A smooth geometrically connected curve over the finite field [Formula: see text] with gonality has at most rational points. Faber and Grantham conjectured that there exist curves of every sufficiently large genus achieve this bound. In paper, we show bound can be achieved for an infinite sequence genera using abelian covers projective line. We also argue will not suffice to prove full conjecture.

Let An(K) be the Kostant form of U(sl + n ) and Γ the monoid generated by the positive roots of sln. For each λ ∈ Λ(n, r) we construct a functor Fλ from the category of finitely generated Γ-graded An(K)-modules to the category of finite-dimensional S(n, r)-modules, with the property that Fλ maps (minimal) projective resolutions of the one-dimensional An(K)module KA to (minimal) projective resol...

In 1966, Michael [11] introduced the concept of compact-covering maps. Since many important kinds of maps are compact-covering, such as closed maps on paracompact spaces, much work has been done to seek the characterizations of metric spaces under various compact-covering maps, for example, compact-covering (open) s-maps, pseudosequence-covering (quotient) s-maps, sequence-covering (quotient) s...

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...

We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...

The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...

Let T be a right exact functor from an abelian category ℬ into another $${\mathscr A}$$ . Then there exists p the product A} \times {\mathscr B}$$ to comma ( $$\left( {T \downarrow A}} \right)$$ ). In this paper, we study property of extension closure some classes objects in ), exactness and detailed description orthogonal given class $${\rm{P}}\left( {{\cal X},{\cal Y}} Moreover, characterize ...

Evaluators and researchers often have to deal with situations in which conventional research tools are impossible to use, either because of the characteristics of a population or unclear research variables. This paper presents a technique that succeeds in overcoming this kind of problem--a projective technique, but one that differs from the usual approach to projective techniques. The approach ...

During recent years, several studies have revealed that human-dog relationships are based on a well-established and complex bond. There is now evidence suggesting that the dog-human affectional bond can be characterized as an "attachment". The present study investigated possible association between the owners' attachment profile assessed throughout a new semi-projective test (the 9 Attachment P...

For a monoid S, a (left) S-act is a non-empty set B together with a mapping S × B → B sending (s, b) to sb such that s(tb) = (st)b and 1b = b for all s, t ∈ S and b ∈ B. Right S-acts A can also be defined, and a tensor product A⊗S B (a set) can be defined that has the customary universal property with respect to balanced maps from A×B into arbitrary sets. Over the past three decades, an extensi...