Finitely maxitive T-conditional possibility theory: Coherence and extension

Starting from the axiomatic definition of finitely maxitive T-conditional possibility (where T is a continuous triangular norm), the paper aims at a comprehensive and self-contained treatment of coherence and extension of a possibilistic assessment defined on an arbitrary set of conditional events. Coherence (or consistence with a T-conditional possibility) is characterized either in terms of existence of a linearly ordered class of finitely maxitive possibility measures (T-nested class) agreeing with the assessment, or in terms of solvability of a finite sequence of nonlinear systems for every finite subfamily of conditional events. Coherence reveals to be a necessary and sufficient condition for the extendibility of an assessment to any superset of conditional events and, in the case of T equal to the minimum or a strict t-norm, the set of coherent values for the possibility of a new conditional event can be computed solving two optimization problems over a finite sequence of nonlinear systems for every finite subfamily of conditional events.     

Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.     

On statistical properties of the lyapunov exponent of the generalized skew tent map

The statistical properties of the Lyapunov exponent of the chaotic generalized skew tent map is studied. Expressions of the mean and the variance of this Lyapunov exponent at each discrete time index are obtained. A sufficient condition for weakly mixing of the chaotic generalized skew tent map is derived, and the asymptotic distribution of its Lyapunov exponent is provided.     

IMPORTANCE MEASURE OF CORRELATED VARIABLES IN POLYNOMIAL OUTPUT

为了解决一般工程问题中输出量为多项式情况下相关正态输入变量的贡献识别问题，以二次不含交叉项的多项输出量为例，利用多维相关正态分布及其条件分布的性质，解析地推导了相关正态输入变量对输出量总方差的独立贡献及相关贡献，采用算例验证了所推导的解析表达式的正确性．文中所推导的相关正态变量独立贡献和相关贡献的表达式可直接用于输出量为二次不含交叉项多项式或一次多项式情况下的输入变量贡献的识别，并且为其他新的算法提供了对照解，另外此方法亦可以推广至含交叉项的高阶多项式，解决更为复杂输出量情况下输入量的贡献识别问题．     

线缆系统电磁脉冲效应测量系统研制和试验

分析了实验室瞬态X射线产生的系统电磁脉冲(SGEMP)效应测试所面临的技术问题,提出了解决方法、措施以及实验室模拟瞬态X射线的SGEMP模拟试验方法。通过电子屏蔽、电磁屏蔽、光电隔离、信号对称提取等特殊技术处理,解决了SGEMP效应模拟试验方法和测量系统抗X射线、抗电磁辐射等技术问题,并在大型瞬态X射线模拟源上,测出了瞬态X射线辐照时金属腔内线缆的SGEMP效应波形及幅值。     

Data envelopment analysis models of investment funds

This paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return-risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research.     

Dahlberg's theorem in higher co-dimension

In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension $n?1$ in ${\mathbb{R}}^n$, and later this result has been extended to more general non-tangentially accessible domains and beyond.In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph Γ of dimension d in ${\mathbb{R}}^n$, $d<n?1$, with a small Lipschitz constant. We construct a linear degenerate elliptic operator L such that the corresponding harmonic measure ${\omega }_L$ is absolutely continuous with respect to the Hausdorff measure on Γ. More generally, we provide sufficient conditions on the matrix of coefficients of L which guarantee the mutual absolute continuity of ${\omega }_L$ and the Hausdorff measure.     

Informational analysis of seismic sequences by applying the Fisher Information Measure and the Shannon entropy: An application to the 2004–2010 seismicity of Aswan area (Egypt)

The interevent-time (IET) and interevent-distance (IED) series of seismic events occurred at Aswan area (Egypt) from 2004 to 2010 were investigated by means of the Fisher Information Measure and the Shannon entropy. The analysis was performed varying the depth and the magnitude thresholds. The results point out to an increase of level of organization and order with the decrease of magnitude threshold and the increase of depth threshold for the IET series, while the IED series are characterized by a level of uncertainty approximately constant with the threshold magnitude. The complexity measure, calculated as the product of the Fisher Information Measure and the Shannon entropy power, presents very similar pattern for both the types of seismic series, indicating an increasing complexity with the decrease of the threshold magnitude and the increase of the threshold depth.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Markov processes conditioned on their location at large exponential times

Suppose that ${\left(X_t\right)}_{t\ge 0}$ is a one-dimensional Brownian motion with negative drift $?\mu$. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like $X$ conditioned to hit 0, after which time it behaves as $X$ killed at the last time $X$ visits 0. Equivalently, the limit process has the dynamics of the killed “bang–bang” Brownian motion that evolves like Brownian motion with positive drift $+\mu$ when it is negative, like Brownian motion with negative drift $?\mu$ when it is positive, and is killed according to the local time spent at 0.An extension of this result holds in great generality for a Borel right process conditioned to be in some state $a$ at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the “bang–bang” construction for a general Markov process.As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the $h$-transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest.