Bracket Product Research Articles

Process Improvement Using Selected Quality Management Methods

Abstract A key element of any quality management system is continuous improvement and a systematic approach to managing non-conformances. The aim of this paper is to use selected statistical methods and quality control techniques to present a way in which an organisation can achieve quality improvement. The 8D methodology was used to solve the observed problem, which was a customer complaint due to a nonconforming dimension on a Brake Bracket product using a structured eight-step Plan-Do-Check-Act (PDCA) approach to problem solving. The subject of the analysis in Knott spol. s.r.o. is the product Brake holder 300x60 S-Nocken /AGS/ABS/. Using the 8D methodology and supporting tools such as the Ishikawa diagram or 5Why, the root cause of the problem was identified and permanent corrective actions were planned and implemented as recommended in the 8D report to reduce the likelihood of the problem recurring and increase customer satisfaction.

Frames of translates for model sets

We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection between model sets and almost periodic functions and rely strongly on a Poisson summations formula for model sets to introduce the so-called bracket product, which then plays a crucial role in our approach. As a corollary to our main results we obtain a density statement for semi-regular Gabor frames.

Comparison of multiforce nickel-titanium wires to multistrand wires without force zones in bending and torque measurements.

The aim was to compare rectangular multiforce nickel-titanium (NiTi) wires to rectangular wires with only one force zone. Both types of wires are primarily intended for use during the levelling phase of orthodontic treatment. Thus, basic mechanical properties were examined by means of athree-point bending test. Torque expression, which is dependent on both wire parameters and interslot distances, was analyzed using the Orthodontic Measurement and Simulation System (OMSS). Four multizone products were tested: DuoForce™ (Forestadent, Pforzheim, Germany), TriTanium™ (American Orthodontics, Sheboygan, WI, USA), Triple Force™ (ODS, Kisdorf, Germany), Bio-Active™ (GC, Breckerfeld, Germany), and two multistrand products without force zones: anine-strand NiTi, TurboWire™ (Ormco, Orange, CA, USA) and an eight-strand stainless steel (SS) wire, Multibraid™ (GAC, Dentsply Sirona, York, PA, USA). All the wires had the dimension 0.40 mm × 0.56 mm (0.016 inch × 0.022 inch) except the nine-strand NiTi wire TurboWire™, which had a dimension of 0.43 mm × 0.65 mm (0.017 inch × 0.025 inch). Six different bracket systems in the 0.018 inch slot system were chosen: the conventional brackets discovery® and discovery® smart (Dentaurum, Ispringen, Germany), the active self-ligating brackets InOvation™ and InOvation™ mini (GAC, Dentsply Sirona, York, PA, USA) and the passive self-ligating brackets Carrière™ (ODS, Kisdorf, Germany) and BioPassive® (Forestadent, Pforzheim, Germany). The first set-up was athree-point bending test according to DIN EN ISO 15841. For the second experiment, the bracket products glued on amaxilla model were combined with the wire products. The torque moments arising during torqueing of the wires between +20° and -20° were measured in three positions: first incisor, canine and second bicuspid. Bending tests confirmed variation of the force corresponding to the force zones. The nine-strand NiTi wire TurboWireTM and the eight-strand SS wire Multibraid™ did not show any variation dependent on the tested area. Torque-moments generated by the multizone wires were higher compared to the braided wires. The nine-strand NiTi wire showed the lowest moments in spite of the higher dimension. As expected, increasing the interbracket distance reduced the torque moments. The tests verified the existence of multiple force zones in the NiTi wires for forces and moments, respectively. As the torque-moments arising from the multizone wires were rather high, it is not recommended to use these wires as afirst "leveling wire" in orthodontic treatment, especially in extremely crowded cases.

$$\phi (L)$$-Factorable Operators on $$L^{P}(G)$$ for a Locally Compact Abelian Group

Let G be a locally compact abelian group, $$\phi $$ be a topological isomorphism on G, and L be a uniform lattice in G. We provide a development of the $$L^{ 1} (G/\phi (L)) $$ function-valued product on $$ L^{ p} (G)$$ called $$(\phi (L),p)$$ -bracket product, where $$ 1<p<\infty $$ . Among other things, we study $$\phi (L)$$ -factorable operators and we prove Riesz representation type theorem for $$ L^{ p} (G)$$ .

