Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations

We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.     

Exponentially damped operators for a harmonic oscillator linearly coupled to a heat bath

We consider the problem of the dissipative dynamics of a harmonic oscillator linearly coupled to a heat bath. We demonstrate that in addition to the mean energy, there exists an infinite series of quantities exponentially decreasing in time that are means of polynomials of the system Hamiltonian. We obtain the spectrum of the corresponding relaxation times. We propose a method for representing the time characteristics of the system in terms of operators corresponding to the exponentially damped observables. We obtain a recurrence relation for these operators.     

Asymptotic analysis of contact problems between an elastic material and thin-rigid plates

We consider an elastic material in contact with a three-dimensional rigid plate of varying thickness. We suppose that a perfect adhesion occurs along thin zones disposed in a self-similar way on the interface between the two materials. We suppose that the elasticity coefficients in the plate depend on its thickness and tend to infinity as this thickness tends to zero. We derive the effective material properties using Γ-convergence methods.     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.     

Comatrix Coring Generalized and Equivalences of Categories of Comodules

We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings. We apply our results to corings coming from entwining structures and graded structures, and we obtain new results in the setting of entwining structures and in the graded ring theory.     

Some problems of the theory of quantum statistical systems with an energy spectrum of the fractional-power type

We consider the problem of the effective interaction potential in a quantum many-particle system leading to the fractional-power dispersion law. We show that passing to fractional-order derivatives is equivalent to introducing a pair interparticle potential. We consider the case of a degenerate electron gas. Using the van der Waals equation, we study the equation of state for systems with a fractional-power spectrum. We obtain a relation between the van der Waals constant and the phenomenological parameter ??, the fractional-derivative order. We obtain a relation between energy, pressure, and volume for such systems: the coefficient of the thermal energy is a simple function of ??. We consider Bose??Einstein condensation in a system with a fractional-power spectrum. The critical condensation temperature for 1 < ?? < 2 is greater in the case under consideration than in the case of an ideal system, where ?? = 2.     

Fractal methods and the problem of estimating scaling exponents: A new approach based on upper and lower linear bounds

The characterization of irregular objects with fractal methods often leads to the estimation of the slope of a function which is plotted versus a scale parameter. The slope is usually obtained with a linear regression. The problem is that the fit is usually not acceptable from the statistical standpoint. We propose a new approach in which we use two straight lines to bound the data from above and from below. We call these lines the upper and lower linear bounds. We propose to define these bounds as the solution of an optimization problem. We discuss the solution of this problem and we give an algorithm to obtain its solution. We use the difference between the upper and lower linear bounds to define a measure of the degree of linearity in the scaling range. We illustrate our method by analyzing the fluctuations of the variogram in a microresistivity well log from an oil reservoir in the North Sea.     

A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition

We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling’s technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.     

Complex classical fields: An example

We study complex, classical, scalar fields within a new framework introduced in a previous work. We replace the usual functional integral by a complex functional arising from a boosted Hamiltonian. We generalize the Feynman–Kac relation to this setting, and use it to establish the spectral condition on a cylinder. We consider also positive-temperature states.     

Quiver-graded Richardson orbits

In Lie theory, a dense orbit in the nilpotent radical of a parabolic group under the operation of the parabolic is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalizing the classical definition in the case of the general linear group. We define a quasi-hereditary algebra called the nilpotent quiver algebra whose isomorphism classes of Δ-filtered modules correspond to orbits in our generalized setting. We translate the existence of a Richardson orbit into the existence of a rigid Δ-filtered module of a given dimension vector. We study an idempotent recollement of this algebra whose associated intermediate extension functor can be used to produce Richardson orbits in some situations. This can be explicitly calculated in examples. We also give examples where no Richardson orbit exists.     

On Equilibria when Agents Have Multiple Priors

We discuss the existence and the qualitative properties of equilibria when agents have multiple priors and there is only one good in each state of the world. We first prove a general existence result in infinite dimension economies. We then fully describe the equilibria in two special cases. We first consider the case of CEU maximizers that have same capacities. We next consider the case of no aggregate uncertainty. We prove that if agents have non-random initial endowments and are uncertainty averse and maximize the minimal expected utility according to a set of possible priors, then the existence of a common prior is equivalent to the existence of a unique equilibrium, the no-trade equilibrium. We lastly give a mild assumption for indeterminacy of equilibria and compute the dimension of indeterminacy.     

The impact of liberalization on the productive efficiency of Indian commercial banks

We examine the productive efficiency of 70 Indian commercial banks during the early stages (1986–1991) of the ongoing period of liberalization. We use data envelopment analysis to calculate radial technical efficiency scores. We then use stochastic frontier analysis to attribute variation in the calculated efficiency scores to three sources: a temporal component, an ownership component, and a random noise component. We find publicly-owned Indian banks to have been the most efficient, followed by foreign-owned banks and privately-owned Indian banks. We also find a temporal improvement in the performance of foreign-owned banks, virtually no trend in the performance of privately-owned Indian banks, and a temporal decline in the performance of publicly-owned Indian banks. We attempt to explain these patterns in terms of the government's evolving regulatory policies.     

