Abstract Let $f\,:\,C\,\longrightarrow \,D$ be a nonconstant separable morphism between irreducible smooth projective curves defined over an algebraically closed field. We say that $f$ is genuinely ramified if ${\mathcal O}_D$ the maximal semistable subbundle of $f_*{\mathcal O}_C$ (equivalently, induced homomorphism $f_*\,:\, \pi _1^{\textrm{et}}(C)\,\longrightarrow \, _1^{\textrm{et}}(D)$ éta...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

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...

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...

Recently, in [DvZa], we have introduced EMV -algebras which resemble MV -algebras but the top element is not guaranteed for them. For σ-complete EMV -algebras, we prove an analogue of the Loomis–Sikorski Theorem showing that every σ-complete EMV -algebra is a σ-homomorphic image of an EMV -tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological pr...

Abstract We introduce a generalization of the notion negligible morphism and study associated tensor ideals thick ideals. These are defined by considering deformations given monoidal category $${\mathcal {C}}$$ C over local ring R . If maximal ideal is generated single element, we show that any admits an expl...

Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. For p sufficiently large (explicitly given in terms of r, g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of degree zero up to isomorphism). This is done by exhibiting a surjective morphism from...