On curvature approximation in 2D and 3D parameter–free shape optimization

Manufacturing constraints considered in shape optimization often need to be expressed in terms of curvature. Within the scope of a sensitivity–based parameter–free shape optimization approach, curvature constraints have to be formulated in terms of the FE node coordinates in order to derive the required first order gradients with respect to the design node coordinates. In this contribution we introduce approaches to approximate the curvature of a FE model using the coordinates of the FE nodes at the boundary of the geometry, as a smooth representation of the design boundary is not available. Therefore, in the 2D case we present two different smooth curves which represent the design boundary and for which the curvature can be computed analytically. In a third 2D, as well as in our 3D approach, we use geometric information of the discretization such as the distance to neighboring boundary nodes and edge normals to approximate the curvature at the respective boundary node under consideration.     

An integral–differential equation approach for the free vibration of a SDOF system with hysteretic damping

An integral–differential equation (IDE) in the time domain is proposed for the free vibration of a single-degree-of-freedom (SDOF) system with hysteretic damping which is different from the conventional complex stiffness model as employed in the frequency domain. The integral of the Hilbert transform is embedded in the IDE and is calculated in the Cauchy principal value sense by using a numerical folding technique. Numerical experiments show that the free vibration obtained by the frequency domain approach satisfies the IDE in the time domain. A successive iteration algorithm is employed to solve the IDE subject to forced vibration, and a convergent solution for the hysteresis loop is constructed, which matches the solution found by using the frequency domain approach. Both models, the time domain and frequency domain approaches, present the noncasual effect since they are equivalent in the mathematical sense.     

A technical note on AC-Unification. The number of minimal unifiers of the equation αx1 + ⋯ + αxp ≐AC βy1 + ⋯ + βyq

We show in this note that the equation αx₁ + #x22EF; +αx_p?_ACβy₁ + α +βy_q where + is an AC operator and αx stands for x+...+x (α times), has exactly $$\left( { - 1} \right)^{p + q} \sum\limits_{i = 0}^p {\sum\limits_{j = 0}^q {\left( { - 1} \right)^{1 + 1} \left( {\begin{array}{*{20}c} p \\ i \\ \end{array} } \right)\left( {\begin{array}{*{20}c} q \\ j \\ \end{array} } \right)} 2^{\left( {\alpha + \begin{array}{*{20}c} {j - 1} \\ \alpha \\ \end{array} } \right)\left( {\beta + \begin{array}{*{20}c} {i - 1} \\ \beta \\ \end{array} } \right)} } $$ minimal unifiers if gcd(α, β)=1.     

Numerical approach of a free boundary in the junction field effect transistor – MESFET

This paper presents the numerical approach of the free boundary by using shape optimization method. The numerical simulation field effect transistor MESFET is possible with the Laplace–Poisson model, which introduces two regions, respectively, known by “charge neutrality region” and “depletion region”, separated by some free boundary.     

On an infinite family of graphs with information ratio 2 − 1/k

In this paper we consider the secret sharing problem on special access structures with minimal qualified subsets of size two, i.e. secret sharing on graphs. This means that the participants are the vertices of the graph and the qualified subsets are the subsets of V(G) spanning at least one edge. The information ratio of a graph G is denoted by R(G) and is defined as the ratio of the greatest size of the shares a vertex has to remember and of the size of the secret. Since the determination of the exact information ratio is a non-trivial problem even for small graphs (i.e. for V(G) = 6), every construction can be of particular interest. Let k be the maximal degree in G. In this paper we prove that R(G) = 2 ? 1/k for every graph G with the following properties: (A) every vertex has at most one neighbour of degree one; (B) vertices of degree at least 3 are not connected by an edge; (C) the girth of the graph is at least 6. We prove this by using polyhedral combinatorics arguments and the entropy method.     

Fast evaluation of the hypergeometric function p F p−1(a; b; z) at the singular point z = 1 by means of the Hurwitz zeta function ζ(α, s)

A method for fast and highly accurate evaluation of the generalized hypergeometric function _p F _p?1(a ₁, ..., a _p ; b ₁, ..., b _p?1; 1) = Σ _{k = 0} ^∞ f _k by means of the Hurwitz zeta function ζ(α, s) is developed. Based on asymptotic analysis of the coefficients f _k , an expansion of _p F _p?1 is constructed as a combination of the functions ζ(α, s) with explicit coefficients expressed in terms of the generalized Bernoulli polynomials. An appropriate selection of the parameter α and the number of terms of the asymptotic expansion makes it possible to obtain the result with any desired degree of accuracy. The use of computer algebra methods, efficient numerical algorithms, and stochastic optimization methods considerably improve the efficiency of the suggested method.     

On the law (a·b'')''=b+a''·b'' in de Morgan algebras and orthomodular lattices

This paper's goal is to prove that the only de Morgan algebras and the only orthomodular lattices in which the law (a·b)=b+a·b, posed by Charles Elkan in [1] holds, are those that are boolean algebras. That is, that among both families of de Morgan algebras and orthomodular lattices, Elkan's formula is only characteristic of boolean algebras.Authors are actually in debt with an anonymous referee that helped them to considerably improve the first version of this paper.This paper has been partially supported by CICYT(Spain) under project TIC2000-1420     

On the “scattering law” for Kasner parameters in the model with a one-component anisotropic fluid

A multidimensional cosmological model with a one-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We single out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits τ → +0 and τ → +∞, where τ is the synchronous time variable. A relation between two sets of Kasner parameters α _∞ and α ₀ is found. This formula (“scattering law”) coincides with that obtained earlier for the S-brane solution (where scalar fields are absent).     

Postfix — a secure alternative to Sendmail: A new frontier in the reaim of free mailers

It is now widely recognized that Sendmail, the most widely used UNIX mailer, has certain security gaps, many of which are discovered and reported on a daily basis by researchers and users. One such researcher is Wietse Venema. Venema is a programmer and inventor of numerous irreplaceable tools for UNIX administrators. Examples include SATAN (created together with the equally well known researcher, Dan Farmer) and TCPWrappers, of note recently for allegedly having been illicitly distributed with a Trojan horse inside by a group of malicious hackers. For some time now, Venema has been pointing out to the scientific community just why Sendmail will never be completely secure. Naturally, criticism of a product should be accompanied by suggestions — or better yet — alternatives. Thus, Venema, during his time with the T.J. Watson research laboratories, was driven to launch the Postfix project (a.k.a. Vmailer or Secure Mailer) under the auspices of IBM. As Venema says, there is a dual objective: to give the user an alternate Mail Transfer Agent (MTA) to Sendmail while creating a secure mailer like the well-known Qmail, another program in this category, created by Dan Bernstein.     

On the validity of the arithmetic–geometric mean method to locate the optimal solution in a supply chain system

Cardenas-Barron [Cardenas-Barron, L.E. (2010) ‘A Simple Method to Compute Economic order Quantities: Some Observations’, Applied Mathematical Modelling, 34, 1684–1688] indicates that there are several functions in which the arithmetic–geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), ‘A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives’, Applied Mathematical Modelling, 33, 4388–4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), ‘Comment on ‘Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives’, International Journal of Systems Science, 40, 1095–1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), ‘A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage’, Production Planning and Control, 19, 601–604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic–geometric mean method of Teng et al. (2009), Teng and Goyal (2009 Teng, JT, Chen, J and Goyal, SK. 2009. A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives. Applied Mathematical Modelling, 33: 4388–4396. [Crossref], [Web of Science ®] , [Google Scholar]) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.