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81.
缪正武 《浙江大学学报(理学版)》2019,46(6):680-685
提出利用拉格朗日乘子法重新证明σ 2 ![]()
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算子的最优凹性,并定义了一个凸锥Γ 3 ? = λ = ( λ 1 , λ 2 , ? , λ n ) ∈ R n : σ 1 ( λ ) > 0 , σ 2 ( λ | i ) > 0 , 1 ≤ i ≤ n ![]()
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。利用σ 2 ![]()
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算子的最优凹性,给出了σ 2 H e s s i a n 方 程 P o g o r e l o v ![]()
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型C 2 ![]()
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内估计,进而证明了σ 2 ( D 2 u ( x ) ) = 1 , x ∈ R n ![]()
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的满足二次多项式增长条件的Γ 3 ? - ![]()
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凸整解为二次多项式。 相似文献
82.
张四保 《数学的实践与认识》2020,(7):273-276
设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1. 相似文献
83.
In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with -growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case. 相似文献
84.
Apeng Chen Joann J. Lu Congying Gu Min Zhang Kyle B. Lynch Shaorong Liu 《Analytica chimica acta》2015
Toward developing a micro HPLC cartridge, we have recently built a high-pressure electroosmotic pump (EOP). However, we do not recommend people to use this pump to deliver an organic solvent directly, because it often makes the pump rate unstable. We have experimented several approaches to address this issue, but none of them are satisfactory. Here, we develop an innovative approach to address this issue. We first create an abruption (a dead-volume) within a fluid conduit. We then utilize an EOP to withdraw, via a selection valve, a train of eluent solutions having decreasing eluting power into the fluid conduit. When these solutions are further aspirated through the dead-volume, these solutions are partially mixed, smoothening concentration transitions between two adjacent eluent solutions. As these solutions are pushed back, through the dead-volume again, a smooth gradient profile is formed. In this work, we characterize this scheme for gradient formation, and we incorporate this approach with a high-pressure EOP, a nanoliter injection valve, and a capillary column, yielding a micro HPLC system. We then couple this micro HPLC with an electrospray ionization – mass spectrometer for peptide and protein separations and identifications. 相似文献
85.
86.
For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates. 相似文献
87.
Let M be an -dimensional closed orientable submanifold in an -dimensional space form . We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on M defined by , where T is a general symmetric, positive definite and divergence-free -tensor on M. The upper bound is given in terms of an integration involving tr T and , where tr T is the trace of the tensor T and is a normal vector field associated with T and the second fundamental form A of M. Furthermore, we give the sufficient and necessary conditions when the upper bound is attained. Our main theorem can be viewed as an extension of the famous “Reilly inequality”. The operator can be regarded as a natural generalization of the well-known operator which is the linearized operator of the first variation of the -th mean curvature for hypersurfaces in a space form. As applications of our main theorem, we generalize the results of Grosjean [17] and Li–Wang [20] in codimension one to arbitrary codimension. 相似文献
88.
89.
Shumin Li 《Applicable analysis》2013,92(11):2335-2356
In this article, we consider Maxwell's equations in an isotropic, inhomogeneous and non-stationary medium. We discuss an inverse problem of determining the t-independent components of the coefficients ?, μ in the constitutive relations from a finite number of interior measurements. We prove a Lipschitz stability estimate for the inverse problem by applying the argument on the basis of Carleman estimate. 相似文献
90.
Xiaqi Ding 《数学物理学报(B辑英文版)》2012,(1):209-218
This paper gives some estimates of a quadratic functional related with Riemann Hypothesis. 相似文献