12,954 research outputs found
The Kakeya Set Conjecture for for general
No full textWe prove the Kakeya set conjecture for for general
as stated by Hickman and Wright [HW18]. This entails extending and
combining the techniques of Arsovski [Ars21a] for and the author and
Dvir [DD21] for the case of square-free . We also prove stronger lower
bounds for the size of -Kakeya sets over
by extending the techniques of [Ars21a] using
multiplicities as was done in [SS08, DKSS13]. In addition, we show our bounds
are almost sharp by providing a new construction for Kakeya sets over
and .Comment: To be published in Advances in Combinatorics 2024:2, 26p
On the Rationality and Transcendentality of Solutions to the Equation x^n + y^n = z^n
No full textIn this paper, the author develops 2 theorems that serve as extensions to the well-known Fermat’s Last Theorem in the field of number theory. The first proposed theorem in this paper states that if there exist numbers x, y, and an integer z such that x^n + y^n = z^n for any integer n > 2, then both/either x and/or y must be irrational. The second proposed theorem in this paper states that if there exist a number x, a transcendental number y, and an integer z such that x^n + y^n = z^n for any integer n > 2, then x must be irrational. The proposed theorems in this paper expand on the notion that if there exist numbers x, y, and an integer z such that x^n + y^n = z^n for any integer n > 2, then at least x or y is not an integer, which is stated in Fermat’s Last Theorem
Discovery of a single faint AGN in a large sample of z > 5 Lyman break galaxies
No full textAs part of a large spectroscopic survey of z > 5 Lyman break galaxies (LBGs), we have identified a single source which is clearly hosting an active galactic nucleus (AGN). Out of a sample of more than 50 spectroscopically confirmed R-band dropout galaxies at z∼ 5 and above, only J104048.6−115550.2 at z= 5.44 shows evidence for a high ionization potential emission line indicating the presence of a hard ionizing continuum from an AGN. Like most objects in our sample the rest-frame-UV spectrum shows the UV continuum breaking across a Lyα line. Uniquely within this sample of LBGs, emission from N V is also detected, a clear signature of AGN photoionization. The object is spatially resolved in Hubble Space Telescope (HST) imaging. This, and the comparatively high Lyα/N V flux ratio indicates that the majority of the Lyα (and the UV continuum longward of it) originates from stellar photoionization, a product of the ongoing starburst in the LBG. Even without the AGN emission, this object would have been photometrically selected and spectroscopically confirmed as a Lyman break in our survey. The measured optical flux (IAB= 26.1) is therefore an upper limit to that from the AGN and is of order 100 times fainter than the majority of known quasars at these redshifts. The detection of a single object in our survey volume is consistent with the best current models of high redshift AGN luminosity function, providing a substantial fraction of such AGN is found within luminous starbursting galaxies. We discuss the cosmological implications of this discovery
Lyman break galaxies and the star formation rate of the Universe at z ~ 6
No full textWe determine the space density of UV-luminous starburst galaxies at z≈ 6 using deep HST ACS SDSS-i′ (F775W) and SDSS-z′ (F850LP) and VLT ISAAC J and Ks band imaging of the Chandra Deep Field South. We find eight galaxies and one star with (i′−z′) > 1.5 to a depth of z′AB= 25.6 (an 8σ detection in each of the 3 available ACS epochs). This corresponds to an unobscured star formation rate of ≈15 h−270 M⊙ yr−1 at z= 5.9, equivalent to L* for the Lyman-break population at z= 3–4 (ΩΛ= 0.7, ΩM= 0.3). We are sensitive to star-forming galaxies at 5.6 ≲z≲ 7.0 with an effective comoving volume of ≈1.8 × 105h−370 Mpc3 after accounting for incompleteness at the higher redshifts due to luminosity bias. This volume should encompass the primeval subgalactic-scale fragments of the progenitors of about a thousand L* galaxies at the current epoch. We determine a volume-averaged global star formation rate of (6.7 ± 2.7) × 10−4h70 M⊙ yr−1 Mpc−3 at z∼ 6 from rest-frame UV selected starbursts at the bright end of the luminosity function: this is a lower limit because of dust obscuration and galaxies below our sensitivity limit. This measurement shows that at z∼ 6 the star formation density at the bright end is a factor of ∼6 times less than that determined by Steidel et al. for a comparable sample of UV-selected galaxies at z= 3–4, and so extends our knowledge of the star formation history of the Universe to earlier times than previous work and into the epoch where reionization may have occurred
Triangular Constellations in Flows
No full textParticles advected on the surface of a fluid can exhibit fractal clustering. The local structure of a fractal set is described by its dimension , which is the exponent of a power-law relating the mass in a ball to its radius : . It is desirable to characterise the {\em shapes} of constellations of points sampling a fractal measure, as well as their masses. The simplest example is the distribution of shapes of triangles formed by triplets of points, which we investigate for fractals generated by chaotic dynamical systems. The most significant parameter describing the triangle shape is the ratio of its area to the radius of gyration squared. We show that the probability density of has a phase transition: is independent of and approximately uniform below a critical flow compressibility , which we estimate. For the distribution appears to be described by two power laws: when , and when
Self-archiving practice and the influence of publisher policies in the social sciences
