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  1. null (Ed.)
    We prove that the higher rho invariant is a homomorphism from the structure group of a compact manifold to the K-group of certain geometric C*-algebra. In particular, we apply this result to show that the structure group is infinitely generated for a class of manifolds. 
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  2. Free, publicly-accessible full text available June 1, 2024
  3. null (Ed.)
  4. In this paper, we prove bounds for the unique, positive zero of O  G (z) := 1 −O G (z) , where O G ( z ) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplic- ity and cardinalities of the vertex orbits of a graph. In [1] , we have shown that the unique, positive zero δ≤1 of O  G (z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ. 
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  5. Free, publicly-accessible full text available June 1, 2024
  6. Abstract

    The Cryogenic Underground Observatory for Rare Events (CUORE) is the first cryogenic experiment searching for$$0\nu \beta \beta $$0νββdecay that has been able to reach the one-tonne mass scale. The detector, located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy, consists of an array of 988$${\mathrm{TeO}}_{2}$$TeO2crystals arranged in a compact cylindrical structure of 19 towers. CUORE began its first physics data run in 2017 at a base temperature of about 10 mK and in April 2021 released its$$3{\mathrm{rd}}$$3rdresult of the search for$$0\nu \beta \beta $$0νββ, corresponding to a tonne-year of$$\mathrm{TeO}_{2}$$TeO2exposure. This is the largest amount of data ever acquired with a solid state detector and the most sensitive measurement of$$0\nu \beta \beta $$0νββdecay in$${}^{130}\mathrm{Te}$$130Teever conducted . We present the current status of CUORE search for$$0\nu \beta \beta $$0νββwith the updated statistics of one tonne-yr. We finally give an update of the CUORE background model and the measurement of the$${}^{130}\mathrm{Te}$$130Te$$2\nu \beta \beta $$2νββdecay half-life and decay to excited states of$${}^{130}\mathrm{Xe}$$130Xe, studies performed using an exposure of 300.7 kg yr.

     
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