Uncertainty Principles for Heisenberg Motion Group

In this article, we will recall the main properties of the Fourier transform on the Heisenberg motion group G = ℍ n ⋊ K , where K = U n and ℍ n = ℂ n × ℝ denote the Heisenberg group. Then, we will present some uncertainty principles associated to this transform as Beurling, Hardy, and Gelfand-Shilov.

Cutting efficiency of two heat-treated files in rotation and reciprocation motions

Background This study aimed at assessing the effect of different kinematics as well as different instrument designs on efficiency of cutting of two heat-treated nickel–titanium systems. Forty resin canals with 30°-angle of curvature and a length of 16 mm were utilized in this research. They were divided into four groups depending on the instrument and the operating kinematic, group I; Azure rotary system in rotation motion, group II; Azure rotary system in Reciprocation motion, group III; Fanta AF One rotary system in rotation motion and group IV; Fanta AF One rotary system in reciprocation motion. Blocks were labeled and then weighed pre- and post-preparation with delta weight (Δ wt = wt pre − wt post) and data were documented for statistics evaluation. Results Resin canals prepared using Fanta AF One rotary system showed significantly higher weight loss than Azure rotary system in both rotation and reciprocation (P < 0.001). Insignificant difference was reported for rotation and reciprocation movements in both file systems. Conclusion The instrument’s cross section revealed a more significant impact on cutting efficiency than the motion used.

Pelvic Sagittal Rotation in Patients With Hip Joint Disease

Objective: The functional orientation of the acetabular cup depends on the pelvic orientation when standing. Therefore, predicting the standing orientation of the pelvis after total hip arthroplasty( THA )is important to the preoperative plan. This study aimed to explore the rule suitable for different categories of patients.Methods: A total of 262 patients who had undergone hip arthroplasty in our hospital from 2011 to 2019 were retrospectively analyzed. Based on the spine and hip joint, they were divided into 5 categories: no flexion contracture of the hip joint - good lumbar range of motion (group A); no flexion contracture of the hip joint - limited lumbar motion (group B: B1, tanterior pelvic plane tilt (APPt)>0 °; B2, APPt<0 °); hip flexion contracture - good lumbar range of motion (group C); and hip flexion contracture - limited lumbar motion (group D). Changes of the pelvic sagittal parameter before and after THA were analyzed. Results: In group A, there was no significant difference in pelvic incidence (PI) and sagittal vertical axia (SVA) between preoperation and postoperation (P>0.05), but the mean value of sacral slope (SS) (from 44.99 °to 40.50 °), lumbar lordosis( LL) (from 51.42 to 47.45), pelvic tilt (PT) (from 8.71 °to 11.91°), and tanterior pelvic plane tilt (APPt) (from 4.5 °to 1.27 °) had statistic difference (P<0.05); In group B1 and B2, PI, SVA, SS, PT, LL, and APPt had no significant difference before and after operation (P>0.05); In group C, significant difference was not observed in PI (P>0.05), but found (P<0.05) in LL (from 52.17° to 43.43°), SS(44.90° to 38.34°), PT (from 5.70° to 13.36°), APPt (from 9.18° to 2.18°), and SVA (from 3.46cm to 1.16cm). In group D: the pelvis was in supination state before and after operation, and the spine sagittal position was imbalanced. Neither was there significant difference in SVA, PI, SVA, SS, ll and APPt between preoperation and postoperation (P>0.05). In addition, Harris scores of different groups changed accordingly. Conclusion: The sagittal rotation of the pelvis caused by different conditions of the spine-hip has a certain change law after total hip arthroplasty.

