Remarks on embeddable semigroups in groups and a generalizationof some Cuthbert′s results [PDF]
Let (U(t)) t≥0 be a C0‐semigroup of bounded linear operators on a Banach space X. In this paper, we establish that if, for some t0 > 0, U(t0) is a Fredholm (resp., semi‐Fredholm) operator, then (U(t)) t≥0 is a Fredholm (resp., semi‐Fredholm) semigroup.
Latrach, Khalid, Dehici, Abdelkader
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Maximum number of zeroes of polynomials on weighted projective spaces over a finite field
Abstract We compute the maximum number of rational points at which a homogeneous polynomial can vanish on a weighted projective space over a finite field, provided that the first weight is equal to 1. This solves a conjecture by Aubry, Castryck, Ghorpade, Lachaud, O'Sullivan and Ram, which stated that a Serre‐like bound holds with equality for weighted
Jade Nardi, Rodrigo San‐José
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Nonlinear Markov semigroups and interacting Lévy type processes [PDF]
Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X.
Kolokoltsov, V. N. (Vasiliĭ Nikitich)
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A group-theoretical interpretation of the word problem for free idempotent generated semigroups [PDF]
The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the semigroup in question. This leads to the construction of a free idempotent generated semigroup $\mathsf{IG}(\mathcal{E})$ - the `free-est' semigroup with a given biordered ...
Gould, Victoria Ann Rosalind +2 more
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Isotopy and equivalence of knots in 3‐manifolds
Abstract Two knots K$K$ and J$J$ in S3$S^3$ are isotopic if and only if they are related by an orientation‐preserving diffeomorphism of S3$S^3$. This claim follows from the fact that any orientation‐preserving self‐diffeomorphism of S3$S^3$ is isotopic to the identity. We show that this same idea applies to any prime oriented closed 3‐manifold.
Paolo Aceto +4 more
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Presentations of inverse semigroups, their kernels and extensions [PDF]
"Part of this work was done while Gray was an EPSRC Postdoctoral Research Fellow at the University of St Andrews, Scotland"Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K.
Ruskuc, Nik +8 more
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Note on semigroups generated by positive Rockland operators on graded homogeneous groups [PDF]
If \(L\) is a positive Rockland operator of homogeneous degree \(d\) on a graded homogeneous Lie group \(G\) and \((p_t)_{t > 0}\) the convolution kernel of the semigroup generated by \(L\) then the authors prove that for each left-invariant differential operator \(\partial\) on \(G\) of homogeneous degree \(j\) and all \(k \in \{0, 1, \ldots\}\) there
Dziubański, Jacek +2 more
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A priori bounds for the generalised parabolic Anderson model
Abstract We show a priori bounds for solutions to (∂t−Δ)u=σ(u)ξ$(\partial _t - \Delta) u = \sigma (u) \xi$ in finite volume in the framework of Hairer's Regularity Structures [Invent Math 198:269–504, 2014]. We assume σ∈Cb2(R)$\sigma \in C_b^2 (\mathbb {R})$ and that ξ$\xi$ is of negative Hölder regularity of order −1−κ$- 1 - \kappa$ where κ<κ¯$\kappa <
Ajay Chandra +2 more
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Completely regular semigroup varieties generated by mal'cev products with groups
For \(S\) a completely regular semigroup, let \(C^*(S)\) be the least subsemigroup of \(S\) that contains the set \(E(S)\) of idempotents of \(S\) and contains \(a^{-1}ta\) whenever it contains \(t\) (where \(a^{-1}\) is the \(\mathcal H\)-related inverse of \(a\)).
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Stochastic Dynamics From Maximum Entropy in Action Space
ABSTRACT We develop an information‐theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint distribution of actions and endpoints, subject to normalization and a constraint on the mean action, we ...
Fabricio Souza Luiz +3 more
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