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1.
M. B. Nathanson 《Acta Mathematica Hungarica》2000,87(3):179-195
Let A be a set of positive integers with gcd (A) = 1, and let p
A
(n) be the partition function of A. Let c
0 = 2/3. If A has lower asymptotic density and upper asymptotic density , then lim inf log p
A
(n)/c
0 n and lim sup log p
A
(n)/c
0 n . In particular, if A has asymptotic density > 0, then log p
A
(n) c0n. Conversely, if > 0 and log p
A
(n) c
0 n, then the set A has asymptotic density . 相似文献
2.
Lucilla Bassotti Rizza 《Annali di Matematica Pura ed Applicata》1987,148(1):173-205
Summary Let be an open subset of n, Wm() the linear space of m-vector valued functions defined on , G{} a group of orthogonal matrices mapping onto itself and T{T()} a linear representation of order m of G. A suitable groupC(G,T) of linear operators of Wm(), which leads to a general definition of T-invariant linear operator with respect to G, is here introduced. Characterization theorems concerning the linear differential and integral T-invariant operators are also given. When G is a finite group, projection operators are explicitly obtained; they define a «maximal» decomposition of Wm() into a direct sum of subspaces each of them invariant with respect to any T-invariant linear operator of Wm(). Some examples are givenc.
Lavoro eseguito nell'ambito del progetto nazionale di ricerca «Analisi numerica e matematica computazionale» nell'anno 1985–86. 相似文献
Lavoro eseguito nell'ambito del progetto nazionale di ricerca «Analisi numerica e matematica computazionale» nell'anno 1985–86. 相似文献
3.
, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1]. 相似文献
4.
L
p
, 0<<1, . 相似文献
5.
Pavel Valtr 《Discrete and Computational Geometry》1992,7(1):135-152
For a finite setA of points in the plane, letq(A) denote the ratio of the maximum distance of any pair of points ofA to the minimum distance of any pair of points ofA. Fork>0 letc
(k) denote the largest integerc such that any setA ofk points in general position in the plane, satisfying
for fixed
, contains at leastc convex independent points. We determine the exact asymptotic behavior ofc
(k), proving that there are two positive constants=(), such thatk
1/3c
(k)k
1/3. To establish the upper bound ofc
(k) we construct a set, which also solves (affirmatively) the problem of Alonet al. [1] about the existence of a setA ofk points in general position without a 7-hole (i.e., vertices of a convex 7-gon containing no other points fromA), satisfying
. The construction uses Horton sets, which generalize sets without 7-holes constructed by Horton and which have some interesting properties. 相似文献
6.
Exact estimates for partially monotone approximation 总被引:2,自引:0,他引:2
G. L. Iliev 《Analysis Mathematica》1978,4(3):181-197
f(x) — , - [–1,1], (f, ) — , as— f, . . (- ) (x
i,x
i+ 1) (i=0, 1, ...,s–1; =–1,x
s,=1), f(x) . , n=0,1,...
n() , [– 1,1] signf(x) sign
n(x) 0, ¦f(x)–
n(x)¦ C(s) (f, 1/n+1, C(s) s. , - , « » . 相似文献
7.
There are described the subgroups of the general symplectic group =GSp(2n, R) over a commutative semilocal ring R, containing the group of symplectic diagonal matrices. For each such subgroup P there is uniquely defined a symplectic D-net a such that ()pN(), where () is the net subgroup in corresponding to (cf. RZhMat, 1977, 5A288), and N() is its normalizer. The quotient group N × ()/() is calculated. There are also considered subgroups in Sp(2n, R). Analogous results for subgroups of the general linear group were obtained earlier in RZhMat, 1978, 9A237.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 31–47, 1980. 相似文献
8.
J. Lippus 《Analysis Mathematica》1984,10(3):213-231
- ()N2,L
F
(
) — , 2- , {s
m()
f} -L.
— . (L
F(
),L
F(
) ={(k)} (kZ2) , fLF(
) f
,
, L
F(
). - ={()} ={()} , n(())m()n(()+())
. R() , ..
- . , . (L
F
(
),L
F
(
)) , R(,)=O(1) (x).
The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper. 相似文献
The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper. 相似文献
9.
S. S. P. Shen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(1):122-138
Critical long surface waves forced by locally distributed external pressure applied on the free surface in channels of arbitrary cross section are studied in this paper. The fluid under consideration is inviscid and has constant density. The upstream flow is uniform and the upstream velocity is assumed to be near critical, i.e.,u
0=u
c
++0(2), where 0<1 andu
c
is the critical velocity determined by the geometry of the channel. The external pressure applied on the free surface as the forcing is
2
P(x). Then the first order perturbation of the free surface elevation satisfies a forced Korteweg-de Vries equation (fK-dV). It is shown in this paper that: (i) If
(supercritical), the stationaryfK-dV has two cusped solitary wave solutions; (ii) if
(subcritical), the stationaryfK-dV has a downstream cnoidal wave solution; (iii) when=
L
, the unique stationary solution of thefK-dV is a wave free hydraulic fall; (iv) if=
d
=–
L
, thefK-dV has a jump solution; and (v) if
L
<<
c
, thefK-dV does not have stationary solutions. Some free surface profiles and bifurcation diagrams are presented. 相似文献
10.
