共查询到20条相似文献,搜索用时 109 毫秒
1.
Walter Benz 《Aequationes Mathematicae》1992,43(2-3):177-182
Summary The following theorem holds true.
Theorem.
Let X be a normed real vector space of dimension 3 and let k > 0 be a fixed real number. Suppose that f: X X and g: X × X are functions satisfying x – y = k f(x) – f(y) = g(x, y)(x – y) for all x, y X. Then there exist elements and t X such that f(x) = x + t for all x X and such that g(x, y) = for all x, y X with x – y = k. 相似文献
2.
Prof. Dr. Karl Strubecker 《Monatshefte für Mathematik》1977,84(4):303-339
One determines all the minimal surfaces of the isotropic space, which simultaneously are affinminimal surfaces. A characteristic property of those surfaces is that the isotropic spherical imagines of the asymptotic lines of form two orthogonal pencils of circles. There are three types of such surfaces : first the well known right helicoid
I
, second an interesting transcendental surface
II
, and third the isotropic analogy
III
of the minimal surface ofEnneper. The surfaces permit cinematic generations. Especially
II
and
III
can be generated byClifford screws in a certain indefinite quasielliptic space.In the isotropic space conjugate to the surfaces are isotropic minimal surfaces
* with plane lines of curvature. There are also three types of such surfaces:
I
*
is a logarithmic surface of revolution,
II
*
is an interesting transcendental surface, and
III
*
is again the isotropic minimal surface ofEnnerper. 相似文献
3.
Dr. Johannes Schoißengeier 《Monatshefte für Mathematik》1979,87(1):21-52
In this paper we give the connection between the zeros of the -function and sequences(g(p)), p prime, mod 1 ifg(x)=x
for 0, >0 or ifg(X) is a polynomial in . 相似文献
4.
Dr.-Ing. P.-Th. Wilrich 《Mathematical Methods of Operations Research》1968,12(1):185-209
Zusammenfassung Die zeitabhängige (instationäre) Lösung für die Zustandswahrscheinlichkeiten und für einige Kenngrößen von Warteschlangensystemen mit einer Bedienungsstation, unendlich vielen Warteplätzen, exponentiellem Zu- und Abgang und beliebigem Anfangszustand wird bestimmt. Die ZustandswahrscheinlichkeitenP
v
(), d. h. die Wahrscheinlichkeiten für Einheiten im System zur Zeit, ergeben sich als Integrale, in denen modifizierteSessel-Funktionen 1. Art auftreten. Der ErwartungswertL () und die VarianzV() der Zahl von Einheiten im System lassen sich als Integrale darstellen, in denen nur die ZustandswahrscheinlichkeitP
0() auftritt.Für<1 und erreichen die Systeme einen stationären Zustand (für den die Lösung bekannt ist); für1 und giltP
v
()0 für alle, L(),V().Ist>1, dann wachsenL() undV() für große linear mit; ihre Asymptoten werden berechnet. Ist=1, dann wachsenL() und die Standardabweichung() für große mit
; einfache Näherungsformeln werden gefunden.
Vorgel. v.:J. Nitsche. 相似文献
Summary The time dependent solution is determined for the state probabilities and for some characteristic values of queuing systems with a single server, an infinite number of waiting places, exponentially distributed inter-arrival and service times, and any initial state. The state probabilitiesP v (), i.e. the probabilities for units in the system at time, are given in the form of integrals in which modifiedBessel functions of the first kind occur. Integrating the state probalityP 0() over leads to the meanL() and the varianceV() of the number of units in the system.For<1 and the systems tend to a steady state (for which the solution is known); for1 and we haveP v ()0 for all, L(),V().If>1 asymptotic expansions for large are found givingL() andV() proportional to. If=1 simple approximate formulas for large are obtained givingL() and the standard deviation() proportional to .
Vorgel. v.:J. Nitsche. 相似文献
5.
Jean-Paul Bézivin 《Aequationes Mathematicae》1992,44(1):84-99
Résumé Soitq un nombre algébrique de module 1, qui ne soit pas une racine de l'unité, etP
[X, Y
0,Y
1] un polynôme non nul. Dans cet article, nous montrons que toute solution de l'équation fonctionnelleP(z, (z), (qz))=0, qui est une série formelle (z) dansQ[[z]], a un rayon de convergence non nul.
Summary Letq Q be an algebraic number of modulus one that is not a root of unity. LetP Q[X, Y 0,Y 1] be a non zero polynomial. In this paper, we show that every formal power series,(z) Q[[z]], solution of the functional equationP(z), (z), (qz)) = 0 has a non zero radius of convergence.相似文献
6.
B. D. Bojanov 《Analysis Mathematica》1980,6(3):185-197
(v
k)
1
n
, 1v
kr, v1+...+vn
r, p(;r) — =(x
1,v
1),...,(x
n,v
n), v
1+...+v
n-r
(r(;·)=1. , (*;t) [, ] (;t) x
1<... n v
1 ...,v
n. (*;t) . 相似文献
7.
