Rudimentary Languages and Second-Order Logic

The aim of this paper is to point out the equivalence between three notions respectively issued from recursion theory, computational complexity and finite model theory. One the one hand, the rudimentary languages are known to be characterized by the linear hierarchy. On the other hand, this complexity class can be proved to correspond to monadic second-order logic with addition. Our viewpoint sheds some new light on the close connection between these domains: We bring together the two extremal notions by providing a direct logical characterization of rudimentary languages and a representation result of second-order logic into these languages. We use natural arithmetical tools, and our proofs contain no ingredient from computational complexity.     

Anisotropic Second-Order Fluid

A classification of fluids is presented in accordance with the terminology of the school of rational mechanics. Rheological equations of state are formulated for an anisotropic second-order fluid. A qualitative assumption is made in regard to the rheological behavior of a dilute suspension of rigid ellipsoids of revolution whose dispersion medium is modeled by a second-order fluid.     

模糊选择函数的合理性及拟传递合理性的刻画

首先给出模糊选择函数合理性的一个充分必要条件。然后将普通情况下Schw artz所提出的收缩扩张公理模糊化,在选择集为正规模糊集的前提下,研究了模糊选择函数拟传递合理性的刻画问题。我们指出,该模糊化后的条件仍是选择函数拟传递合理的必要条件,但已不再是拟传递合理的充分条件(我们用例子说明了这一点)。因此,在文章的最后,给出了比较强的一个充分条件。     

Constant-Rank Condition and Second-Order Constraint Qualification

The constant-rank condition for feasible points of nonlinear programming problems was defined by Janin (Math. Program. Study 21:127–138, 1984). In that paper, the author proved that the constant-rank condition is a first-order constraint qualification. In this work, we prove that the constant-rank condition is also a second-order constraint qualification. We define other second-order constraint qualifications.     

Wisdom, Knowledge and Rationality

After surveying the strengths and weaknesses of several well-known approaches to wisdom, I argue for a new theory of wisdom that focuses on being epistemically, practically, and morally rational. My theory of wisdom, The Deep Rationality Theory of Wisdom, claims that a wise person is a person who is rational and who is deeply committed to increasing his or her level of rationality. This theory is a departure from theories of wisdom that demand practical and/or theoretical knowledge. The Deep Rationality Theory salvages all that is attractive, and avoids all that is problematic, about theories of wisdom that require wise people to be knowledgeable.     

Second-Order Epi-Derivatives of Composite Functionals

We compute two-sided second-order epi-derivatives for certain composite functionals f=gF where F is a C ¹ mapping between two Banach spaces X and Y, and g is a convex extended real-valued function on Y. These functionals include most essential objectives associated with smooth constrained minimization problems on Banach spaces. Our proof relies on our development of a formula for the second-order upper epi-derivative that mirrors a formula for a second-order lower epi-derivative from [7], and the two-sided results we obtain promise to support a more precise sensitivity analysis of parameterized optimization problems than has been previously possible.     

Second-Order Analysis of Penalty Function

By exploiting second-order analysis, in particular sufficient and representation conditions, it is shown how to achieve global exact penalty functions for constrained optimization. Some remarks are made on how to continue such an investigation.     

On Second-Order Almost-Periodic Elliptic Operators

The paper considers second-order, strongly elliptic, operatorsH with complex almost-periodic coefficients in divergence formon R^d. First, it is proved that the corresponding heat kernelis Hölder continuous and Gaussian bounds are derived withthe correct small and large time asymptotic behaviour on thekernel and its Hölder derivatives. Secondly, it is establishedthat the kernel has a variety of properties of almost-periodicity.Thirdly, it is demonstrated that the kernel of the homogenization of H is the leading term inthe asymptotic expansion of t K_t.     

Second-Order Degenerate Identification Differential Problems

We are concerned with second-order degenerate identification problems related to closed operators in a Banach space. Suitable hypotheses on the involved operators are made in order to reduce the given problem to a solvable first-order problem of (weak) parabolic type. Some applications to partial differential equations are given to show the fullness of our abstract results. The last two authors are members of GNAMPA, the Italian Istituto Nazionale di Alta Matematica (INdAM).     

二阶跟踪—微分器的频率特性

本文给出二阶跟踪—微分器的频率特性 ,此频率特性类似于二阶线性低通滤波器的频率特性 ,但具有线性系统所没有的优点 ,即通带内有较小的相移 ,且无谐振现象 .同时 ,文中指出频率特性与跟踪参数和正弦输入信号幅值之间的关系就是一个简单的“平移”     

Preferences for harmony and minority voting

We examine repeated collective decisions in which people care about how others are treated. We formulate the notion of preferences for harmony as the desire of a person that others should not suffer repeatedly from the tyranny of majorities. We suggest that minority voting is a suitable scheme for such problems. Under such a scheme, only members of the minority in one decision are allowed to vote in the next decision. We discuss a variety of applications and avenues for future research.     

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

We consider differential–difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.     

Partial Second-Order Subdifferentials in Variational Analysis and Optimization

This article presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial second-order subdifferentials to Lipschitzian stability of stationary point mappings in parametric constrained optimization and discuss some other applications.     

Second-Order Efficiency Conditions and Sensitivity of Efficient Points

The paper deals with necessary and sufficient efficiency conditions of first and second order in vector differential optimization in Banach spaces. The conditions presented ensure the Fréchet sensitivity of efficient (Pareto) points for a perturbed problem. In finite dimension, weaker conditions ensure the Lipschitz sensitivity and existence of directional derivatives of perturbed efficient points.     

First and Second-Order Lagrange Claims for Set-Valued Maps

In this note, we derive first and second-order necessary (resp. sufficient) conditions for local minimum (resp. strict local minimum) points of optimization problems governed by set-valued maps. This allows us to present and to solve a generalized Lagrange claim in a multivalued setting.     

偏好的对子态可分性

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．     

Optimization of Second-Order Discrete Approximation Inclusions

The present article studies the approximation of the Bolza problem of optimal control theory with a fixed time interval given by convex and non-convex second-order differential inclusions (P _C ). Our main goal is to derive necessary and sufficient optimal conditions for a Cauchy problem of second-order discrete inclusions (P _D ). As a supplementary problem, discrete approximation problem (P _DA ) is considered. Necessary and sufficient conditions, including distinctive transversality, are proved by incorporating the Euler-Lagrange and Hamiltonian type of inclusions. The basic concept of obtaining optimal conditions is the locally adjoint mappings (LAM) and equivalence theorems, one of the most characteristic features of such approaches with the second-order differential inclusions that are peculiar to the presence of equivalence relations of LAMs. Furthermore, the application of these results are demonstrated by solving some non-convex problem with second-order discrete inclusions.     

二阶动态亚格子尺度应力模型

提出了一个基于亚格子尺度应力与速度梯度张量之间关系的二阶动态模型.然后利用在高雷诺数的流场直接数值解的结果对此二阶模型进行检验.直接数值解的流场包括均匀各向同性强迫湍流,衰减湍流以及均匀旋转湍流.数值检验结果发现与一阶动态模型相比,二阶模型的相关系数提高.