Rotation Of Group Research Articles

Rotation Group Bias in Current Smoking Prevalence Estimates Using TUS-CPS

This paper examined whether the sample rotation scheme of the Current Population Survey (CPS) results in an underestimation of current smoking prevalence in the Tobacco Use Supplement to the Current Population Survey (TUS-CPS). The TUS-CPS has been administered as part of the CPS, which has eight rotation groups of households in each month that are repeatedly interviewed based on a sample rotation scheme. Previous research has found that even though all eight rotation groups in the CPS are independent random samples of the population, some estimates, such as unemployment rates, tend to be significantly higher in the first rotation group than among other rotation groups. The probit regression results of this paper showed that although current smokers are more likely to attrite than nonsmokers in all years of the TUS-CPS, for the six waves of TUS-CPS before 2003 there is no evidence that current smoking prevalence estimates were significantly affected by the rotation scheme of the CPS. For the three waves of TUS-CPS since 2003, however, the results showed that current smoking prevalence has been underestimated likely due to differential panel attrition. It appears that rotation group bias in these waves was caused by the substantially increased number of additional questions current smokers had to answer.

Primitive Monodromy Groups of Rational Functions with One Multiple Pole

Primitive monodromy groups of rational functions P/Q, where Q is a polynomial with no multiple roots and deg P > deg Q+1 are classified. There are 17 families of such functions which are not Belyi functions. Only one family from the list contains functions that have five critical values. All the remaining families consist of functions with at most four critical values and constitute one-dimensional strata in the Hurwitz space. The action of the braid group on generators of their monodromy groups is computed and the corresponding megamaps are drawn. The result extends the classification of primitive edge rotation groups of weighted trees obtained by the author and Zvonkin and is also a generalization of the classification of primitive monodromy groups of polynomials obtained by P. Muller.

On the duality between rotational minimal surfaces and maximal surfaces

We investigate the duality between minimal surfaces in Euclidean space and maximal surfaces in Lorentz–Minkowski space in the framework of rotational surfaces. We study if the dual surfaces of two congruent rotational minimal (or maximal) surfaces are congruent. We analyze the duality process when we deform a rotational minimal (maximal) surface by a one-parametric group of rotations. In this context, the family of Bonnet minimal (maximal) surfaces and the Goursat transformations play a remarkable role.

An explicit formula for the cup-length of the rotation group

This paper gives an explicit formula for the $\mathbb Z_2$-cup-length of the rotation group $\mathrm{SO}(n)$.

POVM construction: A simple recipe with applications to symmetric states

We propose a simple method for constructing positive operator-valued measures (POVMs) using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the [Formula: see text]-dimensional subspace of the [Formula: see text]-dimensional Hilbert space of [Formula: see text] qubits comprising the permutationally symmetric states. Using the notion of vectorization, the constructed POVMs are interpretable as projection operators in a higher-dimensional space. We then describe a method to physically realize the constructed POVMs for symmetric states using the Clebsch–Gordan decomposition of the tensor product of irreducible representations of the rotation group. We illustrate the proposed construction on a spin-1 system, and show that it is possible to generate entangled states from separable ones.

The Hidden Curriculum of Veterinary Education: Mediators and Moderators of Its Effects.

The "hidden curriculum" has long been supposed to have an effect on students' learning during their clinical education, and in particular in shaping their ideas of what it means to be a professional. Despite this, there has been little evidence linking specific changes in professional attitudes to the individual components of the hidden curriculum. This study aimed to recognize those components that led to a change in students' professional attitudes at a UK veterinary school, as well as to identify the attitudes most affected. Observations were made of 11 student groups across five clinical rotations, followed by semi-structured interviews with 23 students at the end of their rotation experience. Data were combined and analyzed thematically, taking both an inductive and deductive approach. Views about the importance of technical competence and communication skills were promoted as a result of students' interaction with the hidden curriculum, and tensions were revealed in relation to their attitudes toward compassion and empathy, autonomy and responsibility, and lifestyle ethic. The assessment processes of rotations and the clinical service organization served to communicate the messages of the hidden curriculum, bringing about changes in student professional attitudes, while student-selected role models and the student rotation groups moderated the effects of these influences.

