1 Affine Morphisms Definition 1. Let f : X −→ Y be a morphism of schemes. Then we say f is an affine morphism or that X is affine over Y , if there is a nonempty open cover {Vα}α∈Λ of Y by open affine subsets Vα such that for every α, fVα is also affine. If X is empty (in particular if Y is empty) then f is affine. Any morphism of affine schemes is affine. Any isomorphism is affine, and the aff...

We define a morphism based upon a Latin square that generalizes the Thue-Morse morphism. We prove that fixed points of this morphism are overlap-free sequences, generalizing results of Allouche Shallit and Frid.

• The first work that can correct attributes while preserving the original meaning of each attribute dimension. plug-in module aims to facilitate existing approaches and makes ZSL models eligible or even GZSL tasks. corrected better reflect visual contexts without losing integrability in attributes. While Zero Shot Learning recognize new classes training examples, they often fails incorporate b...

1 is unique (1 = 11 = 1, so any left identity equals any right identity). A morphism takes 1 to the identity of φX (since φ(x) = φ(1x) = φ(1)φ(x)), but φ(1) = 1 is an extra property that ought to be satisfied by morphisms; its kernel is the sub-algebra φ(1); zero object is { 1 }; not Cartesian-closed (the terminal and initial objects are the same, yet not all groups are isomorphic). A quasi-gro...

Abstract: This paper proposes a new analysis method for photovoltaic (PV) modules. The main objectives are to obtain the resistance parameters of PV modules by adjusting I-V equation and voltage equation of diode and to find the relationship between resistance parameters and power. Firstly, values of serial resistance and parallel resistance at maximum power point are concluded. Secondly, the c...

Let R be a commutative Noetherian ring, I an ideal of R and M a non-zero R-module. In this paper we calculate the extension of annihilator of local cohomology modules H^t_I(M), t≥0, under the ring extension R⊂R[X] (resp. R⊂R[[X]]). By using this extension we will present some of the faithfulness conditions of local cohomology modules, and show that if the Lynch's conjecture, i...