共查询到20条相似文献,搜索用时 15 毫秒
1.
A. V. Domrina 《Theoretical and Mathematical Physics》2014,178(3):265-277
Any finite-energy solution of a noncommutative sigma model has three nonnegative integer-valued characteristics: the normalized energy e(Φ), canonical rank r(Φ), and minimum uniton number u(Φ). We prove that r(Φ) ≥ u(Φ) and e(Φ) ≥ u(Φ)(u(Φ) + 1)/2. Given any numbers e, r, u ∈ ? that satisfy the slightly stronger inequalities r ≥ u and e ≥ r +u(u ? 1)/2, we construct a finite-energy solution Φ with e(Φ) = e, r(Φ) = r, and u(Φ) = u. 相似文献
2.
A.J.E.M. Janssen 《Journal of Fourier Analysis and Applications》1994,1(1):39-65
In this paper we present a technique for proving bounds of the Boas-Kac-Lukosz type for unsharply restricted functions with
nonnegative Fourier transforms. Hence we consider functions F(x) ≥ 0, the Fourier transform f(u) of which satisfies |f(u)|
≤ ε for all u in a subset of (-∞,-1] ⋃ [1,∞), and are interested in bounds on |f(u)| for |u| ≤ 1. This technique gives rise
to several "epsilonized" versions of the Boas-Kac-Lukosz bound (which deals with the case f(u) = 0, |u| ≥ 1). For instance,
we find that |f(u)| ≤ L(u) + O(ε2/3), where L(u) is the Boas-Kac-Lukosz bound, and show by means of an example that this version is the sharpest possible with
respect to its behaviour as a function of ε as ε ↓ 0. The technique also turns out to
be sufficiently powerful to yield the best bound as ε ↓ 0 in various other cases with less severe restrictions on f. 相似文献
3.
K. J. Wirths 《分析论及其应用》1996,12(3):98-100
Let
be such that |p(eiq)|≤1 for ϕ∈R and |p(1)|=a∈[0,1]. An inequality of Dewan and Govil for the sum |av|+|an|, 0≤u<v≤n is sharpened. 相似文献
4.
§1IntroductionInthispaper,weconsiderthelargetimebehaviorofaproblem,ut=Δu+up,x∈RN+,t>0,-ux1=uq,x1=0,t>0,u(x,0)=u0(x),x∈RN+,(... 相似文献
5.
E. G. Goluzina 《Journal of Mathematical Sciences》1998,89(1):958-966
Let TR be the class of functions
that are regular and typically real in the disk E={z:⋱z⋱<1}. For this class, the region of values of the system {f(z0), f(r)} for z0 ∈ ℝ, r∈(-1,1) is studied. The sets Dr={f(z0):f∈TR, f(r)=a} for −1≤r≤1 and Δr={(c2, c3): f ∈ TR, −f(−r)=a} for 0<r≤1 are found, where aε(r(1+r)−2, r(1−r)−2) is an arbitrary fixed number. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 69–79. 相似文献
6.
M. Hosseini Aliabadi 《Journal of Applied Mathematics and Computing》2000,7(3):673-683
In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method
on the differential delay equation defined byw(u) = 1/u for 1 ≤u ≤ 2 and(uw(u))′ = w(u-1) foru ≥ 2, which was introduced by Buchstab. As Khajah et al.[l] applied the Recursive Tau Method on this problem, they had to
apply that Method under theMathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran
code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations.
The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities
of this Method to handle problems in different applications. 相似文献
7.
Huan-song Zhou Hong-bo Zhu 《应用数学学报(英文版)》2007,23(4):685-696
In this paper,we consider the following ODE problem(P)where f ∈ C((0, ∞)×R,R),f(r,s)goes to p(r)and q(r)uniformly in r>0 as s→0 and s→ ∞,respectively,0≤p(r)≤q(r)∈ L~∞(0,∞).Moreover,for r>0,f(r,s)is nondecreasing in s≥0.Some existenceand non-existence of positive solutions to problem(P)are proved without assuming that p(r)≡0 and q(r)hasa limit at infinity.Based on these results,we get the existence of positive solutions for an elliptic problem. 相似文献
8.
