Working in a semi-abelian context, we use Janelidze’s theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out...

As a promising power source to boost up advent of next-generation ubiquitous era, high-energy density lithium-ion batteries with reliable electrochemical properties are urgently requested. Development of the advanced lithium ion-batteries, however, is staggering with thorny problems of performance deterioration and safety failures. This formidable challenge is highly concerned with electrochemi...

Making use of noncommutative motives we relate exceptional collections (and more generally semi-orthogonal decompositions) to motivic decompositions. On one hand we prove that the Chow motive M(X )Q of every smooth and proper Deligne-Mumford stack X , whose bounded derived category D(X ) of coherent schemes admits a full exceptional collection, decomposes into a direct sum of tensor powers of t...

We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive characteristic. The proof relies on lc abritrary fields, proved by Tanaka, and technique Hacon Xu to descend semi-ampleness from normalization. also present applications dlt threefold pairs, mixed characteristic families surfaces.

Abstract Using the 1.32 $$\hbox {pb}^{-1}$$ pb - 1 statistics collected at $$J/\psi $$ J / ψ peak with KEDR detector VEPP-4M $$e^{+}e^{-\, }$$ e +</...

In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin its systematic study with an effective view point. Our last section will apply this representation to investigate the intersection of two bi-cubic surfaces, these surfaces are widely used in Computer...

Let K be the function field of a connected regular scheme S of dimension 1, and let f : X → Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) ≥ 2. Suppose that f can be extended to a finite cover X → Y of semi-stable models over S (it is known that this is always possible up to finite separable extension of K). Then there exists a unique minimal such c...

The representations of dimension vector α of the quiver Q can be parametrised by a vector space R(Q,α) on which an algebraic group Gl(α) acts so that the set of orbits is bijective with the set of isomorphism classes of representations of the quiver. We describe the semi–invariant polynomial functions on this vector space in terms of the category of representations. More precisely, we associate...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category O associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category O and its parabolic generalizations for classical Lie superalgebras are categories with fu...