Existence of Pulsating Roll-Waves for the Saint Venant System

The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic travelling waves) follows from a classical work due to DRESSLER [6]. The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation. Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions.     

Battery-Aware Routing for Streaming Data Transmissions in Wireless Sensor Networks

Recent technological advances have made it possible to support long lifetime and large volume streaming data transmissions in sensor networks. A major challenge is to maximize the lifetime of battery-powered sensors to support such transmissions. Battery, as the power provider of the sensors, therefore emerges as the key factor for achieving high performance in such applications. Recent study in battery technology reveals that the behavior of battery discharging is more complex than we used to think. Battery powered sensors might waste a huge amount of energy if we do not carefully schedule and budget their discharging. In this paper we study the effect of battery behavior on routing for streaming data transmissions in wireless sensor networks. We first give an on-line computable energy model to mathematically model battery discharge behavior. We show that the model can capture and describe battery behavior accurately at low computational complexity and thus is suitable for on-line battery capacity computation. Based on this battery model we then present a battery-aware routing (BAR) protocol to schedule the routing in wireless sensor networks. The routing protocol is sensitive to the battery status of routing nodes and avoids energy loss. We use the battery data from actual sensors to evaluate the performance of our protocol. The results show that the battery-aware protocol proposed in this paper performs well and can save a significant amount of energy compared to existing routing protocols for streaming data transmissions. Network lifetime is also prolonged with maximum data throughput. As far as we know, this is the first work considering battery-awareness with an accurate analytical on-line computable battery model in sensor network routing. We believe the battery model can be used to explore other energy efficient schemes for wireless networks as well.     

Performance modeling and evaluation of data/voice services in wireless networks

Application-level performance is a key to the adoption and success of the CDMA 2000. To predict this performance in advance, a detailed end-to-end simulation model of a CDMA network is built to include application traffic characteristics, network architecture, network element details using the proposed simulation methodology. We assess the user-perceived application performance when a RAN and a CN adopt different transport architectures such as ATM and IP. To evaluate the user-perceived quality of voice service, we compare the end-to-end packet delay for different vocoder schemes such as G.711, G.726 (PCM), G.726 (ADPCM), and vocoder bypass scheme. By the simulation results, the vocoder bypass scenario shows 30% performance improvement over the others. We also compare the quality of voice service with and without DPS scheduling scheme. We know that DPS scheme keep the voice delay bound even if the service traffic is high. For data packet performance, HTTP v.1.1 shows better performance than that of HTTP v.1.0 due to the pipelining and TCP persistent connection. We may conclude that IP transport technology is better solution for higher FER environment since the packet overhead of IP is smaller than that of ATM for web browsing data traffic, while it shows opposite effect to the small size voice packet in RAN architecture. We show that the 3G-1X EV-DO system gives much better packet delay performance than 3G-1X RTT. The main conclusion is that end-to-end application-level performance is affected by various elements and layers of the network and thus it must be considered in all phases of the development process. Jae-Hyun Kim He received the B.S., M.S., and Ph.D. degrees, all in computer science and engineering, from Hanyang University, Ansan, Korea, in 1991, 1993, and 1996 respectively. In 1996, he was with the Communication Research Laboratory, Tokyo, Japan, as a Visiting Scholar. From April 1997 to October 1998, he was a post-doctoral fellow at the department of electrical engineering, University of California, Los Angeles. From November 1998 to February 2003, he worked as a member of technical staff in Performance Modeling and QoS management department, Bell laboratories, Lucent Technologies, Holmdel, NJ. He has been with the department of electrical engineering, Ajou University, Suwon, Korea, as an assistant professor since 2003. His research interests include QoS issues and cross layer optimization for high-speed wireless communication. Dr. Kim was the recipient of the LGIC Thesis Prize and Samsung Human-Tech Thesis Prize in 1993 and 1997, respectively. He is a member of the Korean Institute of Communication Sciences (KICS), Korea Institute of Telematics and Electronis (KITE), Korea Information Science Society (KISS), and IEEE. Hyun-Jin Lee received the B.S. degree in electrical engineering from Ajou University, Suwon, Korea, in 2004, and is working toward the M.S. degree and Ph. D. degree in electrical engineering at Ajou University. He has been awarded Samsung Human-Tech Thesis Prize in 2004. His research interests QoS, especially network optimization and wireless packet scheduling. He is a member of the KICS. Sung-Min Oh received the B.S. and M. S. degrees in electrical engineering form Ajou University, Suwon, Korea, in 2004, and is working toward the Ph. D. degree in electrical engineering at Ajou University. His research interests QoS performance analysis and 4G network. He is a member of the KICS. Sung-Hyun Cho received his B.S., M.S., and Ph.D. in computer science and engineering from Hanyang University, Korea, in 1995, 1997, and 2001, respectively. From 2001 to 2005, he has been with Samsung Advanced Institute of Technology, where he has been engaged in the design and standardization of MAC and upper layers of B3G, IEEE 802.16e, and WiBro systems. He is currently a MAC part leader in the telecommunication R&D center of Samsung Electronics. His research interests include 4G air interface design, radio resource management, cross layer design, and handoff in wireless systems.     

Radially symmetric wave maps from (1 + 2)-dimensional Minkowski space to general targets

Extending our previous work [5] on this subject we show global existence of smooth solutions to the Cauchy problem for wave maps from the (1 + 2)-dimensional Minkowski space to an arbitrary smooth, compact Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. Received: 14 December 2001 / Accepted: 1 March 2002 / Published online: 6 August 2002     

Nonvanishing derivatives and normal families

We consider the differential operators Ψ _k , defined by Ψ₁(y) =y and Ψ _k+1(y)=yΨ _k y+d/dz(Ψ _k (y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ _k F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z ²+β z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ _k (F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ _k (f ^′/f) =f ^(k)/f, we deduce in particular that iff andf ^(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f ^′/f :f ∈F} is normal. The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999, and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank Günter Frank for helpful discussions.     

cos πρ theorems for δ-subharmonic functions

For ϕ a δ-subharmonic function, sharp results are obtained that connectA(r, ϕ), B(r, ϕ) andT(r, ϕ), whereA(r, ϕ)=inf_|z|=r ϕ(z),B(r, ϕ)=sup_|z|=r ϕ(z), andT(r, ϕ) is the Nevanlinna characteristics.     

Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations

The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L ₂-estimates) and the least absolute deviation estimates (L ₁-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.