Note on a Result of Kerman and Weit

A result in Kerman and Weit (J.?Fourier Anal. Appl. 16:786?C790, 2010) states that a real valued continuous function f on the unit circle and its nonnegative integral powers can generate a dense translation invariant subspace in the space of all continuous functions on the unit circle if f has a unique maximum or a unique minimum. In this note we endeavour to show that this is quite a general phenomenon in harmonic analysis.     

关于华的一个结果的注记

本文证明除了至多N20/21 ε个例外整数外,所有满足必要条件n=1 or 3(mod 6)的正整数n≤N均可表为两个素数的平方与一个素数的三次方的和．     

A Further Note on a Result of Bank, Frank, and Laine

In this paper, we generalize a result of Bank, Frank, and Laine [2] and a result of Wang [8]. Under certain conditions on the coefficients P_j in equation (1.1), we show that solutions ? of (1.1) must satisfy λ(?) = ρ(?) or ? has only finitely many zeros.     

Remark on a Result of Constantine

In this short note we construct codes of length 4n with 8n+8 codewords and minimum distance 2n?2 whenever 4n+4 is the order of a Hadamard matrix. This generalises work of Constantine who obtained a similar result in the special case that n is a prime power.

     

Variations on a Result of Bressoud

The well-known Rogers-Ramanujan identities have been a rich source of mathematical study over the last fifty years. In particular, Gordon’s generalization in the early 1960s led to additional work by Andrews and Bressoud in subsequent years. Unfortunately, these results lacked a certain amount of uniformity in terms of combinatorial interpretation. In this work, we provide a single combinatorial interpretation of the series sides of these generating function results by using the concept of cluster parities. This unifies the aforementioned results of Andrews and Bressoud and also allows for a strikingly broader family of q-series results to be obtained. We close the paper by proving congruences for a “degenerate case” of Bressoud’s theorem.     

Some Remarks on a Result of Atanackovic

In a recent paper Atanackovi gave an a priori estimate of themaximal deflection of an elastic column. In this note we showhow to improve those results using a sharper form of a "complement"of H?lder's inequality.     

Note on a Riegels-type integral

Zusammenfassung Die vorliegende Arbeit befasst sich mit einer Klasse von Integralen, die bei der Untersuchung der Strömung um Ringflügel von elliptischem Querschnitt auftreten. Es wird gezeigt, dass sich die fraglichen Integrale mittels Riegels'scher und vollständiger elliptischer Integrale darstellen lassen, ferner werden Reihenentwicklung nach Potenzen des Moduls angegeben und Rekursionsformeln für die numerische Berechnung der Integrale mitgeteilt.     

Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)     

Note on a conjecture of Kojima and Saigal

We prove there exist a finite set of (real) matrices of order n with positive determinant that, collectively, “see” all such matrices.     

Note on a theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.     

Note on a result of Chen and Lev

Periodica Mathematica Hungarica - Let $${\mathbb {N}}$$ be the set of all nonnegative integers. For a given set $$S\subset {\mathbb {N}}$$ the representation function $$R_S(n)$$ is defined as the...     

Note on a Theorem of Munkres

We prove that given a Riemannian manifold with boundary, having a finite number of compact boundary components, any fat triangulation of the boundary can be extended to the whole manifold. We also show that this result extends to manifolds and to embedded PL manifolds of dimensions 2, 3 and 4. We employ these results to prove that manifolds of the types above admit quasimeromorphic mappings onto As an application we prove the existence of G-automorphic quasimeromorphic mappings, where G is a Kleinian group acting on Dedicated to the memory of Robert BrooksThis paper represents part of the authors Ph.D. thesis written under the supervision of Prof. Uri Srebro.