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1.
Alessandro Morando Paola Trebeschi Tao Wang 《Journal of Differential Equations》2019,266(9):5397-5430
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme. 相似文献
2.
This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but ) nonlinearities. 相似文献
3.
1-read/1-write (1R1W) register file (RF) is a popular memory configuration in modern feature rich SoCs requiring significant amount of embedded memory. A memory compiler is constructed using the 8T RF bitcell spanning a range of instances from 32 b to 72 Kb. An 8T low-leakage bitcell of 0.106 μm2 is used in a 14 nm FinFET technology with a 70 nm contacted gate pitch for high-density (HD) two-port (TP) RF memory compiler which achieves 5.66 Mb/mm2 array density for a 72 Kb array which is the highest reported density in 14 nm FinFET technology. The density improvement is achieved by using techniques such as leaf-cell optimization (eliminating transistors), better architectural planning, top level connectivity through leaf-cell abutment and minimizing the number of unique leaf-cells. These techniques are fully compatible with memory compiler usage over the required span. Leakage power is minimized by using power-switches without degrading the density mentioned above. Self-induced supply voltage collapse technique is applied for write and a four stack static keeper is used for read Vmin improvement. Fabricated test chips using 14 nm process have demonstrated 2.33 GHz performance at 1.1 V/25 °C operation. Overall Vmin of 550 mV is achieved with this design at 25 °C. The inbuilt power-switch improves leakage power by 12x in simulation. Approximately 8% die area of a leading 14 nm SoC in commercialization is occupied by these compiled RF instances. 相似文献
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For z1,z2,z3∈Zn, the tristance d3(z1,z2,z3) is a generalization of the L1-distance on Zn to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticodeAd of diameter d is a subset of Zn with the property that d3(z1,z2,z3)?d for all z1,z2,z3∈Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z2 for all diameters d?1. We then generalize this result to two related distance models: a different distance structure on Z2 where d(z1,z2)=1 if z1,z2 are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z2 is replaced by the hexagonal lattice A2. We also investigate optimal tristance anticodes in Z3 and optimal quadristance anticodes in Z2, and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multi-dimensional interleaving schemes and to connectivity loci in the game of Go. 相似文献
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9.
M. Brokate D. Rachinskii 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):385-411
The paper is concerned with the study of plasticity models described by differential equations with stop and play operators.
We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the
vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another
class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions.
The paper was written during the research stay of D. Rachinskii at the Technical University Munich supported by the research
fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grant No. 01-01-00146, 03-01-00258), and the Grants of the President of Russia (Grant No. MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged. 相似文献
10.
In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G. 相似文献