Estimating Sampling Errors in REA Survey: A Model Approach for the Synthetic Presentation of Results for Main Variables Involved in Economic Analysis

A new sample business survey for agriculture, the REA survey, and a project of integration with the FADN network (RICA in Italy) have significantly changed the production of statistical information nowadays available with reference to the agricultural sector. On the basis of this relevant information, new economic analyses are being developed on farms’ performance, agricultural households’ income and the Common Agricultural Policy (CAP). In this paper the authors estimate the relationship between the levels of variables of interest and their sampling errors using models in order to improve the accessibility of the information on estimates accuracy to the final users (agricultural analysts, policy makers). The paper is the result of a joint research of the three authors. Sections 1–3 and 6 by Pizzoli, Sects. 4 and 5 by Rondinelli, Sect. 7 by Filiberti, conclusions joint to the three authors.     

Experimental verification of some elastic properties of unidirectional composites

The first part of the paper deals with homogenization models of unidirectional composites, in which each phase of the material is bounded by parallel cylindrical surfaces. For a GFRP with epoxy resin and glass fibres, five elastic constants for six models of the composite are calculated. In the second part, the results of strain gauge tests, photoelasticity investigations, and scanning electron inspection are discussed. With these data, some elastic constants of the composite in tension and compression are found. A comparison of experimental and analytical results is presented. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 195–206, March–April, 2008.     

Acceleration of the EM algorithm using the vector epsilon algorithm

The expectation–maximization (EM) algorithm is a very general and popular iterative computational algorithm to find maximum likelihood estimates from incomplete data and broadly used to statistical analysis with missing data, because of its stability, flexibility and simplicity. However, it is often criticized that the convergence of the EM algorithm is slow. The various algorithms to accelerate the convergence of the EM algorithm have been proposed. The vector ε algorithm of Wynn (Math Comp 16:301–322, 1962) is used to accelerate the convergence of the EM algorithm in Kuroda and Sakakihara (Comput Stat Data Anal 51:1549–1561, 2006). In this paper, we provide the theoretical evaluation of the convergence of the ε-accelerated EM algorithm. The ε-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm, and thus it keeps the flexibility and simplicity of the EM algorithm.     

Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients

This paper is one of a series underpinning the authors’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT, 41 (2001), pp. 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be fully implicit, nonlinear, and contain derivatives of order higher than one. Algorithmic details are given. Second, it proves that either the method succeeds in the sense of computing TCs of the local solution, or one of a number of detectable error conditions occurs. AMS subject classification (2000) 34A09, 65L80, 65L05, 41A58     

Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite

Within the framework of a unified mathematical model based on the Markov chain theory, an attempt is made to describe the distribution of static strength, the fatigue curve, and the accumulation of fatigue damages. It is assumed that the fatigue failure of a test specimen occurs after the destruction of some its critical microvolume consisting of two — elastic (brittle fibers) and plastic (matrix) — parts. In the second part, plastic strains accumulate as soon as the cyclic load exceeds some level. Numerical examples are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 615–630, September–October, 2006.     

Strength and deformation characteristics of poly(ethylene terephtalate)/elastomer blends

Changes in the toughness of crystalline poly(ethylene terephtalate) upon addition of two elastomers — ethylene-propylene-diene terpolymer and ethylene-α-octene copolymer — are investigated. Blends with increasing elastomer content (up to 30 wt.%) were obtained and modified by γ-radiation up to a 300-kGy absorbed dose. The interrelation between the toughness and certain tensile characteristics (elastic modulus, yield stress, ultimate stress, elongation at break, and specific fracture energy) of the blends, with various structural features of components (crystallinity and the degree of cross-linking) and morphology of the blends, is discussed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 521–534, July–August, 2008.     

On the adaptive coupling of FEM and BEM in 2–d–elasticity

Summary. This paper concerns the combination of the finite element method (FEM) and the boundary element method (BEM) using the symmetric coupling. As a model problem in two dimensions we consider the Hencky material (a certain nonlinear elastic material) in a bounded domain with Navier–Lamé differential equation in the unbounded complementary domain. Using some boundary integral operators the problem is rewritten such that the Galerkin procedure leads to a FEM/BEM coupling and quasi–optimally convergent discrete solutions. Beside this a priori information we derive an a posteriori error estimate which allows (up to a constant factor) the error control in the energy norm. Since information about the singularities of the solution is not available a priori in many situation and having in mind the goal of an automatic mesh–refinement we state adaptive algorithms for the –version of the FEM/BEM–coupling. Illustrating numerical results are included. Received April 15, 1994 / Revised version received January 8, 1996     

Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition

In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.     