Hans-Heinrich Kairies 《Aequationes Mathematicae》1996,51(1-2):115-128
Summary The following Artin type characterization of : + + is proved: Assume thatf: + + satisfies the Gauss multiplication formula for some fixedp 2,f is absolutely continuous on [l/p, 1 + ] for some > 0 and lim
x 0
xf(x) = 1. Thenf(x) = (x) forx > 0.The optimality of this result is checked by means of counterexamples. For instance, it is shown that the result is no longer true, if f is absolutely continuous is replaced by f is continuous and of finite variation. 相似文献
8.
T. Jerofsky 《Analysis Mathematica》1977,3(4):257-262
[0,1], - H
.
This paper was written during the author's scholarship at the State University of Odessa in the USSR. 相似文献
This paper was written during the author's scholarship at the State University of Odessa in the USSR. 相似文献
9.
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
10.
Р. С. Юлмухаметов 《Analysis Mathematica》1985,11(3):257-282
The following statement is proved. Letu be a subharmonic function in the region and
u
the associated measure. Then there exists a functionf holomorphic in and such that if
f
is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for=
u
and for=
f
. In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.
. . . 相似文献
. . . 相似文献
11.
It is shown that two real functionsf andg, defined on a real intervalI, satisfy the inequalitiesf(x + (1 – )y) g(x) + (1 – )g(y) andg(x + (1 – )y) f(x) + (1 – )f(y) for allx, y I and [0, 1], iff there exists an affine functionh: I such thatf h g. As a consequence we obtain a stability result of Hyers—Ulam type for affine functions. 相似文献
12.
V. A. Slousch 《Journal of Mathematical Sciences》2003,115(2):2267-2271
Let A be a self-adjoint operator, let (, ) be an inner gap in the spectrum of the operator A, and let B(t) = A + tW
*
W, where the operator W(A – iI)-1 is not necessarily bounded. Conditions are obtained under which the spectrum of B(t) in (, ) is discrete. Let N(, A, W, ), (, ), > 0, be the number of eigenvalues of the operator B(t) passing the point (, ) as t increases from 0 to . The asymptotics of N(, A, W, ) as + is obtained in terms of the spectral asymptotics of a certain self-adjoint compact operator. Bibliography: 5 titles. 相似文献
13.
We prove the following generalization of a theorem of Ferry concerning selections of strongly regular multivalued maps onto the class of paracompact spaces: Let : X (Z, ) be a map of a paracompact space X into a metric space (Z, ) whose values (x) are complete subspaces of Z and absolute extensors (AE), for every x X. Suppose that can be represented as = , where : X Y is a continuous singlevalued map of X onto some finite-dimensional paracompact space Y and : Y (Z, ) is a strongly regular map. Then for every closed subset A X and every selection r : A Z of the map |A : A Z, there exists an extension
: X Z of r such that
is a selection of the map . We also prove a local version of this theorem. 相似文献
14.
Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in
p
,
n
, respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in
n
. The function c:
p+n
is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in
n
. Computational experiments show that the resulting algorithms work well for problems with smalln. 相似文献
15.
V. F. Gapoškin 《Analysis Mathematica》1982,8(2):103-124
(2), k1, >0, L
p
(0,), 1p L
=C. , , p, k, (C, )- L
p
(0,), , , {sinnx}
n
=k/
(C, )- L
p
(0,) |x|p
. , 1p, {x
sinnx}
n=k
, k2 2k–2–1/p<2k–1/p, (C, )- L
p
[0,] , >–(p–1)/. 相似文献
16.
K. Tandori 《Analysis Mathematica》1980,6(2):157-164
. . . : sn(x) — , n-(, 1)- n
L
2. , . , :
a
k
l
2
n
() [0,1] , (*) , (**) .
a
k
l
2
u
n
() [0,1] , (**), (*) . 相似文献
17.
Alan S. McRae 《Geometriae Dedicata》2001,84(1-3):321-330
If denotes the curvature and the torsion of a closed, generic, and oriented polygonal space curve X in
, then we show that
X
(2 + 2) ds =
X
ds +
X
| | ds > 4 if is positive. We also show that
X
(2 + 2) ds 2n if no four consecutive vertices lie in a plane and X has linking number n with a straight line. These extend theorems of Milnor and Totaro. 相似文献
18.
Anders Lundberg 《Aequationes Mathematicae》1992,43(2-3):127-144
Summary A real solution of the functional equation(x + (y – x)) = f(x) + g(y) + h(x)k(y) on a set 2 is a 6-tuple (f, g, h, k, , ) of real valued functions such that the equation is identically fulfilled on. Except for cases known before—e.g. when is linear—we present all real solutions in an arbitrary region where the functions have derivatives of second order. 相似文献
19.
М. Г. Григорян 《Analysis Mathematica》1985,11(3):201-216
, . . Q
k
[0,2],k=1,2, — . F(x, y)L(T), T=[0, 2]2, G(x, y)L(T) , G(x,y)=F(x,y) Q=Q
1
×Q
2
- . 相似文献
20.
. . 相似文献