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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 nonreflexive differencedifferential ideal in the algebra of differencedifferential 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 nonreflexive 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 differencedifferential equations.

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 differencedifferential field extensions with arbitrary partitions of sets of basic operators. We also describe some properties of multivariate dimension polynomials and their invariants.

We present a difference algebraic technique for the evaluation of the Einstein's strength of quasilinear 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 reactiondiffusion equations.

We consider Hilberttype 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 quasipolynomials that can be represented as alternating sums of Ehrhart quasipolynomials 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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A bstract A search is presented for new particles produced at the LHC in protonproton collisions at $$ \sqrt{s} $$ s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb − 1 , collected in 2017–2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initialstate radiation and events with largeradius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with anmore »Free, publiclyaccessible full text available November 1, 2022

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