In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-△u=F（u,Du） u（0,x）=f（x）∈H^s,δtu（0,x）=g（x）∈H^s-1...In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-△u=F（u,Du） u（0,x）=f（x）∈H^s,δtu（0,x）=g（x）∈H^s-1,where F is quadratic in Du with D = （δr, δx1,…, δxn）.We proved that the range of s is s ≥n＋1/2 ＋ δ, respectively, with δ 〉 1/4 if n = 2, and δ 〉 0 if n = 3, and δ ≥0 if n ≥ 4. Which is consistent with Lindblad＇s counterexamples [3] for n = 3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.展开更多
Datapath accounts for a considerable part of power consumption in VLSI circuit design. This paper presents a method for physical implementation of datapath to achieve low power consumption. Regularity is a characteris...Datapath accounts for a considerable part of power consumption in VLSI circuit design. This paper presents a method for physical implementation of datapath to achieve low power consumption. Regularity is a characteristic of datapath and the key of the proposed method, where synthesis is tightly combined with placement to make full use of regularity, so that low power consumption is achieved. In This paper, a new concept of Synthesis In Relative Placement (SIRP) is given to deal with the semi-regularity in some datapath. Experimental results of a sample circuit validated the proposed method.展开更多
基金Supported by the NSF of China(10225102, 10301026)Supported by the South-west Jiaotong University Foundation(20005B05)
文摘In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-△u=F（u,Du） u（0,x）=f（x）∈H^s,δtu（0,x）=g（x）∈H^s-1,where F is quadratic in Du with D = （δr, δx1,…, δxn）.We proved that the range of s is s ≥n＋1/2 ＋ δ, respectively, with δ 〉 1/4 if n = 2, and δ 〉 0 if n = 3, and δ ≥0 if n ≥ 4. Which is consistent with Lindblad＇s counterexamples [3] for n = 3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.
基金Project (No. 2002 AA1Z1140) supported by the Hi-Tech Research and Development Program (863) of China and the Fork Ying Tong Education Foundation (No. 94031), China
文摘Datapath accounts for a considerable part of power consumption in VLSI circuit design. This paper presents a method for physical implementation of datapath to achieve low power consumption. Regularity is a characteristic of datapath and the key of the proposed method, where synthesis is tightly combined with placement to make full use of regularity, so that low power consumption is achieved. In This paper, a new concept of Synthesis In Relative Placement (SIRP) is given to deal with the semi-regularity in some datapath. Experimental results of a sample circuit validated the proposed method.
