Analysis of the core of multisided Böhm-Bawerk assignment markets

We introduce the class of multisided Böhm-Bawerk assignment games which generalizes the well-known two-sided Böhm-Bawerk assignment games to markets with an arbitrary number of sectors. We reach the core and the corresponding extreme allocations of any multisided Böhm-Bawerk assignment game by means of an associated convex game defined on the set of sectors instead of the set of sellers and buyers. We also study when the core of a multisided Böhm-Bawerk assignment game is stable in the sense of von Neumann–Morgenstern.     

The core and nucleolus of games: A note on a paper by Göthe-Lundgren et al.

In the paper “On the nucleolus of the basic vehicle routing game”, Mathematical Programming 72, 83–100 (1996), G?the-Lundgren et al. develop a constraint generation method to compute the pre-nucleolus of a game. Their method assumes that constraints that are redundant in the representation of the core can be ignored in the computation of the pre-nucleolus. We provide an example that shows that for a game with an empty core such an assumption is, in general, not valid. Further, we show that a statement made by G?the-Lundgren et al. about an intuitive interpretation of the pre-nucleolus is misleading. Received: January 1996 / Accepted: February 2000?Published online January 17, 2001     

Pseudoisotopies and the Bökstedt trace

In this paper we study the group of isotopy classes of pseudoisotopies of a compact manifold of high dimension. We set up Igusa’s exact sequence from the point of view of A-theory and use the Bökstedt trace map to detect elements coming from the \({Wh^+_1}\) -term. The main result relates the non-vanishing of \({\pi_0\mathcal{P}(M)}\) to a curious question in group theory.     

The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schrödinger Operators

We give a necessary and sufficient condition for the maximum principle of Schrödinger operators in terms of the bottom of the spectrum of time-changed processes. As a corollary, we obtain a sufficient condition for the Liouville property of Schrödinger operators.     

The Schrödinger kernel of the twisted Laplacian and cyclic models

We give a rigorous derivation of the integral kernel of the Schrödinger equation governed by the twisted Laplacian and give an interpretation in terms of cyclic models in physics.     

The structure of solutions of the Schrödinger equation

The goal of the paper is to study the structure of the eigenfunctions of the one-dimensional Schrödinger equation from the point of view of the Euler theorem. It turns out that analog of exponent is exponentially increasing solution. Sometimes linear combinations of such solutions cancel each other at infinity and then we obtain an eigenfunction from L₂(R¹).     

On the freeness of Böröczky line arrangements

Periodica Mathematica Hungarica - In the present note, we focus on the freeness and some combinatorial properties of line arrangements in the projective plane having only double and triple points....     

Solving the Rectangular assignment problem and applications

The rectangular assignment problem is a generalization of the linear assignment problem (LAP): one wants to assign a number of persons to a smaller number of jobs, minimizing the total corresponding costs. Applications are, e.g., in the fields of object recognition and scheduling. Further, we show how it can be used to solve variants of the LAP, such as the k-cardinality LAP and the LAP with outsourcing by transformation. We introduce a transformation to solve the machine replacement LAP.     

The elliptic-in-t solutions of the nonlinear Schrödinger equation

Four various anzatzes of the Krichever curves for the elliptic-in-t solutions of the nonlinear Schrödinger equation are considered. An example is given.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 188–200, May, 1996.Translated by V. I. Serdobol'skii.     

The Dynamics of Zeros of Finite-Gap Solutions of the Schrödinger Equation

We study a system of particles on a Riemann surface with a puncture. This system describes the behavior of zeros of finite-gap solutions of the Schrödinger equation corresponding to a degenerate hyperelliptic curve. We show that this system is Hamiltonian and integrable by constructing action-angle type coordinates.     

The number of eigenvalues of the two-particle discrete Schrödinger operator

We consider the two-particle discrete Schrödinger operator associated with the Hamiltonian of a system of two particles (fermions) interacting only at the nearest neighbor sites. We find the number and the location of the eigenvalues of this operator depending on the particle interaction energy, the system quasimomentum, and the dimension of the lattice ? ^ν , ν ≥ 1.     

Realization of Configurations and the Löwner Ellipsoid

It is proved that any subset of an (m-1)-dimensional sphere of volume larger than l(m+ 1) of the volume of the entire sphere contains l+ 1 points forming a regular l-dimensional simplex. As a corollary, it is obtained that, if the exterior of a given m-dimensional filled ellipsoid contains no more than the 1/(m+ 1) fraction of some sphere, then the volume of the ellipsoid is no less than the volume of the corresponding ball. The existence of a pair of points a given spherical distance apart in a set of positive measure is examined.     

The r-Stirling numbers of the first kind in terms of the Möbius function

The Ramanujan Journal - The main result of this paper is an identity expressing the r-Stirling number of the first kind as a sum involving binomial coefficients and the Möbius function of the...     

On FC-Purity and I-Purity of Modules and Köthe Rings

In this article, several characterizations of certain classes of rings via FC-purity and I-purity are considered. Among others results, it is shown that every I-pure injective left R-module is projective if and only if every FC-pure projective left R-module is injective, if and only if, R is a semisimple ring. In particular, the structures of FC-pure projective and I-pure projective modules over a left Artinian ring are completely described. Also, it is shown that every left R-module is FC-pure projective if and only if every indecomposable left R-module is a finitely presented cyclic R-module, if and only if, R is a left Köthe ring. Finally, we introduce FC-pure flatness and I-pure flatness of modules and several characterizations of these notions are given. In particular, we show that a commutative ring R is quasi-Frobenius if and only if R is an Artinian ring and I-pure injective, if and only if, R is an Artinian ring and the injective envelope E(R) is an FC-pure projective R-module.     

The Equivalence of the DFA and OFA Automate

ＴｈｅＥｑｕｉｖａｌｅｎｃｅ　ｏｆｔｈｅＰＦＡａｎｄＯＦＡＡｕｔｏｍａｔａＴｈｅＥｑｕｉｖａｌｅｎｃｅｏｆｔｈｅＰＦＡａｎｄＯＦＡＡｕｔｏｍａｔａ￥／／ＬｉＧｕｏｃａｉａｎｄＷａｎｇＣｈｕａｎｈｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，...     

The quantum mechanical virial theorem and the absence of positive energy bound states of Schrödinger operators

For a class of potentialsq which may become as singular asr ^?2 at the origin we show that the eigenfunctionsu of the Friedrichs extensionT _Fof (?Δ+q)?C ₀ ^∞ (R ⁿ /{0}) satisfy the virial theorem 2(?Δu,u)=(u,rq,u). Two proofs of this relation are given. One extends the Fock-Weidmann method of scale transformations, the other makes an argument by Finkelstein rigorous and can be viewed of as a substitute of the “commutator proof” of (*) employed in the physical literature. The virial theorem provides a convenient tool for proving the nonexistence of eigenvalues embedded in the continuum or the total absence of eigenvalues ofT _F.