Influence of Continuous or Reciprocating Optimum Torque Reverse Motion on Cyclic Fatigue Resistance of Two Single-File Nickel-Titanium Rotary Instruments

Different single-file instruments and kinematics have been introduced on the market. It is important to know the cyclic fatigue performance of these instruments in these new kinematics such as reciprocation of Optimum Torque Reverse (OTR) motion. The aim of this study was to evaluate the resistance to cyclic fatigue of F6 SkyTaper and OneShape used in continuous rotation (proper rotation) or in reciprocating OTR motion.A total of forty-eight nickel-titanium files were tested. Twenty-four instruments of both brands were divided into two groups (n=12) on the basis of the motion tested: continuous rotation (group 1) or reciprocating OTR motion (group 2). Resistance to cyclic fatigue was determined by recording time to fracture (TtF) in a stainless steel artificial canal with a 60° angle of curvature and 5 mm radius of curvature. Data were analysed by two-way analysis of variance and post-hoc Bonferroni tests for multiple comparisons with P<0.05 as the level of significance.F6 SkyTaper showed higher TtF compared with OneShape, both in continuous and in OTR motion (P<0.0001). The two tested instruments showed higher cyclic fatigue resistance in reciprocating OTR motion than continuous rotation (P<0.0001).OTR motion significantly improves cyclic fatigue resistance of the tested instruments. In addition, F6 SkyTaper showed higher cyclic fatigue resistance than OneShape in both motions.

Influence of Continuous or Reciprocating Optimum Torque Reverse Motion on Cyclic Fatigue Resistance of Two Single-File Nickel-Titanium Rotary Instruments

Objective:Different single-file instruments and kinematics have been introduced on the market. It is important to know the cyclic fatigue performance of these instruments in these new kinematics such as reciprocation of Optimum Torque Reverse (OTR) motion. The aim of this study was to evaluate the resistance to cyclic fatigue of F6 SkyTaper and OneShape used in continuous rotation (proper rotation) or in reciprocating OTR motion.Methods:A total of forty-eight nickel-titanium files were tested. Twenty-four instruments of both brands were divided into two groups (n=12) on the basis of the motion tested: continuous rotation (group 1) or reciprocating OTR motion (group 2). Resistance to cyclic fatigue was determined by recording time to fracture (TtF) in a stainless steel artificial canal with a 60° angle of curvature and 5 mm radius of curvature. Data were analysed by two-way analysis of variance and post-hoc Bonferroni tests for multiple comparisons with P<0.05 as the level of significance.Results:F6 SkyTaper showed higher TtF compared with OneShape, both in continuous and in OTR motion (P<0.0001). The two tested instruments showed higher cyclic fatigue resistance in reciprocating OTR motion than continuous rotation (P<0.0001).Conclusion:OTR motion significantly improves cyclic fatigue resistance of the tested instruments. In addition, F6 SkyTaper showed higher cyclic fatigue resistance than OneShape in both motions.

Concussion management knowledge among residents and students and how to improve it.

Aim:Recognition and management of concussion is an area of growing importance. The objective was to measure concussion knowledge among residents and medical students (MS).Methods:Baseline knowledge was assessed by a standardized questionnaire. Control group (family medicine [FM], pediatric medicine [PM] and emergency medicine) residents were given reading material, and intervention group rotated in a clinic (sports medicine residents and MS). Subjects were retested after 36.82 (16.1) days. Pre- and post-intervention test scores were compared.Results:The average baseline knowledge scores were 79.2% for emergency medicine residents, 61.4% for FM, 68.5% for PM, 71.7% for sports medicine residents and 68.0% for MS. Knowledge increase for control group was 1.16% compared with 14.41% for the clinical rotation group (p < 0.0001).Conclusion:PM and FM residents can benefit from more focused education about concussion.

Constraint Control of Nonholonomic Mechanical Systems

We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection of the body frame angular velocity on a given direction $\boldsymbol{\xi}$. We derive the optimal control formulation, first for an arbitrary group, and then in the classical realization of Suslov's problem for the rotation group $SO(3)$. We show that it is possible to control the system using the constraint $\boldsymbol{\xi}(t)$ and demonstrate numerical examples in which the system tracks quite complex trajectories such as a spiral.

