共查询到20条相似文献,搜索用时 34 毫秒
1.
We consider the boundary-value problem u
tt + u
t + (1 + cos2)sin u =2
u
xx, u
x|x=0=ux|x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number. 相似文献
2.
Let T be a homogeneous tree of homogeneity q+1. Let denote the boundary of T, consisting of all infinite geodesics b=[b
0,b
1,b
2,] beginning at the root, 0. For each b, 1, and a0 we define the approach region ,a
(b) to be the set of all vertices t such that, for some j, t is a descendant of b
j
and the geodesic distance of t to b
j
is at most (–1)j+a. If >1, we view these as tangential approach regions to b with degree of tangency . We consider potentials Gf on T for which the Riesz mass f satisfies the growth condition
T
f
p
(t)q
–|t|<, where p>1 and 0<<1, or p=1 and 0<1. For 11/, we show that Gf(s) has limit zero as s approaches a boundary point b within ,a
(b) except for a subset E of of -dimensional Hausdorff measure 0, where H
(E)=sup>0inf
i
q
–|t
i|:E a subset of the boundary points passing through t
i
for some i,|t
i
|>log
q
(1/). 相似文献
3.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 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.
Serge Alinhac 《Inventiones Mathematicae》1993,111(1):627-670
Résumé Nous considérons le système des équations d'Euler isentropiques en dimension deux; pour des données initiales invariantes par rotation et perturbations de taille d'un état de repos, on établit un équivalent du temps de vieT
de la solution classique (lim
2
T
=
*
2
).De plus, on donne, pour
une estimation de la vraie solution, en calculant la taille de son écart à une solution approchée construite dans un précédent travail.
Oblatum 2-XII-1991 & 24-IX-1992 相似文献
Summary We consider the 2D isentropic Euler equations; for rotationnally invariant data which are a perturbation of size of a rest state, we establish the first term asymptotic of the life spanT of the classical solution (lim 2 T = * 2 ).Moreover, we give, for an estimate of the true solution, by computing the size of its difference with an approximate solution obtained in a previous work.
Oblatum 2-XII-1991 & 24-IX-1992 相似文献
6.
Dr. Alexander Kovačec 《Monatshefte für Mathematik》1981,92(1):19-35
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional :
n
, such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map
n
n
, which is functional increasing (i.e. for each x
n
(which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)(
u))(
2(u))...
n
(u)). Under quite general conditions one finds that the sequence {
n
(u)}
n converges tov=v(u). As a consequence one obtains the inequality (u)(v). 相似文献
7.
M. Truszczyński 《Periodica Mathematica Hungarica》1988,19(4):273-286
A family of subtrees of a graphG whose edge sets form a partition of the edge set ofG is called atree decomposition ofG. The minimum number of trees in a tree decomposition ofG is called thetree number ofG and is denoted by(G). It is known that ifG is connected then(G) |G|/2. In this paper we show that ifG is connected and has girthg 5 then(G) |G|/g + 1. Surprisingly, the case wheng = 4 seems to be more difficult. We conjecture that in this case(G) |G|/4 + 1 and show a wide class of graphs that satisfy it. Also, some special graphs like complete bipartite graphs andn-dimensional cubes, for which we determine their tree numbers, satisfy it. In the general case we prove the weaker inequality(G) (|G| – 1)/3 + 1. 相似文献
8.
I. A. Taimanov 《Acta Appl Math》1994,36(1-2):119-124
The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier 相似文献
9.
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
10.
A polyhedron on a surface is called a clean triangulation if each face is a triangle and each triangle is a face. LetS
p
(resp.N
p
) be the closed orientable (resp. nonorlentable) surface of genusp. If (S) is the smallest possible number of triangles in a clean triangulation ofS, the results are: (N
1)=20, (S
1)=24, lim(S
p
)p
–1=4, lim(N
p
)p
–1=2 forp. 相似文献
11.
Wolfgang Bischoff 《Annals of the Institute of Statistical Mathematics》1992,44(2):229-238
Let * be an exact D-optimal design for a given regression model Y
= X
+ Z
. In this paper sufficient conditions are given for sesigning how the covariance matrix of Z
may be changed so that not only * remains D-optimal but also that the best linear unbiased estimator (BLUE) of stays fixed for the design *, although the covariance matrix of Z
* is changed. Hence under these conditions a best, according to D-optimality, BLUE of is known for the model with the changed covariance matrix. The results may also be considered as determination of exact D-optimal designs for regression models with special correlated observations where the covariance matrices are not fully known. Various examples are given, especially for regression with intercept term, polynomial regression, and straight-line regression. A real example in electrocardiography is treated shortly. 相似文献
12.
Amitava Chakravorti 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1959,10(4):333-338
Zusammenfassung Die vorliegende Notiz behandelt das Problem der Auffindung des Biegungszentrums eines aus isotropem Material bestehenden Balkens, der einen durch eine parabolische und eine geradlinige Kante begrenzten Querschnitt besitzt. Die Last ist parallel zur geradlinigen Kante angenommen. Der Verfasser benützt zur Lösung der Aufgabe dasselbe Verfahren, dasSokolnikoff [1] für die Auffindung des Biegungszentrums eines halbkreisförmigen Balkens verwendete.