New Insight Into the Evaluation of Abnormal Left Ventricular Wall Motion

BackgroundEvaluation of mechanical dyssynchrony using echocardiography has failed to improve refractory heart failure in patients treated with cardiac resynchronization therapy. Previous predictors may not accurately reflect cardiac dyssynchrony. It was hypothesized that the spatially and temporary continuous information of the whole endocardium is required when the mechanical dyssynchrony is assessed using echocardiography. This study aimed to examine differences in the locus of the centroid of the left ventricle between abnormal and normal wall motion. MethodsTwenty-seven patients with dilated cardiomyopathy (left ventricular ejection fraction [LVEF]: 43±7%) and 45 old myocardial infarction patients with aneurysm (LVEF: 38±11%) were compared with 188 individuals with normal wall motions (LVEF: 61±5%). In an off-line system, the border of the endocardium was defined for each coordinate via the two-dimensional speckle tracking method. The centroid of the three-dimensional left ventricle was defined as the central point between both centroids calculated from four- and two-chamber images using an original application. ResultsThe locus of the centroid of the left ventricle in the normal wall motion group showed a horizontally inverted β shape, whereas this shape was absent in the other groups. When corrected by left ventricular end-systolic volume, the total and each directional length of the locus of the centroid of the left ventricle in the abnormal wall motion groups were clearly reduced compared with those recorded in the normal wall motion group. The acceleration of the centroid was also reduced in the abnormal wall motion groups. Multiple regression analysis with a stepwise method revealed a corrected antero-posterior shift of the centroid of left ventricle by left ventricular end-systolic volume and N-terminal pro-brain natriuretic peptide, which strongly correlated with the LVEF (adjusted R2: 0.6818, p≤2.2e-16).ConclusionUse of the locus of the centroid of the left ventricle provides novel insight into the evaluation of abnormal left ventricular contractions. Trial registrationretrospectively registered

Star Product on the Euclidean Motion Group in the Plane

In this work, we perform exact and concrete computations of star-product of functions on the Euclidean motion group in the plane, and list its $C$-star-algebra properties. The star-product of phase space functions is one of the main ingredients in phase space quantum mechanics, which includes Weyl quantization and the Wigner transform, and their generalizations. These methods have also found extensive use in signal and image analysis. Thus, the computations we provide here should prove very useful for phase space models where the Euclidean motion groups play the crucial role, for instance, in quantum optics.

Cyclic fatigue resistance of VDW.ROTATE and Reciproc Blue nickel-titanium files at root canal temperature

Background. This study aimed to compare the VDW.ROTATE instruments with the Reciproc Blue instruments in different kinematics in terms of the cyclic fatigue resistance. Methods. Sixty instruments, 40 VDW.ROTATE and 20 Reciproc Blue instruments, were divided into three groups (n=20): VDW.ROTATE was used in both continuous rotation and reciprocation, and Reciproc Blue was used in reciprocation only. The cyclic fatigue resistance test was carried out in an artificial canal (60°, r=3 mm) at an intracanal temperature of 35±2°C until fracture, and the time to fracture was recorded in seconds. The data were analyzed statistically using Kruskal–Wallis and Tamhane’s T2 tests (P<0.05). Results. DAll the reciprocating motion groups resulted in a longer mean duration to failure than the continuous rotation motion group (P<0.05). Conclusion. It was observed that the Reciproc Blue instruments had higher cyclic fatigue resistance than VDW.ROTATE instruments (P<0.05). Recent studies have shown that reciprocal movement increases cyclic fatigue resistance compared to rotational movement. The VDW.ROTATE instrument, which has a similar size, design, and alloy as the Reciproc Blue instrument, can also be used by clinicians in reciprocating motion with endo motors capable of reciprocating in different directions. However, even if the cyclic fatigue resistance increases by using VDW.ROTATE instruments in reciprocation, the cyclic fatigue resistance is lower than Reciproc Blue instruments.

Commutative Hypercomplex Numbers and the Geometry of Two Sets

The main task of the theory of phenomenologically symmetric geometries of two sets is the classification of such geometries. In this paper, by complexing with associative hypercomplex numbers, functions of a pair of points of new geometries are found by the functions of a pair of points of some well- known phenomenologically symmetric geometries of two sets (FS GDM). The equations of the groups of motions of these geometries are also found. The phenomenological symmetry of these geometries is established, that is, functional relationships are found between the functions of a pair of points for a certain finite number of arbitrary points. In particular, the s + 1-component functions of a pair of points of the same ranks are determined by single-component functions of a pair of points of the FS of GDM ranks (n,n) and (n + 1,n). Finite equations of motion group and equation expressing their phenomenological symmetry are found

Deforming discontinuous groups for Heisenberg motion groups

We study in this paper the local rigidity proprieties of deformation parameters of the natural action of a discontinuous group [Formula: see text] acting on a homogeneous space [Formula: see text], where [Formula: see text] stands for a closed subgroup of the Heisenberg motion group [Formula: see text]. That is, the parameter space admits a locally rigid (equivalently a strongly locally rigid) point if and only if [Formula: see text] is finite. Moreover, Calabi–Markus’s phenomenon and the question of existence of compact Clifford–Klein forms are also studied.