We use the vector wedge product in geometric algebra to show that Poisson commutator brackets measure preservation of phase space areas. We also use the vector dot product to define the Poisson anticommutator bracket that measures the preservation of phase space angles. We apply these brackets to the paraxial meridional complex height-angle ray vectors that transform via a 2×2 matrix, and we sh...

Problem statement: To evaluate the frictional forces generated by five different orthodontic brackets when used in combination with stainless steel and NiTi archwires in dry conditions at physiological temperature. Approach: Five different types of maxillary canine brackets (Damon 3 MX, Step, Quick, Sprint, Mini Mono) with a slot size 0.022 inch were coupled with 0.016” and 0.019”×0.025” stainl...

INTRODUCTION The aim of this study was to compare the rate of en-masse space closure with sliding mechanics between passive self-ligating SmartClip brackets (3M Unitek, Monrovia, Calif) and conventional twin brackets ligated with stainless steel ligatures. METHODS Nineteen patients including 20 arches participated in this prospective trial with 0.018-in slot brackets. All patients had first p...

AIM To compare the clinical failure rates over six months of indirectly bonded brackets with and without methyl methacrylate monomer (MMM) conditioned custom bases. METHODS Thirty-six consecutive patients satisfying the selection criteria were randomly assigned to two groups in a split-mouth study design. In Group 1, the maxillary right and mandibular left quadrants were indirectly bonded aft...

OBJECTIVE To assess the color stability of five types of ceramic brackets after immersion in potentially staining solutions. METHODS Ninety brackets were divided into 5 groups (n = 18) according to brackets commercial brands and the solutions in which they were immersed (coffee, red wine, coke and artificial saliva). The brackets assessed were Transcend (3M/Unitek, Monrovia, CA, USA), Radianc...

OBJECTIVE This in vitro study was undertaken to evaluate the physical, chemical, and biological properties of commercially available metal orthodontic brackets in South Korea, because national standards for these products are lacking. METHODS FOUR BRACKET BRANDS WERE TESTED FOR DIMENSIONAL ACCURACY, (MANUFACTURING ERRORS IN ANGULATION AND TORQUE), CYTOTOXICITY, COMPOSITION, ELUTION, AND CORRO...

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent ∆ operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie br...

In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov’s method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this that all Poisson brackets on an arbitrary field of characteristic zero can be quantized. The well...

introduction: this study was performed to determine the shear bond strength of rebonded mechanically retentive ceramic brackets after recycling with erbium-doped yttrium aluminum garnet (er:yag) laser or sandblasting. methods: twenty-eight debonded ceramic brackets plus 14 intact new ceramic brackets were used in this study. debonded brackets were randomly divided into 2 groups of 14. one group...

Background and aims. The aim of this study was to compare shear bond strength (SBS) of metal and ceramic brackets bonded to enamel using acid versus Er:YAG laser etching. Materials and methods. Eighty premolars were divided into 4 groups: AM (acid etching/ metal brackets), AC (acid etching/ ceramic brackets), LM (laser etching/ metal brackets) and LC (laser etching/ ceramic brackets). Enamel co...