Results 21 to 30 of about 89 (69)
Generic root counts and flatness in tropical geometry
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We use tropical and nonarchimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space Y$Y$. In particular, we are interested in the choices of parameters for which the generic root count is attained.
Paul Alexander Helminck, Yue Ren
wiley +1 more source
The singular series of a cubic form in many variables and a new proof of Davenport's Shrinking Lemma
Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 681-691, March 2025.Abstract We study the singular series associated to a cubic form with integer coefficients. If the number of variables is at least 10, we prove the absolute convergence (and hence positivity) under the assumption of Davenport's Geometric Condition, improving on a result of Heath‐Brown. For the case of nine variables, we give a conditional treatment. We
Christian Bernert
wiley +1 more source
Maximal dimensional subalgebras of general Cartan‐type Lie algebras
Bulletin of the London Mathematical Society, Volume 57, Issue 2, Page 605-624, February 2025.Abstract Let k$\mathbb {k}$ be a field of characteristic zero and let Wn=Der(k[x1,…,xn])$\mathbb {W}_n = \operatorname{Der}(\mathbb {k}[x_1,\ldots,x_n])$ be the nth$n{\text{th}}$ general Cartan‐type Lie algebra. In this paper, we study Lie subalgebras L$L$ of Wn$\mathbb {W}_n$ of maximal Gelfand–Kirillov (GK) dimension, that is, with GKdim(L)=n ...
Jason Bell, Lucas Buzaglo
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The Journal of Engineering, Volume 2025, Issue 1, January/December 2025.The article shows how novel general two‐degree‐of‐freedom feedback loop factorisation for single‐input single‐output systems is applied to oscillating plants with time delay, periodic changes of controlled plant parameters and astatism using the D‐K iteration and algebraic approach.
Marek Dlapa
wiley +1 more source
The structure and density of k$k$‐product‐free sets in the free semigroup and group
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract The free semigroup F$\mathcal {F}$ on a finite alphabet A$\mathcal {A}$ is the set of all finite words with letters from A$\mathcal {A}$ equipped with the operation of concatenation. A subset S$S$ of F$\mathcal {F}$ is k$k$‐product‐free if no element of S$S$ can be obtained by concatenating k$k$ words from S$S$, and strongly k$k$‐product‐free ...
Freddie Illingworth +2 more
wiley +1 more source
Parameter Constraints and Real Structures in Quadratic Semicomplete Vector Fields on C3
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.It is a remarkable fact that among the known examples of quadratic semicomplete vector fields on C3, it is always possible to find linear coordinates where the corresponding vector field has all—or “almost all”—coefficients in the real numbers. Indeed, the coefficients are very often integral.
Daniel de la Rosa Gómez, Shikha Binwal
wiley +1 more source
Analytic Nullstellensätze and the model theory of valued fields
Mathematische Nachrichten, Volume 297, Issue 8, Page 2873-2917, August 2024.Abstract We present a uniform framework for establishing Nullstellensätze for power series rings using quantifier elimination results for valued fields. As an application, we obtain Nullstellensätze for p$p$‐adic power series (both formal and convergent) analogous to Rückert's complex and Risler's real Nullstellensatz, as well as a p$p$‐adic analytic ...
Matthias Aschenbrenner, Ahmed Srhir
wiley +1 more source
Retrospective‐cost‐based model reference adaptive control of nonminimum‐phase systems
International Journal of Adaptive Control and Signal Processing, Volume 38, Issue 7, Page 2404-2422, July 2024.Abstract This paper presents a novel approach to model reference adaptive control inspired by the adaptive pole‐placement controller (APPC) of Elliot and based on retrospective cost optimization. Retrospective cost model reference adaptive control (RC‐MRAC) is applicable to nonminimum‐phase (NMP) systems assuming that the NMP zeros are known.
Nima Mohseni, Dennis S. Bernstein
wiley +1 more source
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract Genus Theory is a classical feature of integral binary quadratic forms. Using the author's generalization of the well‐known correspondence between quadratic form classes and ideal classes of quadratic algebras, we extend it to the case when quadratic forms are twisted and have coefficients in any principal ideal domain (PID) R$R$. When R=K[X]${
William Dallaporta
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Fortschritte der Physik, Volume 72, Issue 5, May 2024.Abstract The diffeomorphism class of simply connected smooth Calabi‐Yau threefolds with torsion‐free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class.
Aditi Chandra +4 more
wiley +1 more source