Balancing assembly lines effectively – A computational comparison

We report on results of a numerical experiment including the most effective branch and bound procedures for solving type 1 of the simple assembly line balancing problem (SALBP-1), namely Johnson's (1988) FABLE, Nourie and Venta's (1991) OptPack, Hoffmann's (1992) Eureka and Scholl and Klein's (1997) SALOME. It appears that SALOME clearly outperforms the other procedures with respect to hard instances of a new challenging data set. Beyond that, it is shown that the performance of SALOME can greatly be improved by adding some further features including dynamic renumbering and dominance rules.     

On comparison of ℓ-stable vector optimization results

Two papers with similar optimality conditions were published by I. Ginchev, and by D. Bedna?ík and K. Pastor independently in Nonlinear Analysis in 2011. We compare these results. We also show the equivalence of two definitions of ?-stability of vector functions. Moreover, we generalize another result given by I. Ginchev and V. I. Ivanov [J. Math. Anal. Appl. 340 (2008), 646–657] and compare it with the previously mentioned optimality conditions.     

Some comparison theorems for K?hler manifolds

In this work, we will verify some comparison results on K?hler manifolds. They are: complex Hessian comparison for the distance function from a closed complex submanifold of a K?hler manifold with holomorphic bisectional curvature bounded below by a constant, eigenvalue comparison and volume comparison in terms of scalar curvature. This work is motivated by comparison results of Li and Wang (J Differ Geom 69(1):43–47, 2005).     

A comparison theorem and an inequality of redhefferf†

For equations of the form w″+B(e^z)w = 0, where B(ζ) is a rational function which is analytic on 0<|ζ|∞, we determine the regions where the bulk of the zeros of a solution must be located. In the special case of the general Mathieu equation, these results complement earlier results of E. Hille (1924) who considered the special case of real Mathieu equations     

Grothendieck’s comparison theorem and multivariable Fredholm theory

We use a variant of Grothendieck’s comparison theorem to show that, for a Fredholm tuple T ∈ L(X)ⁿ on a complex Banach space, there are isomorphisms . We conclude that a Fredholm tuple T ∈ L(X)ⁿ satisfies Bishop’s property (β) at z = 0 if and only if the vanishing conditions hold for . We apply these observations and results from commutative algebra to show that a graded tuple on a Hilbert space is Fredholm if and only if it satisfies Bishop’s property (β) at z = 0 and that, in this case, its cohomology groups can grow at most like k^p. Received: 14 January 2009     

On local comparison between various metrics on Teichmüller spaces

There are several Teichmüller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). Such spaces include the quasiconformal Teichmüller space, the length spectrum Teichmüller space, the Fenchel-Nielsen Teichmüller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between them. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions between them. In this paper, we obtain local metric comparison results on these inclusions, namely, we show that the inclusions are locally bi-Lipschitz under certain hypotheses. To obtain these results, we use some hyperbolic geometry estimates that give new results also for surfaces of finite type. We recall that in the case of a surface of finite type, all these Teichmüller spaces coincide setwise. In the case of a surface of finite type with no boundary components (but possibly with punctures), we show that the restriction of the identity map to any thick part of Teichmüller space is globally bi-Lipschitz with respect to the length spectrum metric on the domain and the classical Teichmüller metric on the range. In the case of a surface of finite type with punctures and boundary components, there is a metric on the Teichmüller space which we call the arc metric, whose definition is analogous to the length spectrum metric, but which uses lengths of geodesic arcs instead of lengths of closed geodesics. We show that the restriction of the identity map to any “relative thick” part of Teichmüller space is globally bi-Lipschitz, with respect to any of the three metrics: the length spectrum metric, the Teichmüller metric and the arc metric on the domain and on the range.     

