Given an abelian, CM extension K of any totally real number field k, we restate and generalise two conjectures ‘of Stark type’ made in [So5]. The Integrality Conjecture concerns the image of a p-adic map sK/k,S determined by the minus-part of the S-truncated equivariant L-function for K/k at s = 1. It is connected to the Equivariant Tamagawa Number Conjecture of Burns and Flach. The Congruence ...

We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain “Relative Morse Inequalities” relating the homology of the manifold to the number of interior critical cells. We also derive a Ball Theorem, in analogy to Forman’s Sphere Theorem. The main corollaries of our work are: ...

Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

irrigation with distillery effluent, besides influencing crop yield, may have considerable impact on physical properties of soil because of its high salt and organic carbon contents. this experimental study was conducted to evaluate the effect of distillery effluent on hydraulic conductivity of a sandy loam alluvial soil and compare the effect of inorganic salts of potassium (k) with that of di...

We consider a generalization of the house-selling problem to selling k houses. Let the offers, X1,X2, . . ., be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N1, . . . , Nk , one for each component. The payoff is the sum over j of the jth component of XNj ...