46,078 research outputs found

    Going Beyond Counting First Authors in Author Co-citation Analysis

    Full text link
    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed

    Uncertainty principles for the Weinstein transform

    Full text link
    summary:The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi's theorem, Beurling's theorem, and Donoho-Stark's uncertainty principle are obtained for the Weinstein transform

    Introduction

    No full text
    Harriet Beecher Stowe's most famous introduction took place on or around Thanksgiving Day, 1862, when she was introduced to President Abraham Lincoln, who allegedly greeted her with these memorable words, “So you're the little woman who wrote the book that made this great war! ” Even if we grant Lincoln's statement its obvious degree of ironic intention, he, nevertheless, makes quite a claim for the impact of Uncle Tom's Cabin on American history. One glance at virtually any of Lincoln's speeches reveals that he, like Stowe, believed that the power of words could alter the minds and hearts of individuals. Stowe's faith in the transforming capacity of language makes a great deal of sense, given that she came from a distinguished family of ministers and social activists - in an 1851 letter to Frederick Douglass, she writes, “I am a ministers daughter - a ministers wife & I have had six brothers in the ministry . . . & I certainly ought to know something of the feelings of ministers.” Stowe here refers to her father, Lyman Beecher, President of Lane Seminary, her husband, Calvin Stowe, who served at various times as Professor at Lane Seminary, Professor of the Chair of Sacred Literature at Andover Theological Seminary and Professor at Bowdoin College, and her brothers, the most famous of whom was Henry Ward Beecher, head of the prestigious Congregationalist Plymouth Church in Brooklyn and anti-slavery activist. This list, it should be noted, doesn’t even mention her influential sisters, Catharine Beecher, founder of the Hartford Female Seminary and author of many tracts, including A Treatise on Domestic Economy, and Isabelle Beecher Hooker, whose close ties to Elizabeth Cady Stanton and Susan B. Anthony made Isabelle an important figure in the campaign for women’s rights. To what extent Stowe’s own words of ministration and protest catapulted the nation toward Civil War is an unanswerable question, but clearly Stowe wanted her novel to bring about great social change and Lincoln thought she had succeeded

    A counterexample to the singular Weinstein conjecture

    No full text
    © 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND licenseIn this article, we study the dynamical properties of Reeb vector fields on b-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key properties of escape orbits and singular periodic orbits, which play a central role in formulating singular counterparts to the Weinstein conjecture and the Hamiltonian Seifert conjecture. In fact, we prove that the above-mentioned constructions lead to counterexamples of these conjectures as stated in [20]. Our construction shows that there are b-contact manifolds with no singular periodic orbits and no regular periodic orbits away from Z. We do not know whether there are constructions with no generalized escape orbits whose a and ¿-limits both lie on Z (a generalized singular periodic orbit). This is the content of the generalized Weinstein conjecture.Peer ReviewedPostprint (published version

    On the singular Weinstein conjecture and the existence of escape orbits for b-Beltrami fields

    No full text
    Motivated by Poincaré’s orbits going to infinity in the (restricted) three-body problem (see [26] and [6]), we investigate the generic existence of heteroclinic-like orbits in a neighbourhood of the critical set of a b-contact form. This is done by using the singular counterpart [3] of Etnyre– Ghrist’s contact/Beltrami correspondence [9], and genericity results concerning eigenfunctions of the Laplacian established by Uhlenbeck [29]. Specifically, we analyze the b-Beltrami vector fields on b-manifolds of dimension 3 and prove that for a generic asymptotically exact b-metric they exhibit escape orbits. We also show that a generic asymptotically symmetric b-Beltrami vector field on an asymptotically flat b-manifold has a generalized singular periodic orbit and at least 4 escape orbits. Generalized singular periodic orbits are trajectories of the vector field whose α- and ω-limit sets intersect the critical surface. These results are a first step towards proving the singular Weinstein conjecturePostprint (author's final draft
    corecore