scholarly journals The Owen Value of Stochastic Cooperative Game

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Cheng-Guo E ◽  
Quan-Lin Li ◽  
Shi-Yong Li
Keyword(s):  
Explicit Expression ◽  
Cooperative Game ◽  
Existence And Uniqueness ◽  
Classical Case ◽  
Owen Value ◽  
Definition Of

We consider stochastic cooperative game and give it the definition of the Owen value, which is obtained by extending the classical case. Then we provide explicit expression for the Owen value of the stochastic cooperative game and discuss its existence and uniqueness.

scholarly journals Owen-stable coalition partitions in games with vector payoffs

2019 ◽  
Vol 10 (3) ◽  
pp. 3-23 ◽  
Author(s):  
Василий Гусев ◽  
Vasily Gusev ◽  
Владимир Мазалов ◽  
Vladimir Mazalov
Keyword(s):  
Characteristic Function ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Owen Value ◽  
Stable Coalition ◽  
Vector Payoffs ◽  
Definition Of ◽  
Games With Vector Payoffs

The paper is devoted to the study of multicriteria cooperative games with vector payoffs and coalition partition. The imputation which is based on the concept of the Owen value is proposed. We use it for the definition of stable coalition partition for bicriteria games. In three person cooperative game with 0-1 characteristic function the conditions under which the coalition partition is stable are found.

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

scholarly journals Theory of existence and uniqueness for the nonlinear Maxwell-Boltzmann equation I

1977 ◽  
Vol 16 (3) ◽  
pp. 379-414 ◽  
Author(s):  
Aleksander Glikson
Keyword(s):  
Boltzmann Equation ◽  
Existence And Uniqueness ◽  
Broad Class ◽  
Physical Space ◽  
Uniqueness Result ◽  
Cauchy Problems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Boltzmann Gas ◽  
Definition Of

A review of the development of the theory of existence and uniqueness of solutions to initial-value problems for mostly reduced versions of the nonlinear Maxwell-Boltzmann equation with a cut-off of intermolecular interaction, precedes the formulation and discussion of a somewhat generalized initial-value problem for the full nonlinear Maxwell-Boltzmann equation, with or without a cut-off. This is followed by a derivation of a new existence-uniqueness result for a particular Cauchy problem for the full nonlinear Maxwell-Boltzmann equation with a cut-off, under the assumption that the monatomic Boltzmann gas in the unbounded physical space X is acted upon by a member of a broad class of external conservative forces with sufficiently well-behaved potentials, defined on X and bounded from below. The result represents a significant improvement of an earlier theorem by this author which was until now the strongest obtained for Cauchy problems for the full Maxwell-Boltzmann equation. The improvement is basically due to the introduction of equivalent norms in a Banach space, the definition of which is connected with an exponential function of the total energy of a free-streaming molecule.

scholarly journals About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof

2019 ◽  
Vol 22 (4) ◽  
pp. 871-898 ◽  
Author(s):  
Jacky Cresson ◽  
Anna Szafrańska
Keyword(s):  
Local Group ◽  
Type Theorem ◽  
Classical Case ◽  
Alternative Proof ◽  
Lagrangian Systems ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Definition Of ◽  
Variational Symmetries ◽  
Discrete Setting

Abstract Recently, the fractional Noether’s theorem derived by G. Frederico and D.F.M. Torres in [10] was proved to be wrong by R.A.C. Ferreira and A.B. Malinowska in (see [7]) using a counterexample and doubts are stated about the validity of other Noether’s type Theorem, in particular ([9], Theorem 32). However, the counterexample does not explain why and where the proof given in [10] does not work. In this paper, we make a detailed analysis of the proof proposed by G. Frederico and D.F.M. Torres in [9] which is based on a fractional generalization of a method proposed by J. Jost and X.Li-Jost in the classical case. This method is also used in [10]. We first detail this method and then its fractional version. Several points leading to difficulties are put in evidence, in particular the definition of variational symmetries and some properties of local group of transformations in the fractional case. These difficulties arise in several generalization of the Jost’s method, in particular in the discrete setting. We then derive a fractional Noether’s Theorem following this strategy, correcting the initial statement of Frederico and Torres in [9] and obtaining an alternative proof of the main result of Atanackovic and al. [3].

