共查询到20条相似文献,搜索用时 31 毫秒
1.
R. Schäfke 《Journal of Mathematical Sciences》2004,124(6):5364-5389
First, in joint work with S. Bodine of the University of Puget Sound, Tacoma, Washington, USA, we consider the second-order differential equation 2 y'=(1+2 (x, ))y with a small parameter , where is analytic and even with respect to . It is well known that it has two formal solutions of the form y±(x,)=e±x/h±(x,), where h±(x,) is a formal series in powers of whose coefficients are functions of x. It has been shown that one (resp. both) of these solutions are 1-summable in certain directions if satisfies certain conditions, in particular concerning its x-domain. We show that these conditions are essentially necessary for 1-summability of one (resp. both) of the above formal solutions. In the proof, we solve a certain inverse problem: constructing a differential equation corresponding to a certain Stokes phenomenon. The second part of the paper presents joint work with Augustin Fruchard of the University of La Rochelle, France, concerning inverse problems for the general (analytic) linear equations
r
y' = A(x,) y in the neighborhood of a nonturning point and for second-order (analytic) equations y' - 2xy'-g(x,) y=0 exhibiting resonance in the sense of Ackerberg-O'Malley, i.e., satisfying the Matkowsky condition: there exists a nontrivial formal solution
such that the coefficients have no poles at x=0. 相似文献
2.
When do Toeplitz and Hankel operators commute? 总被引:1,自引:0,他引:1
Rubén A. Martínez-Avendaño 《Integral Equations and Operator Theory》2000,37(3):341-349
We completely classify all Toeplitz and Hankel operators which commute; namely, we prove that that a non-trivial Hankel operator and a non-trivial Toeplitz operator commute if and only if the Hankel operator has symbolz, where is the symbol of the Toeplitz operator, and is an affine function of the characteristic function of certain anti-symmetric sets of the unit circle. 相似文献
3.
Bolesław Gaweł 《Aequationes Mathematicae》1996,52(1):55-71
Summary In the paper we consider, from a topological point of view, the set of all continuous functionsf:I I for which the unique continuous solution:I – [0, ) of(f(x)) (x, (x)) and(x, (x)) (f(x)) (x, (x)), respectively, is the zero function. We obtain also some corollaries on the qualitative theory of the functional equation(f(x)) = g(x, (x)).
No assumption on the iterative behaviour off is imposed. 相似文献
4.
A. S. Zinov'ev 《Mathematical Notes》1972,12(5):743-746
We obtain sufficient conditions for the absolute convergence of Fourier series for functions of L
d
2
depending on the properties of the function being expanded and the rate of growth of the sums
of the system of functions {k(t)} orthonormalized in [a, b] with respect to d(t). We show that if at some point x [a, b] the function (t) has a discontinuity, at that point the Fourier series of any functionf(t) L
d
2
, converges absolutely.Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 511–516, November, 1972. 相似文献
5.
Johann Hartl 《Journal of Geometry》1988,31(1-2):89-95
If , , are linear mappings out of a projective space (P,G) into a projective space (P', G') and , then is said to belong to the pencil <,<> of linear mappings spanned by and if in the main (x), (x), (x) are collinear for all x P. We give some sufficient conditions for x P and , , such that (x) is uniquely determined by giving, and (z), z P.
Herrn Prof. Dr.Helmut Karzel zum 60. Geburtstag gewidmet 相似文献
Herrn Prof. Dr.Helmut Karzel zum 60. Geburtstag gewidmet 相似文献
6.
Johann Schröder 《manuscripta mathematica》1977,21(2):135-171
The paper is concerned with Range-Domain Implications MvCvK, where M is a given operator and C,K denote given sets. Sufficient conditions are derived by a very general continuity principle. Various special cases are considered such as inverse-positivity, MvMwvw, and a generalization H(,[,])MvH(,[,]) v, where Mu=H(u,u) and [,] denotes an order interval. These results are applied to differential operators related to boundary or initial value problems. The goal is to furnish a simple uniform approach, to explain its application, and to provide a kind of survey on what problems have been treated in this way. 相似文献
7.
We propose an approach to problems of group classification. By using this approach, we perform a complete group classification of nonlinear Schrödinger equations of the form i
t
+ + F(, *) = 0. 相似文献
8.
