共查询到20条相似文献,搜索用时 31 毫秒
1.
A. A. Tolchennikov 《Russian Journal of Mathematical Physics》2008,15(1):128-139
For the kernel of the Laplace operator ΔΛ with potential Σ
j=1
k
c
j
δ
q
j
(x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ
k
⊕ ℂ
k
), an isomorphism Γ: ker ΔΛ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH
Λ)) are found.
Dedicated to the memory of V. A. Geyler 相似文献
2.
A trajectory attractor is constructed for the 2D Euler system containing an additional dissipation term −ru, r > 0, with periodic boundary conditions. The corresponding dissipative 2D Navier-Stokes system with the same term −ru and with viscosity v > 0 also has a trajectory attractor, . Such systems model large-scale geophysical processes in atmosphere and ocean (see [1]). We prove that → as v → 0+ in the corresponding metric space. Moreover, we establish the existence of the minimal limit of the trajectory attractors as v → 0+. We prove that is a connected invariant subset of . The connectedness problem for the trajectory attractor by itself remains open.
Dedicated to the memory of Leonid Volevich
Partially supported by the Russian Foundation for Basic Research (projects no 08-01-00784 and 07-01-00500). The first author
has been partially supported by a research grant from the Caprio Foundation, Landau Network-Cento Volta. 相似文献
3.
A. S. Demidov 《Russian Journal of Mathematical Physics》2010,17(2):145-153
For a given domain ω ⋐ ℝ2 with boundary γ = ∂ω, we study the cardinality of the set $
\mathfrak{A}_\eta \left( \Phi \right)
$
\mathfrak{A}_\eta \left( \Phi \right)
of pairs of numbers (a, b) for which there is a function u = u
(a,b): ω → ℝ such that ∇2
u(x) = au(x) + b ⩾ 0 for x ∈ ω, u|
γ
= 0, and ||∇u(s)| − Φ(s) ⩽ η for s ∈ γ. Here η ⩾ 0 stands for a very small number, Φ(s) = |∇(s)| / ∫
γ
|∇v| d
γ, and v is the solution of the problem ∇2
v = a
0
v + 1 ⩾ 0 on ω with v|
γ
= 0, where a
0 is a given number. The fundamental difference between the case η = 0 and the physically meaningful case η > 0 is proved. Namely, for η = 0, the set $
\mathfrak{A}_\eta \left( \Phi \right)
$
\mathfrak{A}_\eta \left( \Phi \right)
contains only one element (a, b) for a broad class of domains ω, and a = a
0. On the contrary, for an arbitrarily small η > 0, there is a sequence of pairs (a
j
, b
j
) ∈ $
\mathfrak{A}_\eta \left( \Phi \right)
$
\mathfrak{A}_\eta \left( \Phi \right)
and the corresponding functions u
j
such that ‖f
u
j+1‖ − ‖f
u
j
‖ > 1, where ‖f
u
j
= max
x∈ω
|f
u
j
(x)| and f
u
j
(x) = a
j
u
j
(x) + b
j
. Here the mappings f
u
j
: ω → ℝ necessarily tend as j → ∞ to the δ-function concentrated on γ. 相似文献
4.
N. M. Panyunin 《Russian Journal of Mathematical Physics》2008,15(4):511-521
In the paper, evolution pseudodifferential equations in the space of superanalytic functions (X) of an infinite-dimensional argument with symbols in the space (Y) of Fourier supertransforms of distributions on the dual superspace are considered. For these equations, the “weak” Cauchy
problem is posed and the existence theorem for the solutions of this problem is proved. The main result of the paper is the
theorem concerning the representation of solutions of the “weak” Cauchy problem by the Feynman path integral in the phase
superspace (the Feynman-Kac formula). The Feynman integral is understood in the sequential sense. Thus, the Feynman formula
becomes an immediate consequence of the Feynman-Kac formula. 相似文献
5.
We study the Verma modules M((μu)) over the Yangian Y
associated with a simple Lie algebra
. We give necessary and sufficient conditions for irreducibility of M(μ(u)). Moreover, regarding the simple quotient L((μu)) of M((μu)) as an
-module, we give necessary and sufficient conditions for finite-dimensionality of the weight subspaces of L((μu)). 相似文献
6.
We prove a maximal regularity result for operators corresponding to rotation invariant symbols (in space) which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary-value
problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining
it with abstract results on the -calculus and -bounded operator families. As an application, we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson
correction.
Dedicated to the memory of Leonid Romanovich Volevich 相似文献
7.
V. A. Bednyakov Ju. A. Budagov A. V. Gladyshev D. I. Kazakov E. V. Khramov D. I. Khubua 《Physics of Atomic Nuclei》2009,72(4):619-637
Prospects for observation of a SUSY-like signal from two gluinos are investigated within a certain region of the mSUGRA parameter space, where the cross section of the two-gluino production
in pp-collisions at the LHC ( = 14 TeV) is estimated at a rather high level of 17.3 pb. In this so-called EGRET-preferred region, the lightest stable neutralinos
χ
10 can serve as cold-dark-matter particles and can naturally explain the excess of diffuse Galactic gamma rays observed by the
EGRET space apparatus. The -event selection relies on a clear signature when decay products of each gluino contain one b
pair, one or two l
pair(s) or one or two light q
pair(s), and a neutralino. Rather high transverse missing energy carried away by the two neutralinos is the essential signature
of the events using of which allows the relevant Standard Model background to be reduced significantly. Furthermore, distributions
of the reconstructed invariant masses of two opposite-charged-lepton or light-jet pairs produced by the χ
20 → χ
10
l
+
l
− and χ
20 → χ
10
q
three-body decays have kinematic end points which measure the difference between masses of χ
20 and χ
10. In particular, it was found that these signatures of selected processes demonstrate good prospects for discovery of gluinos
at the LHC. These signatures allow one to distinguish different mSUGRA parameters m
1/2 within the EGRET-preferred region (at a higher than 6σ confidence level with 300 fb−1 data).
The text was submitted by the authors in English. 相似文献
8.
V. S. Rabinovich 《Russian Journal of Mathematical Physics》2009,16(2):300-308
We consider the class of matrix h-pseudodifferential operators Op h (a) with symbols a = (a ij ) i,j=1 N , where the coefficients a ij ∈ C ∞(? x n × ? ξ n ? C(0, 1] satisfy the estimates |? x β g6 ξ α α ij (x, ξ, h)| ? C αβ 〈ξ〉 m and 〈ξ〉 = (1 + |ξ|2)1/2 for every multi-indices α, β. We also assume that a ij (x, ξ) is analytically continued with respect to ξ to a tube domain ? n + i $ \mathcal{B} We consider the class of matrix h-pseudodifferential operators Op
h
(a) with symbols a = (a
ij
)
i,j=1N, where the coefficients a
ij
∈ C
∞(ℝ
x
n
× ℝ
ξ
n
⊗ C(0, 1] satisfy the estimates |ϖ
x
β
g6
ξ
α
α
ij
(x, ξ, h)| ⩽ C
αβ
〈ξ〉
m
and 〈ξ〉 = (1 + |ξ|2)1/2 for every multi-indices α, β. We also assume that a
ij
(x, ξ) is analytically continued with respect to ξ to a tube domain ℝ
n
+ i
, where is a bounded domain in ℝ
n
containing the origin. The main results of the paper are the local estimates for solutions of h-pseudodifferential equations.
Let H
h
s
(ℝ
n
, ℂ
N
) be the space of distributions with values in ℂ
N
which is equipped with the norm , let Ω ⊂ ℝ
n
be a bounded open set, let v ∈ C
∞(ℝ
n
), let ▿v(x) ∈ for any x ∈ Ω, and let . Let u
h
(∈ H
h
s
(ℝ
n
,‒
N
)) be a solution of the equation Op
h
(α)u = 0. In this case, for every ϕ ∈ C
0∞ (Ω) such that ϕ(x) = 1 on Supp v and for a sufficiently small h
0 > 0, there exists a constant C > 0 such that the following estimate holds for every h ∈ (0, h
0]:
We apply estimate (1) to local tunnel exponential estimates for the behavior as h → 0 of the eigenfunctions of matrix Schr?dinger, Dirac, and square-root Klein-Gordon operators.
To the memory of Professor V. A. Borovikov 相似文献
((1)) |
9.
