A characterization of the Kalai–Smorodinsky bargaining solution by disagreement point monotonicity

We provide a new axiomatization of the Kalai–Smorodinsky bargaining solution, which replaces the axiom of individual monotonicity by disagreement point monotonicity and a restricted version of Nash’s IIA.     

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows one to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.     

On the size of the set A(A + 1)

Let F _p be the field of a prime order p. For a subset A ì F_p{A \subset F_p} we consider the product set A(A + 1). This set is an image of A ×  A under the polynomial mapping f(x, y) = xy +  x : F _p ×  F _p → F _p . In the present note we show that if |A| <  p ^1/2, then

Extensions of solution concepts by means of multiplicative ɛ-tax games

Multiplicative ɛ-tax games are introduced that are obtained from a game by imposing a tax on any proper coalition. The imposed tax is proportional to the relative reward to the coalition for its formation from the individuals. Of particular interest is the balanced (quasi-balanced, respectively) ɛ-tax game for which the imposed tax is minimal. This least balanced (quasi-balanced) ɛ-tax game is used to extend the concept of the core (τ-value). In a similar way the stable core of a game is introduced by considering the least convex ɛ-tax game.     

A simple characterization of the set ofμ-entropy pairs and applications

We present simple characterizations of the setsE _μ andE _X of measure entropy pairs and topological entropy pairs of a topological dynamical system (X, T) with invariant probability measureμ. This characterization is used to show that the set of (measure) entropy pairs of a product system coincides with the product of the sets of (measure) entropy pairs of the component systems; in particular it follows that the product of u.p.e. systems (topological K-systems) is also u.p.e. Another application is to show that the proximal relationP forms a residual subset of the setE _X . Finally an example of a minimal point distal dynamical system is constructed for whichE _X ∩(X ₀×X ₀)≠ , whereX ₀ is the denseG _δ subset of distal points inX.     

A short proof for the polyhedrality of the Chvátal–Gomory closure of a compact convex set

Recently Schrijver’s open problem, whether the Chvátal–Gomory closure of an irrational polytope is polyhedral was answered independently in the seminal works of Dadush et al. (2011) and Dunkel and Schulz (2010); the former even applies to general compact convex sets. We present a very short, easily accessible proof.     

A continuous extension of the de la Vallée Poussin means

Among the many interesting results of their 1958 paper, G. Pólya and I. J. Schoenberg studied the de la Vallée Poussin means of analytic functions. These are polynomial approximations of a given analytic function on the unit disk obtained by taking Hadamard products of the functionf with certain polynomialsV _n (z), wheren is the degree of the polynomial. The polynomial approximationsV _n *f converge locally uniformly tof asn→∞. In this paper, we define a subordination chainV _λ (z),γ>0, |z|<1, of convex mappings of the disk that for integer values is the same as the previously definedV _n (z). Iff is a conformal mapping of the diskD onto a convex domain, thenV _λ *f→f locally uniformly as λ→∞, and in fact when λ₂ > λ₁. We also consider Hadamard products of theV _λ with complex-valued harmonic mappings of the disk. This work was supported by the Volkswagen Stiftung (RiP-program at Oberwolfach). S. R. received partial support also from INTAS (Project 99-00089) and the German-Israeli Foundation (grant G-643-117.6/1999).     

No characterization of generators in ℓp (1

《Comptes Rendus Mathematique》2008,346(11-12):645-648

A characterization of arithmetical invariants by the monoid of relations

The investigation and classification of non-unique factorization phenomena have attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P. García-Sánchez, together with several co-authors, derived a method to calculate the catenary and tame degree from the monoid of relations, and they applied this method successfully in the case of numerical monoids. In this paper, we investigate the algebraic structure of this approach. Thereby, we dispense with the restriction to finitely generated monoids and give applications to other invariants of non-unique factorizations, such as the elasticity and the set of distances.     

A characterization of finite simple groups by the orders of solvable subgroups

Let G be a finite group and S be a finite simple group. In this paper, we prove that if G and S have the same sets of all orders of solvable subgroups, then G is isomorphic to S, or G and S are isomorphic to Bn(q), Cn(q), where n≥3 and q is odd. This gives a positive answer to the problem put forward by Abe and Iiyori.     

