On a Class of Recursively Enumerable Sets

We define a class of so-called ∑(n)-sets as a natural closure of recursively enumerable sets W_n under the relation “∈” and study its properties.     

Experimental and numerical study of installing a dune model in a 90° bend in the horizontal-vertical pneumatic conveying system

In the pneumatic conveying process, particles move to the bend under the influence of inertia to form a particle rope, which will cause serious wear between the particles and the pipe wall, and then the dune model is designed and installed in the 90° bend to reduce energy consumption and wear in this study. Firstly, the minimum pressure drop velocity of particles transported by different size dune models was obtained through experimental study. Then the energy saving mechanism of the dune model is studied by CFD-DEM coupling. The experimental results show that the installation of the dune model reduces the minimum pressure drop velocity. The numerical simulation results show that the number of collisions between the particles and the tube wall in the vertical tube decreases after the installation of the dune model, which reduces the energy loss. Moreover, the increasing of tail size of the dune model is beneficial to the diffusion and acceleration of the particles in the vertical tube.     

Tiny families of functions with random properties: A quality-size trade-off for hashing

We present three explicit constructions of hash functions, which exhibit a trade-off between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudorandom property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing property—mapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction property—mapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle, respectively, the extreme situations when the range is very large or very small. We provide lower bounds showing that our constructions are nearly optimal, and mention some applications of the new constructions. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 315–343 (1997)     

随机利率下的风险模型

考虑随机利率情形下关于风险损失(或赔款)的随机风险模型.当随机利率取一般的独立增量过程时,得到了总索赔额精算现值的各阶矩.特别地,当独立增量过程为Wiener过程,损失分布为Pareto分布的情形下,给出了总索赔额精算现值各阶矩的具体表达式.     

Uncomputability and undecidability in economic theory

Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory[Noam Nisan, Tim Roiughgarden, Éva Tardos, Vijay V. Vazirani (Eds.), Algorithmic Game Theory, Cambridge University Press, Cambridge, 2007] and Algorithmic Statistics[Péter Gács, John T. Tromp, Paul M.B. Vitányi, Algorithmic statistics, IEEE Transactions on Information Theory 47 (6) (2001) 2443-2463] are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory - and its applied branches, say computational complexity theory or algorithmic information theory - and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general - but concise - analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory (The qualification ‘recursive’ here has nothing to do with ‘recursion theory’. Instead, this is a reference to the mathematical formalizations of the rational economic agent’s intertemporal optimization problems, in terms of Markov Decision Processes, (Kalman) Filtering and Dynamic Programming, where a kind of ‘recursion’ is invoked in the solution methods. The metaphor of the rational economic agent as a ‘signal processor’ underpins the recursive macroeconomic paradigm.), are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics.     

The complexity of recursive constraint satisfaction problems

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem.     

可见-近红外光谱技术结合递归变量选择算法对土壤全氮与有机质含量测定研究

应用可见-近红外光谱技术进行定量分析时,变量选择起着十分重要的作用。不同土壤样品之间的预测机制可能存在很大差异,当待测样品出现新的特征信息时,基于建模集选择的特征变量不一定能够很好地代表待测样品的有效信息,继续采用原有特征变量建模就易导致预测误差增大。该研究采用递归变量选择方法在预测过程中递归更新土壤全氮与有机质的特征变量,以保持预测模型的鲁棒性;比较了偏最小二乘法(PLS),递归偏最小二乘法(RPLS)和不同递归变量选择方法,如： 变量投影重要性与RPLS相结合(VIP-RPLS), VIP-RPLS, 无信息变量消除法与PLS相结合(UVE-PLS)对于土壤全氮与有机质含量的预测效果。所用195份土壤样品来自浙江省文成县8个乡镇的农田。土壤样品随机分成两部分,一部分作为建模集包含120份样品,另一部分作为预测集包含75份样品。结果表明： VIP-RPLS建立的模型对于预测土壤全氮与有机质含量取得了最优的结果,获得的决定系数(R2)分别为0.85与0.86,获得的预测相对分析误差(RPD)分别为2.6%与2.7%。说明VIP-RPLS通过不断更新模型的特征变量,能够捕获新加入到建模集样品的有效信息。相比于本研究中的其他方法,VIP-RPLS对于土壤全氮与有机质含量具有更高的预测精度。     

Postbuckling Behavior of Thin-Walled Open Cross-Section Compression Members

ABSTRACT

The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated by means of the general nonlinear theory of elastic stability. Fourth-order terms in the series expansion of the total potential energy are disregarded.

It is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one. If the buckling modes are not simultaneous, the equilibrium is neutral in both cases. Finally, the equilibrium at bifurcation is usually unstable if the cross section has no axis of symmetry.     

Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models

This paper presents a new parameter and state estimation algorithm for single-input single-output systems based on canonical state space models from the given input–output data. Difficulties of identification for state space models lie in that there exist unknown noise terms in the formation vector and unknown state variables. By means of the hierarchical identification principle, those noise terms in the information vector are replaced with the estimated residuals and a new least squares algorithm is proposed for parameter estimation and the system states are computed by using the estimated parameters. Finally, an example is provided.     

Recursive state estimation for hybrid systems

The paper deals with recursive state estimation for hybrid systems. An unobservable state of such systems is changed both in a continuous and a discrete way. Fast and efficient online estimation of hybrid system state is desired in many application areas. The presented paper proposes to look at this problem via Bayesian filtering in the factorized (decomposed) form. General recursive solution is proposed as the probability density function, updated entry-wise. The paper summarizes general factorized filter specialized for (i) normal state-space models; (ii) multinomial state-space models with discrete observations; and (iii) hybrid systems. Illustrative experiments and comparison with one of the counterparts are provided.