M. Janek V. P. Ladygin L. S. Azhgirey T. Uesaka Yu. V. Gurchin M. Hatano K. Itoh A. Yu. Isupov J. -T. Karachuk H. Kato T. Kawabata V. A. Krasnov A. N. Khrenov A. S. Kiselev V. A. Kizka J. Kliman A. K. Kurilkin P. K. Kurilkin N. B. Ladygina A. N. Livanov Y. Maeda A. I. Malakhov V. Matousek M. Morhach J. Nishikawa Yu. K. Pilipenko T. Ohnishi H. Okamura S. M. Piyadin S. G. Reznikov T. Saito S. Sakaguchi H. Sakai N. Sakamoto S. Sakoda Y. Sasamoto Y. Satou K. Sekiguchi K. Suda M. A. Shikhalev A. Tamii I. Turzo N. Uchigashima T. A. Vasiliev K. Yako L. S. Zolin 《Physics of Atomic Nuclei》2008,71(9):1495-1501
The investigation of the spin structure of d, 3H, and 3He has been performed at the RIKEN acceleration research facility and VBLHE. Vector A
y
and tensor A
yy
, A
xx
, A
xz
analyzing powers for
d → 3Hen and
d → 3Hp are presented at 270 MeV. Themirror channels (3Hen and 3Hp) are comparedto each other in order to find possible manifestation of charge-symmetry breaking. The preliminary results on
the polarization observables for
d → 3Hp at 200MeV are also presented. The obtained data are compared with one-nucleon-exchange calculations.As a byproduct,
d → pX and
12C → pX breakup reactions are investigated at 140, 200, and 270MeV. The experimental data on
p elastic scattering were obtained at 270, 880, and 2000 MeV at the Nuclotron. The polarization of the deuteron beam was measured
at 270 MeV at the internal target station. The preliminary data on the vector A
y
and tensor A
yy
, A
xx
analyzing powers for the
p elastic scattering at 880 MeV are presented. The calculations on A
y
, A
yy
, and A
xx
analyzing powers for the
p elastic scattering at 880 MeV were performed in the framework of the multiple-scattering model.
The text was submitted by the authors in English. 相似文献
10.
A.?Bartl W.?Majerotto K.?M?nig A.?N.?Skachkova N.?B.?Skachkov 《Physics of Particles and Nuclei Letters》2009,6(3):181-189
We study pair production of scalar top quarks (stop, ) in e
+
e
− collisions with the subsequent decay of the top squarks into b quarks and charginos . We simulate this process by using PYTHIA6.4 for the beam energy 2E
b
= = 350, 400, 500, 800, 1000 GeV. A set of criteria for physical variables is proposed, which provides good separation of stop
signal events from top quark pair production being the main background. These criteria allow us to reconstruct the mass of
the top squark with an integrated luminosity of 1000 fb−1 provided that the neutralino mass is known.
The article is published in the original. 相似文献
11.
I. D. Gorlachev B. B. Knyazev A. Kuketayev F. M. Pen’kov 《Bulletin of the Russian Academy of Sciences: Physics》2009,73(2):245-248
A new modification of the least squares method (LSM) is proposed. The main idea is to consider the fitting parameters β
i
as independent random variables with a certain distribution density F(β1, β2, ..., β
k
; φ1, ..., φ
m
), which depends on a set of m experimental points φ
j
. Within this approach, the estimates of the parameters minimize squared deviations and are equivalent to means of the probability distribution = = ∫β
i
F(β1, β2, ..., β
k
; φ1, ..., φ
m
)dβ1
dβ2...dβ
k
.
Original Russian Text ? I.D. Gorlachev, B.B. Knyazev, A. Kuketayev, F.M. Pen’kov, 2009, published in Izvestiya Rossiiskoi
Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 257–260. 相似文献
12.
B. Paneah 《Russian Journal of Mathematical Physics》2008,15(2):291-296
The new identifying problem is formulated for general linear functional operators
F = Σc
j
F ○ a
j
which significantly generalizes in particular the well-known Ulam stability problem. The results obtained can be very useful
when processing experimental data of any kind as they enable to determine with high precision the structure of a compactly
supported Banach-valued function F by using a rather restricted information concerning
F.
Dedicated to the memory of Leonid Volevich 相似文献
13.
