Search results for "Mathematica"

On Ibn Ezra's Procedure and Shapley Value

2014

We examine ibn Ezra's procedure (Rabinovitch 1973; O'Neill 1982) historically used to solve the Rights Arbitration problem in the general framework of bankruptcy problems. When the greatest claim is larger than or equal to the estate, the procedure is a maximal game (Aumann 2010). However, when the greatest claim is smaller than the estate, the axioms of efficiency (the whole estate is distributed) and satiation are difficult to satisfy simultaneously. We discuss both axioms to show that their importance and necessity are radically different. From then, for the part of the estate not covered by the greatest claim, we examine four possible procedures: the minimal overlap rule, Alcalde et al.…

Seminararbeiten von Semester 71/72, 72, 72/73

1801

Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian

2017

Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.

Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method

2015

ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…

A generalized integration formula for indefinite integrals of special functions

2020

An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...

A third integrating factor for indefinite integrals of special functions

2020

An integrating factor f ~ x is presented involving the terms in y ′ ′ x and q x y x of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey se...

On the time function of the Dulac map for families of meromorphic vector fields

2003

Given an analytic family of vector fields in Bbb R2 having a saddle point, we study the asymptotic development of the time function along the union of the two separatrices. We obtain a result (depending uniformly on the parameters) which we apply to investigate the bifurcation of critical periods of quadratic centres.

An abstract doubly nonlinear equation with a measure as initial value

2007

Abstract The solvability of the abstract implicit nonlinear nonautonomous differential equation ( A ( t ) u ( t ) ) ′ + B ( t ) u ( t ) + C ( t ) u ( t ) ∋ f ( t ) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A ( t ) x and B ( t ) x + C ( t ) x is bounded below.

On the construction of lusternik-schnirelmann critical values with application to bifurcation problems

1987

An iterative method to construct Lusternik-Schnirelmann critical values is presented. Examples of its use to obtain numerical solutions to nonlinear eigenvalue problems and their bifurcation branches are given

A hierarchy of simplified constitutive models within isotropic strain gradient elasticity

2017

Abstract Simplified isotropic models of strain gradient elasticity are presented, based on the mutual relationship between the inherent (dual) gradient directions (i.e. the gradient direction of any strain gradient source and the lever arm direction of the promoted double stress). A class of gradient-symmetric materials featured by gradient directions obeying a reciprocity relation and by 4 independent h.o. (higher order) coefficients is envisioned, along with the sub-classes of hemi-collinear materials (3 h.o. coefficients, gradient directions in part coincident), collinear materials (2 h.o. coefficients, equal gradient directions) and micro-affine materials (1 h.o. coefficient, behavioral…