An extension of Günther’s volume comparison theorem

The aim of this note if to give an extension of a classical volume comparison theorem for Riemannian manifolds with sectional curvature bounded above (see Günther, P. Einige Sätze über das Volumenelement eines Riemannschen Raumes, Publ. Math. Debrecen 7, 78–93 (1960)). For the case of a n-dimensional simply connected complete Riemannian manifold with nonpositive sectional curvature our theorem states that the function tarea(S _t (p))/t ^n–2 is convex for every pM where S _t (p) denotes the sphere of radius t with center p. In view of area(S ₀ (p))=0, it is easy to see that our theorem implies the classical result. A similar result holds true for simply connected manifolds with sectional curvature bounded above by a negative constant.Research partially supported by Fondecyt Grant # 1000713 and by UTFSM Grant # 120023     

Massive vector gauge theory and comparison with Higgs—Connes—Lott

A massive vector gauge theory constructed from the matrix derivative approach of non-commutative geometry is compared with the Higgs—Connes—Lott theory. In the massive vector gauge theory, a new extra shift-like symmetry which is due to the one form constant matrix derivative allows the theory to have a mass term while keeping the gauge symmetry intact. In the Higgs—Connes—Lott theory, the transformation of scalar field makes up the deficiency of symmetry due to the mass term. Thus, when the scalar field is absent there remains no gauge symmetry just like the Proca model. In the massive vector gauge theory, the shift-like symmetry makes up the deficiency of symmetry due to the mass term even in the absence of the scalar field.     

Existence and comparison results for quasilinear parrabolic inclusions woth state-dependent subdifferentials ∗

In this paper we consider initial boundary value problems for quasilinear parabolic differential inclusions governed by nonmonotone operators of Leray-Lions type and state-dependent subdifferentials. Our main goal is to prove the existence of solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof are abstract results on nonlinear evolution equations, regularization, comparison and truncation techniques as well as special test function techniques     

FEM-analysis of a multiferroic nanocomposite – comparison of experiment and numerical simulation

The combination of electric and magnetic materials opens new possibilities in the field of sensor technologies and data storage [1]. These magneto-electric (ME) materials have the property to change a physical ferroic quantity into another, i.e. a magnetic field can change the electric polarization and vice versa. The combination of multiple ferroic characteristics within materials is called multiferroic. Since magneto-electric single-phase materials are rare in nature and typically operate only at very low temperature, they are not favorable in technical applications. However, ME composites, consisting of ferroelectric and ferromagnetic phases, produce a strain-induced magneto-electric product property at room temperature [2]. In these composites, two different effects can be differentiated, the direct and the converse ME effect. The first one describes a polarization which is magnetically caused. In detail, a magnetic field is applied which produces a deformation of the magneto-active phase which is transferred to the electro-active phase and as a consequence this phase exhibits a polarization. Therefore, one can discover a strain-induced polarization. The second effect to observe is a magnetization caused by an electric field. In our contribution, we focus on a (1-3) composite, where cobalt ferrite nanopillars are embedded in a barium titanate matrix, see the experiments described in [3]. In the numerical simulations we compare the changes of the strain-induced inplane polarizations of the ferroelectric matrix with experimental measurements. Furthermore, we analyze the magneto-electric coupling coefficient. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An ‘apples to apples’ comparison of various tests for exponentiality

The exponential distribution is a popular model both in practice and in theoretical work. As a result, a multitude of tests based on varied characterisations have been developed for testing the hypothesis that observed data are realised from this distribution. Many of the recently developed tests contain a tuning parameter, usually appearing in a weight function. In this paper we compare the powers of 20 tests for exponentiality—some containing a tuning parameter and some that do not. To ensure a fair ‘apples to apples’ comparison between each of the tests, we employ a data-dependent choice of the tuning parameter for those tests that contain these parameters. The comparisons are conducted for various samples sizes and for a large number of alternative distributions. The results of the simulation study show that the test with the best overall power performance is the Baringhaus and Henze test, followed closely by the test by Henze and Meintanis; both tests contain a tuning parameter. The score test by Cox and Oakes performs the best among those tests that do not include a tuning parameter.     

