An Adaptive Algorithm for Vector Partitioning

The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes, we are able to develop an adaptive algorithm for the vector partition problem that runs in time O(q(L)v) and in space O(L), where q is a polynomial function, L is the input size and v is the number of vertices of the associated partition polytope. It is based on an output-sensitive algorithm for enumerating all vertices of the partition polytope. Our adjacency characterization also implies a polynomial upper bound on the combinatorial diameter of partition polytopes. We also establish a partition polytope analogue of the lower bound theorem, indicating that the output-sensitive enumeration algorithm can be far superior to previously known algorithms that run in time polynomial in the size of the worst-case output.     

On Hadamard Inequality for Log-Concave Functions

Some improvements and generalizations of Finks results about Hadamards inequality for log-concave functions are given.AMS Subject Classification: 26D07, 26D15, 26A51.     

Minimal Modules Over Serial Rings

We investigate several model theoretic minimalities in the framework of modules over a given serial ring R.     

Stability of the intersection of solution sets of semi-infinite systems

Many mathematical programming models arising in practice present a block structure in their constraint systems. Consequently, the feasibility of these problems depends on whether the intersection of the solution sets of each of those blocks is empty or not. The existence theorems allow to decide when the intersection of non-empty sets in the Euclidean space, which are the solution sets of systems of (possibly infinite) inequalities, is empty or not. In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the sets is preserved by sufficiently small perturbations or not. This paper focuses on the stability of the non-empty (empty) intersection of the solutions of some given systems, which can be seen as the images of set-valued mappings. We give sufficient conditions for the stability, and necessary ones as well; in particular we consider (semi-infinite) convex systems and also linear systems. In this last case we discuss the distance to ill-posedness.     

Sequence and phosphorylation level determination of two donkey β‐caseins by mass spectrometry

Two coeluting components, with experimentally measured M_r values of 25529 and 24606 Da, were identified by reversed‐phase high‐performance liquid chromatography (RP‐HPLC) and mass spectrometric analysis in the dephosphorylated casein fraction of a milk sample collected from an individual donkey belonging to the Ragusano breed of the east of Sicily. By coupling enzymatic digestions, matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS) and RP‐HPLC/nano‐electrospray ionization tandem mass spectrometry (nESI‐MS/MS) analysis, the two proteins were identified as donkey β‐CNs and their sequences characterized completely, using the two known β‐CNs from mare as references. The two donkey β‐CNs, showing a mass difference of 923 Da, differ by the presence of the domain E²⁷SITHINK³⁴ in the full‐length component (M_r 25529 Da). In comparison with the mare's β‐CNs used as reference, they present nine amino acid substitutions: L→S³⁷, R→H⁵², S→N⁸¹, P→V⁸⁴, L→V⁹¹, R→Q²⁰³, P→L/I²⁰⁶, L→F²¹⁰ and A→P²¹⁹. Together, these substitutions account for the increase of 18 Da in the M_r of the donkey β‐CNs with respect to the counterparts from the mare. The molecular mass determination by ESI‐MS for the phosphorylated proteins showed that the full‐length component was composed of highly multi‐phosphorylated isoforms with five to seven phosphate groups. By analogy with the homologous mare's β‐CNs, the full‐length (226 amino acids) β‐CN was termed variant A, whereas the shorter (218 amino acids) β‐CN was termed variant A^Δ5. Copyright © 2009 John Wiley & Sons, Ltd.     

Ferrocenylalkyl azoles: bioactivity,synthesis, structure

The toxicity of ferrocenylethyl benzotriazole ( 1 ) and other ferrocene compounds including ferrocenylmethyl benzimidazoles ( 4,5,6,11 ), ferricenium salts ( 3,9,10 ) and ferrocenylmethyl adenine ( 7 ), was studied. All ferrocene complexes under investigation showed low or medium toxicities. On the basis of an earlier model of chemical carcinogenesis, the antitumor activity of ferrocenylalkyl azoles 1, 8 and ferricenium salts 9, 10 was studied in vivo in the so‐called sub‐capsular test on human tumors. This effectiveness was compared with that of cisplatin. A series of ferrocenylalkyl azoles were synthesized by interacting azoles either with α‐hydroxyalkyl ferrocenes FcC(OH)R₁R₂ in organic solvent in the presence of aqueous HBF₄ in quantitative yields or with trimethyl(aminomethyl)ferrocene iodide in an aqueous‐basic medium in good yields. The X‐ray determinations of molecular and crystal structures of α‐(1‐benzotriazolyl)ethylferrocene ( 1 ) and α‐(1‐naphthatriazolyl)ethylferrocene ( 12 ) were performed. Copyright © 2008 John Wiley & Sons, Ltd.     

Monotonicity properties of wholesale price contracts

This paper contributes to the supply chain contracts literature in economics and operations by performing qualitative sensitivity analysis of a wholesale price contract in a two-echelon supply chain setting. Order-theory tools are used to derive sufficient conditions for monotonicity of contract parameters.The upstream supplier is modeled as a Stackelberg leader. The supplier is assumed to have complete information about the costs and revenue function of the downstream retailer. It is shown that an equilibrium wholesale price weakly increases with an increase in the supplier production cost rate, but it may increase or decrease with an increase in the retailer cost rate. As either the supplier production cost or the retailer cost increases, the supplier profit decreases weakly. Additional sensitivity analysis is performed assuming certain properties of the retailer revenue function.Several well-known results in the supply chain contracting literature can be considered as special cases of the more general theorems developed here. In particular, this paper reexamines the analysis of a newsvendor supply chain problem by Lariviere and Porteus [Lariviere, M.A., Porteus, E.L., 2001. Selling to the newsvendor: An analysis of price-only contracts. Manufacturing & Service Operations Management 3, 293–305]. This paper generalizes and extends their work, by establishing properties of the newsvendor demand distribution that guarantee monotonicity of the contract parameters, without requiring a unique contract solution.