共查询到20条相似文献,搜索用时 46 毫秒
1.
We give the asymptotics of the sum
, where
, for the multiplicative functions
, and
. 相似文献
2.
The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations. III 总被引:1,自引:1,他引:0
In the canonical smooth fiber bundles
endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups
(1, n) and construct
(1, n)-invariant generalized differential-geometric connections. In both regular and special cases of the representations of the considered groups
(1, n), we find all affine nonholonomic
, and 1,2-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations
(1, n) and also describe the corresponding
(1, n)invariant planar connections. 相似文献
3.
We study the problem of asymptotic integration of the linear integro-differential equation
, and the achievement of an asymptotic formula for the solutions of the equation
. 相似文献
4.
C. Baxa 《Acta Mathematica Hungarica》1999,83(1-2):125-130
Let log
. We prove that there exist non-denumerably many pairwise not equivalent irrational numbers such that
and
where qn() denotes the denominator of the nth convergent of . 相似文献
5.
Consider a path-integral
which is the solution to a diffusion version of the generalized Schro¨dinger's equation
. Here
, where A is an infinitesimal generator of a strongly continuous Markov Semigroup corresponding to the diffusion process
. For
and V replaced by
one obtains
, which represents a quantum mechanical Hamiltonian corresponding to a particle of mass 1 (in atomic units) subject to interaction with potential V. This paper is concerned with computer calculations of the second eigenvalue of
by generating a large number of trajectories of an ergodic diffusion process. 相似文献
6.
We show that ifP
, |P|=d+k,dk1 andO int convP, then there exists a simplexS of dimension
with vertices inP, satisfyingO rel intS, the bound being sharp. We give an upper bound for the minimal number of vertices of facets of a (j-1)-neighbourly convex polytope in
withv vertices.Research (partially) supported by Hung. Nat. Found. for Sci. Research, grant no. 1817Research (partially) supported by Hung. Nat. Found. for Sci. Research, grant no. 326-0213 相似文献
7.
K. ONO 《Compositio Mathematica》1997,106(3):349-360
If E is an elliptic curve over
, then let E(D) denote theD-quadratic twist of E. It is conjectured that there are infinitely many primesp for which E(p) has rank 0, and that there are infinitely many primes
for which
has positive rank. For some special curvesE we show that there is a set S of primes p with density
for which if
is a squarefree integer where
, then E(D) has rank 0. In particular E(p) has rank 0 for every
. As an example let E1 denote the curve
.Then its associated set of primes S1 consists of the prime11 and the primes p for which the order of the reduction ofX0(11) modulo p is odd. To obtain the general result we show for primes
that the rational factor of L(E(p),1) is nonzero which implies thatE(p) has rank 0. These special values are related to surjective
Galois representations that are attached to modularforms. Another example of this result is given, and we conclude with someremarks regarding the existence of positive rank prime twists via polynomialidentities. 相似文献
8.
Conditions are found upon satisfaction of which the differential equation
相似文献
9.
Tatsuya Maruta 《Geometriae Dedicata》1999,74(3):305-311
Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q –
q - \sqrt q + 2$$
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and for
when
, which is a generalization of [18, Them. 2.4]. 相似文献
10.
Consider the Dirichlet problem for the parabolic equation
in
, where
$\Omega$ is a bounded domain in
and f has superlinear subcritical growth in u.
If f is independent of t and satisfies some
additional conditions then using a dynamical method we find multiple (three, six or infinitely many) nontrivial
stationary solutions. If f has the form
where m is periodic, positive and m,g satisfy some technical
conditions then we prove the existence of a positive periodic solution and
we provide a locally uniform bound for all global solutions. 相似文献
11.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
12.
13.
Gerold Wagner 《Monatshefte für Mathematik》1981,92(3):239-245
Letf be a periodic function on with period 1, piecewise continuously differentiable, satisfying
. For an arbitrary sequence = (
i
) in [0,1) put
and
. If
then
n
(f,) >c· logn holds for some positive constantc (depending onf only) and almost alln. In a certain sense the converse is also true: there is a class of functionsf with
such that
n
(f,) =o (logn).Support has been received from Netherlands Organization for the Advancement of Pure Research (Z. W. O.). 相似文献
14.
H. Fiedler 《Numerische Mathematik》1987,51(5):571-581
Summary Interpolatory quadrature formulae consist in replacing
by
wherep
f
denotes the interpolating polynomial off with respect to a certain knot setX. The remainder
may in many cases be written as
wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP
X
(t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis. 相似文献
15.
Sufficient conditions of solvability and unique solvability of the boundary value problem
are established, where
are measurable functions and the vector function
is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument. 相似文献
16.
B. Bajnok and S. Shahriari proved that in 2[n], the Boolean lattice of order n, the width (the maximum size of an antichain) of a non-trivial cutset (a collection of subsets that meets every maximal chain and does not contain or [n]) is at least n-1. We prove that, for n5, in the Boolean lattice of order n, given
-1 disjoint long chains, we can enlarge the collection to a cutset of width n-1. However, there exists a collection of
long chains that cannot be so extended. 相似文献
17.
We study level surfaces of non-degenerate functions inR
n+1. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field
for level surfaces of a non-degenerate function and give certain characterizations of when
is transversal, by the shape operatorS, the transversal connection , and consider the difference between
and the affine normal. 相似文献
18.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):477-495
Given a nonempty set
and two multifunctions
, we consider the following generalized quasi-variational inequality problem associated with X, : Find
such that
. We prove several existence results in which the multifunction is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case (x(X. 相似文献
19.
И. Н. Пак 《Analysis Mathematica》1990,16(1):57-64
We generalize and sharpen certain results concerning Fourier series from the Lipschitz class. In particular, for
sinnx we prove the following: Let ¦bn¦n–2L(n) where L(x) is a continuous and slowly oscillating function. Then
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