Related papers: Polar coordinates view on KM-arcs
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.
The multidimensional extension of the Aleskerov-Golubenko polarization index is developed. Several versions of the polarization index are proposed based on different distance functions. Basic properties of the index are examined.
Advances in vectorial polarisation-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis. Imaging polarimetry requires determination of the Mueller matrix (MM) at every…
We prove that the polar degree of an arbitrarily singular projective hypersurface can be decomposed as a sum of non-negative numbers which represent local vanishing cycles of two different types. This yields lower bounds for the polar…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
The polarization of the cosmic microwave background radiation will have a distribution of singularities and anti-singularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities…
We analyze polarization-adjusted convolutional codes using the algebraic representation of polar and Reed-Muller codes. We define a large class of codes, called generalized polynomial polar codes which include PAC codes and Reverse PAC…
Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce…
Possible instrumental set--ups for the measurement of CMB polarization are reviewed in this article. We discuss existing and planned instruments, putting special emphasis on observational, instrumental, and data processing issues for the…
In this paper we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon non-paraxially propagating a…
We find upper bounds, sharp in most cases, on the number of real hyperplane sections of real smooth polarized $K3$-surfaces that split into lines. Most bounds coincide with their complex counterparts.
We give a method for constructing Kummer covers with many points over finite fields.
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…
We propose a unified view of the polarity of functions, that encompasses all specific definitions, generalizes several well-known properties and provides new results. We show that bipolar sets and bipolar functions are isomorphic lattices.…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.