On Some Feasibility Conditions in MPEC

This article discusses feasibility conditions in mathematical programs with equilibrium constraints （MPECs）. The authors prove that two sufficient conditions guarantee the feasibility of these MPECs. The authors show that the two feasibility conditions are different from the feasibility condition in [2, 3], and show that the sufficient condition in [3] is stronger than that in [2].     

A nonlocal nonlinear diffusion equation in higher space dimensions

We study the initial-value problem for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation, in the whole RN, N?1, or in a bounded smooth domain with Neumann or Dirichlet boundary conditions. First, we prove the existence, uniqueness and the validity of a comparison principle for solutions of these problems. In RN we show that if initial data is bounded and compactly supported, then the solutions is compactly supported for all positive time t, this implies the existence of a free boundary. Concerning the Neumann problem, we prove that the asymptotic behavior of the solutions as t→∞, they converge to the mean value of the initial data. For the Dirichlet problem we prove that the asymptotic behavior of the solutions as t→∞, they converge to zero.     

An acceleration of Erlenkotter-Körkel’s algorithms for the uncapacitated facility location problem

This contribution is focused on an acceleration of branch and bound algorithms for the uncapacitated facility location problem. Our approach is based on the well-known Erlenkotters’ procedures and Körkels’ multi-ascent and multi-adjustment algorithms, which have proved to be the efficient tools for solving the large-sized instances of the uncapacitated facility location problem. These two original approaches were examined and a thorough analysis of their performance revealed how each particular procedure contributes to the computational time of the whole algorithms. These analyses helped us to focus our effort on the most frequent procedures. The unique contribution of this paper is a new dual ascent procedure. This procedure leads to considerable acceleration of the lower bound computation process and reduces the resulting computational time. To demonstrate more efficient performance of amended algorithms we present the results of extensive numerical experiments.     

线性互补问题的一类新的带参数价值函数的阻尼牛顿法

本文给出了线性互补问题LCP(q ,M)的一类新的带参数光滑价值函数 ,基此价值函数提出了一种阻尼牛顿类算法 ,并证明了当M为P 矩阵时 ,该算法全局收敛且有限步终止 .通过数值实验说明了该算法高效可靠 .与互补问题的磨光方程组中所采用的带参数价值函数不同 ,这里的参数最终并不趋向于零 ,而是趋向于被称作解的乘子向量 (与凸非线性极小极大问题的Lagrange乘子完全一致 ) ,这一思想是本文作者首次提出来的 ,同时本文中所采用的阻尼牛顿类方法也有其独到之处 ,在互补问题的研究中有进一步发展的潜力     

Robustness and nondegenerateness for linear complementarity problems

In this paper the main focus is on a stability concept for solutions of a linear complementarity problem. A solution of such a problem is robust if it is stable against slight perturbations of the data of the problem. Relations are investigated between the robustness, the nondegenerateness and the isolatedness of solutions. It turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated. Since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set, attention is paid to Garcia's classG _n of linear complementarity problems. The nondegenerate problems inG _n form an open set.     

研测动态问题的旋转孔径散斑照相法Ⅰ:双孔、四扇孔

本文提出一种研测动态问题的实验新方法——旋转孔径散斑照相法。该法设备简单,利用一个旋转孔径装置,能在一张散斑图上记录下物体动态变形的全过程,然后在全场波滤分析时把各瞬时的信息分离出来,可得任意时刻的瞬态位移场。转孔法能应用于振动和非周期性动态问题,并以三个实验证实其可行性。实验结果表明,散斑条纹清晰可靠,定量分析与其它方法所得结果一致。     

A complete closed form vectorial solution to the Kepler problem

The paper gives an exact vectorial solution to the Kepler problem. A vectorial regularization that linearizes the Kepler problem is given using a Sundman transformation. Closed form expressions describing the Keplerian motion are deduced. A unified approach to the classic Kepler problem is offered, by studying both rectilinear and non-rectilinear Keplerian motions with the same instrument. The approach is an elementary one and only simple vectorial computations are involved.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

A Traditional Scientific Perspective on the Integrated Information Theory of Consciousness

This paper assesses two different theories for explaining consciousness, a phenomenon that is widely considered amenable to scientific investigation despite its puzzling subjective aspects. I focus on Integrated Information Theory (IIT), which says that consciousness is integrated information (as ϕ^Max) and says even simple systems with interacting parts possess some consciousness. First, I evaluate IIT on its own merits. Second, I compare it to a more traditionally derived theory called Neurobiological Naturalism (NN), which says consciousness is an evolved, emergent feature of complex brains. Comparing these theories is informative because it reveals strengths and weaknesses of each, thereby suggesting better ways to study consciousness in the future. IIT’s strengths are the reasonable axioms at its core; its strong logic and mathematical formalism; its creative “experience-first” approach to studying consciousness; the way it avoids the mind-body (“hard”) problem; its consistency with evolutionary theory; and its many scientifically testable predictions. The potential weakness of IIT is that it contains stretches of logic-based reasoning that were not checked against hard evidence when the theory was being constructed, whereas scientific arguments require such supporting evidence to keep the reasoning on course. This is less of a concern for the other theory, NN, because it incorporated evidence much earlier in its construction process. NN is a less mature theory than IIT, less formalized and quantitative, and less well tested. However, it has identified its own neural correlates of consciousness (NCC) and offers a roadmap through which these NNCs may answer the questions of consciousness using the hypothesize-test-hypothesize-test steps of the scientific method.