantages from orthodontic fixed appliances and to achieve the desired final occlusion, correct bracket positioning is highly necessary. in order to measure and determine bracket’s height, diverse gauges have been used. the objective of the present study is to determine and compare bracket positioning accuracy by using height bracket positioning gauge (hb...

BACKGROUND Fixed orthodontic mechanotherapy is associated with friction between the bracket - wire - ligature interfaces during the sliding mechanics. A sound knowledge of the various factors affecting the magnitude of friction is of paramount importance. The present study was done to analyze and compare the frictional forces generated by a new ceramic (Clarity Advanced) bracket with the conven...

The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their nonholomorphic analogs and show their connection to values of L-functions outside the critical strip.