FOCUS SHAPING OF CYLINDRICALLY POLARIZED VORTEX BEAMS BY A LINEAR AXICON

Focus shaping of cylindrically polarized vortex beams (CPVBs) by linear axicon is studied theoretically. Vector diffraction theory has been used to derive the expressions of the light field in the focal region. It is shown that a different intensity distribution in the focal region can be obtained by adjusting the topological charge, the polarization rotation angle and the numerical aperture maximal angle. A focal spot, a dark channel and a flat-topped shapes are formed by choosing proper values of parameters. A controllable polarization state of dark channel is obtained. The different focal region shapes may find wide applications such as material processing and optical tweezers.

The maximal angle between 5×5 positive semidefinite and 5×5 nonnegative matrices

The paper is devoted to the study of the maximal angle between the $5\times 5$ semidefinite matrix cone and $5\times 5$ nonnegative matrix cone. A signomial geometric programming problem is formulated in the process to find the maximal angle. Instead of using an optimization problem solver to solve the problem numerically, the method of Lagrange Multipliers is used to solve the signomial geometric program, and therefore, to find the maximal angle between these two cones.

Association between medial gastrocnemius muscle-tendon unit architecture and ankle dorsiflexion range of motion with and without consideration of slack angle

Joint flexibility is theoretically considered to associate with muscle-tendon unit (MTU) architecture. However, this potential association has not been experimentally demonstrated in humans in vivo. We aimed to identify whether and how MTU architectural parameters are associated with joint range of motion (RoM), with a special emphasis on slack angle. The fascicle length, pennation angle, tendinous tissue length, MTU length, and shear modulus of the medial gastrocnemius (MG) were assessed during passive ankle dorsiflexion using ultrasound shear wave elastography in 17 healthy males. During passive dorsiflexion task, the ankle joint was rotated from 40° plantar flexion to the maximal dorsiflexion joint angle at which each subject started experiencing pain. From the ankle joint angle-shear modulus relationship, the angle at which shear modulus began to rise (slack angle) was calculated. Two dorsiflexion RoMs were determined as follows; 1) range from the anatomical position to maximal angle (RoManat-max) and 2) range from the MG slack angle to maximal angle (RoMslack-max). The MTU architectural parameters were analyzed at the anatomical position and MG slack angle. The resolved fascicle length (fascicle length × cosine of pennation angle) and ratios of resolved fascicle or tendinous tissue length to MTU length measured at the MG slack angle significantly correlated with the RoMslack-max (r = 0.491, 0.506, and -0.506, respectively). Any MTU architectural parameters assessed at the anatomical position did not correlate with RoManat-max or RoMslack-max. These results indicate that MTUs with long fascicle and short tendinous tissue are advantageous for joint flexibility. However, this association cannot be found unless MTU architecture and joint RoM are assessed with consideration of muscle slack.

Flow responses alteration by geometrical effects of tubercles on plates under the maximal angle of attack

Plates with leading-edge tubercles experience beneficially more gradual aerodynamics stalling when entering the post-stall regime. Little is known, however, about the corresponding aquatic flow responses when these tubercles-furnished plates are subjected to the maximal angle of attack, with the flow direction perpendicular to their planar area. Hence, this study presents numerically, by means of the flow behavior solver ANSYS, the flow responses alteration in terms of the geometrical effects of tubercles on plates through changes in amplitudes (5 mm, 10 mm, 15 mm) and wavelengths (50 mm, 100 mm, 150 mm) under the maximal angle of attack in comparison to a control case, i.e., without tubercles. Additional to the commonly examined flow velocity and pressure, characteristics such as wake (area, reattachment length, flow recirculation intensity) and newly defined downstream vortical parameters (area, perimeter, and Feret diameters) for the vortex region have been proposed and assessed. It is found that the drag increases with the tubercle wavelength but corresponds inversely with the tubercle amplitude. By correlating with the best beneficial velocity and pressure profiles, it has been characterized that the optimally performing plate is the one that generates the greatest flow recirculation intensity, wake area, and reattachment length, corresponding to the capability to produce also the highest vortical area, perimeter, and major Feret diameter. Compared to the control case, all plates with tubercles alter beneficially these flow behaviors. In conclusion, plates with tubercles contribute favorably to the flow behaviors under the maximal angle of attack compared to the control case while the newly proposed downstream parameters could serve capably as alternatives in corroborating the flow physics description in future studies.

Sex-dependent differences in single-leg squat kinematics and their relationship to squat depth in physically active individuals

The purpose of this study is to compare recreationally physically active females and males with regard to spine, pelvis and lower limb joints peak angles in each plane of motion during a single leg squat (SLS). The second aim is to investigate the relationship between kinematics and SLS depth in females and males. Fifty-eight healthy, young adults performed 5 repetitions of a single right leg squat to maximal depth while keeping their balance. Kinematic data were obtained using an optical motion capture system. At the hip, greater adduction and greater internal rotation were observed in females than in males. Females had more extended spines and less outward bended knees throughout the SLS than did men. In males, squat depth was significantly, positively correlated with the maximal angle of the ankle (r = 0.60, p < 0.001), the knee (r = 0.87, p < 0.001), the hip (r = 0.73, p < 0.001) and the pelvis (r = 0.40, p = 0.02) in the sagittal plane. A positive significant correlation was found between SLS depth and maximal angle of the knee (r = 0.88, p < 0.001) and the ankle (r = 0.53, p = 0.01) in the sagittal plane in females. Males and females used different motor strategies at all levels of the kinematic chain during SLS.

Surgical Clipping of an Unruptured Large Inferiorly Projecting Anterior Communicating Artery Aneurysm With Chiasmopathy: 2-Dimensional Operative Video

Anterior communicating artery (ACoA) aneurysms are a frequently encountered cerebrovascular entity that is associated with a high rupture rate at a smaller size and debilitating morbidity and mortality following rupture. The surgical management of ACoA aneurysms is highly dependent on the spatial orientation of the saccular projection, which is categorized as inferior, superior, anterior, or posterior. The inferiorly projecting aneurysms constitute a minority of all aneurysms involving the ACoA. The adherence of the aneurysm dome near the chiasm predisposes these patients to dome avulsion during frontal lobe retraction. This patient presented with a 1-mo history of progressive vision loss and was found to have a large inferiorly projecting ACoA saccular aneurysm measuring 2.04 cm × 1.54 cm with resultant chiasmopathy. The lesion was approached via a right modified orbitozygomatic craniotomy, which can provide a more favorable maximal angle of approach to the ACoA complex to avoid brain retraction. Intraoperative adenosine was administered to provide relaxation of the aneurysm dome to augment clip placement. Postoperatively, the patient's chiasmopathy demonstrated near-complete resolution. The patient gave informed consent for surgery and video recording. Institutional review board approval was deemed unnecessary. Used with permission from Barrow Neurological Institute, Phoenix, Arizona.

On the maximal angle between copositive matrices

Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle θ_{max}(C_n) between two copositive matrices of order n [J.-B. Hiriart-Urruty and A. Seeger. A variational approach to copositive matrices. SIAM Rev., 52:593–629, 2010.]. They have proved that θ_{max}(C_2) = (3/4)pi and conjectured that θ_{max}(C_n) is equal to (3/4)pi for all n ≥ 2. In this note, their conjecture is disproven by showing that lim_{n→∞} θ_{max}(C_n) = pi. The proof uses a construction from algebraic graph theory. The related problem of finding the maximal angle between a nonnegative matrix and a positive semidefinite matrix of the same order is considered in this paper.