Search results for " Conformal"
showing 10 items of 51 documents
Lie properties of symmetric elements in group rings
2009
Abstract Let ∗ be an involution of a group G extended linearly to the group algebra KG . We prove that if G contains no 2-elements and K is a field of characteristic p ≠ 2 , then the ∗-symmetric elements of KG are Lie nilpotent (Lie n -Engel) if and only if KG is Lie nilpotent (Lie n -Engel).
Star calculus on Jacobi manifolds
2002
Abstract We study the Gerstenhaber bracket on differential forms induced by the two main examples of Jacobi manifolds: contact manifolds and l.c.s. manifolds. Moreover, we obtain explicit expressions of the generating operators and the derivations on the algebra of multivector fields. We define star operators for contact manifolds and l.c.s. manifolds and we study some of its properties.
The graded Lie algebra structure of Lie superalgebra deformation theory
1989
We show how Lie superalgebra deformation theory can be treated by graded Lie algebras formalism. Rigidity and integrability theorems are obtained.
Next-to-next-to-leading order prediction for the photon-to-pion transition form factor
2003
We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$-function in the so-called conformal scheme. The Wilson--coefficients appearing in the non-forward kinematics are then entirely determined from those of the polarized deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$-function, and discuss numerical predictions calculated in different kinemati…
Incidence of mandibular osteoradionecrosis (MORN) after intensity modulated radiotherapy (IMRT) versus 3D conformal radiotherapy (3D-CRT): A systemat…
2022
Background: Analyze the incidence of MORN after head and neck radiotherapy by two novel irradiation techniques. 3DCRT and IMRT and compare the success rates of distinct authors. Material and Methods: An electronic search in Pubmed (MEDLINE), Ovid. Google Scholar and Cochrane Library (Wiley). databases was conducted with the key words Radiotherapy, Conformal[Mesh] OR Radiotherapy. Intensity-Modulated[Mesh]) AND Osteoradionecrosis[Mesh] for all databases. The inclusion criteria randomized controlled trials (RCT), as well as prospective and retrospective cohort studies published in English; MORN patients treated with 3D-CRT y IMRT. Results: 27 articles were selected from 194 initially found. 1…
Mass-flux-based outlet boundary conditions for the lattice Boltzmann method
2009
We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is fu…
Annihilators of tensor density modules
2007
Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …
Hom-Lie quadratic and Pinczon Algebras
2017
ABSTRACTPresenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.
An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm
2022
Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, ar…
Analysis of cardiac and pulmonary complication probabilities after radiation therapy for patients with early-stage breast cancer
2009
Objective. The purpose of this study was to evaluate the radiobiological implications of clinical use of respiratory-gated techniques for postoperative radiation therapy of early-stage left-sided breast cancer after breast-conserving surgery. Material and methods. Radiation therapy treatment plans of 80 patients with early-stage breast cancer (stage I–II), receiving whole breast irradiation after breast-conserving therapy, were analyzed. The control group consisting of 47 patients received standard radiation therapy, and the respiratory-gated group consisting of 33 patients received deep inspiration-gated radiation therapy. Normal tissue complication probabilities (NTCP) for cardiac mortali…