Derivation of the inverse Schulze-Hardy rule.

Aggregation of Colloidal Particles in the Presence of Multivalent Co-Ions: The Inverse Schulze-Hardy Rule.

Shifts of the critical coagulation concentration (CCC) in particle suspensions in salt solutions containing multivalent co-ions and monovalent counterions are rationalized. One observes that the CCC is inversely proportional to the valence, and this behavior is referred to as the inverse Schulze-Hardy rule. This dependence is established by means of measurements of the stability ratio for posit...

ar X iv : 0 90 3 . 21 97 v 2 [ m at h . A C ] 2 5 Ju n 20 09 Hardy type derivations on generalized series fields

We consider the valued field K := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

2 00 9 Hardy type derivations on generalized series fields ∗

We consider the valued field K := R((Γ)) of generalized series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

Hardy type derivations on generalised series fields

We consider the valued fieldK := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a derivat...

Derivation of conflict resolution rule-curves in multi-purpose multi-reservoir system for inter-basin water transfer during drought