Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

Die Behandlung englischen Kulturgutes im Wiener fin de siècle:am Beispiel von Hugo von Hofmannsthal, Hermann Bahr und Peter Altenberg

This study explores the fascination which English culture represented in turn-of-the-century Vienna. The writers that are going to be discussed are the renowned Anglophile Hugo von Hofmannsthal, the more ambivalent Hermann Bahr and the idealizing, but Janus-faced Peter Altenberg. With the more widely known poet, prose writer and playwright, Hofmannsthal, individual aspects of his engagement with English culture have already been well researched; the same, however, cannot be said in the case of Hermann Bahr, whose extensive literary oeuvre has now largely been forgotten, and who has, instead, come to be valued as a prominent figure in the culture life of modernist Vienna, and Peter Altenberg, whose literary fame rests mainly on his prose poems and who, a legend in his life-time, has in recent years also increasingly attracted research interest as a phenomenon and ‘embodiment’ of the culture of his time: while their engagement with French literature, for example, has long received its due share of attention, their debt to English culture has, until now, been neglected. This thesis, therefore, sets out to explore Hofmannsthal’s, Bahr’s and Altenberg’s perception and portrayal of English civilization – ranging from English character and stereotypes, to what they saw as the principles of British society; it goes on to investigate the impulses they derive from Pre-Raphaelite art (Rossetti, Burne-Jones, Whistler) and the art and crafts-movement centred around William Morris, as well as their inspiration by the art criticism of John Ruskin and Walter Horatio Pater. In English literature one of the focal points will be their reading and evaluation of aestheticism as it was reflected in the life and writings of the Dubliner Oscar Wilde, who was perceived, by these Austrian authors, as a predominant figure of London’s cultural life. Similarly, they regarded his compatriot George Bernard Shaw as a key player in turn-of-the-century English (and European) culture. Hermann Bhar largely identified with him. Hofmannsthal, on the other hand, while having some reservations, acknowledged his importance and achievements, whereas Peter Altenberg saw in Shaw a model to reassure him, as his writings were becoming more openly didactic and even more miniaturistic than they had already been. He turned to Shaw, too, to explain and justify his new goal of making his texts more intelligent to a wider circle of readers.

Binary sparse nonnegative matrix factorization

This paper presents a fast part-based subspace selection algorithm, termed the binary sparse nonnegative matrix factorization (B-SNMF). Both the training process and the testing process of B-SNMF are much faster than those of binary principal component analysis (B-PCA). Besides, B-SNMF is more robust to occlusions in images. Experimental results on face images demonstrate the effectiveness and the efficiency of the proposed B-SNMF.

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Analysis of Wiener-Hammerstein equalizer for downlink LTE system

We propose a Wiener-Hammerstein (W-H) channel estimation algorithm for Long-Term Evolution (LTE) systems. The LTE standard provides known data as pilot symbols and exploits them through coherent detection to improve system performance. These drivers are placed in a hybrid way to cover up both time and frequency domain. Our aim is to adapt the W-H equalizer (W-H/E) to LTE standard for compensation of both linear and nonlinear effects induced by power amplifiers and multipath channels. We evaluate the performance of the W-H/E for a Downlink LTE system in terms of BLER, EVM and Throughput versus SNR. Afterwards, we compare the results with a traditional Least-Mean Square (LMS) equalizer. It is shown that W-H/E can significantly reduce both linear and nonlinear distortions compared to LMS and improve LTE Downlink system performance.

Postcards of the Wiener Werkstätte Selections from the Leonard A. Lauder Collection

Postcards of the Wiener Werkstätte: Selections from the Leonard A. Lauder Collection With additional works from the collection of The Wolfsonian--Florida International University, Miami Beach, Florida The exhibition is organized by the Neue Galerie New York and curated by Christian Witt-Dörring and Janis Staggs. Exhibition on view at The Wolfsonian--FIU November 15, 2012--March 31, 2013 The Wolfsonian's presentation was curated by Silvia Barisione and designed by Richard Miltner.

Schnell zu ersehende Gewichts-Reduction der vorzüglichsten europäischen Länder und Städte : nach dem Wiener Gewicht von 1 bis 10000 Pfund

von M.L. Michelup, geprüftem Hauptschullehrer

3D adaptive Wiener filter to restore brain SPECT image with reference MRI

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

3D adaptive Wiener filter to restore brain SPECT image with reference MRI

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.