Optimal shape design in a fibre orientation model

We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown. This research was supported by the Charles University Grant Agency under Contract 6/2005/R, MSM 0021620839 (MŠMT ČR), and the Academy of Finland, Grant #204741.     

On the Self-adjointness of the Product Operators of Two ruth-Order Differential Operators on [0, ＋∞）

In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, ∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.     

Note on implementing the new sphere method for LP using matrix inversions sparingly

A new IPM (interior point method) for LPs has been discussed in Murty (Algorithmic Oper Res 1:3–19, 2006; Tutorials in OR, INFORMS, pp 1–36, 2006) based on a centering step that attempts to maximize the radius of the inscribed sphere with center on the current objective plane, and using descent directions derived without using matrix inversions. The method is a descent method and may be called the sphere method for LP. In contrast to all the existing IPMs which involve heavy matrix inversions in each step, an advantage of the new method is that it can be implemented with no matrix inversions, or using them only sparingly. We discuss various techniques for implementing this method. These implementations offer the prospect of extending the superior performance of existing software systems for LP, to models that do not have the property of being very sparse.     

Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function

 We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd–Omojokun class of algorithms, each step is composed of a quasi-normal and a tangential step. Both steps are required to satisfy a decrease condition for their respective trust-region subproblems. The proposed mechanism for accepting steps combines nonmonotone decrease conditions on the constraint violation and/or the Lagrangian function, which leads to a flexibility and acceptance behavior comparable to filter-based methods. We establish the global convergence of the method. Furthermore, transition to quadratic local convergence is proved. Numerical tests are presented that confirm the robustness and efficiency of the approach. Received: December 14, 2000 / Accepted: August 30, 2001 Published online: September 27, 2002 Key words. nonmonotone trust-region methods – sequential quadratic programming – penalty function – global convergence – equality constraints – local convergence – large-scale optimization Mathematics Subject Classification (2000): 65K05, 90C30     

Lorentz Gas with Thermostatted Walls

In a planar periodic Lorentz gas, a point particle (electron) moves freely and collides with fixed round obstacles (ions). If a constant force (induced by an electric field) acts on the particle, the latter will accelerate, and its speed will approach infinity (Chernov and Dolgopyat in J Am Math Soc 22:821–858, 2009; Phys Rev Lett 99, paper 030601, 2007). To keep the kinetic energy bounded one can apply a Gaussian thermostat, which forces the particle’s speed to be constant. Then an electric current sets in and one can prove Ohm’s law and the Einstein relation (Chernov and Dolgopyat in Russian Math Surv 64:73–124, 2009; Chernov et al. Comm Math Phys 154:569–601, 1993; Phys Rev Lett 70:2209–2212, 1993). However, the Gaussian thermostat has been criticized as unrealistic, because it acts all the time, even during the free flights between collisions. We propose a new model, where during the free flights the electron accelerates, but at the collisions with ions its total energy is reset to a fixed level; thus our thermostat is restricted to the surface of the scatterers (the ‘walls’). We rederive all physically interesting facts proven for the Gaussian thermostat in Chernov, Dolgopyat (Russian Math Surv 64:73–124, 2009) and Chernov et al. (Comm Math Phys 154:569–601, 1993; Phys Rev Lett 70:2209–2212, 1993), including Ohm’s law and the Einstein relation. In addition, we investigate the superconductivity phenomenon in the infinite horizon case.     