Optimal AK composite estimators in current population survey

ABSTRACTThe Current Population Survey (CPS) is a monthly household sample survey with a sample consisting of eight rotation groups. Sampled individuals of a rotation group are interviewed four consecutive months and another four consecutive months after resting eight consecutive months. A composite-type estimator is adopted in the CPS for the estimation of the monthly population total, which combines sample information from the current month's survey and previous months using the fact that 75% households have data for two consecutive months. There are two values, A and K, in the composite estimator to decide how to combine the available information, and thus this estimator is called the AK composite estimator. In this paper, we use a formula of the mean-squared error of AK composite estimator and propose an easy-to-use method of choosing A and K based on data, which evolves the estimation of some population quantities using the method of moments and replication. Some numerical studies are conducted to illustrate the effectiveness of the proposed method.

Entropic inequalities for matrix elements of rotation group irreducible representations

Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups SU(2) and SU(1, 1) like Jacoby polynomials and Gauss’ hypergeometric functions, respectively, are used.

Effects of Scapular Stabilization Exercise Training on Scapular Kinematics, Disability, and Pain in Subacromial Impingement: A Randomized Controlled Trial

ObjectiveTo investigate the effects of 2 different exercise programs on 3-dimensional scapular kinematics, disability, and pain in participants with subacromial impingement syndrome (SIS). DesignRandomized controlled trial. SettingOutpatient clinic and research laboratory. ParticipantsParticipants who were diagnosed with SIS and who also exhibited scapular dyskinesis (N=30). InterventionsThe participants were randomized in 2 different exercise groups: (1) shoulder girdle stretching and strengthening with additional scapular stabilization exercises based on a kinetic chain approach (intervention group), and (2) shoulder girdle stretching and strengthening exercises only (control group). Main Outcome MeasuresThree-dimensional scapular kinematics, self-reported shoulder pain, and disability were evaluated at baseline, after 6 weeks of training, and after 12 weeks of training. ResultsSignificant differences were observed between the control and intervention groups in external rotation and posterior tilt after 6 weeks of training and in external rotation, posterior tilt, and upward rotation after 12 weeks of training. All groups showed improvement in self-reported pain and disability scores; however, there were no significant differences between the groups. ConclusionsProgressive exercise training independent from specific scapular stabilization exercises provides decreased disability and pain severity in impingement syndrome.

Biomechanical evaluation of different osteosynthesis methods after mandibular sagittal split osteotomy in major advancements

The aim of this study was to assess the biomechanical stability of six different osteosynthesis methods after sagittal split osteotomy. Sixty polyurethane hemimandibles were divided into two groups, with six subgroups in each. After 10-mm advancement of the distal segment (group 1) and 10-mm advancement combined with 20° counterclockwise rotation (group 2), the bone segments were fixed using 2.0-mm plates/screws as follows: subgroup A, one conventional straight plate; subgroup B, two conventional straight plates; subgroup C, one conventional sagittal plate; subgroup D, one locking straight plate; subgroup E, two locking straight plates; subgroup F, one locking sagittal plate. The hemimandibles were tested for compressive strength by three-point biomechanical test, until there was 3mm of displacement between the segments. The fixations showed better performance in group 1 than in group 2 in all cases, with statistical significance for subgroups A, C, and D. In both groups, the use of two straight miniplates showed the most resistance, followed by the sagittal miniplates. However, in counterclockwise rotations, no statistically significant difference was found between two conventional straight plates and the sagittal locking plate. This study shows that the use of two plates is the form of fixation with the minimum displacement. If the clinician opts to use one plate, a sagittal plate is the best alternative.

The role of angular momentum in the superrotor theory for rovibrational motion of extremely flexible molecules

Recently, we proposed a novel approach to the description of the rotation-vibration motion for extremely flexible molecules (Schmiedt et al., 2016, 2017). Such molecules have multiple very “soft” vibrational modes and so, they lack a well-defined equilibrium structure. We have applied the new superrotor model to the prototype example of an extremely flexible molecule, CH5+, for which we combine two, essentially free vibrational modes (describing internal rotation) with the over-all rotation of the molecule and consider the resulting motion as a free rotation in five-dimensional space, with a Hamiltonian whose symmetry is described by SO(5), the five-dimensional rotation group. In the present work we discuss the correlation between the superrotor energies and those obtained in the more usual situation of the internal and over-all rotations being separable, and we give an initial discussion of the selection rules for electric dipole transitions obtained in the superrotor approach. Such selection rules are required for a detailed comparison between the superrotor predictions and the available, experimentally derived energy spacings (Asvany et al., 2015; Brackertz, 2016).

