Vervollständigungsverfahren für Basen von Polynomidealen und Axiomensysteme von Gleichungstheorien

@article{RISC7121,
author = {E. Hoxhaj and J. Schicho},
title = {{How to reconstruct a planar map from its branching curve}},
language = {english},
journal = {Math. Comp.},
volume = {94},
pages = {935--952},
isbn_issn = {ISSN 1088-6842},
year = {2025},
refereed = {yes},
length = {18},
url = {https://doi.org/10.1090/mcom/3988}
}

@article{RISC7068,
author = {P. Paule and C. Schneider},
title = {{Creative Telescoping for Hypergeometric Double Sums}},
language = {english},
abstract = {We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute rational solutions of parameterized linear recurrences.},
journal = {J. Symb. Comput.},
volume = {128},
number = {102394},
pages = {1--30},
isbn_issn = {ISSN: 0747-7171},
year = {2025},
note = {Symbolic Computation and Combinatorics: A special issue in memory and honor of Marko Petkovšek, edited by Shaoshi Chen, Sergei Abramov, Manuel Kauers, Eugene Zima},
refereed = {yes},
keywords = {creative telescoping; symbolic summation, hypergeometric multi-sums, contiguous relations, parameterized recurrences, rational solutions},
length = {30},
url = {https://doi.org/10.1016/j.jsc.2024.102394}
}

@article{RISC6755,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The first--order factorizable contributions to the three--loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},
language = {english},
abstract = {The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$contain first--order factorizable and non--first--order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first--order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color--$zeta$ factors for the cases in which also non--first--order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin $N$--space, and correspondingly, on Kummer--Poincar'e and square--root valued alphabets in Bjorken--$x$ space. We present a complete discussion of the possibilities of solving the present problem in $N$--space analytically and we also discuss the limitations in the present case to analytically continue the given $N$--space expressions to $N in mathbb{C}$ by strict methods. The representation through generating functions allows a well synchronized representation of the first--order factorizable results over a 17--letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in $x$--space, also containing up to weight {sf w = 5} special constants, which can be rationalized to Kummer--Poincar'e iterated integrals at special arguments. The analytic $x$--space representation requires separate analyses for the intervals $x in [0,1/4], [1/4,1/2], [1/2,1]$ and $x > 1$. We also derive the small and large $x$ limits of the first--order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high--precision numerical solution of the problems.},
journal = {Nuclear Physics B},
volume = {999},
number = {116427},
pages = {1--42},
isbn_issn = {ISSN 0550-3213},
year = {2024},
note = {arXiv:2311.00644 [hep-ph]},
refereed = {yes},
keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, nested integrals, nested sums},
length = {42},
url = {https://doi.org/10.1016/j.nuclphysb.2023.116427}
}

@article{RISC7058,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},
language = {english},
abstract = {The non-first-order-factorizable contributions to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method basedon series expansions and utilize the first-order differential equations for the master integrals whichdoes not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(ep^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x in ]0,infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.},
journal = {Physics Letter B},
volume = {854},
number = {138713},
pages = {1--8},
isbn_issn = {ISSN 0370-2693},
year = {2024},
note = {arXiv:2403.00513 [[hep-ph]},
refereed = {yes},
keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, numerics},
length = {8},
url = {https://doi.org/10.1016/j.physletb.2024.138713}
}

@article{RISC7113,
author = {Fabián Fernando Serrano Suárez and Thaynara Arielly de Lima and Mauricio Ayala-Rincón},
title = {{Compactness Theorem for Propositional Logic and Combinatorial Applications}},
language = {english},
journal = {Arch. Formal Proofs},
volume = {2024},
pages = {--},
isbn_issn = { ISSN 2150-914x},
year = {2024},
refereed = {yes},
length = {0},
url = {https://www.isa-afp.org/entries/Prop_Compactness.html}
}

@article{RISC7116,
author = {Lucas A. da Silveira and Thaynara A. de Lima and Mauricio Ayala-Rincón},
title = {{On reconfiguring heterogeneous parallel island models}},
language = {english},
abstract = {This work introduces a new Parallel Island Model (PIM) that encompasses the benefits of heterogeneity and algorithmic reconfigurability. The former feature, heterogeneity, means that different islands may execute different evolutionary algorithms. The latter, reconfigurability, means that each island can change the algorithm being executed during the evolutionary process. Allowing such features increases the usual diversity obtained by the communication topologies and migration policies by homogeneous PIMs (HoPIMs). Previous (non-reconfigurable) heterogeneous PIMs (HePIMs) were able to provide competitive solutions regarding the HoPIMs. By adding the reconfiguration capability, PIMs can change dynamically from executing one evolutionary algorithm to another. In this manner, the required diversity and flexibility to outperform HoPIMs and HePIMs is achieved. This paper discusses policies to profit from the feature of reconfigurability on HePIM models and provides an innovative and successful stagnation-based reconfiguration policy. The benefits of the new reconfigurable model are verified using the unsigned reversal distance optimization problem as a case study.},
journal = {Swarm and Evolutionary Computation},
volume = {89},
pages = {101624--101624},
isbn_issn = { ISSN 2210-6502},
year = {2024},
refereed = {yes},
keywords = {Island-based bioinspired algorithms, Parallel island models, Heterogeneous models, Reconfigurability, Evolutionary algorithms, Unsigned reversal distance},
length = {0},
url = {https://www.sciencedirect.com/science/article/pii/S2210650224001627}
}

@article{RISC7130,
author = {Diego Dominici and Juan Carlos García-Ardila and Francisco Marcellán},
title = {{Symmetrization process and truncated orthogonal polynomials}},
language = {english},
abstract = {https://doi.org/10.1007/s13324-024-00974-3},
journal = { Analysis and Mathematical Physics},
volume = {14},
pages = {0--0},
isbn_issn = { 1664-2368},
year = {2024},
month = {11},
refereed = {yes},
length = {51}
}