Maximin share and minimax envy in fair-division problems

For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envy-minimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions.     

Stable attachment of redox groups for modified electrodes via cyanuric chloride

Methylaminopropylviologen (MAV) was covalently attached to glassy carbon electrodes via cyuranic chloride. X-ray photoelectron spectroscopy (XPS) analysis confirmed the presence of bound MAV on the electrode surfaces. Electrochemical experiments of these electrodes indicated that the bound MAV was stable and electrochemically active for extended periods of time in aqueous media. The surface coverage of MAV was in the range, of 2.0–3.0×10^?10 mol cm^?2.     

A non-sulfide scheme of inorganic qualitative microanalysis

Summary A non-sulfide scheme of inorganic qualitative microanalysis is presented with solutions of HCl, CH₃COONa, H₂SO₄, and NaOH as group reagents. Color reactions (spot tests) are also included in this scheme. The purpose of this new approach to qualitative analysis is to eliminate disagreeable odor and corosive action of hydrogen sulfide as also to introduce complete group separations leading to more definite analytical results.

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Zusammenfassung Ein Schema für die qualitative anorganische Analyse ohne Schwefelwasserstoff mit Salzsäure, Na-Acetat, Schwefelsäure und Natronlauge als Gruppenreagenzien wird vorgelegt. Farbreaktionen (Tüpfelproben) werden im Laufe des Analysenganges verwendet. Die Geruchsbelästigung und die Korrosion durch Schwefelwasserstoff wird vermieden und gleichzeitig eine Gruppentrennung mit eindeutigeren Ergebnissen erzielt.

     

Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.