401 research outputs found
Chebyshev solution of large linear systems
AbstractThe general problem considered is that of solving a linear system of equations which is singular or almost singular. A method is described which obtains a “solution” to the system which is stable with respect to small changes in the matrix elements. This method will solve an overdetermined system in m variables and n equations (m<n) even when the system rank is less than m, and should therefore be very useful in many statistical applications. In this case the error of the system is minimized in the Chebyshev norm using a linear programming formulation and solution. A numerical example using the Hilbert matrix is described in detail
A collocation method for parabolic quasilinear problems on general domains
AbstractA collocation method is described which obtains approximate solutions to quasilinear parabolic problems on a general two-dimensional domain. The method is best suited for obtaining robust solutions to smooth problems with the accuracy required in most engineering applications. The solution is obtained in terms of a finite element, B-spline basis. An interactive computer graphics system is used for both problem formulation and the subsequent display of selected results. The theoretical basis for the method is discussed, and some typical computational results are presented
Bounds for the solution set of linear complementarity problems
AbstractWe give here bounds for the feasible domain and the solution norm of Linear Complementarity Problems (LCP). These bounds are motivated by formulating the LCP as a global quadratic optimization problem and are characterized by the eigenstructure of the corresponding matrix. We prove boundedness of the feasible domain when the quadratic problem is concave, and give easily computable bounds for the solution norm for the convex case. We also obtain lower and upper bounds for the solution norm of the general nonconvex problem
Adiabatic following criterion, estimation of the nonadiabatic excitation fraction and quantum jumps
An accurate theory describing adiabatic following of the dark, nonabsorbing
state in the three-level system is developed. An analytical solution for the
wave function of the particle experiencing Raman excitation is found as an
expansion in terms of the time varying nonadiabatic perturbation parameter. The
solution can be presented as a sum of adiabatic and nonadiabatic parts. Both
are estimated quantitatively. It is shown that the limiting value to which the
amplitude of the nonadiabatic part tends is equal to the Fourier component of
the nonadiabatic perturbation parameter taken at the Rabi frequency of the
Raman excitation. The time scale of the variation of both parts is found. While
the adiabatic part of the solution varies slowly and follows the change of the
nonadiabatic perturbation parameter, the nonadiabatic part appears almost
instantly, revealing a jumpwise transition between the dark and bright states.
This jump happens when the nonadiabatic perturbation parameter takes its
maximum value.Comment: 33 pages, 8 figures, submitted to PRA on 28 Oct. 200
A spatially-VSL gravity model with 1-PN limit of GRT
A scalar gravity model is developed according the 'geometric conventionalist'
approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach
1957, Gruenbaum1973). In principle this approach allows an alternative
interpretation and formulation of General Relativity Theory (GRT), with
distinct i) physical congruence standard, and ii) gravitation dynamics
according Hamilton-Lagrange mechanics, while iii) retaining empirical
indistinguishability with GRT. In this scalar model the congruence standards
have been expressed as gravitationally modified Lorentz Transformations
(Broekaert 2002). The first type of these transformations relate quantities
observed by gravitationally 'affected' (natural geometry) and 'unaffected'
(coordinate geometry) observers and explicitly reveal a spatially variable
speed of light (VSL). The second type shunts the unaffected perspective and
relates affected observers, recovering i) the invariance of the locally
observed velocity of light, and ii) the local Minkowski metric (Broekaert
2003). In the case of a static gravitation field the model retrieves the
phenomenology implied by the Schwarzschild metric. The case with proper source
kinematics is now described by introduction of a 'sweep velocity' field w: The
model then provides a hamiltonian description for particles and photons in full
accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972,
Will 1993).Comment: v1: 11 pages, GR17 conf. paper, Dublin 2004, v2: WEP issue solved,
section on acceleration transformation added, text improved, more references,
same results, v3: typos removed, footnotes, added and references updated, v4:
appendix added, improved tex
Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management
We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier’s profit depends not only on its own delivery frequency, but also on other suppliers’ frequencies through their impact on manufacturer’s purchase allocation to the suppliers. We first solve the follower’s (manufacturer’s) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders’ (suppliers’) game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved
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