On a Liouville-type comparison principle for solutions of quasilinear elliptic inequalities

We characterize in terms of monotonicity basic properties of quasilinear elliptic partial differential operators which make it possible to obtain a Liouville-type comparison principle for entire solutions of quasilinear elliptic partial differential inequalities of the form A(u)+|u|^q?1u?A(v)+|v|^q?1v, which belong only locally to the corresponding Sobolev spaces on $\text{R}{}^{\mathrm{n}}\text{,}\text{n?2}$. We establish that such properties are inherent for a wide class of quasilinear elliptic partial differential operators. Typical examples of such operators are the p-Laplacian and its well-known modifications for 1<p?2. To cite this article: V.V. Kurta, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Stochastic comparison and preservation of positive correlations for Lévy-type processes

The stochastic comparison and preservation of positive correlations for Levy-type processes on R^d are studied under the condition that Levy measure v satisfies f{0〈｜z｜≤1）｜z｜｜v（x, dz） - v（x, d（-z））｜ 〈 ∞, x∈ R^d, while the sufficient conditions and necessary ones for them are obtained. In some cases the conditions for stochastic comparison are not only sufficient but also necessary.     

Forecasting mortality in subpopulations using Lee–Carter type models: A comparison

The relative performance of multipopulation stochastic mortality models is investigated. When targeting mortality rates, we consider five extensions of the well known Lee–Carter single population extrapolative approach. As an alternative, we consider similar structures when mortality improvement rates are targeted. We use a dataset of deaths and exposures of Italian regions for the years 1974–2008 to conduct a comparison of the models, running a battery of tests to assess the relative goodness of fit and forecasting capability of different approaches. Results show that the preferable models are those striking a balance between complexity and flexibility.     

A comparison of feasible direction methods for the stochastic transportation problem

The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.     

Learning fraction comparison by using a dynamic mathematics software – GeoGebra

GeoGebra is a mathematics software system that can serve as a tool for inquiry-based learning. This paper deals with the application of a fraction comparison software, which is constructed by GeoGebra, for use in a dynamic mathematics environment. The corresponding teaching and learning issues have also been discussed.     

A generalization of Lehmann’s Theorem on the comparison of uniform location experiments

Summary We generalize a result of Lehmann on the comparison of location experiments with uniform distributions on intervals. We compare a location experiment consisting of uniform distributions on parallelepipeds with a location experiment consisting of uniform distributions on convex bodies. We show that the first experiment can only be more informative than the second one if the convex bodies in the second experiment are themselves parallelepipeds. Further we show that the length of the edges of these parallelepipeds must fulfill a condition similar to the condition on the length of the intervals in Lehmanns result.     

The comparison between the DRBEM and DQM solution of nonlinear reaction–diffusion equation

In this study, both the dual reciprocity boundary element method and the differential quadrature method are used to discretize spatially, initial and boundary value problems defined by single and system of nonlinear reaction–diffusion equations. The aim is to compare boundary only and a domain discretization method in terms of accuracy of solutions and computational cost. As the time integration scheme, the finite element method is used achieving solution in terms of time block with considerably large time steps. The comparison between the dual reciprocity boundary element method and the differential quadrature method solutions are made on some test problems. The results show that both methods achieve almost the same accuracy when they are combined with finite element method time discretization. However, as a method providing very good accuracy with considerably small number of grid points differential quadrature method is preferrable.     

Application and comparison of kernel functions for linear parameter varying model approximation of nonlinear systems

In this paper, a comparative study for kernel-PCA based linear parameter varying(LPV) model approximation of sufficiently nonlinear and reasonably practical systems is carried out. Linear matrix inequalities(LMIs) to be solved in LPV controller design process increase exponentially with the increase in a number of scheduling variables. Fifteen kernel functions are used to obtain the approximate LPV model of highly coupled nonlinear systems. An error to norm ratio of original and approximate LPV ...