Optimization of probabilistic multiple response surfaces

Response surface methodology (RSM) is a statistical-mathematical method used for analyzing and optimizing the experiments. In analysis process, experts usually face several input variables having effect on several outputs called response variables. Simultaneous optimization of the correlated response variables has become more important in complex systems. In this paper multi-response surfaces and their related stochastic nature have been modeled and optimized by Goal Programming (GP) in which the weights of response variables have been obtained through a Group Decision Making (GDM) process. Because of existing uncertainty in the stochastic model, some stochastic optimization methods have been applied to find robust optimum results. At the end, the proposed method is described numerically and analytically.     

Mathematical study of trade-off relations in logistics systems

This paper presents a mathematical model of trade-off relations arising in third party logistics using Pareto optimal solutions for multi-objective optimization problems. The model defines an optimal set of distribution costs and service levels constituting a trade-off relation. An analogy to the concept of the indifference curve in the field of economics is discussed. Numerical experiments for a simplified problem are performed, demonstrating an increasing process of the utility of logistics.     

Balancing the fit and logistics costs of market segmentations

Segments are typically formed to serve distinct groups of consumers with differentiated marketing mixes, that better fit their specific needs and wants. However, buyers in a segment are not necessarily geographically closely located. Serving a geographically dispersed segment with one marketing mix can increase the logistics costs in the form of high transportation costs and long lead times.This study proposes a segmentation method that balances the fit of a segmentation strategy against the corresponding logistics costs. An application to the problem of segmenting a set of European regions, using consumers’ store attribute preferences as a segmentation basis, suggests segment-specific retail positioning strategies that reflect different decisions about store image attributes such as price, assortment, and atmosphere. This approach designates transnational segments that require acceptable logistics costs and offer the highest possible level of within segment homogeneity.     

Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter

In this paper, we consider the asymptotic behavior of the fractional mean curvature when $s\to 0^{+}$. Moreover, we deal with the behavior of s-minimal surfaces when the fractional parameter $s\in (0,1)$ is small, in a bounded and connected open set with $C^2$ boundary $\mathrm{\Omega }?{\mathbb{R}}^n$. We classify the behavior of s-minimal surfaces with respect to the fixed exterior data (i.e. the s-minimal set fixed outside of Ω). So, for s small and depending on the data at infinity, the s-minimal set can be either empty in Ω, fill all Ω, or possibly develop a wildly oscillating boundary.Also, we prove the continuity of the fractional mean curvature in all variables, for $s\in [0,1]$. Using this, we see that as the parameter s varies, the fractional mean curvature may change sign.     

Running error for the evaluation of rational Bézier surfaces through a robust algorithm

Running error analysis of the corner cutting algorithm for rational Bézier surfaces is carried out and the sharpness of the corresponding error bounds is shown.     

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.     

On the associated family of Delaunay surfaces

We use the generalised Weierstraßrepresentation of Dorfmeister, Pedit and Wu to obtain the associated family of Delaunay surfaces and derive a formula for the neck size of the surface in terms of the entries of the holomorphic potential.

     

New examples of maximal space like surfaces in the anti-de Sitter space

Let be the three-dimensional anti-de Sitter space. In this paper we will construct new examples of complete maximal space like surfaces in . Moreover, we will prove that any complete maximal space like surface in with principal curvatures ±κ bounded away from zero must be isometric to the hyperbolic cylinder. Since the new examples that we have constructed have exactly two principal curvatures everywhere, we conclude that the condition on the principal curvatures on the previous result, i.e. the condition |κ(m)|>c>0, cannot be replaced by the condition |κ(m)|>0.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

On the convergence of metric and geometric properties of polyhedral surfaces

We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in Euclidean 3-space. Under the assumption of convergence of surfaces in Hausdorff distance, we show that convergence of the following properties are equivalent: surface normals, surface area, metric tensors, and Laplace–Beltrami operators. Additionally, we derive convergence of minimizing geodesics, mean curvature vectors, and solutions to the Dirichlet problem. This work was supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.     

On the construction of interpolation mesh surfaces

A method for constructing two-dimensional interpolation mesh functions is proposed that is more flexible than the classical cubic spline method because it makes it possible to construct interpolation surfaces that fit the given function at specified points by varying certain parameters. The method is relatively simple and is well suited for practical implementation.     

A finite group acting on the moduli space of K3 surfaces

We consider the natural action of a finite group on the moduli space of polarized K3 surfaces which induces a duality defined by Mukai for surfaces of this type. We show that the group permutes polarized Fourier-Mukai partners of polarized K3 surfaces and we study the divisors in the fixed loci of the elements of this finite group.

     

RATIONALITY OF THE OFFSETS TO ALGEBRAIC CURVES AND SURFACES

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In response to the article by Ivan Kausz: A discriminant and an upper bound for w 2 for hyperelliptic arithmetic surfaces

We define a natural discriminant for a hyperelliptic curve X of genus g over a field K as a canonical element of the (8g+4)th tensor power of the maximal exterior product of the vectorspace of global differential forms on X. If v is a discrete valuation on K and X has semistable reduction at v, we compute the order of vanishing of the discriminant at v in terms of the geometry of the reduction of X over v. As an application, we find an upper bound for the Arakelov self-intersection of the relative dualizing sheaf on a semistable hyperelliptic arithmetic surface.     

On the nondegeneracy of constant mean curvature surfaces

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces are nondegenerate; that is, the Jacobi operator Δ_f + | A_f |² has no L² kernel. In fact, if ∑ has genus zero with k ends, and if f (∑) is embedded (or Alexandrov immersed) in a half-space, then we find an explicit upper bound for the dimension of the L² kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising characterization of CMC surfaces via spinning spheres. R.K. partially supported by NSF grants DMS-0076085 at GANG/UMass and DMS-9810361 at MSRI, and by a FUNCAP grant in Fortaleza, Brazil. J.R. partially supported by an NSF VIGRE grant at Utah. Received: January 2005; Accepted: June 2005     

A bi-level programming model and solution algorithm for the location of logistics distribution centers

In this paper, by considering benefits of customers and logistics planning departments, a bi-level programming model is presented to seek the optimal location for logistics distribution centers. The upper-level model is to determine the optimal location by minimizing the planners’ cost, and the lower gives an equilibrium demand distribution by minimizing the customers’ cost. Based on the special form of constraints, a simple heuristic algorithm is proposed. Finally, a numerical example is used to illustrate the application of the method, which shows that the algorithm is feasible and advantageous.     

Isotrivially fibred isles in the moduli space of surfaces of general type

We complement Catanese's results on isotrivially fibred surfaces by completely describing the components containing an isotrivial surface with monodromy group . We also give an example for deformation equivalent isotrivial surfaces with different monodromy group.

     

A survey of literature on automated storage and retrieval systems

Automated Storage and Retrieval Systems (AS/RSs) are warehousing systems that are used for the storage and retrieval of products in both distribution and production environments. This paper provides an overview of literature from the past 30 years. A comprehensive explanation of the current state of the art in AS/RS design is provided for a range of issues such as system configuration, travel time estimation, storage assignment, dwell-point location, and request sequencing. The majority of the reviewed models and solution methods are applicable to static scheduling and design problems only. Requirements for AS/RSs are, however, increasingly of a more dynamic nature for which new models will need to be developed to overcome large computation times and finite planning horizons, and to improve system performance. Several other avenues for future research in the design and control of AS/RSs are also specified.