Combining approximate solutions for linear discrete ill-posed problems

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems.     

How do we know who to include in collaborative research? Toward a method for the identification of experts

Collaborative research, defined as research involving actors participating in the problem situation under study, has an important role in operational research, strategic management and systems thinking. In a recent study, we found that a strong organizational focus incorporated into many soft operational research (OR) approaches is inadequate for studying societal problem situations, which are fragmented and have no clear boundary. Specifically, we failed to find a process of identifying individuals that is capable of representing the perspectives of actors and sufficient for research into societal problem situations. We found no clear terminology accounting for ontological differences between actors, individuals representing them and conceptual representations of acting entities. In response to this gap in the literature, we propose terminology that differentiates among actors (individuals or collective entities in the real world), experts (individuals capable of representing the perspective of an actor) and agents (ideal-typical representations of actors). Based on this terminology, we propose an iterative method to guide the assembly of an expert group to undertake collaborative research into societal problem situations. To demonstrate the application of our method, we present selected insights from our study in an electronic supplement.     

Coupling particle sets of contours and streamline methods for solving convection problems

In this work a particle sets of contours method is coupled with a streamline technique in order to obtain accurate approximations of transport problems. A modified streamline technique is proposed and several bench tests arising in the field of porous media are then simulated to validate the new method.     

Autocorrelation measures for the quadratic assignment problem

In this article we provide an exact expression for computing the autocorrelation coefficient ξ and the autocorrelation length ? of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition. We also provide empirical evidence of the autocorrelation length conjecture in QAP and compute the parameters ξ and ? for the 137 instances of the QAPLIB. Our goal is to better characterize the difficulty of this important class of problems to ease the future definition of new optimization methods. Also, the advance that this represents helps to consolidate QAP as an interesting and now better understood problem.     

Existence of solutions for fractional differential equations with multi-point boundary conditions

We discuss the existence of solutions for a nonlinear multi-point boundary value problem of integro-differential equations of fractional order q ∈ (1, 2]. Our analysis relies on the contraction mapping principle and the Krasnoselskii’s fixed point theorem. Example is provided to illustrate the theory.     

Positive solutions of singular Caputo fractional differential equations with integral boundary conditions

In this paper, we investigate the existence of positive solutions of singular super-linear (or sub-linear) integral boundary value problems for fractional differential equation involving Caputo fractional derivative. Necessary and sufficient conditions for the existence of C³[0, 1] positive solutions are given by means of the fixed point theorems on cones. Our nonlinearity f(t, x) may be singular at t = 0 and/or t = 1.     

Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive numbers ρ<R, there exists a radially symmetric stationary solution with tumor boundary r=R and necrotic core boundary r=ρ. The system depends on a positive parameter μ, which describes the tumor aggressiveness. There also exists a sequence of values μ₂<μ₃<? for which branches of symmetry-breaking stationary solutions bifurcate from the radially symmetric solution branch.     

On the existence of weak solutions to the equations of steady flow of heat-conducting fluids with dissipative heating

We study a system of partial differential equations describing the steady flow of a heat conducting incompressible fluid in a bounded three dimensional domain, where the right-hand side of the momentum equation includes the buoyancy force. In the present work we prove the existence of a weak solution under both the smallness and a sign condition on physical parameters α₀ and α₁ which appear on the right hand side.     

(R,S,μ)对称矩阵逆问题和最佳逼近问题及扰动分析

称R∈C^m×m为k次轮换矩阵若 R的最小多项式为x^k-1(k≥2).令μ∈{0,1,…,k-1}和ζ=e^2πi/k.若R∈C^m×m和S∈C^n×n为k次轮换矩阵,则称A∈C^m×m为(R,S,μ)对称矩阵若RAS^-1=ζ^μA.本文研究了(R,S,μ) 对称矩阵的逆问题和最佳逼近问题,得到了解的表达式. 并讨论了最佳逼近解的扰动分析,得到了比较满意的理论结果, 最后通过数值算例验证了该理论结果的正确性.