A structural characterization of numéraires of convex sets of nonnegative random variables

We introduce the concept of numéraire s of convex sets in ${L^0_{+}}$ , the nonnegative orthant of the topological vector space L ⁰ of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set ${\mathcal{C} \subseteq L^0_{+}}$ to be a numéraire of ${\mathcal{C}}$ is given, inspired from ideas in financial mathematics.     

On the Chvátal–Gomory closure of a compact convex set

In this paper, we show that the Chvátal–Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver (Ann Discret Math 9:291–296, 1980) for irrational polytopes, and generalizes the same result for the case of rational polytopes (Schrijver in Ann Discret Math 9:291–296, 1980), rational ellipsoids (Dey and Vielma in IPCO XIV, Lecture Notes in Computer Science, vol 6080. Springer, Berlin, pp 327–340, 2010) and strictly convex bodies (Dadush et al. in Math Oper Res 36:227–239, 2011).     

Approximations of functions defined on the real axis by means of de la Vallée-Poussin operators

Asymptotic equations for upper bounds of deviations of the de la Vallée-Poussin operators on C classes in the uniform metric are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 682–691, May, 1992.     

A generalization of the Egalitarian and the Kalai–Smorodinsky bargaining solutions

We characterize the class of weakly efficient n-person bargaining solutions that solely depend on the ratios of the players’ ideal payoffs. In the case of at least three players the ratio between the solution payoffs of any two players is a power of the ratio between their ideal payoffs. As special cases this class contains the Egalitarian and the Kalai–Smorodinsky bargaining solutions, which can be pinned down by imposing additional axioms.     

On the (n − 2)-transversals of n convex subsets of the plane

In this paper we consider families of distinct ovals in the plane, with the property that certain subfamilies have stabbing lines (transversals). Our main result says that if any k member of the family can be stabbed by a line avoiding all the other ovals and k is large enough, then the family consists of at most k+1 ovals. For any n4 we show a family of n ovals, whose n–2 element subfamilies have, but the n–1 element subfamilies do not have, transversals.     

Solution of the neutron transport equation by means of hermite-S ∞-theory

Summary A stable numerical approximation (H -S ) is obtained through the use of Hermite's method of order (H ) in the spatial integration of the 1D neutron transport equation. The theory for =1 is applied to a one-group shielding problem.Numerical calculations show the new method to converge much faster than earlier versions ofS -theory. Comparison ofH ₁-S with the well-knownS _N -code ANISN indicates a large gain in computing time for the former.

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Zusammenfassung Durch Anwendung der Hermiteschen Integrationsmethode der Ordnung (H ) auf die Ortsintegration der 1D Neutronentransportgleichung entsteht eine numerisch stabile Approximation (H -S ). Diese Methode wurde für =1 auf ein 1 Gruppen-Abschirmungsproblem angewandt.Numerische Rechnungen zeigen die wesentlich raschere Konvergenz der Methode verglichen mit den ursprünglichen Versionen derS -Theorie. Durch Vergleich mit dem bekanntenS _N -Code ANISN wurde gezeigt, dass mit derH ₁-S -Methode ein grosser Rechenzeitgewinn erzielt wird.

     

On the divergence of de la Vallée Poussin means of Fourier series

Пусть {λ _{n 1} ^t8 — монотонн ая последовательнос ть натуральных чисел. Дл я каждой функции fεL(0, 2π) с рядом Фурье строятся обобщенные средние Bалле Пуссена $$V_n^{(\lambda )} (f;x) = \frac{{a_0 }}{2} + \mathop \sum \limits_{k = 1}^n (a_k \cos kx + b_k \sin kx) + \mathop \sum \limits_{k = n + 1}^{n + \lambda _n } \left( {1 - \frac{{k - n}}{{\lambda _n + 1}}} \right)\left( {a_k \cos kx + b_k \sin kx} \right).$$ Доказываются следую щие теоремы.

1. Если λ_n=o(n), то существуе т функция fεL(0, 2π), для кот орой последовательность {V_n ^(λ)(?;x)} расходится почти вс юду.
2. Если λ_n=o(n), то существуе т функция fεL(0, 2π), для кот орой последовательность $$\left\{ {\frac{1}{\pi }\mathop \smallint \limits_{ - \pi /\lambda _n }^{\pi /\lambda _n } f(x + t)\frac{{\sin (n + \tfrac{1}{2})t}}{{2\sin \tfrac{1}{2}t}}dt} \right\}$$ расходится почти всю ду

.