共查询到20条相似文献,搜索用时 15 毫秒
1.
《纯数学与应用数学通讯》2018,71(3):577-614
We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z > 0 can bind at most Z + C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas‐Fermi theory which, as a by‐product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.© 2017 Wiley Periodicals, Inc. 相似文献
2.
Ansgar Jüngel 《Mathematical Methods in the Applied Sciences》1996,19(5):401-424
The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi–Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage–current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device. 相似文献
3.
Nakao Hayashi Masahiro Ikeda Pavel I. Naumkin 《Mathematical Methods in the Applied Sciences》2011,34(8):896-910
We prove the existence of the wave operator for the system of the massive Dirac–Klein–Gordon equations in three space dimensions x∈ R 3 where the masses m, M>0. We prove that for the small final data , (?, ?)∈ H 2 + µ, 1 × H 1 + µ, 1, with and , there exists a unique global solution for system (1) with the final state conditions Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
Nelson José Rodrigues Faustino 《Mathematical Methods in the Applied Sciences》2017,40(11):4118-4127
Starting from the representation of the (n ? 1) + n ? dimensional Lorentz pseudo‐sphere on the projective space , we propose a method to derive a class of solutions underlying to a Dirac–Kähler type equation on the lattice. We make use of the Cayley transform to show that the resulting group representation arises from the same mathematical framework as the conformal group representation in terms of the general linear group . That allows us to describe such class of solutions as a commutative n ? ary product, involving the quasi‐monomials ) with membership in the paravector space . Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
5.
Ravi P. Agarwal Donal O'Regan Panos K. Palamides 《Mathematical Methods in the Applied Sciences》2006,29(1):49-66
This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above‐mentioned upper–lower solutions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
金永阳 《数学物理学报(A辑)》2009,29(5):1434-1441
该文得到了在Ω上以下问题
{Lp,ku+f(u)=0, ,
u|∂Ω=0
非负解的不存在性结果. 其中Ω为Heisenberg型群G中的区域(有界或无界), Lp, ku=divX (| X u|p-2 X u)为对应于Greiner型向量场 X 的一类次P-Laplace算子. 相似文献
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We consider the family of graphs with a fixed number of vertices and edges. Among all these graphs, we are looking for those minimizing the sum of the square roots of the vertex degrees. We prove that there is a unique such graph, which consists of the largest possible complete subgraph plus only one other non‐isolated vertex. The same result is proven for any power of the vertex‐degrees less than one half. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 230–240, 2002; DOI 10.1002/jgt.10025 相似文献
9.
Otto Rendón Leonardo Di G. Sigalotti Jaime Klapp 《Mathematical Methods in the Applied Sciences》2017,40(18):6642-6648
In this paper, we derive an asymptotic expansion for the semi‐infinite sum of Dirac‐δ functions centered at discrete equidistant points defined by the set . The method relies on the Laplace transform of the semi‐infinite sum of Dirac‐δ functions. The derived series distribution takes the form of the Euler‐Maclaurin summation when the distributions are defined for complex or real‐valued continuous functions over the interval . For n=1, the series expansion contributes with a term equal to δ(x)/2, which survives in the limit when a→0+. This term represents a correction term, which is in general omitted in calculations of the density of states of quantum confined systems by finite‐size effects. 相似文献
10.
In this paper, we shall prove that there is no [3q4-q3-q2-3q-1,5,3q4-4q3-2q+1]q code over the finite field for q11. Thus, we conclude the nonexistence of a [gq(5,d),5,d]q code for 3q4-4q3-2q+1d3q4-4q3-q. 相似文献
11.
Hartmut Schwetlick Daniel C. Sutton Johannes Zimmer 《Journal of Nonlinear Science》2012,22(6):917-934
The nonexistence of heteroclinic travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two stable phases. We demonstrate that there is no travelling wave joining bounded strains in the different wells of this potential for a range of wave speeds significantly lower than the speed of sound. We achieve this using a profile-corrector method previously used to show existence of travelling waves for the same model at higher subsonic velocities. 相似文献
12.
Homogenization and Hydrodynamic Limit for Fermi‐Dirac Statistics Coupled to a Poisson Equation 下载免费PDF全文
This paper deals with the diffusion approximation of a Boltzmann‐Poisson system modeling Fermi‐Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in [19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in [19], here we use two‐scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of [3]. © 2015 Wiley Periodicals, Inc. 相似文献
13.
关于一类Ginzburg-Landau型泛函径向极小元的注记 总被引:1,自引:0,他引:1
考虑的是Bethuel,Brczis和Helcin在[1]中提出的问题7.针对Ginzburg-Landau泛函的径向极小元,作者给出了这一问题的肯定回答. 相似文献
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16.
Nonexistence of Nonconstant Positive Steady
States of a Diffusive Predator-prey Model with
Fear Effect 下载免费PDF全文
In this paper, we investigate a diffusive predator-prey model with
fear effect. It is shown that, for the linear predator functional response case,the positive constant steady state is globally asymptotically stable if it ex-ists. On the other hand, for the Holling type II predator functional response
case, it is proved that there exist no nonconstant positive steady states for
large conversion rate. Our results limit the parameters range where complex
spatiotemporal pattern formation can occur. 相似文献
17.
We consider the poset SO(n) of all words over an n-element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i. e. there is a theorem of Kruskal–Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip-order can be chosen.Daykin introduced the V-order which generalizes the vip-order to the n2 case. He conjectured that the V-order gives a Kruskal–Katona type theorem for SO(n).We show that this conjecture fails for all n3 by explicitly giving a counterexample. Based on this, we prove that for no n3 the subword order SO(n) is a Macaulay poset. 相似文献
18.
We study a special case of Shigesada–Kawasaki–Teramoto (SKT) model for two competing species with the Dirichlet boundary conditions. In our case, one of the species is not influenced by self‐diffusion or cross‐diffusion. We specify the explicit range of parameters by contradiction such that there are no coexisting steady‐state solutions to the model. 相似文献
19.
We consider the system
20.
Florin Catrina 《Journal of Differential Equations》2005,215(1):19-36
In this paper, we discuss positive solutions for certain weighted elliptic equations with critical Sobolev exponent in RN. The weights depend on a positive parameter γ, which is allowed to increase to infinity. While for small values of γ solutions are completely classified, an attempt to such a classification is much more difficult for large values of the parameter. In the present work we prove the nonexistence of solutions with bounded energy as γ increases to infinity. We also prove a multiplicity result for high energy solutions. 相似文献