Valter Moretti 《Communications in Mathematical Physics》2006,268(3):727-756
This work concerns some features of scalar QFT defined on the causal boundary
of an asymptotically flat at null infinity spacetime and based on the BMS-invariant Weyl algebra
.(a) (i) It is noticed that the natural BMS invariant pure quasifree state λ on
, recently introduced by Dappiaggi, Moretti and Pinamonti, enjoys positivity of the self-adjoint generator of u-translations with respect to every Bondi coordinate frame
on
, (
being the affine parameter of the complete null geodesics forming
and
complex coordinates on the transverse 2-sphere). This fact may be interpreted as a remnant of the spectral condition inherited from QFT in Minkowski spacetime (and it is the spectral condition for free fields when the bulk is the very Minkowski space). (ii) It is also proved that the cluster property under u-displacements is valid for every (not necessarily quasifree) pure state on
which is invariant under u displacements. (iii) It is established that there is exactly one algebraic pure quasifree state which is invariant under u-displacements (of a fixed Bondi frame) and has positive self-adjoint generator of u-displacements. It coincides with the GNS-invariant state λ. (iv) Finally it is shown that in the folium of a pure u-displacement invariant state ω (like λ but not necessarily quasifree) on
is the only state invariant under u-displacement.(b) It is proved that the theory can be formulated for spacetimes asymptotically flat at null infinity which also admit future time completion i
+ (and fulfill other requirements related with global hyperbolicity). In this case a -isomorphism ı exists - with a natural geometric meaning - which identifies the (Weyl) algebra of observables of a linear field propagating in the bulk spacetime with a sub algebra of
. Using ı a preferred state on the field algebra in the bulk spacetime is induced by the BMS-invariant state λ on
. 相似文献
14.
Serban Belinschi Amir Dembo Alice Guionnet 《Communications in Mathematical Physics》2009,289(3):1023-1055
We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N × N symmetric matrix whose (i, j) entry is , where (x
ij
, 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-stable law, , and σ is a deterministic function. For random diagonal D
N
independent of and with appropriate rescaling a
N
, we prove that converges in mean towards a limiting probability measure which we characterize. As a special case, we derive and analyze
the almost sure limiting spectral density for empirical covariance matrices with heavy tailed entries.
Supported in part by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada and a University
of Saskatchewan start-up grant.
Research partially supported by NSF grant #DMS-0806211. 相似文献
15.
We present results for the universal anomalous dimension γ
uni(j) of Wilson twist-2 operators in the = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory.
The text was submitted by the authors in English. 相似文献
16.
17.
A Helmholtz resonator is a shell Ωshell separating a compact cavity Ωint from a noncompact outer domain Ωout. A small opening Ω
δ
in the shell connects the cavity with the outer domain, causing the transformation of real eigenfrequencies of the Neumann
Laplacian in the cavity into the complex scattering frequencies of the full spectral problem for the Neumann Laplacian on
Ω = ℝ3\Ωshell.
The Kirchhoff model of 1882, see [21], gives a convenient ansatz
for the approximate calculation of the outer component of the scattered wave of the full spectral problem on Ω in terms of
the scattered wave Ψout
N
(x, ν, λ) and the Green function G
out
N
(x, a, λ) of the Neumann Laplacian on the outer domain, with a pole at the pointwise opening Ω
δ
≈ a.
In this paper, we suggest an explicit formula for the Kirchhoff coefficient A
out, based on the construction of a fitted solvable model for the Helmholtz resonator with a narrow short channel Ω
δ
connecting the cavity with the outer domain. The correcting term of the scattering matrix of the model serves as a rational
approximation, on a certain spectral interval, for the correcting term of the full scattering matrix of the Helmholtz resonator.
Dedicated to the memory of Vladimir Andreevich Borovikov, who often chose a problem as an engineer and solved it by creating
new and surprising mathematics 相似文献
((1)) |
18.
Lucy Gow 《Communications in Mathematical Physics》2007,276(3):799-825
We describe a Gauss decomposition for the Yangian of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie
superalgebra Y(A(m − 1, n − 1)) (for m ≠ n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians and Y(A(n, n)). We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian . This was conjectured by Nazarov in 1991. 相似文献
19.
T. Branz T. Gutsche V. Lyubovitskij 《The European Physical Journal A - Hadrons and Nuclei》2008,37(3):303-317
We discuss a possible interpretation of the f
0(980)-meson as a hadronic molecule —a bound state of K and mesons. Using a phenomenological Lagrangian approach we calculate the strong f
0(980) → ππ and electromagnetic f
0(980) → γγ decays. The compositeness condition provides a self-consistent method to determine the coupling constant between
f
0 and its constituents, K and . Form factors governing the decays of the f
0(980) are calculated by evaluating the kaon loop integrals. The predicted f
0(980) → ππ and f
0(980) → γγ decay widths are in good agreement with available data and results of other theoretical approaches. 相似文献
20.
In this paper, an error in the proof of Theorem 4.9 in Gudder’s paper (Int. J. Theor. Phys. 47(1):268–279, 2008) is pointed out and it is proved that if
such that E
i
∈ℂI∖{0} and E
j
∉ℂI for some i,j in {1,2,…,n}, then
.
This subject is supported by the NNSF of China (No. 10571113, 10871224). 相似文献