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  1. We use the method of characteristic sets with respect to two term orderings to prove the existence and obtain a method of computation of a bivariate dimension polynomial associated with a non-reflexive difference-differential ideal in the algebra of difference-differential polynomials with several basic derivations and one translation. As a consequence, we obtain a new proof and a method of computation of the dimension polynomial of a non-reflexive prime difference ideal in the algebra of difference polynomials over an ordinary difference field. We also discuss applications of our results to systems of algebraic difference-differential equations.
  2. Multivariate dimension polynomials associated with finitely generated differential and difference field extensions arise as natural generalizations of the univariate differential and difference dimension polynomials. It turns out, however, that they carry more information about the corresponding extensions than their univariate counterparts. We extend the known results on multivariate dimension polynomials to the case of difference-differential field extensions with arbitrary partitions of sets of basic operators. We also describe some properties of multivariate dimension polynomials and their invariants.
  3. We present a difference algebraic technique for the evaluation of the Einstein's strength of quasi-linear partial difference equations and some systems of such equations. Our approach is based on the properties of difference dimension polynomials that express the Einstein's strength and on the characteristic set method for computing such polynomials. The obtained results are applied to the comparative analysis of difference schemes for some chemical reaction-diffusion equations.
  4. We consider Hilbert-type functions associated with finitely generated inversive difference field extensions and systems of algebraic difference equations in the case when the translations are assigned positive integer weights. We prove that such functions are quasi-polynomials that can be represented as alternating sums of Ehrhart quasi-polynomials of rational conic polytopes. In particular, we generalize the author's results on difference dimension polynomials and their invariants to the case of inversive difference fields with weighted basic automorphisms.
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  8. A bstract A search is presented for a heavy W′ boson resonance decaying to a B or T vector-like quark and a t or a b quark, respectively. The analysis is performed using proton-proton collisions collected with the CMS detector at the LHC. The data correspond to an integrated luminosity of 138 fb − 1 at a center-of-mass energy of 13 TeV. Both decay channels result in a signature with a t quark, a Higgs or Z boson, and a b quark, each produced with a significant Lorentz boost. The all-hadronic decays of the Higgs or Z boson and of the t quark are selected using jet substructure techniques to reduce standard model backgrounds, resulting in a distinct three-jet W′ boson decay signature. No significant deviation in data with respect to the standard model background prediction is observed. Upper limits are set at 95% confidence level on the product of the W′ boson cross section and the final state branching fraction. A W′ boson with a mass below 3.1 TeV is excluded, given the benchmark model assumption of democratic branching fractions. In addition, limits are set based on generalizations of these assumptions. These are the most sensitive limits to datemore »for this final state.« less
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