The class V, consisting of the smooth functions f(t), ot1, satisfying the condition
0
1
[f
(r)
(t)]dt1, where the function (t) is nonnegative and r is a natural number, is studied. Under certain restrictions on the function (t) ensuring the compactness of the class V, the order of decrease of the Kolmogorov diameters dn(V) is computed. The analogous problem for the case r=1 is solved also for functions of several variables.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 671–678, November, 1977. 相似文献
9.
Hiroaki Taniguchi 《Geometriae Dedicata》2000,80(1-3):99-123
Let k, K be fields, and assume that |k| 4 and n, m 2, or |k| = 3 and n 3, m 2. Then, for any embedding of AG(n, k) into PG(m, K), there exists an isomorphism from k into K and an (n+1) × (m+1) matrix B with entries in K such that can be expressed as (x1,x2,...,xn) = [(1,x1
,x2
,...,xn
)B], where the right-hand side is the equivalence class of (1,x1
,x2
,...,xn
)B. Moreover, in this expression, is uniquely determined, and B is uniquely determined up to a multiplication of element of K*. Let l 1, and suppose that there exists an embedding of AG(m+l, k) into PG(m, K) which has the above expression. If we put r = dim
k
K, then we have r 3 and m > 2 l-1)/(r-2). Conversely, there exists an embedding of AG(l+m, k) into PG(m, K) with the above expression if K is a cyclic extension of k
with dim
k
K=r 3, and if m 2l/(r-2) with m even or if m 2l/(r-2) +1 with m odd. 相似文献
10.
Yves Péraire 《Archive for Mathematical Logic》1995,34(4):269-277
The results established in this paper are in connection with the Relative Internal Set Theory (R.I.S.T.). The main result is the general principle of choice: Let be a level and let (x, y) be anexternalbounded formula of the language of R.I.S.T.. Suppose that to each elementx, dominated by , corresponds an elementy
x
such that (x, y
x
) holds, then there exists a function of choice such that, which is a very general principle of choice, for everyx dominated by , (x, (x)) holds. More than that, we establish that if all the elementsy
x
are uniformly dominated by a level then we can prescribe that the function of choice is also dominated by . 相似文献
11.
12.
Ludwig Baringhaus Norbert Henze 《Annals of the Institute of Statistical Mathematics》1991,43(3):551-564
The Laplace transform (t=E[exp(–tX)]) of a random variable with exponential density exp(–x), x0, satisfies the differential equation (+t)(t)+(t=0, t0). We study the behaviour of a class of consistent (omnibus) tests for exponentiality based on a suitably weighted integral of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaacaGGBbGaaiikai% qbeU7aSzaajaWaaSbaaSqaaGqaciaa-5gaaeqaaOGaey4kaSIaamiD% aiaacMcacqaHipqEcaWFNaWaaSbaaSqaaiaad6gaaeqaaOGaaiikai% aadshacaGGPaGaey4kaSIaeqiYdK3aaSbaaSqaaiaad6gaaeqaaOGa% aiikaiaadshacaGGPaGaaiyxamaaCaaaleqabaGaaGOmaaaaaaa!4C69!\[[(\hat \lambda _n + t)\psi '_n (t) + \psi _n (t)]^2 \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqpepeea0xe9qqVa0l% b9peea0lb9sq-JfrVkFHe9peea0dXdarVe0Fb9pgea0xa9pue9Fve9% Ffc8meGabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH7oaBgaqcam% aaBaaaleaaieGacaWFUbaabeaaaaa!3A66!\[\hat \lambda _n \] is the maximum-likelihood-estimate of and n is the empirical Laplace transform, each based on an i.i.d. sample X
1,...,X
n
. 相似文献
13.
Richard Koch 《Journal of Geometry》1998,62(1-2):176-189
In Euclidean space E3, let be a (regular C-) minimal surface without planar points having locally (without loss of generality) the spherical representation n(u,v)=(cos v/cosh u, sin v/cosh u, tanh u), (u,v)G2. The corresponding (isothermal) parametrization : x(u,v), (u,v)G can be expressed using agenerating Function (u,v) which satisfies uu +
vv – 2utanh u + =0; the v-curves (coordinate curves u=u0) in , along each of which the angle between the normal n(u,v) of and the x3-axis is constant, are thevertical- isophotes of , the u-curves (v=v0) being their orthogonal trajectories (theorems 1, 2). Considering u-curves and/or v-curves of having additional geometric properties (curves of constant/steepest slope, curves of constant Gaussian curvature, asymptotic curves, lines of curvature or geodesies of ) we prove many newgeometric characterizations of theright helicoid, thecatenoid andScherk's second surface (theorems 3–7). All of these surfaces areminimal hélicoidal surfaces. 相似文献
14.