No full textAuthors in different disciplines exhibit very different behaviours on the so-called ‘green’ road to open access, i.e. self-archiving. This study looks at the self-archiving behaviour of authors publishing in leading journals in six social science disciplines. It tests the hypothesis that authors are self-archiving according to the norms of their respective disciplines rather than following self-archiving policies of publishers, and that, as a result, they are self-archiving significant numbers of publisher PDF versions. It finds significant levels of
self-archiving, as well as significant self-archiving of
the publisher PDF version, in all the disciplines
investigated. Publishers’ self-archiving policies have
no influence on author self-archiving practice
Microscopic origin of shape coexistence in the N=90, Z=64 region
No full textA microscopic explanation of the nature of shape coexistence in the N=90, Z=64 region is suggested, based on calculations of single particle energies through standard covariant density functional theory. It is suggested that shape coexistence in the N=90 region is caused by the protons, which create neutron particle-hole (p-h) excitations across the N=112 3-dimensional isotropic harmonic oscillator (3D-HO) magic number, signaling the start of the occupation of the 1i13/2 intruder orbital, which triggers stronger proton-neutron interaction, causing the onset of the deformation and resulting in the shape/phase transition from spherical to deformed nuclei described by the X(5) critical point symmetry. A similar effect is seen in the N=60, Z=40 region, in which p-h excitations across the N=70 3D-HO magic number occur, signaling the start of the occupation of the 1h11/2 intruder orbital. © 2022 The Author(s
Manifolds associated with (Z(2))(n+1)-colored regular graphs
No full textIn this article we describe a canonical way to expand a certain kind of (Z(2))(n+1)-colored regular graphs into closed n-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial n-manifold can be obtained in this way. When n <= 3, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a (Z(2))(n+1)-colored regular graph admits an n-skeletal expansion, then it is realizable as the induced graph of an (n + 1)-dimensional closed (Z(2))(n+1)-manifold.Mathematics, AppliedMathematicsSCI(E)1ARTICLE1121-1492
Type and class vectors and matrices in Z(n). Application to Z(6), Z(7), and Z(12)
No full text[EN]
In post-tonal theory, set classes are normally elements of Z(12) and are characterized by their interval-class vector. Those being non-inversionally-symmetrical can be split into two set types related by inversion, which can be characterized by their trichord-type vector. In this paper, I consider the general case of set classes and types in Z(n) and their m-class and m-type vectors, m ranging from 0 to n, which are properly grouped into matrices. As well, three relevant cases are considered: Z(6) (hexachords), Z(7) (heptatonic scales), and Z(12) (chromatic scale), where all those type and class matrices are computed and provided in supplementary files; and, in the first two cases, also in the form of tables. This completes the corresponding information given in previous publications on this subject and can directly be used by researchers and composers. Moreover, two computer programs, written in MATLAB, are provided for obtaining the above-mentioned and other related matrices in the general case of Z(n). Additionally, several theorems on type and class matrices are provided, including a complete version of the hexachord theorem. These theorems allow us to obtain the type and class matrices by different procedures, thus providing a broader perspective and better understanding of the theory.The author thanks the editor Darrell Conklin and the two anonymous reviewers for their valuable comments and suggestions, which contributed to improve the quality of this paper. He also thanks the ITACA Institute for contributing to support the open access publication.Nuño Fernández, L. (2023). Type and class vectors and matrices in Z(n). Application to Z(6), Z(7), and Z(12). Journal of Mathematics and Music. 17(2):244-265. https://doi.org/10.1080/17459737.2022.2120214S24426517
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Identifying idiolect in forensic authorship attribution: an n-gram textbite approach
No full textForensic authorship attribution is concerned with identifying authors of disputed or anonymous documents, which are potentially evidential in legal cases, through the analysis of linguistic clues left behind by writers. The forensic linguist “approaches this problem of questioned authorship from the theoretical position that every native speaker has their own distinct and individual version of the language [. . . ], their own idiolect” (Coulthard, 2004: 31). However, given the diXculty in empirically substantiating a theory of idiolect, there is growing concern in the Veld that it remains too abstract to be of practical use (Kredens, 2002; Grant, 2010; Turell, 2010). Stylistic, corpus, and computational approaches to text, however, are able to identify repeated collocational patterns, or n-grams, two to six word chunks of language, similar to the popular notion of soundbites: small segments of no more than a few seconds of speech that journalists are able to recognise as having news value and which characterise the important moments of talk. The soundbite oUers an intriguing parallel for authorship attribution studies, with the following question arising: looking at any set of texts by any author, is it possible to identify ‘n-gram textbites’, small textual segments that characterise that author’s writing, providing DNA-like chunks of identifying material
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