The main result in this paper is the equivalence, for any Banach space B , between (i) "Every normalized basic sequence (an)nEN in B is weakly null" , and (ii) "For every normalized basic sequence (an)nFN in B , Pelczyfiski proved that (i) characterizes the fact of B being reflexive. So, the same holds for (ii) and we have a "geometrical" characterization of reflexivity. We finish quoting some equivalent version of the above result. AMS Subject Class. 1980 : 46 b 10 , 46 b 15
An asymmetric link problem is a considerable effect in vehicular network, but usually overlooked by many researchers.Most of researches concerning this problem are extensions on unicasting routing protocols which have a primary route of data transmission. However, reliable broadcasting protocols such as Density-Aware Reliable Broadcasting protocol (DECA) have no exact route for sending data but do data dissemination. Therefore, in this paper, we focus on making a solution for broadcasting protocols. Specifically, we design a method to select the most efficient preferred node with broadly transmission range and vastly neighbor coverage. In this paper, we propose a RSSI-Voting algorithm as a new node selection algorithm. Each node votes a neighbor who has the highest Received Signal Strength Indicator (RSSI). When a sender wants to broadcast a message, it will select a preferred forwarder node who gains a majority vote. The simulation results show that our mechanism can improve protocol performance up to 17% and decrease its retransmission overhead up to 28%.Keywords-Asymmetric Link, Reliable Broadcasting Protocol , NS-3, Vehicular Network L INTRODUCTIONVehicular Ad-hoc Networks (VANETs) is a famous topic on ad-hoc networks, which many researchers pay attention to. This is because V ANET can support many applications on Intelligent Transportation System (ITS). The applications such as driver assistant or safety transport application need reliable broadcasting protocols to provide accuracy and reliable service.However, most of researches in V ANETs were evaluated on simulation that does not require any equipment, high-cost devices and vehicles. So the simulation does not include many problems on the real world such as building effects and signal interference effect. The previous reliable broadcasting protocols such as DECA[5], POCA[14], EAEP[15], AckPBSM[16], DV Cast[17] are the protocols that proficiently operate on their simulations. But these protocols do not provide the realistic scenario evaluation that can affect their performance and overhead. So we choose DECA as a case study to observe its behavior on the real world. We have developed DECA [5] on NS-3[4]. We can evaluate our protocol on both simulation and emulation (real world) using NS-3. Moreover, NS-3 also has more benefit and better performance than NS-2 [1][2][3]. In real world *Corresponding author 978-1-4577-2166-3/11/$26.00 ©2011 IEEE experiment with NS-3's emulation, we have found a problem.While we deployed four laptops running DECA, we found that DECA's overhead increased more than happened in simulation (this issue will be discussed in Section lILA). We observed that the protocol selected inefficient forwarder nodes. This is due to an asymmetric link problem. The reason is that on the real world system, each computer has different capabilities of wireless devices and antenna. These affect to computer's transmission range. However, this problem is usually ignored because most of researchers use the same transmission range for every node in their...
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