Nomenclature x, y, z rectangular co-ordinates - l, m, n direction cosines of outward drawn normal - x , y , z normal components of stress parallel tox, y, z axes - xy , yz , zx shearing stress components in rectangular co-ordinates - u, v, w components of displacement - T (x, y) stress function in rectangular coordinates - Poisson's ratio - shear modulus - yz , zx , xy shearing strain components in rectangular coordinates 相似文献
Nomenclature x, y, z rectangular co-ordinates - l, m, n direction cosines of outward drawn normal - x , y , z normal components of stress parallel tox, y, z axes - xy , yz , zx shearing stress components in rectangular co-ordinates - u, v, w components of displacement - T (x, y) stress function in rectangular coordinates - Poisson's ratio - shear modulus - yz , zx , xy shearing strain components in rectangular coordinates 相似文献
13.
A. Yu. Shevlyakov 《Journal of Mathematical Sciences》1993,67(4):3237-3243
Let w(x, y), x 0 and y 0 be a Wiener field on the plane; be a curve given parametrically x=x() and y=y(), [0, 1], where x() is a positive, continuous, nondecreasing function; y() is a positive, continuous, nonincreasing function. A best estimate in the mean-square sense is constructed for w(u, v)(u, v) , based on the values w(x, y), (x, y) and its error is found.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 87–93, 1988. 相似文献
14.
Summary Necessary and sufficient conditions are given in order that a sequence of probability measures, weakly convergent relative to a given topology
0 and associated -field (
0), are weakly convergent (and satisfy a continuity theorem) relative to the (
0)-measurable functions which are continuous in some finer topology
1, even if does not extend to (
0). These conditions are shown to be applicable to a sequence of translated renewal measures. Alternate conditions (tightness, uniformity of weak convergence) are investigated and shown to be inappropriate.This research was partially supported by UMC Summer Faculty Research Fellowships 相似文献
15.
We study the class of bounded C
0-semigroups T=(T
t
)
t0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X
0(T)<, where X
0(T):={x X:limt T
t
x=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality. 相似文献
16.
On Idempotent Ranks of Semigroups of Partial Transformations 总被引:2,自引:0,他引:2
A subset U of a semigroup S is a generating set for S
if every element of S may be written as a finite product of
elements of U. The rank of S is the size of a minimal
generating set of S, and the idempotent rank of S is
the size of a minimal generating set of S consisting of
idempotents in S. A partition of a q-element subset of the set Xn={1,2,...,
n} is said to be of type if the sizes of its classes form
the partition of q n. A non-trivial partition
of a positive integer q consists of k < q elements. For a
non-trivial partition of q n, the semigroup
S(), generated by all the transformations with kernels of
type , is idempotent-generated. It is known that if is a non-trivial partition of n, that
is, S() consists of total many-to-one transformations, then
the rank and the idempotent rank of S() are both equal to
max{nd, N()}, where
N() is the number of partitions of Xn of type
. We extend this result to semigroups of partial
transformations, and prove that if is a non-trivial
partition of q < n, then the rank and the idempotent rank of
S() are both equal to N(). 相似文献
17.
Norbert Polat 《Czechoslovak Mathematical Journal》2001,51(3):477-492
For an end and a tree T of a graph G we denote respectively by m() and m
T
() the maximum numbers of pairwise disjoint rays of G and T belonging to , and we define tm() := min{m
T(): T is a spanning tree of G}. In this paper we give partial answers — affirmative and negative ones — to the general problem of determining if, for a function f mapping every end of G to a cardinal f() such that tm() f() m(), there exists a spanning tree T of G such that m
T
() = f() for every end of G. 相似文献
18.
We express the real connective K-theory groups
o4k–1(B
Q
) ofthe quaternion group Q
of order = 2
j
8 in terms of therepresentation theory of Q
by showing
o4k–1(B
Q
) =
Sp(S
4k+3/Q
)where is any fixed point free representation of Q
in U(2k + 2). 相似文献
19.
Prog. Dr. Erhard Heinz 《manuscripta mathematica》1979,28(1-3):81-88
Let T be the domain in N defined by the inequalities O < 1 < ... < N < +. Put N+k = /2(1+k) (k=1,2,3), N+4=1+2, and denote byF() the set of functions x=x(u,v)=(x1(u,v),...,xp(u,v)), (p2) of class
, where B is the unit disk u2+v2<1, which maps the circular arcs k={w=ei:k<<K+1} (k=1,..., N+3) into the straight lines containing the edges ak, ak+1 (aN+4=a1) of a polygon IRp. Then we show that the function ()=
inf
xF()
D(x) is analytic in T. This generalizes and sharpens an unproved result of I. Marx and M. Shiffman (see [4]).
Hans Lewy und Charles B. Morrey gewidmet 相似文献
Hans Lewy und Charles B. Morrey gewidmet 相似文献
20.
Martin Krüskemper 《manuscripta mathematica》1989,65(2):225-243
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT
L/F
()=1 andTr
L/F
(i)=i fori=2,...n. 相似文献