On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e

For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645]. These solutions contain not only those obtained by Zhang, Yang, and Cao but also some which are neither diagonally nor permutation equivalent to those obtained by Zhang, Yang, and Cao. Therefore, the open problem proposed by Zhang, Yang, and Cao in the cited paper is solved

Human-centred design: An emergent conceptual model

(Human-centred design: an emergent conceptual module by Zhang T and Dong H) Understanding human needs and how design responds to human needs are essential for human-centred design (HCD). By combining Maslow’s hierarchy of needs model and Küthe’s “design and society” model, this paper proposes a conceptual model of human-centred design which marries psychology and sociology in investigating the relationship between design and human needs. The study reveals a tendency that design evolution responds to the hierarchy of human needs. Nowadays design tends to care for more levels of human needs

Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems

In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system $\ddot{u}-L(t)u(t)+W_u(t,u)=0$, $\forall t\in\mathbb{R}$, by means of the minmax arguments in the critical point theory, where $L(t)$ is unnecessary uniformly positively definite for all $t\in \mathbb{R}$ and $W_u(t, u)$ sastisfies the asymptotically linear condition.Comment: published in International Mathematical Forum, Vol. 6, 2011, no. 4, 159 - 17

Yingjin Zhang, ed. China in a polycentric world : essays in Chinese comparative literature

This article reviews the book China in a Polycentric World: Essays in Chinese Comparative Literature edited by Yingjin Zhang

On the spectral characterization of pineapple graphs

The pineapple graph $K_p^q$ is obtained by appending $q$ pendant edges to a vertex of a complete graph $K_{p}$ ($q\geq 1,\ p\geq 3$). Zhang and Zhang ["Some graphs determined by their spectra", Linear Algebra and its Applications, 431 (2009) 1443-1454] claim that the pineapple graphs are determined by their adjacency spectrum. We show that their claim is false by constructing graphs which are cospectral and non-isomorphic with $K_p^q$ for every $p\geq 4$ and various values of $q$. In addition we prove that the claim is true if $q=2$, and refer to the literature for $q=1$, $p=3$, and $(p,q)=(4,3)$

Explicit eigenvalues of certain scaled trigonometric matrices

In a very recent paper "\emph{On eigenvalues and equivalent transformation of trigonometric matrices}" (D. Zhang, Z. Lin, and Y. Liu, LAA 436, 71--78 (2012)), the authors motivated and discussed a trigonometric matrix that arises in the design of finite impulse response (FIR) digital filters. The eigenvalues of this matrix shed light on the FIR filter design, so obtaining them in closed form was investigated. Zhang \emph{et al.}\ proved that their matrix had rank-4 and they conjectured closed form expressions for its eigenvalues, leaving a rigorous proof as an open problem. This paper studies trigonometric matrices significantly more general than theirs, deduces their rank, and derives closed-forms for their eigenvalues. As a corollary, it yields a short proof of the conjectures in the aforementioned paper.Comment: 7 pages; fixed Lemma 2, tightened inequalitie

Using Combined Lane Change and Variable Speed Limit Control Techniques Can Ease Congestion and Reduce Fuel Use and Emissions

Traffic during peak hours is getting worse over time and the duration of the peak is increasing in most metropolitan areas as more drivers try to use limited roadway capacity. Bottlenecks caused by traffic incidents or road construction limit roadway capacity even further and can cause traffic “shock waves.” When an incident causes a highway lane to close unexpectedly, vehicles are forced to change lanes close to the incident and at low speeds. These forced lane changes interfere with traffic flow in open lanes and decrease the overall flow of the roadway. Heavy-duty trucks can exacerbate congestion because they are larger and slower than passenger vehicles. Advanced technologies may help to improve traffic flow in these situations. Variable speed limits can change based on road, traffic, and weather conditions. Speed limits can be reduced in real time when congestion is imminent to smooth traffic flow and handle more traffic volume at a slower, but not stop-and-go, speed. Lane change control systems provide lane change recommendations well upstream of blocked lanes, spreading lane changes over a greater distance and minimizing bottlenecks that disrupt traffic flow.This policy brief summarizes findings from researchers at the University of Southern California who simulated traffic patterns along a section of Interstate 710 near the Ports of Long Beach/Los Angeles, a congested area that gets substantial truck traffic. They simulated the use of variable speed limit and lane change control systems to evaluate the potential traffic impacts of these systems.This brief is based on research from two NCST projects: Eco-Friendly Intelligent Transportation System Technology for Freight Vehicles, and Reducing Truck Emissions and Improving Truck Fuel Economy via ITS Technologies

Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541

On the Renormalization of the Kardar-Parisi-Zhang equation

The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally subtracted perturbation expansion about d = 2. For the KPZ roughening transition in dimensions d > 2, this renormalization group yields the dynamic exponent z* = 2 and the roughness exponent chi* = 0, which are exact to all orders in epsilon = (2 - d)/2. The expansion becomes singular in d = 4, which is hence identified with the upper critical dimension of the KPZ equation. The implications of this perturbation theory for the strong-coupling phase are discussed. In particular, it is shown that the correlation functions and the coupling constant defined in minimal subtraction develop an essential singularity at the strong-coupling fixed point.Comment: 21 pp. (latex, now texable everywhere, no other changes), with 2 fig