We give a completion theorem for ordered magmas (i.e. ordered algebras with monotone operations) in a general form. Particular instances of this theorem are already known, and new results follow. The semantics of programming languages is the motivation of such investigations. Key wordscomplete partial orders, semantics of programming languages. Introduction. When defining recursive functions by...

Let φ : P → P be a morphism of degree d ≥ 2 defined over C. The dynamical Mordell–Lang conjecture says that the intersection of an orbit Oφ(P ) and a subvariety X ⊂ P is usually finite. We consider the number of linear subvarieties L ⊂ P such that the intersection Oφ(P ) ∩ L is “larger than expected.” When φ is the d-power map and the coordinates of P are multiplicatively independent, we prove ...

We present in this paper a systematic study on how to morph a well-trained neural network to a new one so that its network function can be completely preserved. We define this as network morphism in this research. After morphing a parent network, the child network is expected to inherit the knowledge from its parent network and also has the potential to continue growing into a more powerful one...

We consider dynamical systems arising from iterating a morphism of a projective variety defined over the field of fractions of a discrete valuation ring. Our goal is to obtain information about the dynamical system over the field of fractions by studying the dynamical system over the residue field. In particular, we aim to bound the possible primitive periods for a periodic point. This is discu...

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, either necessarily adjointable or arbitrary ones. As a consequence of these investigations, we obtain a set of equivalent conditions characteri...

Let φ,ψ : PN → PN be morphisms of degree at least 2 whose canonical heights ĥφ and ĥψ are identical. We draw various conclusions about the Green functions, Julia sets, and canonical local heights of φ and ψ. We use this information to completely characterize φ and ψ in the following cases: (i) φ and ψ are polynomial maps in one variable; (ii) φ is the dth-power map; (iii) φ is a Lattès map. Int...

This work concerns the problem of relating characteristic numbers of onedimensional holomorphic foliations of PC to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional holomorphic foliation F of M is a morphism Φ : L −→ TM where L is a holomorphic line bundle on M . The singular set of F is the analytic subvariety sing(F) = {p ...

We construct families of rank two bundles Et on P4, in characteristic two, where for t 6= 0, Et is a sum of line bundles, and E0 is non split. We construct families of rank two bundles Et on P3, in characteristic p, where for t 6= 0, Et is a sum of line bundles, and E0 is non split. 1. A degenerating family of split bundles on P in characteristic 2 We will construct a family of rank two bundles...

Let X a smooth quasi-projective algebraic surface, L a line bundle on X. Let X [n] the Hilbert scheme of n points on X and L the tautological bundle on X [n] naturally associated to the line bundle L on X. We explicitely compute the image Φ(L) of the tautological bundle L for the Bridgeland-King-Reid equivalence Φ : D(X ) → DbSn(X ), in terms of a complex C L of Snequivariant sheaves in DbSn(X ...