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.     

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.

---

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.

     

Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C(3))- or four (T(d), tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by F?rster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.     

Multisample probe for fast-atom bombardment / mass spectrometry

An inexpensive multisample fast-atom bombardment (FAB) probe assembly was designed for high-throughput analysis of samples on a VG ZAB-SE mass spectrometer. The system consists of a vacuum lock system and a FAB probe whose tip contains five or more sample wells. The probe enters the mass spectrometer source region perpendicular to the secondary ion beam axis, The probe is maintained at high voltage on contact with a spring clip attached to the screen plate of the source block. Sample throughput with the multisample probe is twice that of a coaxial probe, with about twice the sensitivity and no sample cross contamination.     

Rearrangements of 3-heterobicyclo[3.2.0]hept-6-enes

Studies directed at a synthesis of dihydrothiepin 1b have resulted in the elucidation of several factors which effect cyclobutene ring opening in the 3-heterobicyclo[3.2.0]hept-6-ene ring system. We report the unexpected rearrangement of 4a, 4b, 13b and 13c to the synthetically useful a-vinyl-2,5-dihydrothiophenes 7a, 7b, 15a and 15b, respectively. Conversion of 4a to 6 is suggested to occur by a 1,3-rearrangement of 4a to isomeric 3-thiabicyclo[3.2.0]hept-6-ene 19 followed by cyclobutene ring opening in 19.     

Some Inequalities for Derivatives of Trigonometric and Algebraic Polynomials

We investigate inequalities for derivatives of trigonometric and algebraic polynomials in weighted L ^P spaces with weights satisfying the Muckenhoupt A _p condition. The proofs are based on an identity of Balázs and Kilgore [1] for derivatives of trigonometric polynomials. Also an inequality of Brudnyi in terms of rth order moduli of continuity ω_r will be given. We are able to give values to the constants in the inequalities.     

Artificial genetic systems: exploiting the "aromaticity" formalism to improve the tautomeric ratio for isoguanosine derivatives

The tautomerism of 2'-deoxy-7-deaza-isoguanosine (2) was studied and compared to that of 2'-deoxyisoguanosine (1). The fixed (1)N-methyl (8) and O-methyl (4) derivatives were synthesized to represent the pure extremes of each tautomer. The replacement of the imidazole ring in 1 with a pyrrole ring in 2 makes the keto form in the latter more favored by 2 orders of magnitude (K(TAUT) for 2 approximately 10(3), as opposed to K(TAUT) for 1 approximately 10).