Our procedure will be to embed an arbitrary convex set into a vector space, V (§2.2.1.2), and argue (in the subsequent sections) for progressively adding more structure to V, until it has enough structure to support a theorem to the effect that the convex set of states can in fact ...
At first I will give complete definitions, state and prove simple lemmas, etc., in order to establish common language. As time progresses I expect that things will become a little more high-level, less self-contained, and more technical. Depending on your background and interests, you may ...
Since [Math Processing Error]p∈[2N−μN,2N−μN−2), then by Hardy–Littlewood–Sobolev inequality and Sobolev embedding theorem, it is easy to prove that J is well defined on E and belongs to [Math Processing Error]C1(E,R). Moreover, there holds [Math Processing Error]⟨J′...
Testing excited-state energy density functional and potential with the ionization potential theorem The modified local spin density functional and the related local potentialfor excited states is tested by employing the ionization potential theorem. Thefu... M Hemanadhan,M Shamim,MK Harbola - 《Journa...
In this work, a comparison of the thermo-hydraulic performance and the entropy generation rate for two different types of low temperature solar collectors:... Ramirez-Minguela, J. J,Alfaro-Ayala, J. A,Rangel-Hernandez, V. H,... - 《Solar Energy》 被引量: 0发表: 2018年 加载更多来源...
where V∈ 𝓒1(ℝN, [0, ∞)) satisfies some weak assumptions, and f∈ 𝓒(ℝ, ℝ) satisfies the general Berestycki-Lions assumptions. By introducing some new tricks, we prove that the above problem admits a ground state solution of Pohožaev type and a least energy solution. Th...
We extend the result in Nakanishi and Schlag (J Differ Equ 250:2299–2333, 2011) on the nonlinear Klein–Gordon equation to the nonlinear Schrdinger equation with the focusing cubic nonlinearity in three dimensions, for radial data of energy at most slightly above that of the ground state. ...
\boldsymbol{A} \boldsymbol{A} matrices are important for AMP, and why AMP has a state evolution. In this work, we provide a heuristic derivation of AMP and its state evolution, based on the idea of "first-order cancellation," that provides insights missing from the LBP derivation while ...
Magic states are key ingredients in schemes to realize universal fault-tolerant quantum computation. Theories of magic states attempt to quantify this computational element via monotones and determine how these states may be efficiently transformed into
Thus, it is of great interest to investigate the formation of vacuum state and delta shock wave by taking the perturbed parameter A tend to zero in the solutions to the Riemann problem (1.1), (1.3). The major task of this paper is to prove whether the limits A→0 of solutions to the...