Measurement of loading and operations flexibility in flexible manufacturing systems: An information-theoretic approach

An information-theoretic approach is applied for measuring the flexibility in flexible manufacturing systems (FMSs). The general relation between flexibility and entropy is discussed. The entropy for a Markovian process is obtained and then applied to closed queueing network models of FMSs to discuss loading flexibility which arises from the power to regulate the frequency of the visit of a part to different work stations. The concept of operations entropy as a measure of operations flexibility, which arises from the power to choose the work station and the corresponding operations, is introduced. The operations entropy has been decomposed into entropies within and between operations and entropies within and between groups of operations. This measure has been used to determine the next operation to be performed on a part by using the principle of least reduction of flexibility.The present paper is an improved version of the paper On measurement of flexibility in flexible manufacturing systems: An information-theoretic approach, presented at the II ORSA/TIMS Special Conference on Flexible Manufacturing Systems, held at Ann Arbor in August 1986.     

Constructing the governing equations for a layered composite of regular structure within the limits of the theory of asymmetric elasticity on the basis of energy criteria of equivalence

Within the limits of the theory of asymmetric elasticity, two (kinematic and static) approaches are offered to constructing the governing equations for a layered hybrid composite of regular structure with isotropic constituents. As a criteria of equivalence between the layered composition and a homogeneous transversely isotropic material, the equality of the specific free energy and the specific thermodynamic Gibbs energy in them is used, which allows one to determine the upper and lower bounds for the effective rigidities of the layered material. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 3–16, January–February, 2009.     

Minor summation formula and a proof of Stanley’s open problem

In the open problem session of the FPSAC’03, R.P. Stanley gave an open problem about a certain sum of the Schur functions. The purpose of this paper is to give a proof of this open problem. The proof consists of three steps. At the first step we express the sum by a Pfaffian as an application of our minor summation formula (Ishikawa and Wakayama in Linear Multilinear Algebra 39:285–305, 1995). In the second step we prove a Pfaffian analogue of a Cauchy type identity which generalizes Sundquist’s Pfaffian identities (J. Algebr. Comb. 5:135–148, 1996). Then we give a proof of Stanley’s open problem in Sect. 4. At the end of this paper we present certain corollaries obtained from this identity involving the Big Schur functions and some polynomials arising from the Macdonald polynomials, which generalize Stanley’s open problem.      

Lowest Landau level approach in superconductivity for the Abrikosov lattice close to $$H_{{c}_{2}}$$

We study the Ginzburg–Landau energy for a superconductor submitted to a magnetic field just below the “second critical field” . When the Ginzburg–Landau parameter ε is small, we show that the mean energy per unit volume can be approximated by a reduced energy on a torus. Moreover, we expand this reduced energy in terms of : when this quantity gets small, the problem amounts to a minimization problem on a finite-dimensional space, equivalent to the “lowest Landau level” in other approaches. The functions in this finite-dimensional space can themselves be expressed via the Jacobi Theta function of a lattice. This connects the Ginzburg–Landau energy to the “Abrikosov problem” of locating vortices optimally on a lattice.      

Estimates of deviations from exact solutions of variational inequalities based upon Payne–Weinberger inequality

A new method for obtaining computable estimates for the difference between exact solutions of elliptic variational inequalities and arbitrary functions in the respective energy space is suggested. The estimates are obtained by transforming the corresponding variational inequality without the use of variational duality arguments. These estimates are valid for any function in the energy class and contain no constants depending on the mesh used to find an approximate solution. This method for linear elliptic and parabolic problems was earlier suggested by the author. The guaranteed error bounds we derive can be of two types. Estimates of the first type contain only one global constant, which is a constant in the Friedrichs type inequality. Estimates of the second type are based on the decomposition of Ω into convex subdomains and the Payne–Weinberger inequalities for these subdomains. Bibliography: 20 titles. Translated from Problems in Mathematical Analysis 39 February, 2009, pp. 81–90.     

Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations

In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T]. Five sufficient conditions are given. Our results are motivated by two main ideas: one is to control the accumulation of vorticity alone; the other is to generalize the corresponding geometric conditions of 3-D Euler equations to 3-D ideal magnetohydrodynamic equations.     

Design of helicopter rotor blades with actuators made of a piezomacrofiber composite

For reducing the vibration and noise of helicopter rotor blades, the method of their controlled twisting by using built-in deformation actuators is employed. In this paper, the influence of various design parameters of the blades, including the location of actuators made of a piezomacrofiber material, on the twist angle is evaluated. The results of a parametric analysis performed allowed us to refine the statement of an optimization problem for the rotor blades. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 77–86, January–February, 2008.