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We revisit the problem of Stone duality for lattices with various quasioperators, first studied in [14], presenting a fresh duality result. The new result is an improvement over that of [14] in two important respects. First, the…
Necessary and sufficient conditions are given for a substochastic semigroup on $L^1$ obtained through the Kato--Voigt perturbation theorem to be either stochastic or strongly stable. We show how such semigroups are related to piecewise…
We calculate the effects of polariton bi- and multistability in a semiconductor Bragg microcavity with multiple quantum wells and a chiral photonic crystal on the upper mirror for resonant coherent pumping normal to the structure. Even if…
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe the free objects in varieties of semilattice ordered algebras…
We prove homological stability for standard unitary groups over R, C and H and for general linear groups over skew-fields with infinite centre. We focus on the similarities and differences of these proofs. Both proofs are due to Chih-Han…
We prove that, over a smooth quasi-projective curve, the set of non-isotrivial, smooth and projective families of polarized varieties with a fixed Hilbert polynomial and semi-ample canonical bundle is bounded. This extends the boundedness…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
For a given polarized toric variety, we define the notion of $\lambda$-stability which is a natural generalization of uniform K-stability. At the neighbourhoods of the vertices of the corresponding moment polytope $\Delta$, we consider…
We study graded rings associated to big divisors on LC pairs whose difference with the log-canonical divisor is nef. For divisors that are positive enough at the LC centers of the pair, we prove the finite generation of such rings if the…
We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…
We show that the family of semi log canonical pairs with ample log canonical class and with fixed volume is bounded.
We extend recent orbit counts for finitely generated semigroups acting on $\mathbb{P}^N$ to certain infinitely generated, polarized semigroups acting on projective varieties. We then apply these results to semigroup orbits generated by some…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show…
The rationality of the singularities of the $A_n$-loci is the natural question that arises in the papers devoted to the study of the Thom polynomials and $K$-theoretic invariants of the said loci. In this paper we prove that, in general,…
A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…
The paper gives the polarization of the tau lepton in the semileptonic B decays with respect to the direction of the virtual W boson. The result is given including the nonperturbative HQET corrections.The perturbative QCD corrections are…
We prove that a normal hyperplane section of the Segre variety $\Sigma_{m, n}$ is K-unstable with respect to any polarization if $m\neq n$ or it is not smooth.
We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…