N. B. Lebedinskaya 《Journal of Mathematical Sciences》1985,29(6):1649-1659
The article is devoted to the problem of finding an optimal schedule for a class of functionals ƒ which allows for the existence of a structural set of activities. The functionalƒ(R), where, is defined in the following way: where {i(t)} is a structural set of functions, and the function F is defined on any finite set of arguments and satisfies the following conditions: 1)F(x)=(x); 2) F(x1,x2)=(x1,x2), F(x1,x2,...x3)= (x1, F(x2,...,xs)), S2; 3) and do not decrease in each of their arguments, and moreover, 3a) strictly increases with the increase of both arguments, 3b) if (x1,x2)>(x1, x2 (x2, x3)> (x2,x3), then F(x1,x2,x3)>F(x1,x2,x3).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 5–20, 1983. 相似文献
15.
René L. Schilling 《Journal of Theoretical Probability》1998,11(2):303-330
Let {X
t}
t0 be a Feller process generated by a pseudo-differential operator whose symbol satisfiesÇn|q(Ç,)|c(1=)()) for some fixed continuous negative definite function (). The Hausdorff dimension of the set {X
t:tE}, E [0, 1] is any analytic set, is a.s. bounded above by dim E. is the Blumenthal–Getoor upper index of the Levy Process associated with (). 相似文献
16.
Jelena V. Manojlović 《Czechoslovak Mathematical Journal》2005,55(1):41-60
New oscillation criteria are given for the second order sublinear differential equation
where a C
1 ([t
0, )) is a nonnegative function, , f C() with (x) 0, xf(x) / (x) > 0 for x 0, , f have continuous derivative on \ {0} with [f(x) / #x03C8;(x)] 0 for x 0 and q C([t
0, )) has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x (t) + q(t)x(t) = 0. 相似文献
17.
Arjen E. Ronner 《Probability Theory and Related Fields》1984,66(4):613-620
Summary The consistency and asymptotic normality of p-norm estimators (1<p<2) is established by applying some of the ideas of Huber (1973), where asymptotic normality of the so-called M-estimators for regression parameters is shown. A central role is played by a weight function . Huber assumed that , and are bounded. This is, however, not the case for p-norm estimators with 1<p<2, but some of his ideas can still be applied. 相似文献
18.
宋文华 《应用数学学报(英文版)》1996,12(1):64-70
SONGWENHUA(宋文华)(InstituteofMathematicalScience,DalianUniversityofTechnology,Dalian116024,China)Abstract:AcharacterizationofCh... 相似文献
19.
Maciej Sablik 《Aequationes Mathematicae》1990,39(1):19-39
Summary The functional equation(x) + (y) = (xf(y) + yf(x)) (1) for the unknown functionsf, and mapping reals into reals appears in the title of N. H. Abel's paper [1] from 1827 and its differentiable solutions are given there. In 1900 D. Hilbert pointed to (1), and to other functional equations considered by Abel, in the second part of his fifth problem. He asked if these equations could be solved without, for instance, assumption of differentiability of given and unknown functions. Hilbert's question was recalled by J. Aczél in 1987, during the 25th International Symposium on Functional Equations in Hamburg-Rissen. In particular Aczél asked for all continuous solutions of (1). An answer to his question is contained in our paper. We determine all continuous functionsf: I ,: A
f
(I × I) and: I that satisfy (1). HereI denotes a real interval containing 0 andA
f
(x,y) := xf(y) + yf(x), x, y I. The list contains not only the differentiable solutions, implicitly described by Abel, but also some nondifferentiable ones.Applying some results of C. T. Ng and A. Járai we are able to obtain even a more general result. For instance, the assertion (i.e. the list of solutions) remains unchanged if we replace continuity of and by local boundedness of orf(0)I from above or below. Strengthening a bit the assumptions onf we can preserve a large part of the assertion requiring only the measurability of either orf(0)I. 相似文献
20.
A sharp almost sure bound is derived for limit points of average sum of weakly dependent random variables, which ensures strong laws of large numbers for and -mixing random variables, without assumptions on rate of tending to zero of and -mixing parameters n and n. 相似文献