Accurate interatomic force fields via machine learning with covariant kernels

We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group SO(d) for the relevant dimensionality d. Remarkably, in specific cases the integration can be carried out analytically and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mechanical forces in real materials is investigated by tests on pure and defective Ni, Fe and Si crystalline systems.

Electrodynamics with charged strings

We show that in a four-dimensional space–time a complex scalar field can be associated with a one-dimensionally extended object, called a charged string. The string is said to be charged because the complex scalar field describing it interacts with an electromagnetic field. A charged string is characterized by an extension of the symmetry group of the charge space to a group of stretch rotations. We propose relativistically invariant and gauge-invariant equations describing the interaction of a complex scalar field with an electromagnetic field, and each solution of them corresponds to a charged string. We achieve this by introducing the notion of a charged string index, which, as verified, takes only integer values. We establish equations from which it follows that charged strings fit naturally into the framework of the Maxwell–Dirac electrodynamics.

Multiscale anisotropic fluctuations in sheared turbulence with multiple states

We use high resolution direct numerical simulations to study the anisotropic contents of a turbulent, statistically homogeneous flow with random transitions among multiple energy containing states. We decompose the velocity correlation functions on different sectors of the three dimensional group of rotations, SO(3), using a high-precision quadrature. Scaling properties of anisotropic components of longitudinal and transverse velocity fluctuations are accurately measured at changing Reynolds numbers. We show that independently of the anisotropic content of the energy containing eddies, small-scale turbulent fluctuations recover isotropy and universality faster than previously reported in experimental and numerical studies. The discrepancies are ascribed to the presence of highly anisotropic contributions that have either been neglected or measured with less accuracy in the foregoing works. Furthermore, the anomalous anisotropic scaling exponents are devoid of any sign of saturation with increasing order. Our study paves the way to systematically assess persistence of anisotropy in high Reynolds number flows.

Permutation-symmetric three-particle hyper-spherical harmonics based on the S3 ⊗ SO(3)rot ⊂ O(2)⊗SO(3)rot ⊂ U(3)⋊S2 ⊂ O(6) subgroup chain

We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3⊗SO(3)rot⊂O(2)⊗SO(3)rot⊂U(3)⋊S2⊂O(6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O(2) is the “democracy transformation”, or “kinematic rotation” group for three particles; SO(3)rot is the 3D rotation group, and U(3),O(6) are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3)rot⊂SU(3) degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K≤6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ,ρ) with coefficients given as algebraic numbers unless the “operator method” is chosen for the lifting of the SO(3)rot⊂SU(3) multiplicity and the dimension of the degenerate subspace is greater than four – in which case one must resort to numerical diagonalization; the latter condition is not met by any K≤15 harmonic, or by any L≤7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics) in two ways: 1) by explicit evaluation of integrals and 2) by reduction to known SU(3) Clebsch–Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.

Smooth foliations by circles of with unbounded periods and nonlinearizable multicentres

We give an example of a$C^{\infty }$vector field$X$, defined in a neighbourhood$U$of$0\in \mathbb{R}^{8}$, such that$U-\{0\}$is foliated by closed integral curves of$X$, the differential$DX(0)$at$0$defines a one-parameter group of non-degenerate rotations and$X$isnotorbitally equivalent to its linearization. Such a vector field$X$has the first integral$I(x)=\Vert x\Vert ^{2}$, and its main feature is that its period function islocally unboundednear the stationary point. This proves in the$C^{\infty }$category that the classical Poincaré centre theorem, true for planar non-degenerate centres, is not generalizable to multicentres. Such an example is obtained through a careful study and a suitable modification of a celebrated example by Sullivan [A counterexample to the periodic orbit conjecture.Publ. Math. Inst. Hautes Études Sci. 46(1976), 5–14], by blowing up the stationary point at the origin and through the construction of a smooth one-parameter family of foliations by circles of$S^{7}$whose orbits have unbounded lengths (equivalently, unbounded periods) for each value of the parameter and which smoothly converges to the Hopf fibration$S^{1}{\hookrightarrow}S^{7}\rightarrow \mathbb{CP}^{3}$.