One Facile Preparation of N‐Aroyl‐N′‐arylsulfonylhydrazines by Oxidation of Aromatic Aldehyde N‐Arylsulfonylhydrazones with bis(Trifluoroacetoxy)iodobenzene

N‐aroyl‐N′‐arylsulfonylhydrazines can be obtained by oxidation of aromatic aldehyde N‐arylsulfonylhydrazones with bis(trifluoroacetoxy)iodobenzene in acetone at room temperature in mild to good yields.     

Three Saponins, a Steroid, and a Flavanol Glycoside from Achyrantes aspera

Summary.  Three bisdesmosidic saponins, 20-hydroxyecdysone, and quercetin-3-O-β-D-galactoside were isolated from the methanol extract of the aerial parts of Achyranthes aspera L. (Amaranthaceae). Their structures were established on the basis of NMR spectroscopic analysis; the complete ¹H and ¹³C assignments of the compounds were achieved by means of 2D NMR studies. Received July 21, 1999. Accepted August 26, 1999     

Analysis of an intermediate in a 1,3-dipolar cycloaddition of methylsulfonyl azide

MNDO-PM3 calculations, carried out on an experimentally determined structure of an intermediate in the cycloaddition of an electrophilic azide and a nucleophilic 1,3-dipolarophile, show that the semiempirical MO scheme models this structure closely. Transition structures for formation of the intermediate and ring closure of the latter are described.     

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.     

Linear extension sums as valuations on cones

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.     

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.     

On the Interpretation of Optimal Dual Solutions in Convex Programming

The relationships between multiple optimal dual solutions of a convex programming problem and the corresponding primal optimal value function are established by straightforward arguments on known results in duality theory. The subsequent discussion includes a demonstration that one-sided shadow prices can be found by solving a linear programming problem, conditions for the uniqueness and validity of the classical shadow price interpretation and a specialization of the results to the linear programming case.