A 3 copies of the manuscript A please indicate the corresponding author's details on the manuscript (tel/fax/e-mail) A 3 sets of figures A electronic version of the manuscript (Label the floppy disk with the type of computer and word processing package used, your name and the name of the file on the disk.) A electronic version of the figures For Review Papers: A 3 copies of the manuscript A ple...

A 3 copies of the manuscript A please indicate the corresponding author's details on the manuscript (tel/fax/e-mail) A 3 sets of figures A electronic version of the manuscript (Label the floppy disk with the type of computer and word processing package used, your name and the name of the file on the disk.) A electronic version of the figures For Review Papers: A 3 copies of the manuscript A ple...

François Alphonse Forel (1890) and Willi Ule (1892) composed a colour comparator scale, with tints varying from indigo-blue to cola brown, to quantify the colour of natural waters, like seas, lakes and rivers. For each measurement, the observer compares the colour of the water above a submersed white disc (Secchi disc) with a hand-held scale of pre-defined colours. The scale can be well reprodu...

On primitive roots of unity, divisors of p 2 − 1, and an extension to mod p Abstract Primitive roots of 1 mod p k (k > 2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by p+1. Integer divisors of ...

Over a commutative noetherian ring $R$, the prime spectrum controls, via assignment of support, structure both $\mathsf{Mod}(R)$ and $\mathsf{D}(R)$. We show that, just like in $\mathsf{Mod}(R)$, support classifies hereditary torsion pairs heart any nondegenerate compactly generated $t$-structure Moreover, we investigate whether these $t$-structures induce derived equivalences, obtaining new so...

Abstract Let $\mathcal {P}^{<\infty } ({\Lambda }\text {-mod})$ P < ∞ ( Λ -mod ) be the category of finitely generated left modules finite projective ...