Given an r × r complex matrix T , if T = U |T | is the polar decomposition of T , then, the Aluthge transform is defined by ∆ (T ) = |T |U |T |. Let ∆n(T ) denote the n-times iterated Aluthge transform of T , i.e. ∆0(T ) = T and ∆n(T ) = ∆(∆n−1(T )), n ∈ N. We prove that the sequence {∆n(T )}n∈N converges for every r× r diagonalizable matrix T . We show that the limit ∆∞(·) is a map of class C∞...

Methods In 15 consecutive patients with structural heart disease and without contraindication to MRI, intramural scar was detected by DE-MRI (Fig 1a). All patients underwent endocardial voltage mapping by catheter. Both unipolar and bipolar voltage maps were constructed from the endocardium. The scar on DE-MRI was registered with the electroanatomic map using fiducials (apex, aorta, mitral valv...

New high-resolution data from the Mars Orbiter Laser Altimeter (MOLA) have provided detailed topographic maps for the north and south polar regions. These new data allow one to compare the overall topography and geologic histories of the two polar regions and to highlight some specific outstanding questions in Mars polar studies, following earlier comparisons using Viking and Mars Global Survey...

In a polar map display, the LAD originates from an area corresponding to 11 o’clock, and the relationship between localization of the culprit lesion and diagonal arteries can be inferred by the extent of decreased perfusion extending from 12 o’clock towards 1 o’clock. The location of a lesion in the LCX main trunk can be inferred by whether decreased perfusion is observed at any level within 2〜...

Plant embryogenesis creates a seedling with a basic body plan. Post-embryonically the seedling elaborates with a lifelong ability to develop new tissues and organs. As a result asymmetric cell divisions serve essential roles during embryonic and postembryonic development to generate cell diversity. This review highlights selective cases of asymmetric division in the model plant Arabidopsis thal...

Beginning with a tracking code for the LHC, we construct the canonical generator of the full-turn map in polar coordinates. For very fast mapping we adopt a model in which the momentum is modulated sinusoidally with a period of 130 turns (very close to the synchrotron period). We achieve symplectic mapping of 10 turns in 3.6 hours on a workstation. Quasi-invariant tori are constructed on the Po...

The internal organization of a higher level visual area in the human parietal cortex was mapped. Functional magnetic resonance images were acquired while the polar angle of a peripheral target for a delayed saccade was gradually changed. A region in the superior parietal cortex showed robust retinotopic mapping of the remembered target angle. The map reversed when the direction of rotation of t...

[1] We have measured winds using cloud motion in consecutive Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) wide-angle global map swaths taken during the first mapping year (Ls 135 –360 –111 ). We present a total of 11,200 wind vectors collected in the north polar region during Ls 135 –195 (late summer/early fall) and Ls 20 –55 (mid spring) and in the south polar region during Ls 337 –10 ...

Purpose Current perimeters use fixed grid patterns. We test whether a grid based on an individual's retinal nerve fiber layer (RNFL) thickness profile would find more visual field (VF) defects. Methods We describe the defect-based method for choosing test locations. First, the 26 VF locations with the highest positive predictive value to detect glaucoma from the 24-2 pattern are chosen. An ad...

for a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, dewan et al [k. k. dewan, n. singh and a. mir, extension of some polynomial inequalities to the polar derivative, j. math. anal. appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). in this paper we improve and extend the above inequality. our result generalizes certai...