B. F. Skubenko 《Journal of Mathematical Sciences》1984,25(2):1089-1092
Let M be a complete module of a purely algebraic field of degree n3, let be the lattice of this module and let F(X) be its form. By we denote any lattice for which we have = , where is a nondiagonal matrix satisfying the condition ¦-I¦ , I being the identity matrix. The complete collection of such lattices will be denoted by {}. To each lattice we associate in a natural manner the decomposable form F(X). The complete collection of forms, corresponding to the set {}, will be denoted by {F} It is shown that for any given arbitrarily small interval (N–, N+), one can select an such that for each F(X) from {F} there exists an integral vector X0 such that N– < F(X0) < N+.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 167–171, 1981. 相似文献
11.
Choosing the maximum value from a sequence ofN independent values is a well known problem often called the candidate problem or secretary problem. This paper treats the above problem with a discount penalty (0<<1) for each additional observation taken. It is shown that asN increases indefinitely, the optimal stopping policy is bounded although the maximum expected payoff goes to zero, and that there exists a sequence 0=
0<1<2<<1, such that the asymptotic optimal stopping rule is the same for all
i–1<i. 相似文献
12.
13.
Wolfgang Reichel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):822-838
We consider the equation
(pu)-qu+wu
= f
in (0,1) subject to homogenous boundary conditions at
x = 0
and
x = 1, e.g.,
u(0)
= u(1) = 0. Let
1
be the first eigenvalue of the corresponding Sturm-Liouville problem. If
f 0
but
0 then it is known that there exists
> 0 (independent on
f) such that for
(1,
1 + ]
any solution
u
must be negative. This so-called
uniform anti-maximum principle
(UAMP)
goes back to Clément, Peletier [4]. In this paper we
establish the sharp values of
for which (UAMP) holds. The same phenomenon, including sharp values of
, can be shown for the radially symmetric
p-Laplacian on balls and annuli in
n
provided
1 n <
p. The results are illustrated by
explicitly computed examples. 相似文献
14.
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
15.
Mark S. MacLean 《Journal of Algebraic Combinatorics》2003,17(2):125-147
Let denote a bipartite distance-regular graph with diameter D 4, valency k 3, and distinct eigenvalues 0 > 1 > ··· > D. Let M denote the Bose-Mesner algebra of . For 0 i D, let E
i denote the primitive idempotent of M associated with
i
. We refer to E
0 and E
D as the trivial idempotents of M. Let E, F denote primitive idempotents of M. We say the pair E, F is taut whenever (i) E, F are nontrivial, and (ii) the entry-wise product E F is a linear combination of two distinct primitive idempotents of M. We show the pair E, F is taut if and only if there exist real scalars , such that
i + 1
i + 1 –
i – 1
i – 1 =
i
(
i + 1 –
i – 1) +
i
(
i + 1 –
i – 1) + (1 i D – 1)where 0, 1, ...,
D
and 0, 1, ...,
D
denote the cosine sequences of E, F, respectively. We define to be taut whenever has at least one taut pair of primitive idempotents but is not 2-homogeneous in the sense of Nomura and Curtin. Assume is taut and D is odd, and assume the pair E, F is taut. We show
for 1 i D – 1, where = 1, = 1. Using these equations, we recursively obtain 0, 1, ..., D and 0, 1, ...,
D
in terms of the four real scalars , , , . From this we obtain all intersection numbers of in terms of , , , . We showed in an earlier paper that the pair E
1, E
d is taut, where d = (D – 1)/2. Applying our results to this pair, we obtain the intersection numbers of in terms of k, , 1, d, where denotes the intersection number c
2. We show that if is taut and D is odd, then is an antipodal 2-cover. 相似文献
16.
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
17.
V. N. Sudakov 《Mathematical Notes》1973,14(4):886-888
Let X and Y be locally compact-compact topological spaces, F X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (x, y P (X)×P(Y), a probability measure P(F) such that
X
=
X
–1
,
Y
=
Y
–1
it is necessary and sufficient that, for any pair of Borel sets A X, B Y for which (A× B) F=Ø, the condition
XA+
YB 1 holds.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973. 相似文献
18.
The following Riemann–Hilbert problem is solved: find an analytical function <> from the Smirnov class E
p(D), whose angular boundary values satisfy the condition
The boundary of the domain D is assumed to be a piecewise smooth curve whose nonintersecting Lyapunov arcs form, with respect to D, the inner angles with values , 0 < 2. 相似文献
19.
This paper is a continuation of RZhMat 1980, 5A439, where there was introduced the subgroup () of the Chevalley group G(,R) of type over a commutative ring R that corresponds to a net , i.e., to a set =(),, of ideals of R such that + whenever ,,+ . It is proved that if the ring R is semilocal, then () coincides with the group 0 considered earlier in RZhMat 1976, 10A151; 1977, 10A301; 1978, 6A476. For this purpose there is constructed a decomposition of () into a product of unipotent subgroups and a torus. Analogous results are obtained for sub-radical nets over an arbitrary commutative ring.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 62–76, 1982.In conclusion, the authors would like to thank Z. I. Borevich for his interest in this paper. 相似文献
20.
Jean Michel Morel 《manuscripta mathematica》1985,54(1-2):165-185
In this paper, we describe a method for extending (in some approximated sense) solutions of a nonlinear P.D.E. on a domain , to solutions in a domain containing . Such an extension property, the Runge property, is well known for a large class of linear problems including elliptic equations. We prove here the Runge property for semilinear problems of the kind -u+g(u)=f, with f L
loc
1
(N). (As a consequence, we get infinitely many solutions for these problems). The proof is based on a homotopy method, and requires a refinement of the linear results: We prove that the Runge extension v on of a solution u in for a linear elliptic equation Lu=f can be choosen in order to depend continuously on u and the coefficients of L. 相似文献