水下噪声听觉属性的主观评价与分析

为探求人耳感知水下目标类型的声学因素,研究了水下噪声听觉属性空间的维度数及其各维度的物理解释.首先通过词汇聚类分析和问卷调查确定评价水下噪声听觉属性的汉语描述词,然后完成基于成对比较法和语义细分法的主观评价实验,获得听觉属性的不相似性矩阵及各样本在不同听觉属性下的主观评价分值.最后,利用多维尺度分析确定水下噪声听觉属性空间由五个维度组成,再利用主成分分析得到独立的五个主成分,进而利用相关系数和压力值确定五个主成分分别表示听觉属性空间的五个维度,根据各个主成分对应的汉语描述词所反映的听觉属性对其进行物理解释 关键词： 听觉属性 多维尺度分析 主成分分析     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks

We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial （finite） number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n（·） = Znt（√n·）, where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/4.In addition,if 1/4〈β〈1/2 then n-^（2β-1/2）Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit.     

Exact Anomalous Dimensions of Composite Operators in the Obukhov–Kraichnan Model

We consider two stochastic equations that describe the turbulent transfer of a passive scalar field (x)(t,x) and generalize the known Obukhov–Kraichnan model to the case of a possible compressibility and large-scale anisotropy. The pair correlation function of the field (x) is characterized by an infinite collection of anomalous indices, which have previously been found exactly using the zero-mode method. In the quantum field formulation, these indices are identified with the critical dimensions of an infinite family of tensor composite operators that are quadratic in the field (x), which allows obtaining exact values for the latter (the values not restricted to the -expansion) and then using them to find the corresponding renormalization constants. The identification of the correlation function indices with the composite-operator dimensions itself is supported by a direct calculation of the critical dimensions in the one-loop approximation.     

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

Burgers方程的一类自相似解

利用李群理论中的伸缩变换群,将二阶非线性偏微分方程-Burgers方程化为一类Riccati方程和三类二阶非线性常微分方程,从而Riccati方程和这三类二阶非线性常微分方程给出了Burgers方程的自相似解的表现形式.     

Hopfield neural networks in large-scale linear optimization problems

Hopfield neural networks and affine scaling interior point methods are combined in a hybrid approach for solving linear optimization problems. The Hopfield networks perform the early stages of the optimization procedures, providing enhanced feasible starting points for both primal and dual affine scaling interior point methods, thus facilitating the steps towards optimality. The hybrid approach is applied to a set of real world linear programming problems. The results show the potential of the integrated approach, indicating that the combination of neural networks and affine scaling interior point methods can be a good alternative to obtain solutions for large-scale optimization problems.     

Remarks on asymptotic behaviors of strong solutions to a viscous Boussinesq system

In this paper, we first address the space‐time decay properties for higher‐order derivatives of strong solutions to the Boussinesq system in the usual Sobolev space. The decay rates obtained here are optimal. The proof is based on a parabolic interpolation inequality, bootstrap argument, and some weighted estimates. Secondly, we present a new solution integration formula for the Boussinesq system, which will be employed to establish the existence of strong solutions for small initial data in some scaling invariant function spaces. The smallness conditions are somehow weaker than those presented by Brandolese and Schonbek. We further investigate the asymptotic profiles and decay properties of these strong solutions. Copyright © 2016 John Wiley & Sons, Ltd.