Finishing Line Evaluation of Bracket product FWD RR Spring BT 1702 by Applying 8 Steps 7 Tools Method Toyota Production (Case Study: PT BA)

PT Bakrie Autoparts is a company which runs in foundry and mainly produces cast iron such as wheel hub, brake drum, disc rotor and flywheel. The major problem encountered by this plant is the slow delivery to consumers because the finishing process takes too long time along with the increasing demand while there is no significant improvement. This research focuses on the mapping of the hindrances and problems in the finishing line of Bracket FWD RR Spring BT 1702, how much the actual output is, what causes the problem, and what improvement can be done to remove or reduce the hindrances. The method used is 8 Step 7 Tools Toyota Production System. Time measurement result and Output Standardd calculation is based on finishing line cycle time 142 seconds per pcs and output Standardd 25 pcs per hour. After applying the method of 8 Step 7 Tools Toyota Production System, cycle time line finishing can be reduced to 66 seconds and the output Standardd to 53 pcs per hour. The output line finishing improvement reaches 112% faster than the previous one. Besides that, the improvement makes a better perfomance Standardd in the finishing process of Bracket FWD RR Spring BT 1702 so the product is in better quality and it ensures the operators’s work safety.

On unified Hom–Yetter–Drinfeld categories

In this paper, we discuss properties of the unified Hom–Yetter–Drinfeld categories HHHYD(ℓ), where (H,β) is a Hom–Hopf algebra with bijective antipode S and ℓ∈Z (the set of integers). On one hand, we prove the following results about the symmetry and pseudosymmetry of HHHYD(ℓ): If HHHYD(ℓ) is symmetric then H is trivial; HHHYD(ℓ) is pseudosymmetric if and only if (H,α) is commutative and cocommutative; The relations between u-condition of Hom-type and the symmetry of HHHYD(ℓ); The (co)representation category of (co)triangular Hom–Hopf algebra is symmetric. On the other hand, we focus on the category HHHYD(0). We introduce the notion of (0 degree) unified H-Lie algebra, then show that a Hom-algebra (A,α) satisfying additional conditions gives rise to (0 degree) unified H-Lie algebra with suitable bracket product. And if (A,α) also has two Hom-subalgebras U and X which are (H,β)-commutative such that A=U+X, then we prove that [A,A][A,A]=0.

Gabor Frames for Model Sets

We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: fundamental identity of Gabor analysis, Janssen’s representation of the frame operator and Wexler–Raz biorthogonality relations. Utilizing the connection between model sets and almost periodic functions, as well as Poisson’s summations formula for model sets we develop a form of a bracket product that plays a central role in our approach. Furthermore, we show that, if a Gabor system for a model set admits a dual which is of Gabor type, then the density of the model set has to be greater than one.

Kinetic theory of two-temperature polyatomic plasmas

We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

One-parameter deformations of the diassociative and dendriform operads

Livernet and Loday constructed a polarization of the nonsymmetric associative operad with one operation into a symmetric operad with two operations (the Lie bracket and Jordan product), and defined a one-parameter deformation of , which includes Poisson algebras. We combine this with the dendriform splitting of an associative operation into the sum of two nonassociative operations, and use Koszul duality for quadratic operads, to construct one-parameter deformations of the nonsymmetric dendriform and diassociative operads into the category of symmetric operads.

截面箭图代数的Gerstenhaber 括号积

Based on the minimal projective bimodule resolution, the Gerstenhaber bracket products on the Hochschild cohomology spaces for truncated quiver algebras are described explicitly in terms of parallel paths. As a consequence, for truncated basic cycle algebra Λ, each element in HH2(Λ) defines a noncommutative Poisson structure on Λ, and in turn defines the first multiplication of a one-parameter deformation of Λ.

Intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals

In this paper, the concepts of intuitionistic fuzzy sets are introduced to Lie superalgebras. Intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals of Lie superalgebras are defined and related properties are investigated. As the applications of intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals, the properties of intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals under homomorphisms of Lie superalgebras are studied. The intuitionistic fuzzy bracket product is also introduced and its characterization is established.

Riesz multiwavelet bases generated by vector refinement equation

In this paper, we investigate compactly supported Riesz multiwavelet sequences and Riesz multiwavelet bases for L2(ℝs). Suppose ψ = (ψ1,..., ψr)T and \( \tilde \psi = (\tilde \psi ^1 ,...,\tilde \psi ^r )^T \) are two compactly supported vectors of functions in the Sobolev space (Hμ(ℝs))r for some μ > 0. We provide a characterization for the sequences {ψjkl: l = 1,...,r, j e ℤ, k e ℤs} and \( \tilde \psi _{jk}^\ell :\ell = 1,...,r,j \in \mathbb{Z},k \in \mathbb{Z}^s \) to form two Riesz sequences for L2(ℝs), where ψjkl = mj/2ψl(Mj·−k) and \( \tilde \psi _{jk}^\ell = m^{{j \mathord{\left/ {\vphantom {j 2}} \right. \kern-\nulldelimiterspace} 2}} \tilde \psi ^\ell (M^j \cdot - k) \), M is an s × s integer matrix such that limn→∞M−n = 0 and m = |detM|. Furthermore, let ϕ = (ϕ1,...,ϕr)T and \( \tilde \phi = (\tilde \phi ^1 ,...,\tilde \phi ^r )^T \) be a pair of compactly supported biorthogonal refinable vectors of functions associated with the refinement masks a, \( \tilde a \) and M, where a and \( \tilde a \) are finitely supported sequences of r × r matrices. We obtain a general principle for characterizing vectors of functions ψν = (ψν1,...,ψνr)T and \( \tilde \psi ^\nu = (\tilde \psi ^{\nu 1} ,...,\tilde \psi ^{\nu r} )^T \), ν = 1,..., m − 1 such that two sequences {ψjkνl: ν = 1,..., m − 1, l = 1,...,r, j e ℤ, k e ℤs} and {\( \tilde \psi _{jk}^\nu \) : ν=1,...,m−1,l=1,...,r, j ∈ ℤ, k ∈ ℤs} form two Riesz multiwavelet bases for L2(ℝs). The bracket product [f, g] of two vectors of functions f, g in (L2(ℝs))r is an indispensable tool for our characterization.

Relative vector fields

In this paper relative vector fields by the use of fuzzy sets are presented. A representation for relative vector fields at non-singular points is deduced. Poisson bracket product and Frobenius theorem for relative vector fields are extended.

Wavelets and Hilbert Modules

A Hilbert C*-module is a generalization of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert C*-modules over a group C*-algebra which is generated by the group of translations associated with a wavelet. We shall investigate bracket products and their Fourier transform in the space of square integrable functions in Euclidean space. We will also show that some wavelets are associated with Hilbert C*-modules over the space of essentially bounded functions over higher dimensional tori.

Surface topography and frictional characteristics of ceramic brackets

The surface topography and frictional characteristics of single crystal sapphire and polycrystalline alumina brackets were evaluated in both the dry and the wet state as a function of the four basic wire alloy compositions. On the premise that a particular combination of bracket, wire, and environment must be attained so that the efficiency and reproducibility of tooth movement is improved, a significant reduction in the coefficients of friction was sought. Viscometric measurements were used to show that the characteristics of saliva remained unchanged throughout the investigation. Scanning electron micrographs and laser specular reflection were studied to illustrate the general appearance and quantitative magnitude of roughnesses. Frictional measurements of couples in the dry, the wet, and again in the dry state were evaluated at five different normal loads. The outcomes of the virgin materials show that arch wire alloy, rather than bracket product type or surface roughness, influence the frictional characteristics the most and that titanium wires generally cause higher frictional resistances than either stainless steel or cobalt-chromium wires. Friction tests of specimens that were run multiple times suggest that couples comprised of nickel titanium arch wires against ceramic brackets may actually improve as a result of a break-in period.

Coefficients of friction for arch wires in stainless steel and polycrystalline alumina bracket slots. I. The dry state

The surface roughness and the coefficients of friction were measured for sixteen arch wire-bracket combinations. The sample included one rectangular arch wire product from each of the four principal alloy groups and one bracket product from among the stainless steel and polycrystalline alumina inventory. Although subsamples representing both the 0.018-inch and the 0.022-inch slot sizes were evaluated, no differences were observed in their rankings. When tested over a series of eight incident angles, the optical surface roughness of representative stainless steel and alumina brackets averaged 0.148 and 0.193 microns, respectively. After testing at a single angle (82 degree) and referencing a nomogram, the roughness of the stainless steel, cobalt-chromium, beta-titanium, and nickel-titanium arch wire surfaces averaged 0.053, 0.129, 0.137, and 0.247 microns, respectively. When the various arch wire-bracket couples were pressed against an 0.010-inch stainless steel ligature wire at 34 degrees C and otherwise prevailing atmospheric conditions, the coefficients of friction ranged from stainless steel (lowest) to cobalt-chromium, nickel-titanium, and beta-titanium (highest)--regardless of bracket product or slot size. These results corroborated earlier observations in which the same arch wire products were drawn between stainless steel or alumina contact flats. In the current research, the average coefficient of kinetic friction for the stainless steel couple (0.139) was less than that for the stainless steel arch wire against a polycrystalline alumina bracket (0.174).

A Centennial: Wilhelm Killing and the Exceptional Groups

In his article [3] in the Mathematical Intelligencer (vol. 11, no. 3) A. John Coleman gives a colorful biography of the mathematician Wilhelm Killing and offers an admiring appraisal of his paper [8]. The subject of this paper, the classification of the simple Lie algebras over C, has indeed turned out to be a milestone in the history of mathematics. At the conclusion of his article Coleman lists six reasons why he considers [8] to be such an epoch-making paper, the first one being that it furnished the impetus towards the problem of classifying finite simple groups. Here one could add that the answer to that problem was also motivated by and was partly provided by the classification of simple Lie algebras through Claude Chevalley's paper [2b]. In two sections of his article, entitled "Killing Intervenes" and "The Still Point of the Turning World," Coleman discusses the work of Killing and Elie Cartan on the classification of simple Lie algebras over C. I would like to add a few comments to his discussion (see also [7b]). While Sophus Lie and some of his associates in Leipzig at tempted the problem of classifying all local transformation groups of R n, Killing set himself the problem of finding all possible Zusammensetzungen of r-parameter groups. In other words, he was interested in all possible ways in which a vector space could be turned into a Lie algebra. While Lie was motivated by applications to differential equations, Killing was led to his problem from his work in geometry. Let ~ be a simple Lie algebra over C. Then g is isomorphic to the Lie algebra of linear transformations adX of g given by adX(Y) = IX, Y], with X running through g and [,] denoting the bracket product in the Lie algebra. To study this family it is natural to try to diagonalize the operators ad(X) as effectively as possible. This is the motivation for the definition of a Cartan subalgebra as a subalgebra ~ which is

On the algorithm of Dirac spurs

The spur of the product of any number of Dirac matrices is shown to be square root of a determinant. It can be evaluated directly, however, by means of rules as simple as those of determinant theory. When the number of matrices occurring in the product is ⩾12, further considerations show that many terms of the expansion sum up to give zero total contribution. A final formula is given which takes all such reductions into account. The Appendix contains rules for summing over pairs of λμ which bracket products of Dirac matrices.