Statistical approach to multiple-q modulated structures: average Patterson analysis

Using a statistical approach, the average unit cells have been constructed for modulated structures with different types of modulation, from simple sinusoidal to square-wave functions. The obtained unit cells fully describe diffraction intensities of the main reflections and their satellites. A universal distribution, valid for different lengths of the modulation vector, has been found. Average Patterson functions have been constructed and used to distinguish between different types of modulation.     

Duality Relations for Non-Ohmic Composites, with Applications to Behavior near Percolation

Keller, Dykhne, and others have exploited duality to derive exact results for the effective behavior of two-dimensional Ohmic composites. This paper addresses similar issues in the non-Ohmic context. We focus primarily on three different types of nonlinearity: (a) the weakly nonlinear regime; (b) power-law behavior; and (c) dielectric breakdown. We first make the consequences of duality explicit in each setting. Then we draw conclusions concerning the critical exponents and scaling functions of dual pairs of random non-Ohmic composites near a percolation threshold. These results generalize, unify, and simplify relations previously derived for nonlinear resistor networks. We also discuss some self-dual nonlinear composites. Our treatment is elementary and self-contained; however, we also link it with the more abstract mathematical discussions of duality by Jikov and Kozlov.     

Synthetic Impedance Circuits in Semi-Passive Vibration Control with Piezo-Ceramics - Efficiency and Limitations

Electrical circuits that represent complex impedance connected to the plates of piezo element affect the frequency response function of compound electromechanical systems. The external network consisting of inductance results in absorbing a certain frequency of vibrations. The performance can significantly be increased using negative capacitance. All the negative impedance elements are achievable via semi-passive way with the use of an electronic gyrator realized by operational amplifiers that require power supply. Its performance is limited due to the maximum voltage operational amplifiers can produce. The higher excitation forces require higher output voltages of amplifiers. The aim of the paper is to present the relation between the required voltage on synthetic impedance and force excitation in 1DOF vibrating system regarding parameters of piezo element and mechanical system for absorbing case. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Artificial Protein Crosstalk with a Molecule that Exchanges Binding Partners

Drawing inspiration from allosteric signaling enzymes, whose catalytic and regulatory units are non-covalently linked, we have devised a method to establish unnatural, effector-mediated enzyme activation within native cells. The feasibility of this approach is demonstrated by introducing a synthetic regulatory unit (sRU) onto glycogen synthase kinase 3 (GSK-3) through non-covalent means. Our study reveals that this synthetic regulator mediates an unnatural crosstalk between GSK-3 and lactate dehydrogenase A (LDHA), whose expression is regulated by cellular oxygen levels. Specifically, with this approach, the constitutively active GSK-3 is transformed into an activable enzyme, whereas LDHA is repurposed as an unnatural effector protein that controls the activity of the kinase, making it unnaturally dependent on the cell‘s hypoxic response. These findings demonstrate a step toward imitating the function of effector-regulated cell-signaling enzymes, which play a key biological role in mediating the response of cells to changes in their environment. In addition, at the proof-of-principle level, our results indicate the potential to develop a new class of protein inhibitors whose inhibitory effect in cells is dictated by the cell‘s environment and consequent protein expression profile.     

An Inverse-Ackermann Type Lower Bound For Online Minimum Spanning Tree Verification*

Given a spanning tree T of some graph G, the problem of minimum spanning tree verification is to decide whether T = MST(G). A celebrated result of Komlós shows that this problem can be solved with a linear number of comparisons. Somewhat unexpectedly, MST verification turns out to be useful in actually computing minimum spanning trees from scratch. It is this application that has led some to wonder whether a more flexible version of MST verification could be used to derive a faster deterministic minimum spanning tree algorithm. In this paper we consider the online MST verification problem in which we are given a sequence of queries of the form “Is e in the MST of T ∪{e}?”, where the tree T is fixed. We prove that there are no linear-time solutions to the online MST verification problem, and in particular, that answering m queries requires Ω(mα(m,n)) time, where α(m,n) is the inverse-Ackermann function and n is the size of the tree. On the other hand, we show that if the weights of T are permuted randomly there is a simple data structure that preprocesses the tree in expected linear time and answers queries in constant time. * A preliminary version of this paper appeared in the proceedings of the 43rd IEEE Symposium on Foundations of Computer Science (FOCS 2002), pages 155–163. † This work was supported by Texas Advanced Research Program Grant 003658-0029-1999, NSF Grant CCR-9988160, and an MCD Graduate Fellowship.     

A Linear Bound On The Diameter Of The Transportation Polytope*

We prove that the combinatorial diameter of the skeleton of the polytope of feasible solutions of any m×n transportation problem is at most 8(m+n−2). * Research for this paper was done while the second and third author were visiting the Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. All authors were supported by the TMR Network DONET of the European Community ERB TMRXCT98-0202. † Research partially funded by the Dutch BSIK/BRICKS project.     

Synthesis and Photoinitiated Cationic Polymerization of Epoxidized Castor Oil and Its Derivatives

ABSTRACT

In this communication we describe the synthesis of epoxidized castor oil (ECO) as an interesting and inexpensive biorenewable monomer by an efficient and low cost epoxidation process. Also described are studies of the photoinitiated cationic polymerization of ECO using diaryliodonium salt photoinitiators. The influence of the structure and the concentration of the photoinitiator on the polymerization are reported. The ability of photosensitizers to accelerate the photopolymerization was also studied. Studies comparing the photopolymerization behavior of ECO with other commercially available epoxidized linseed and soybean oils and with other types of synthetic epoxy monomers were conducted. The excellent reactivity of ECO can be ascribed to the presence of both epoxy and hydroxyl groups in the molecule which permits this material to polymerize mainly by an activated monomer mechanism.

     

Operational Research Education for Practitioners and Managers∗

The paper reviews the history of education in operational research and indicates the needs both of a practitioner and of a manager. It describes how these can be met by standard course teaching and suggests some areas of development.