A. V. Komlov 《Theoretical and Mathematical Physics》2007,153(3):1643-1651
We consider a Grassmannian version of the noncommutative U(1) sigma model specified by the energy functional E(P) = ‖[a, P]‖
HS
2
, where P is an orthogonal projection operator in a Hilbert space H and a: H → H is the standard annihilation operator. With
H realized as a Bargmann-Fock space, we describe all solutions with a one-dimensional range and prove that the operator [a,
P] is densely defined in H for a certain class of projection operators P with infinite-dimensional ranges and kernels.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 347–357, December, 2007. 相似文献
9.
Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L
2 Initial Data 总被引:6,自引:0,他引:6
Shang Bin CUI Dong Gao DENG Shuang Ping TAO 《数学学报(英文版)》2006,22(5):1457-1466
In this paper we study solvability of the Cauchy problem of the Kawahara equation 偏导dtu + au偏导dzu + β偏导d^3xu +γ偏导d^5xu = 0 with L^2 initial data. By working on the Bourgain space X^r,s(R^2) associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H^r(R) and -1 〈 r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L^2(R). 相似文献
10.
A. V. Domrin 《Theoretical and Mathematical Physics》2008,154(2):184-200
By Uhlenbeck’s results, every harmonic map from the Riemann sphere S2 to the unitary group U(n) decomposes into a product of so-called unitons: special maps from S2 to the Grassmannians Gr
k(ℂn) ⊂ U(n) satisfying certain systems of first-order differential equations. We construct a noncommutative analogue of this
factorization, applicable to those solutions of the noncommutative unitary sigma model that are finite-dimensional perturbations
of zero-energy solutions. In particular, we prove that the energy of each such solution is an integer multiple of 8π, give examples of solutions that are not equivalent to Grassmannian solutions, and study the realization of non-Grassmannian
zero modes of the Hessian of the energy functional by directions tangent to the moduli space of solutions.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 220–239, February, 2008. 相似文献
11.
In the paper, we characterize the coefficient multiplier spaces of mixed norm spaces (H
p,q
(φ1), H
u,v
(φ2)) for the values of p, q, u, v in three cases: (i) 0 < p ≤ u ≤ ∞, 0 < q ≤ min(1, v) ≤ ∞. (ii) v = ∞, 0 < p ≤ u ≤ ∞, 1 ≤ u, q ≤ ∞. (iii) 1 ≤ v ≤ 2 ≤ q ≤ ∞, and 0 < p ≤ u ≤ ∞ or 1 ≤ p, u ≤ ∞. The first case extends the result of Blasco, Jevtić, and Pavlović in one variable. The third case generalizes partly
the results of Jevtić, Jovanović, and Wojtaszczyk to higher dimensions.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
12.
We prove regularity results for solutions of some nonlinear Dirichlet problems for an equation in the form
where Ω is a bounded open subset of , N ≥ 2, α, θ and p are real constants such that: α > 0, 0 ≤ θ ≤ 1 and 1 < p < N. A limit case is also considered.
相似文献
13.
Existence Results for Superlinear Elliptic Equations with Nonlinear Boundary Value Conditions 下载免费PDF全文
Xiao Hui Yu 《数学学报(英文版)》2019,35(10):1655-1680
In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition
$$\left\{ {\begin{array}{*{20}{c}}
{ - \Delta u + u = {{\left| u \right|}^{r - 2}}u}&{in\;\Omega ,\;\;} \\
{\frac{{\partial u}}{{\partial v}} = {{\left| u \right|}^{q - 2}}u}&{on\;\partial \Omega ,}
\end{array}} \right.$$
where Ω ⊂ ℝN, N ≥ 3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases: (i) Both q and r are subcritical; (ii) r is critical and q is subcritical; (iii) r is subcritical and q is critical; (iv) Both q and r are critical. 相似文献
14.
A. Horwitz 《分析论及其应用》1993,9(2):71-80
Let
and let
, where P
c
n
denoles the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal
rule and the midpoint rule, respectively, and are each exact for all polynomials of degree ≤n+1. We let L(f)=αTM(f)+(1−α)TA(f),
where
, to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem 1). The case n=0
is just the classical Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing
P
(a+b)
2/n+1
(x) by the Hermite cubic interpolant at a and b, we obtain some known formulae by a different approach (see [1] and [2]).
Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each
piece being the Taylor polynomial of f at a and b, respectively. Of course all of our formulae can be compounded over subintervals
of [a,b]. 相似文献
15.
Let ρ be a triangulation of a polygonal domain D⊂R2 with vertices V={vi:l≤i≤Nv} and RSk(D, ρ)={u∈Ck(D): ≠ T∈ρ, u/T is a rational function}. The purpose of this paper is to study the existence and construction of Cμ-rational spline functions on any triangulation ρ for CAGD. The Hermite problem Hμ(V,U)={find u∈U: Dαu(vi)=Dαf(vi),|α|≤μ} is solved by the generalized wedge function method in rational spline function family, i.e. U=RSμ. this solution needs only the knowledge of partial derivatives of order≤μ at vi. The explicit repesentations of all Cμ-GWF(generalized wedge functions)and the interpolating operator with degree of precision at least 2μ+1 for any triangulation
are given. 相似文献
16.
J. R. Cannon 《Annali di Matematica Pura ed Applicata》1964,66(1):155-165
Summary Let u(x, t) satisfy the heat equation in 0<x<1, 0<t≤T. Let u(x, 0)=0 for 0<x<1 and let |u(0, t)|<ε, | ux(0, t) |<ε, and | u(1, t) |<M for 0≤t≤T. Then,
, where M1 and β(x) are given explicitly by simple formulas. The application of the a priori bound to obtain error estimates for a numerical
solution of the Cauchy problem for the heat equation with u(x, 0)=h(x), u(0, t)=f(t), and ux(0, t)=g(t) is discussed.
Work performed under the auspices of the U. S. Atomic Energy Commission. 相似文献
17.
P. I. Plotnikov 《Journal of Mathematical Sciences》1999,93(5):747-766
The following initial-boundary value problem for the forward-backward parabolic equation in a bounded region Ω∈Rd, 1≤d≤3, is considered:
. It is assumed that the function φ decreases monotonically on the interval (−1, 1), increases outside it, and that |u0|≥1. It is proved that this problem has entropy solutions which describe a phase transition process with hysteresis. Bibliography:
11 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 183–209. 相似文献
18.
Factorization and symplectic uniton numbers for harmonic maps into symplectic groups 总被引:7,自引:0,他引:7
It is proved that any harmonic map ϕ : Ω →Sp(N) from a simply connected domain Ω ⊆R
2⋃ | ∞ | into the symplectic groupSp(N) ⊂U(2N) with finite uniton number can be factorized into a product of a finite number of symplectic unitons. Based on this factorization,
it is proved that the minimal symplectic uniton number of ϕ is not larger thanN, and the minimal uniton number of ϕ is not larger than 2N - 1. The latter has been shown in literature in a quite different way. 相似文献
19.
Bruno Pini 《Annali di Matematica Pura ed Applicata》1959,48(1):305-332
Sunto Si studia il problema della determinazione di una soluzione dell'equazione
ak(x)∂ku/∂xk=f(x, y) entro la semistriscia a≤x≤b, y≥0, che assuma assegnati valori per y=0 e per x=a, x1, x2, b (a<x1<x2<b). Analogamente si studia il problema della determinazione di una soluzione dell' equazione
ak(x)∂ku/∂xk+b(x)∂u/∂y=f(x,y), entro la medesima semistriscia, cha assuma assegnati valori per y=0 e per x=a, x1, x2, b e la cui ∂/∂y assuma assegnati valori per y=0.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
20.
张正杰 《应用数学学报(英文版)》2001,17(1):47-52
1. Introduction and Main ResultIn this paper, we consider the echtence of solutions for the following equation:where g(x) 2 0, g(x)' 0, g(x) E H--'(R') andThe homogeneous case, i.e. g(x) H 0 which means zero is a trivial solution of (1.1), itwas introduced in physics. Usually it appears to be a prototype of the so-called nolilocalproblems which arise in many situations[1'2]. Many authors have proved that these equationsat least possess one positive solutionl3--sl.As we know, there is a few … 相似文献