Constructing Carmichael numbers through improved subset-product algorithms

We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property that p-1 divides a highly composite \Lambda.Comment: Table 1 fixed; previously the last 30 digits and number of digits were calculated incorrectl

On the nature of clear-air turbulence (CAT)

CER62ERR11.February 1962.Includes bibliographical references.Scientific interim report.Prepared for Navy Weather Research Facility N189(188)538-28A

A Check-list of the Land Mammals of the Tanganyika territory and the Zanzibar protectorate

Volume: X

The Schwarzian derivative and the Wiman-Valiron property

Consider a transcendental meromorphic function in the plane with finitely many critical values, such that the multiple points have bounded multiplicities and the inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that if the Schwarzian derivative is transcendental then the function has infinitely many multiple points, the inverse function does not have a direct transcendental singularity over infinity, and infinity is not a Borel exceptional value. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method

Derivatives of meromorphic functions of finite order

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative

Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

A 4D Light-Field Dataset and CNN Architectures for Material Recognition

We introduce a new light-field dataset of materials, and take advantage of the recent success of deep learning to perform material recognition on the 4D light-field. Our dataset contains 12 material categories, each with 100 images taken with a Lytro Illum, from which we extract about 30,000 patches in total. To the best of our knowledge, this is the first mid-size dataset for light-field images. Our main goal is to investigate whether the additional information in a light-field (such as multiple sub-aperture views and view-dependent reflectance effects) can aid material recognition. Since recognition networks have not been trained on 4D images before, we propose and compare several novel CNN architectures to train on light-field images. In our experiments, the best performing CNN architecture achieves a 7% boost compared with 2D image classification (70% to 77%). These results constitute important baselines that can spur further research in the use of CNNs for light-field applications. Upon publication, our dataset also enables other novel applications of light-fields, including object detection, image segmentation and view interpolation.Comment: European Conference on Computer Vision (ECCV) 201

Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica

The size of Wiman-Valiron disks

Wiman-Valiron theory and results of Macintyre about "flat regions" describe the asymptotic behavior of entire functions in certain disks around points of maximum modulus. We estimate the size of these disks for Macintyre's theory from above and below.Comment: 20 page