QUANTUM INTEGRAL EQUATIONS OF VOLTERRA TYPE WITH GENERALIZED OPERATOR-VALUED KERNELS

2000 ◽  
Vol 03 (04) ◽  
pp. 505-517 ◽  
Author(s):  
ZHIYUAN HUANG ◽  
CAISHI WANG ◽  
XIANGJUN WANG
Keyword(s):  
Integral Equation ◽  
Explicit Expression ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Uniqueness Of Solutions ◽  
Volterra Type ◽  
Quantum Integral ◽  
Generalized Operator

Quantum integral equation of Volterra type with generalized operator-valued kernel is introduced. Existence and uniqueness of solutions are established, explicit expression of the solution is given, the continuity, continuous dependence on free terms and other properties of the solution are proved.

scholarly journals KHOVANOV HOMOLOGY FOR VIRTUAL KNOTS WITH ARBITRARY COEFFICIENTS

2007 ◽  
Vol 16 (03) ◽  
pp. 345-377 ◽  
Author(s):  
VASSILY OLEGOVICH MANTUROV
Keyword(s):  
Spanning Tree ◽  
Classical Case ◽  
Homology Theory ◽  
Homotopy Equivalent ◽  
Khovanov Homology ◽  
Virtual Knots ◽  
Definition Of

In the present paper, we construct Khovanov homology theory with arbitrary coefficients for arbitrary virtual knots. We give a definition of the complex, which is homotopy equivalent to the initial Khovanov complex in the classical case; our definition works in the virtual case as well. The method used in this work allows us to construct a Khovanov homology theory for "twisted virtual knots" in the sense of Bourgoin and Viro [4, 27] (in particular, for knots in RP3). We also generalize some results of the Khovanov homology for virtual knots with arbitrary atoms (Wehrli and Kofman–Champanerkar spanning tree, minimality problems, Frobenius extensions) and orientable ones (Rasmussen's invariant).

Über die Beziehung der Bispinor-Theorie zur Spinor-Theorie im Riemannschen Raum

1962 ◽  
Vol 17 (9) ◽  
pp. 707-711
Author(s):  
Ernst Schmutzer
Keyword(s):  
Explicit Expression ◽  
Fundamental Notion ◽  
Spinor Geometry ◽  
Mutual Relations ◽  
Definition Of

In the present paper which is a continuation of three earlier works on the theory of spinors and bispinors in RIEMANNean space a general covariant bispinor geometry whithout using any special coordinates or the tedious orthogonal Vierbein-formalism is developped. Departing from the conventional definition of the adjoint bispinor which was the base of SCHRÖDINGER’s generalisation for the RIEMANNean space here a new definition of this fundamental notion is given avoiding many difficulties of SCHRÖDINGER’S theory which are discussed. The whole theory is coincided with the theory of spinor geometry. So it is possible to find an explicit expression for the bispinor affinities. By this work a formal conclusion of the general covariant analytical apparatus of spinor and bispinor theory and of the mutual relations is obtained.

A characterization of probability measures in terms of semi-quantum operators

2019 ◽  
Vol 22 (02) ◽  
pp. 1950009 ◽  
Author(s):  
Gabriela Popa ◽  
Aurel I. Stan
Keyword(s):  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Random Variables ◽  
Finite Family ◽  
Probability Measures ◽  
Existence And Uniqueness Theorem ◽  
Quantum Operators ◽  
Definition Of ◽  
Finite Moments

A canonical definition of the joint semi-quantum operators of a finite family of random variables, having finite moments of all orders, is given first in terms of an existence and uniqueness theorem. Then two characterizations, one for the polynomially symmetric, and another for the polynomially factorizable probability measures, having finite moments of all orders, are presented.

scholarly journals Quantum Turing Machines: Computations and Measurements

2020 ◽  
Vol 10 (16) ◽  
pp. 5551
Author(s):  
Stefano Guerrini ◽  
Simone Martini ◽  
Andrea Masini
Keyword(s):  
Programming Languages ◽  
Classical Case ◽  
Turing Machines ◽  
Quantum Programming Languages ◽  
Quantum Programming ◽  
Definition Of ◽  
Observation Protocol ◽  
Class Of Functions ◽  
Computable Functions ◽  
Arbitrary Quantum

Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not been fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example being the intrinsic infinite nature of any quantum computation. In this paper, we propose a definition of QTM, which extends and unifies the notions of Deutsch and Bernstein & Vazirani. In particular, we allow both arbitrary quantum input, and meaningful superpositions of computations, where some of them are “terminated” with an “output”, while others are not. For some infinite computations an “output” is obtained as a limit of finite portions of the computation. We propose a natural and robust observation protocol for our QTMs, which does not modify the probability of the possible outcomes of the machines. Finally, we use QTMs to define a class of quantum computable functions—any such function is a mapping from a general quantum state to a probability distribution of natural numbers. We expect that our class of functions, when restricted to classical input-output, will not be different from the set of the recursive functions.

scholarly journals Energy and area minimizers in metric spaces

2017 ◽  
Vol 10 (4) ◽  
pp. 407-421 ◽  
Author(s):  
Alexander Lytchak ◽  
Stefan Wenger
Keyword(s):  
Metric Spaces ◽  
Classical Case ◽  
Plateau Problem ◽  
Hölder Exponents ◽  
Area Minimizing ◽  
Definition Of ◽  
Regularity Results ◽  
Quadratic Isoperimetric Inequality ◽  
Energy Minimizers ◽  
Quasi Convexity

AbstractWe show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area has been chosen appropriately. We prove the quasi-convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Hölder exponents of some area-minimizing discs.

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