Approximate performance analysis of CONWIP disciplines in unreliable non homogeneous transfer lines

For a given choice of the maximum allowable total storage parameter, the performance of constant work-in-process (CONWIP) disciplines in unreliable transfer lines subjected to a constant rate of demand for parts, is characterized via a tractable approximate mathematical model. For a (n−1) machines CONWIP loop, the model consists of n multi-state machine single buffer building blocks, separately solvable once a total of (n−1)² unknown constants shared by the building blocks are initialized. The multi-state machine is common to all building blocks, and its n discrete states approximate the joint operating state of the machines within the CONWIP loop; each of the first (n−1) blocks maps into a single internal buffer dynamics, while the nth building block characterizes total work-in-process (wip) dynamics. The blocks correspond to linear n component state equations with boundary conditions. The unknown (shared) constants in the block dynamics are initialized and calculated by means of successive iterations. The performance estimates of interest—mean total wip, and probability of parts availability at the end buffer in the loop—are obtained from the model and validated against the results of Monte Carlo simulations.     

Reliability of manufacturing equipment in complex environments

We present two stochastic failure models for the reliability evaluation of manufacturing equipment that degrades due to its complex operating environment. The first model examines the case when the environment is a temporally nonhomogeneous continuous-time Markov chain, and the second assumes the environment is a temporally homogeneous semi-Markov process on a finite space. Derived are transform expressions for the lifetime distributions. A few examples are provided to illustrate the main results.     

On the Expected Probability of Constraint Violation in Sampled Convex Programs

In this note, we derive an exact expression for the expected probability V of constraint violation in a sampled convex program (see Calafiore and Campi in Math. Program. 102(1):25–46, 2005; IEEE Trans. Autom. Control 51(5):742–753, 2006 for definitions and an introduction to this topic):

Statistical Convergence in Probability for a Sequence of Random Functions

In this paper, we introduce a new type of convergence for a sequence of random functions, namely, statistical convergence in probability, which is a natural generalization of convergence in probability. In this approach, we allow such a sequence to go far away from the limit point infinitely many times by presenting random deviations, provided that these deviations are negligible in some sense of measure. In this context, the set of values of a random function is considered as a probabilistic metric (PM) space of random variables, and some basic results are obtained using the tools of PM spaces.     

Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions

In this paper we present a finite element discretization of the Joule-heating problem. We prove existence of solution to the discrete formulation and strong convergence of the finite element solution to the weak solution, up to a sub-sequence. We also present numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method in the second example we consider an engineering application.     

A multiresolution method for fitting scattered data on the sphere

In this work, we propose an efficient multiresolution method for fitting scattered data functions on a sphere S, using a tensor product method of periodic algebraic trigonometric splines of order 3 and quadratic polynomial splines defined on a rectangular map of S. We describe the decomposition and reconstruction algorithms corresponding to the polynomial and periodic algebraic trigonometric wavelets. As application of this method, we give an algorithm which allows to compress scattered data on spherelike surfaces. In order to illustrate our results, some numerical examples are presented.     

Multi-step methods for choosing the best set of variables in regression analysis

In a recent article (Konno and Yamamoto in ISE 07-01, Department of Industrial and Systems Engineering, Chuo University, February 2007), one of the authors formulated the problem of choosing the best set of explanatory variables from a large number of candidate variables in a linear regression model as a mixed 0–1 integer linear programming problem and showed that it can be solved by the state-of-the-art integer programming software.     

The Poincaré series of divisorial valuations in the plane defines the topology of the set of divisors

With a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables defined by the orders of a function on irreducible components of the curve. The Poincaré series of this filtration turns out to coincide with the Alexander polynomial of the curve germ. For a finite set of divisorial valuations on the ring corresponding to some components of the exceptional divisor of a modification of the plane, in a previous paper there was obtained a formula for the Poincaré series of the corresponding multi-index filtration similar to the one associated with plane germs. Here we show that the Poincaré series of a set of divisorial valuations on the ring of germs of functions of two variables defines “the topology of the set of the divisors” in the sense that it defines the minimal resolution of this set up to combinatorial equivalence. For the plane curve singularity case, we also give a somewhat simpler proof of the statement by Yamamoto which shows that the Alexander polynomial is equivalent to the embedded topology.     

Business value and risk in the presence of price controls: an option-based analysis of margin squeeze rules in the telecommunications industry

Pricing rules specific to the German telecommunications market limit the incumbents flexibility, providing a competitive advantage to all other market participants. More specifically, the incumbent is required not to offer products to its end customers at prices below a predetermined level in order to prevent margin squeezes. In contrast, competitors can freely choose their pricing strategy. In this paper, we propose the imposition of equivalent price barriers on all market participants in order to avoid price margin squeezes and reduce regulatory discrimination at the same time. We tailor a duopoly model to the German context, integrating the regulation of access pricing and price margin squeezes. Under standard parameter assumptions, we demonstrate that no economically significant effects on the value of market participants are observed for the case of market wide price regulation. We conclude that adjusting the current regulatory framework can enhance competition and increase welfare.     

