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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.more » « less

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.more » « less

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.more » « less

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.more » « less

Free, publiclyaccessible full text available December 1, 2024

Free, publiclyaccessible full text available November 1, 2024

Free, publiclyaccessible full text available November 1, 2024

Abstract A description is presented of the algorithms used to reconstruct energy deposited in the CMS hadron calorimeter during Run 2 (2015–2018) of the LHC. During Run 2, the characteristic bunchcrossing spacing for protonproton collisions was 25 ns, which resulted in overlapping signals from adjacent crossings. The energy corresponding to a particular bunch crossing of interest is estimated using the known pulse shapes of energy depositions in the calorimeter, which are measured as functions of both energy and time. A variety of algorithms were developed to mitigate the effects of adjacent bunch crossings on local energy reconstruction in the hadron calorimeter in Run 2, and their performance is compared.
Free, publiclyaccessible full text available November 1, 2024 
Free, publiclyaccessible full text available November 1, 2024

Free, publiclyaccessible full text available November 1, 2024