共查询到20条相似文献,搜索用时 298 毫秒
1.
In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we
prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces
\mathringB1-a¥,q{\mathring{B}^{1-\alpha}_{\infty,q}}, and global well-posedness of the critical quasi-geostrophic equation in
\mathringB0¥,q{\mathring{B}^{0}_{\infty,q}} for all 1 ≤ q < ∞. Here
\mathringBs¥,q {\mathring{B}^{s}_{\infty,q} } is the closure of the Schwartz functions in the norm of Bs¥,q{B^{s}_{\infty,q}}. 相似文献
2.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
tr( (-D)2 - CHRd,2\frac1|x|4 - V(x) )-g £ Cgò\mathbbRd V(x)+g+ \fracd4 dx, g 3 1 - \frac d 4,\mathrm{tr}\left( (-\Delta)^2 - C^{\mathrm{HR}}_{d,2}\frac{1}{|x|^4} - V(x) \right)_-^{\gamma}\leq C_\gamma\int\limits_{\mathbb{R}^d} V(x)_+^{\gamma + \frac{d}{4}}\,\mathrm{d}x, \quad \gamma \geq 1 - \frac d 4, 相似文献
3.
Zhi-song Yu Gui-hua Ren Hong-yi Fan Gen-Chang Cai Nian-Quan Jiang 《International Journal of Theoretical Physics》2012,51(7):2256-2261
We find that the Fock space projector |n〉〈n| is a Weyl ordered Laguerre polynomial 2 ::(-)nLn ( 4afa ) e-2afa ::2{\,}^{:}_{:}(-)^{n}L_{n} ( 4a^{\dagger}a ) e^{-2a^{\dagger}a}{\,}^{:}_{:}, where a † a is the number operator,:: ::,{}^{:}_{:}\ {}^{:}_{:} denotes the Weyl ordering symbol. This brings convenience to derive the Wigner functions of many other quantum states. 相似文献
4.
Xue-xiang Xu 《International Journal of Theoretical Physics》2012,51(7):2056-2065
We theoretically study the squeezing effect in a 3-wave mixing process, generated by the operator S3 o exp[m(a1a2-a1fa2f)+n(a1a3-a1fa3f)]S_{3}\equiv \exp[\mu(a_{1}a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}a_{3}^{\dagger})]. The corresponding 3-mode squeezed vacuum state in Fock space and its uncertainty relation are presented. It turns out that S 3 may exhibit enhanced squeezing. By virtue of integration within an ordered product (IWOP) of operators, we also give the S 3’s normally ordered expansion. Finally, we calculate the Wigner function of 3-mode squeezed vacuum state by using the Weyl ordering invariance under similar transformations. 相似文献
5.
The effective resistance or two-point resistance between two nodes of a resistor network is the potential difference that
appears across them when a unit current source is applied between the nodes as terminals. This concept arises in problems
which deal with graphs as electrical networks including random walks, distributed detection and estimation, sensor networks,
distributed clock synchronization, collaborative filtering, clustering algorithms and etc. In the previous paper (Jafarizadeh
et al. in J. Math. Phys. 50:023302, 2009) a recursive formula for evaluation of effective resistances on the so-called distance-regular networks was given based on
the Christoffel-Darboux identity. In this paper, we consider more general networks called pseudo-distance-regular networks
or QD type networks, where we use the stratification of these networks and show that the effective resistances between a given
node, say α, and all of the nodes β belonging to the same stratum with respect to α, are the same. Then, based on the spectral techniques, for those α,β’s which satisfy
L-1aa=L-1bbL^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}
(L
−1 is the pseudo-inverse of the Laplacian of the network), an analytical formula for effective resistances
Rab(m)R_{\alpha\beta^{(m)}}
(the equivalent resistance between terminals α and β, so that β belongs to the m-th stratum with respect to α) is given in terms of the first and second orthogonal polynomials associated with the network. From the fact that in distance-regular
networks,
L-1aa=L-1bbL^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}
is satisfied for all nodes α,β of the network, the effective resistances
Rab(m)R_{\alpha\beta^{(m)}}
for m=1,2,…,d (d is diameter of the network which is the same as the number of strata) are calculated directly, by using the given formula. 相似文献
6.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
7.