Revisit of the Theorem of Image Trajectories in the Earth-Moon Space

On the occasion of the 50th anniversary of the theorem of the image trajectories in the Earth-Moon space, the author revisits the theorem and clarifies the relation between the class of image trajectories and the class of symmetric free-return trajectories, which were employed in the Apollo program. In a nutshell, the symmetric free-return trajectories are those image trajectories that intersect the Earth-Moon axis orthogonally at some point above the far side of the Moon. Optimization implications are pointed out.     

Equivalent Conditions of Asymptotics for the Density of the Supremum of a Random Walk in the Intermediate Case

This paper obtains some equivalent conditions about the asymptotics for the density of the supremum of a random walk with light-tailed increments in the intermediate case. To do this, the paper first corrects the proofs of some existing results about densities of random sums. On the basis of the above results, the paper obtains some equivalent conditions about the asymptotics for densities of ruin distributions in the intermediate case and densities of infinitely divisible distributions. In the above studies, some differences and relations between the results on a distribution and its corresponding density can be discovered.      

The Method of Virtual Components in the Multivariate Setting

We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the multivariate setting. Two examples of the virtual components for tight wavelet frames based on bivariate box splines on three or four direction mesh are given. As a byproduct, a new construction of tight wavelet frames based on box splines under the quincunx dilation matrix is presented.     

Theoretical analysis of numerical integration in Galerkin meshless methods

In this paper, we study effects of numerical integration on Galerkin meshless methods for solving elliptic partial differential equations with Neumann boundary conditions. The shape functions used in the meshless methods reproduce linear polynomials. The numerical integration rules are required to satisfy the so-called zero row sum condition of stiffness matrix, which is also used by Babuška et al. (Int. J. Numer. Methods Eng. 76:1434–1470, 2008). But the analysis presented there relies on a certain property of the approximation space, which is difficult to verify. The analysis in this paper does not require this property. Moreover, the Lagrange multiplier technique was used to handle the pure Neumann condition. We have also identified specific numerical schemes, diagonal elements correction and background mesh integration, that satisfy the zero row sum condition. The numerical experiments are carried out to verify the theoretical results and test the accuracy of the algorithms.     

Rigidity of the harmonic map heat flow from the sphere to compact Kähler manifolds

A ?ojasiewicz-type estimate is a powerful tool in studying the rigidity properties of the harmonic map heat flow. Topping proved such an estimate using the Riesz potential method, and established various uniformity properties of the harmonic map heat flow from \(\mathbb{S}^{2}\) to \(\mathbb{S}^{2}\) (J. Differential Geom. 45 (1997), 593–610). In this note, using an inequality due to Sobolev, we will derive the same estimate for maps from \(\mathbb{S}^{2}\) to a compact Kähler manifold N with nonnegative holomorphic bisectional curvature, and use it to establish the uniformity properties of the harmonic map heat flow from \(\mathbb{S}^{2}\) to N, which generalizes Topping’s result.     

Density of the polynomials in Hardy and Bergman spaces of slit domains

It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\} and with the property that the analytic polynomials are dense in the Bergman space \mathbbA^t(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma) . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in H^t(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma) ; improving upon a result in an earlier paper.     

A Measure of Non-convexity in the Plane and the Minkowski Sum

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for “not far from convex” regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no “holes”.     

How to get the timing right. A computational model of the effects of the timing of contacts on team cohesion in demographically diverse teams

Lau and Murnighan’s faultline theory explains negative effects of demographic diversity on team performance as consequence of strong demographic faultlines. If demographic differences between group members are correlated across various dimensions, the team is likely to show a “subgroup split” that inhibits communication and effective collaboration between team members. Our paper proposes a rigorous formal and computational reconstruction of the theory. Our model integrates four elementary mechanisms of social interaction, homophily, heterophobia, social influence and rejection into a computational representation of the dynamics of both opinions and social relations in the team. Computational experiments demonstrate that the central claims of faultline theory are consistent with the model. We show furthermore that the model highlights a new structural condition that may give managers a handle to temper the negative effects of strong demographic faultlines. We call this condition the timing of contacts. Computational analyses reveal that negative effects of strong faultlines critically depend on who is when brought in contact with whom in the process of social interactions in the team. More specifically, we demonstrate that faultlines have hardly negative effects when teams are initially split into demographically homogeneous subteams that are merged only when a local consensus has developed.     

A New Regularity Criterion in Terms of the Direction of the Velocity for the MHD Equations

In this paper we obtain a new regularity criterion for weak solutions to the 3D MHD equations. It is proved that if div( \fracu|u|) \mathrm{div}( \frac{u}{|u|}) belongs to L^\frac21-r( 0,T;[(X)\dot]_r( \mathbbR³) ) L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) with 0≤r≤1, then the weak solution actually is regular and unique.     

Large Deviations for Products of Empirical Probability Measures in the τ-Topology

We prove a large deviation principle (LDP) for products of empirical measures, where the state space S of the underlying sequence of i.i.d. random variables is Polish and the set of probability measures on S respectively S×S is endowed with the -topology. An improved form of a LDP for U-statistics and some conclusions from that are obtained as a particular application.