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1.
This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H n. The sharp bounds for the strong type(p, p)(1 ≤ p ≤∞) estimates of n-dimensional Hausdorff operators on H n are obtained. The sharp bounds for strong(p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on H n. The weak type(p, p)(1 ≤ p ≤∞) estimates are also obtained.  相似文献   
2.
Since the quality factor of an acoustic wave resonator (AWR) reached 1011, AWRs have been regarded as a good carrier of quantum information. In this paper, a scheme to construct a NOON state with two AWRs assisted by a nitrogen‐vacancy‐center ensemble (NVE) is proposed. The two AWRs cross each other vertically, and the NVE is located at the center of the crossing. By considering the decoherence of the system and using resonant interactions between the AWRs and the NVE, and the single‐qubit operation of the NVE, a NOON state can be achieved with a fidelity higher than 98.8% when the number of phonons in the AWR is N 3 .  相似文献   
3.
The controlled synthesis and structure determination of a bimetallic nanocluster Au57Ag53(C≡CPh)40Br12 (Au57Ag53) is presented. The metal core has a four‐shell Au2M3@Au34@Ag51 @Au20 (M=1/3 Au+2/3 Ag) architecture. In contrast to the previously reported large nanoclusters that have highly symmetric kernel structures, the metal atoms in Au57Ag53 are arranged in an irregular manner with C1 symmetry. This cluster exhibits excellent thermal stability and is robust under oxidative or basic conditions. The silver precursors play a key role in dictating the structures of the nanoclusters, which suggests the importance of the counteranions used.  相似文献   
4.
A classical perturbation result for nonsingular systems of linear algebraic equations is extended to general consistent systems under any norm. An optimal perturbation result is also obtained for general linear least squares problems under a Euclidean norm.  相似文献   
5.
A facile and simple catalyst‐free protocol has been developed for the condensation of 1,2‐diketones with aromatic 1,2‐diamines in polyethylene glycol (PEG), providing quinoxaline derivatives in good yields. The important features of the methodology are broad substrates scope, simple workup, catalyst free, environmentally benign, and no requirement for metal catalysts. It is noteworthy that the cyclization reaction of 1,2‐diketones with aliphatic 1,2‐diamines is also conducted smoothly to afford pyrazines in good yields under the standard conditions. In addition, PEG could be recovered easily and was reused without evident loss in activity  相似文献   
6.
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier–Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is constructed by approximating the system and regularizing the initial values which may contain vacuum states. Then some global in time estimates on the weak solution are obtained. Based on these uniform estimates, the vacuum states are shown to vanish in finite time and the weak solution we constructed becomes a unique strong one. Consequently, the stability of the rarefaction wave is proved in a weak sense. The theory holds for large-amplitudes rarefaction waves and arbitrary initial perturbations.  相似文献   
7.
The recent successful growth of MoSi2N4 and WSi2N4 monolayers led to the discovery of a new class of the two-dimensional (2D) MA2Z4 materials with no known 3D layered allotropes, which renders great possibilities to integrate diverse properties by proper design of sandwiched “MZ2” building blocks and “A−Z” passivation layers. In this work, the dynamic stability, electronic properties, and surface reactivity of the new MA2Z4 family, in which M is Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, A refers to Si or Ge, and Z is N, P or As, is theoretically probed. Among the proposed 54 possible combinations, about 42 compositions are dynamically stable, which vary from non-magnetic, anti-ferromagnetic, to ferromagnetic semiconductors, metals and half-metals. In particular, the VB (V, Nb, Ta) MA2Z4 possesses robust intrinsic ferromagnetism that is essential for spintronics applications. In regard to surface activity, most MA2Z4, particularly N- or P-terminated IVB and VB MA2Z4, have high catalytic potential for hydrogen evolution, and the ▵GH of non-magnetic MA2Z4 is highly correlated to the highest occupied p electronic states of the surface Z atoms. The photocatalytic activity is also evaluated. MoSi2N4 and WSi2N4 within 4 % tensile strain are capable of photocatalytic overall water splitting. The findings indicate the new 2D MA2Z4 family has fascinating properties and possesses strong potential for applications but not limited to electronics, spintronics and catalysts, which will stimulate the interests of experimental synthesis.  相似文献   
8.
Effectively enhancing the enantioselectivity is a persistent challenge in heterogeneous asymmetric catalysis. Here, the validity of a layered double hydroxides (LDH) nanosheet as an efficient planar substituent to enhance the enantioselectivity has been investigated theoretically; first in vanadium‐catalyzed asymmetric epoxidation of allylic alcohols, and then in zinc‐catalyzed direct asymmetric aldol addition. The computational predication is further confirmed experimentally in zinc‐catalyzed direct asymmetric aldol addition by controlling the location of catalytic sites.  相似文献   
9.
10.
We consider the n-dimensional modified quasi-geostrophic (SQG) equations
tθ + u . ∇θ + κΛαθ = 0,tθ+u.θ+κΛαθ=0,
u = Λα-1 Rθu=Λα-1Rθ
with κ > 0, α ∈ (0,1] and θ0W1, ∞ (?n). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu [5], who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case. The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol [2].  相似文献   
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