Gustav Holzegel 《Communications in Mathematical Physics》2010,294(1):169-197
The massive wave equation ${\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0}
8.
Using chiral perturbation theory we calculate for pion Compton scattering the isospin-breaking effects induced by the difference
between the charged and neutral pion mass. At one-loop order this correction is directly proportional to mp±2-mp02\ensuremath{m_{\pi^\pm}^2-m_{\pi^0}^2} and free of (electromagnetic) counterterm contributions. The differential cross-section for charged pion Compton scattering
p-g? p-g\ensuremath{\pi^-\gamma \rightarrow \pi^-\gamma} gets affected (in backward directions) at the level of a few permille. At the same time the isospin-breaking correction leads
to a small shift of the pion polarizabilities by d(ap- bp) @ 1.3 ·10-5\ensuremath{\delta(\alpha_\pi- \beta_\pi) \simeq 1.3 \cdot 10^{-5}} fm^3. In case of the low-energy gg? p0p0\ensuremath{\gamma\gamma \rightarrow \pi^0\pi^0} reaction isospin breaking manifests itself through a cusp effect at the p+p-\ensuremath{\pi^+\pi^-} threshold. We give an improved estimate for it based on the empirical p \pi
p \pi -scattering length difference a0-a2\ensuremath{a_0-a_2} . 相似文献
9.
We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality.
This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and
is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it
requires that the cosmological constant measured today, t
U
, be L ~ tU-2 ~ 10-122{\Lambda \sim t_{U}^{-2} \sim 10^{-122}} , as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation
determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature
parameter of the universe is Wk0 o -k/a02H2=-0.0055{\Omega _{\mathrm{k0}} \equiv -k/a_{0}^{2}H^{2}=-0.0055} , which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological
history. 相似文献
10.
Oscar M. Perdomo 《Mathematical Physics, Analysis and Geometry》2012,15(1):17-37
In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean
spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures,
in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every
h ? [-1,-\frac2?{n-1}n)h\in[-1,-\frac{2\sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of
S1n-1×\mathbbRS_1^{n-1}\times \mathbb{R} in the (n + 1)-dimensional de Sitter space S1n+1\hbox{\bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and
5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that
can be extended to closed hypersurfaces. 相似文献
11.
J. Stanzel F. Burmeister M. Neeb 《Applied Physics A: Materials Science & Processing》2010,100(1):21-29
We have studied the dynamics of photoexcited tungsten cluster anions Wn-\mathrm{W}_{n}^{-} (n=3,4,…,14) by means of time-resolved two-photon photodetachment spectroscopy. At an excitation energy of h
ν
pump=1.56 eV the photoinduced dynamics is mainly dominated by fast electronic relaxation processes. For the smallest clusters,
i.e., W3-\mathrm{W}_{3}^{-}, W4-\mathrm{W}_{4}^{-}, and W5-\mathrm{W}_{5}^{-}, individual relaxation channels have been identified and resolved on a timescale well below 100 fs. The time constants for
the decay of nascent and secondary electrons have been deduced from a Bloch model. Complete thermalization takes place for
all clusters on a timescale of ∼1 ps. 相似文献
12.
C. S. Fischer T. Goecke R. Williams 《The European Physical Journal A - Hadrons and Nuclei》2011,47(2):28
Using the Dyson-Schwinger and Bethe-Salpeter equations, we calculate the hadronic light-by-light scattering contribution to
the anomalous magnetic moment of the muon am\ensuremath a_\mu , using a phenomenological model for the gluon and quark-gluon interaction. We find am=(84 ±13)×10-11\ensuremath a_\mu=(84 \pm 13)\times 10^{-11} for meson exchange, and am = (107 ±2 ±46)×10-11\ensuremath a_\mu = (107 \pm 2 \pm 46)\times 10^{-11} for the quark loop. The former is commensurate with past calculations; the latter much larger due to dressing effects. This
leads to a revised estimate of am=116 591 865.0(96.6)×10-11\ensuremath a_\mu=116 591 865.0(96.6)\times 10^{-11} , reducing the difference between theory and experiment to ≃ 1.9s \sigma . 相似文献
13.