A nonlinear boundary eigenvalue problem for TM-polarized electromagnetic waves in a nonlinear layer

We consider the propagation of TM-polarized electromagnetic waves in a nonlinear dielectric layer located between two linear media. The nonlinearity in the layer is described by the Kerr law. We reduce the problem to a nonlinear boundary eigenvalue problem for a system of ordinary differential equations. We obtain a dispersion relation and a first approximation for eigenvalues of the problem. We compare the results with those obtained for the case of a linear medium in the layer.     

On the Modified Crystalline Stefan Problem with Singular Data

We study the behavior of solutions of the modified Stefan problem in the plane for polygonal interfaces. We are particularly interested in a solution near a singularity of either the loss of a facet or the breaking of a facet. We establish precise regularity results if a facet disappears. We use them to establish the existence of a weak solution with singular data, i.e., when some of the zero-crystalline-curvature facets have zero length.     

Lagrangean relaxation based heuristics for lot sizing with setup times

We consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only. The demand is dynamic over time and there is a single resource of limited capacity. We show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case. We examine the Lagrangean relaxation (LR) of demand constraints in a strong reformulation of the problem. We then design a primal heuristic to generate upper bounds and combine it with the LR problem within a subgradient optimization procedure. We also develop a simple branch and bound heuristic to solve the problem. Computational results on test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature.     

Thin boundary layers of chiral smectics

We consider a reduced Landau–de Gennes energy functional which describes a chiral smectic liquid crystal with large elastic coefficients. We prove that, according to this model, chiral smectics exhibit behavior which is similar to surface superconductivity: a thin layer of smectics near the boundary, and cholesterics in the bulk of the material. We obtain this behavior for a wide region in the parameter space. We show that in a certain limit case this boundary layer can determine the direction of the helical axis of the cholesterics.     

Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations

In this article, we propose a new estimation methodology to deal with PCA for high-dimension, low-sample-size (HDLSS) data. We first show that HDLSS datasets have different geometric representations depending on whether a ρ-mixing-type dependency appears in variables or not. When the ρ-mixing-type dependency appears in variables, the HDLSS data converge to an n-dimensional surface of unit sphere with increasing dimension. We pay special attention to this phenomenon. We propose a method called the noise-reduction methodology to estimate eigenvalues of a HDLSS dataset. We show that the eigenvalue estimator holds consistency properties along with its limiting distribution in HDLSS context. We consider consistency properties of PC directions. We apply the noise-reduction methodology to estimating PC scores. We also give an application in the discriminant analysis for HDLSS datasets by using the inverse covariance matrix estimator induced by the noise-reduction methodology.     

声誉效应与经理报酬契约的关系研究

探讨了声誉对经理报酬契约的影响 .首先 ,分析了经理效用函数的组成 ,将声誉这个隐性激励约束因素引入经理的效用函数 .随后 ,建立了信息不对称下经理的报酬激励模型 .分析了声誉系数对契约中各要素的影响 ,说明了所有者可以利用经理的声誉效应来设计更加有利的报酬契约 .文章最后给出了主要结论 .     

Inverse problems for multi-valued quasi variational inequalities and noncoercive variational inequalities with noisy data

ABSTRACT

We study the inverse problem of identifying a variable parameter in variational and quasi-variational inequalities. We consider a quasi-variational inequality involving a multi-valued monotone map and give a new existence result. We then formulate the inverse problem as an optimization problem and prove its solvability. We also conduct a thorough study of the inverse problem of parameter identification in noncoercive variational inequalities which appear commonly in applied models. We study the inverse problem by posing optimization problems using the output least-squares and the modified output least-squares. Using regularization, penalization, and smoothing, we obtain a single-valued parameter-to-selection map and study its differentiability. We consider optimization problems using the output least-squares and the modified output least-squares for the regularized, penalized and smoothened variational inequality. We give existence results, convergence analysis, and optimality conditions. We provide applications and numerical examples to justify the proposed framework.     

基于因变量抽样设计下线性回归模型的假设检验问题

在许多大型队列研究中,采用节约成本并能提高效率的抽样机制至关重要,基于因变量的抽样设计正是这样一种有偏抽样机制.这种方法最大的优点在于:能够将资源集中在那些包含有更多的协变量与因变量关系信息的研究群体上.本文研究基于因变量抽样设计下的线性模型中回归方程显著性检验以及回归系数显著性检验问题.基于一种半参数经验轮廓似然的方法,我们分别为回归方程检验与回归系数检验提出了相应的检验统计量,获得了所提出检验统计量的渐近性质.通过模拟研究评估了所提出的检验方法在有限样本下的表现,并应用提出的方法分析了一个孕妇分娩的实际数据.