Finiteness of fixed equilibrium configurations of point vortices in the plane with a background flow

For a dynamic system consisting of n point vortices in an ideal plane fluid with a steady, incompressible and irrotational background flow, a more physically significant definition of a fixed equilibrium configuration is suggested. Under this new definition, if the complex polynomial w that determines the aforesaid background flow is non-constant, we have found an attainable generic upper bound $\frac{(m+n-1)!}{(m-1)!\,n_1!\cdots n_{i_0}!}$ for the number of fixed equilibrium configurations. Here, m = deg w, i0 is the number of species, and each ni is the number of vortices in a species. We transform the rational function system arising from fixed equilibria into a polynomial system, whose form is good enough to apply the BKK theory (named after Bernshtein (1975 Funct. Anal. Appl. 9 183–5), Khovanskii (1978 Funct. Anal. Appl. 12 38–46) and Kushnirenko (1976 Funct. Anal. Appl. 10 233–5)) to show the finiteness of its number of solutions. Having this finiteness, the required bound follows from Bézout's theorem or the BKK root count by Li and Wang (1996 Math. Comput. 65 1477–84).postprin

A companion matrix approach to the study of zeros and critical points of a polynomial

In this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma. © 2005 Elsevier Inc. All rights reserved.preprin

Behavioral transition: A framework for the construction conflict-tension relationship

“© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”Publishe

Exploring the influence of contract governance on construction dispute negotiation

This is an Accepted Manuscript of an article published by the American Society of Civil Engineers in the Journal of Professional Issues in Engineering Education and Practice. October 2008. This material may be downloaded for personal use only. Any other use requires prior permission of the American Society of Civil Engineers. This material may be found at https://doi.org/10.1061/(ASCE)1052-3928(2008)134:4(391)Publishe

Density estimates on composite polynomials

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Logistic regression modeling of construction negotiation outcomes

“© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.”Publishe

Higher-Order, Polar and Sz.-Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle

published_or_final_versio

SPCS: Secure and Privacy-Preserving Charging-Station Searching using VANET

Electric vehicle has attracted more and more attention all around the world in recent years because of its many advan- tages such as low pollution to the environment. However, due to the limitation of current technology, charging remains an important issue. In this paper, we study the problem of finding and making reservation on charging stations via a vehicular ad hoc network (VANET). Our focus is on the privacy concern as drivers would not like to be traced by knowing which charging stations they have visited. Technically, we make use of the property of blind signature to achieve this goal. In brief, an electric vehicle first generates a set of anonymous credentials on its own. A trusted au- thority then blindly signs on them after verifying the identity of the vehicle. After that, the vehicle can make charging station searching queries and reservations by presenting those signed anonymous credentials. We implemented the scheme and show that the credential signing process (expected to be the most time consuming step) can be completed within reasonable time when the parameters are properly set. In particular, the process can be completed in 5 minutes when 1024 bits of RSA signing key is used. Moreover, we show that our scheme is secure in terms of authentication and privacy-preserving.published_or_final_versio

Credential-based privacy-preserving power request scheme for smart grid network

A smart grid network adjusts power allocation by collecting information about the power usage of the customers in real-time. Authentication and user privacy preservation are the two major concerns on smart grid security. Authentication schemes that preserve users' privacy from third parties, but not from the power operator, have been proposed. In this paper, we propose a scheme that preserves users' privacy information, including their daily electricity usage pattern from third parties as well as from the power operator. At the same time, the scheme ensures that authentication can be properly done. These two properties are achieved by using anonymous credential under the principle of blind signature. Basically, a customer generates a set of credentials by himself and asks the control center to blindly sign them. When the customer needs to request more power later on, he presents the signed credential to the control center as proof of his identity. Implementation and analysis show that our scheme is feasible in terms of a number of performance measures such as the signing time and the credential collision rate. © 2011 IEEE.published_or_final_versionThe IEEE Global Communications Conference (GLOBECOM 2011), Houston, TX, USA, 5-9 December 2011. In Proceedings of GLOBECOM, 2011, p. 1-

Study of motoring operation of in-wheel switched reluctance motor drives for electric vehicles

Author name used in this publication: X. D. XueAuthor name used in this publication: K. W. E. ChengAuthor name used in this publication: N. C. CheungAuthor name used in this publication: Z. ZhangAuthor name used in this publication: J. K. LinRefereed conference paper2008-2009 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe