共查询到20条相似文献,搜索用时 46 毫秒
1.
Wolfgang Grotz 《Monatshefte für Mathematik》1979,88(3):219-228
LetK be an algebraic number field, and for every integer K let () andd(), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (). Asymptotic equalities are proved for the sums () and d
2(), where runs through certain finite sets of integers ofK. 相似文献
2.
In this paper, we describe a solution to the register synthesis problem for a class of sequence generators known as algebraic feedback shift registers (AFSRs). These registers are based on the algebra of -adic numbers, where is an element in a ring R, and produce sequences of elements in R/(). We give several cases where the register synthesis problem can be solved by an efficient algorithm. Consequently, any keystreams over R/() used in stream ciphers must be unable to be generated by a small register in these classes. This paper extends the analyses of feedback with carry shift registers and algebraic feedback shift registers by Goresky, Klapper, and Xu. 相似文献
3.
E. M. Matveev 《Mathematical Notes》1996,59(3):293-297
In this note we show that in the well-known Dobrowolski estimate lnM() (ln lnd/ lnd)3,d , where is a nonzero algebraic number of degreed that is not a root of unity andM() is its Mahler measure, the parameterd can be replaced by the quantity=d/()
1/d, where () is the modulus of the discriminant of. To this end, must satisfy the condition deg
p=deg for any primep.Translated fromMatematicheskie Zametki, Vol. 59, No. 3, pp. 415–420, March, 1996. 相似文献
4.
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
5.
We consider solutions of the class of ODEs y=6y
2–x
, which contains the first Painlevé equation (PI) for =1. It is well known that PI has a unique real solution (called a tritronquée solution) asymptotic to
and decaying monotonically on the positive real line. We prove the existence and uniqueness of a corresponding solution for each real nonnegative 1. 相似文献
6.
Fabio Cipriani 《Potential Analysis》1994,3(2):203-218
We give a general criterion for the intrinsic ultracontractivity of Dirichlet Laplacians –
D
on domainsD ofR
d d 3, based on the Lieb's formula. It applies to various classes of domains (e.g. John, Hölder andL
p-averaging domains) and gives new conditions for intrinsic ultracontractivity in terms of the Minkowski dimension of the boundary D. In particular, isotropic self-similar fractals and domains satisfying a c-covering condition are considered. 相似文献
7.
Régis de la Bretèche 《Compositio Mathematica》2001,128(3):261-298
We estimate some sums of the shape
S(X
1,..., X
m
):=1 d1 X1...1 dm Xm
f(d
1,..., d
m
)when m N and f is a nonnegative arithmetical function. We relate them to the behaviour of the associated Dirichlet series
F(s
1,..., s
m
) =
d1 = 1 ...
dm = 1
f(d
1,..., d
m
)/d
1
s1 ... d
m
sm.The main aim of this work is to develop analytic tools to count the rational points of bounded height on toric varieties. 相似文献
8.
Gert K. Pedersen 《Inventiones Mathematicae》1978,45(3):299-305
For each*-derivation of a separableC
*-algebraA and each >0 there is an essential idealI ofA and a self-adjoint multiplierx ofI such that (–ad(ix))|I< and x. 相似文献
9.
We consider a functional differential equation (1) (t)=F(t,) fort[0,+) together with a generalized Nicoletti condition (2)H()=. The functionF: [0,+)×C
0[0,+)B is given (whereB denotes the Banach space) and the value ofF (t, ) may depend on the values of (t) fort[0,+);H: C
0[0,+)B is a given linear operator and B. Under suitable assumptions we show that when the solution :[0,+)B satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2). 相似文献
10.
Guanggui Ding 《数学学报(英文版)》1995,11(4):417-421
IfT is an isomorphism ofL
(A, ) intoL
(B, ) which satisfies the condition T T
–11+, where (A, ) is a -finite measure space, thenT/T is close to an isometry with an error less than 4. 相似文献
11.
We consider Dyson's hierarchical model on a d-dimensional hierarchical lattice and define a renormalization group (RG) transformation for complex values of d as a map in the space of sequences of coupling constants determining the model Hamiltonian. We show that d=4 is a bifurcation value of this transformation for the RG transformation parameter equal to 1+2/d, and we construct a non-Gaussian RG-invariant Hamiltonian in terms of the (4–d)-expansion. We establish that the (–3/2)- and (4–d)-expansion coefficients for a non-Gaussian fixed point in the dimension d=3 have the same asymptotic representation as the size of the elementary cell tends to infinity, thus confirming that both the expansions describe the same nontrivial fixed point in the dimension three. 相似文献
12.
Horst Elmar Winkelnkemper 《Annals of Global Analysis and Geometry》1992,10(3):209-218
Let
t
be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M
n
, whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d
t
and, for each x M, we define a smooth real function
x
(t) : (1 +
i
(t)), where the i(t) are the eigenvalues of AA
T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t
, restricted to v at the point x
-t M
n.Among other things, we prove the
Theorem (Theorem II, below). Assume v is also volume preserving and that
x
'
(t) 0 for all x M and real t; then, if
x
t
: M M is weakly missng for some t, it is necessary that vx 0 at all x M. 相似文献
13.
J. C. Lagarias 《Monatshefte für Mathematik》1993,115(4):299-328
Given a vector of real numbers=(1,...
d
)
d
, the Jacobi-Perron algorithm and related algorithms, such as Brun's algorithm and Selmer's algorithm, produce a sequence of (d+1)×(d+1) convergent matrices {C(n)():n1} whose rows provide Diophantine approximations to . Such algorithms are specified by two mapsT:[0, 1]
d
[0, 1]
d
and A:[0,1]
d
GL(d+1,), which compute convergent matrices C(n)())...A(T())A(). The quality of the Diophantine approximations these algorithms find can be measured in two ways. The best approximation exponent is the upper bound of those values of for which there is some row of the convergent matrices such that for infinitely many values ofn that row of C(n)() has
. The uniform approximation exponent is the upper bound of those values of such that for all sufficiently large values ofn and all rows of C(n)() one has
. The paper applies Oseledec's multiplicative ergodic theorem to show that for a large class of such algorithms and take constant values and on a set of Lebesgue measure one. It establishes the formula where are the two largest Lyapunov exponents attached by Oseledec's multiplicative ergodic theorem to the skew-product (T, A,d), whered is aT-invariant measure, absolutely continuous with respect to Lebesgue measure. We conjecture that holds for a large class of such algorithms. These results apply to thed-dimensional Jacobi-Perron algorithm and Selmer's algorithm. We show that; experimental evidence of Baldwin (1992) indicates (nonrigorously) that. We conjecture that holds for alld2. 相似文献
14.
Rangachari Venkataraman 《Monatshefte für Mathematik》1985,100(1):47-66
An abelian topological group is an group if and only if it is a locally -compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian groupG is topologically isomorphic to G
0 where 0 andG
0 is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra,L
1-algebra, Fourier transforms of abelian groups are given and their properties are studied. 相似文献
15.
Izu Vaisman 《Annals of Global Analysis and Geometry》1990,8(2):137-145
Summary Let (M, J, g) be a compact complex 2-dimensional Hermitian manifold with the Kähler form , and the torsion 1-form defined by d = . In this note we obtain the Euler-Lagrange equations for the variational functionals defined by 2 and d2, whereg runs in the space of all the Hermitian metrics onM. In the first case, the extremals are precisely the Kähler metrics [Gd]. In the second case, we also write down a formula for the second variation.Communicated by J. Szenthe 相似文献
16.
Frédéric Bernardin 《Set-Valued Analysis》2003,11(4):393-415
In this paper we show the strong mean square convergence of a numerical scheme for a R
d
-multivalued stochastic differential equation: dX
t
+A(X
t
)dtb(t,X
t
)dt+(t,X
t
)dW
t
and obtain the rate of convergence O(( log(1/)1/2) when the diffusion coefficient is bounded. By introducing a discrete Skorokhod problem, we establish L
p
-estimates (p2) for the solutions and prove the convergence by using a deterministic result. Numerical experiments for the rate of convergence are presented. 相似文献
17.
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
18.
F. Móricz 《Analysis Mathematica》1979,5(2):135-147
Z
d — k=(k
1, ...,k
d) k
j,d1.d- (8), . .
a
k s
m=
a
k s, >0 N, min (m
1,...,m
d)N, ¦s
m–s¦. , , >0 N, min (m
1,...,m
d)N min (n
1,...,n
d)N, ¦s
m–s
n. . , (8) , >0 N, max (b
1,...,b
d) N, m — Z
d
, m1, ¦s(b, m)¦ where
相似文献
19.
L
p
, 0<<1, . 相似文献