Competitive division of a mixed manna

A mixed manna contains goods (that everyone likes) and bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale–Eisenberg): hence it is welfarist (determined by the set of feasible utility profiles), unique, continuous, and easy to compute. We show that the competitive division of a mixed manna is still welfarist. If the zero utility profile is Pareto dominated, the competitive profile is strictly positive and still uniquely maximizes the product of utilities. If the zero profile is unfeasible (for instance, if all items are bads), the competitive profiles are strictly negative and are the critical points of the product of disutilities on the efficiency frontier. The latter allows for multiple competitive utility profiles, from which no single-valued selection can be continuous or resource monotonic. Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods

Physiological assessment of drought resistance and heat resistance of spring barley varieties by laboratory methods

One of the main conditions for the stable growth of grain production of spring barley is the expansion of sown areas, using varieties with high adaptive properties and capable of providing high yields in a changing climate. The purpose of the work is to determine the drought resistance and heat resistance of varieties and lines of spring barley using laboratory methods. The article presents studies of physiological indicators of resistance at an early stage of plant development to extreme environmental factors (drought and relatively high air temperatures). The physiological method of early diagnostics of seeds and seedlings provides information on the general initial level of physiological and biochemical processes in germinating seeds under stressful conditions and allows one to get an idea of the resistance of adult plants. Such a primary assessment gives grounds for the selection of promising samples for a deeper study of their stability. When determining the resistance of varieties and lines of spring barley to abiotic stressors, samples were identified that, in terms of a set of indicators (drought resistance, heat resistance, degree of depression, index of complex resistance and growth of germinal roots), values significantly exceeding the standard variety Ratnik (36.6; 91, 1; 2.13%; 184.3 rel. units and 2.78 cm, respectively): Zernogradsky 1717 (45.6; 84.0; 5.19%; 194.8 rel. units and 4.76 cm), Zernogradsky 1716 (4.3; 83.4; 5.43%; 188.0 relative units and 3.67 cm), Zernogradsky 1701 (36.2; 87.0; 3.17%; , 4 relative units and 2.56 cm)

Consistent and covariant solutions for TU games

One of the important properties characterizing cooperative game solutions is consistency. This notion establishes connections between the solution vectors of a cooperative game and those of its reduced game. The last one is obtained from the initial game by removing one or more players and by giving them the payoffs according to a specific principle (e.g. a proposed payoff vector). Consistency of a solution means that the restriction of a solution payoff vector of the initial game to any coalition belongs to the solution set of the corresponding reduced game. There are several definitions of the reduced games (cf., e.g., the survey of T. Driessen [2]) based on some intuitively acceptable characteristics. In the paper some natural properties of reduced games are formulated, and general forms of the reduced games possessing some of them are given. The efficient, anonymous, covariant TU cooperative game solutions satisfying the consistency property with respect to any reduced game are described. Copyright Springer-Verlag 2004Cooperative TU game, value, consistency, reduced game,

THE EXTENSION OF DUTTA–RAY'S SOLUTION TO CONVEX NTU GAMES

The egalitarian solution for the class of convex TU games was defined by Dutta and Ray [1989] and axiomatized by Dutta 1990. An extension of this solution — the egalitarian split-off set (ESOS) — to the class of non-levelled NTU games is proposed. On the class of TU games it coincides with the egalitarian split-off set [Branzei et al. 2006]. The proposed extension is axiomatized as the maximal (w.r.t. inclusion) solution satisfying consistency à la Hart–Mas-Colell and agreeing with the solution of constrained egalitarianism for arbitrary two-person games. For ordinal convex NTU games the ESOS turns out to be single-valued and contained in the core. The totally cardinal convexity property of NTU games is defined. For the class of ordinal and total cardinal convex NTU games an axiomatic characterization of the Dutta–Ray solution with the help of Peleg consistency is given.Egalitarian split-off set, consistency

A Flow in a Thin Plastic Layer: Generalizations of the Prandtl’s Problem

The analytical solutions of various generalizations of the classical L.Prandtl’s problem are of great interest in studying the problem of straightening plates using uniaxial stretching beyond the elastic limit. The straightening by stretching allows obtaining a high degree of flatness of thin wide strips and sheets of high-strength steels and special alloys, while the straightening by other methods does not provide satisfactory results. Based on Ilyushin’s theory of flow in a thin plastic layer, generalizations of the classical Prandtl’s problem on plastic strip compression were studied and their solutions were obtained. The planar problem of compression of a plastic strip between two parallel rough planes with accounting for the asymmetry of the conditions on the spreading ends has been solved and the upper estimate of the total compression force of the face-end areas of the plastically stretched strip has been obtained

Linear consistency of values for TU-games

A value on the set {\bf G} of all transferable utility games is said to have a weighted potential representation if there exists a potential function $P: {\bf G} \to {\mathbb{R}}$, associated with a collection of weights, such that, for every game and every player, an appropriately chosen weighted extension of the player's marginal contribution (with respect to the potential) agrees with the player's value in the game. The main theorem states that a value has a weighted potential representation if and only if the value satisfies the well-known efficiency, linearity and symmetry axioms, together with two additional conditions involving a unique collection of constants that describes such a value. Particularly, this unified approach provides various weighted potential representations for the Shapley value, the solidarity value as well and several egalitarian values based on some kind of equity principle. For the class of values that have a weighted potential representation, it is further stated that such a value is consistent (or possesses the reduced game property) with respect to an appropriately chosen type of reduced game (that can be regarded as a generalized version of the known reduced game \`a la Hart and Mas-Colell). Finally, an axiomatic characterization of every value with a weighted potential representation is given in terms of two axioms, namely the corresponding consistency (reduced game) axiom together with a minor axiom referring to some kind of standardness for two-person games

Consistency of the equal split-off set

This paper axiomatically studies the equal split-off set (cf. Branzei et al. 2006) as a solution for cooperative games with transferable utility which extends the well-known Dutta and Ray (1989) solution for convex games. By deriving several characterizations, we explore consistency of the equal split-off set on the domains of exact partition games and arbitrary games

Plastic Flow in a Thin Layer: the Theory, Formulations of the Boundary- Value Problems and the Applications

Two-dimensional, averaged over the thickness of the layer, mathematical theory of the spreading of a plastic layer on the plane has been studied. General and simplified mathematical formulations of boundary value problem were presented. The problem of plastic stretching of a strip by forces applied on its “clamped” ends was investigated. The analysis of various modes of the process was carried out, which are determined by both the total compression force of the ends and the total tensile force. Mathematical analogy between the process of the free spreading of a plastic layer on the plane and the process of heat transfer was studied. For known forms of a domain occupied by a thin plastic layer at the initial time and for a given law of convergence of the plates, the evolution of the boundary of a plastic layer spreading was described. The exact particular solutions of the aforementioned problem was obtained