Magnetocaloric properties of as-quenched Ni50.4Mn34.9In14.7 ferromagnetic shape memory alloy ribbons
Sánchez Llamazares J. L. García C. Hernando B. Prida V. M. Baldomir D. Serantes D. González J. 《Applied Physics A: Materials Science & Processing》2011,103(4):1125-1130
The temperature dependences of magnetic entropy change and refrigerant capacity have been calculated for a maximum field change
of Δ
H=30 kOe in as-quenched ribbons of the ferromagnetic shape memory alloy Ni50.4Mn34.9In14.7 around the structural reverse martensitic transformation and magnetic transition of austenite. The ribbons crystallize into
a single-phase austenite with the L21-type crystal structure and Curie point of 284 K. At 262 K austenite starts its transformation into a 10-layered structurally
modulated monoclinic martensite. The first- and second-order character of the structural and magnetic transitions was confirmed
by the Arrott plot method. Despite the superior absolute value of the maximum magnetic entropy change obtained in the temperature
interval where the reverse martensitic transformation occurs
(|\varDelta SMmax|=7.2 J kg-1 K-1)(|\varDelta S_{\mathrm{M}}^{\max}|=7.2\mbox{ J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}) with respect to that obtained around the ferromagnetic transition of austenite
(|\varDelta SMmax|=2.6 J kg-1 K-1)(|\varDelta S_{\mathrm{M}}^{\max}|=2.6\mbox{ J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}), the large average hysteretic losses due to the effect of the magnetic field on the phase transformation as well as the narrow
thermal dependence of the magnetic entropy change make the temperature interval around the ferromagnetic transition of austenite
of a higher effective refrigerant capacity (RCmagneff=95J kg-1\mathrm{RC}^{\mathrm{magn}}_{\mathrm{eff}}=95\mbox{J}\,\mbox{kg}^{-1} versus RCstructeff=60J kg-1)\mathrm{RC}^{\mathrm{struct}}_{\mathrm{eff}}=60\mbox{J}\,\mbox{kg}^{-1}). 相似文献
14.
Yu. M. Bystritskiy S. R. Gevorkyan E. A. Kuraev 《The European Physical Journal C - Particles and Fields》2009,64(1):47-54
The final state interaction of pions in the decay K
±→π
+
π
−
e
±
ν allows one to obtain the value of the isospin and angular momentum zero pion–pion scattering length a
00. To extract this quantity from experimental data the radiative corrections (RC) have to be taken into account. Based on the
lowest order results and the factorization hypothesis, we get the expressions for RC in the leading and next-to leading logarithmical
approximation. It is shown that the decay width dependence on the lepton mass m
e
through the parameter
s = \fraca2p(ln\fracM2me2-1)\sigma=\frac{\alpha}{2\pi}(\ln\frac{M^{2}}{m_{e}^{2}}-1) has the standard form of the Drell–Yan process and is proportional to the Sommerfeld–Sakharov factor. The numerical estimations
are presented. 相似文献
15.
Siegfried Bethke 《The European Physical Journal C - Particles and Fields》2009,64(4):689-703
Measurements of α
s, the coupling strength of the Strong Interaction between quarks and gluons, are summarised and an updated value of the world
average of as(MZ0)\alpha_{\mathrm{s}}(M_{\mathrm{Z}^{0}}) is derived. Special emphasis is laid on the most recent determinations of α
s. These are obtained from τ-decays, from global fits of electroweak precision data and from measurements of the proton structure function F2, which are based on perturbative QCD calculations up to O(as4)\mathcal{O}(\alpha_{\mathrm{s}}^{4}); from hadronic event shapes and jet production in e+e− annihilation, based on O(as3)\mathcal{O}(\alpha_{\mathrm{s}}^{3}) QCD; from jet production in deep inelastic scattering and from ϒ decays, based on O(as2)\mathcal{O}(\alpha_{\mathrm{s}}^{2}) QCD; and from heavy quarkonia based on unquenched QCD lattice calculations. A pragmatic method is chosen to obtain the world
average and an estimate of its overall uncertainty, resulting in
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