共查询到20条相似文献,搜索用时 31 毫秒
1.
O. N. Karpenkov 《Monatshefte für Mathematik》2007,258(1):217-249
In this paper we develop an integer-affine classification of three-dimensional multistory, completely empty convex marked
pyramids. We apply it to obtain the complete lists of compact two-dimensional faces of multidimensional continued fractions
lying in planes at integer distances 2, 3, 4, … to the origin. The faces are considered up to the action of the group of
integer-linear transformations. 相似文献
2.
August Florian 《Monatshefte für Mathematik》2001,130(4):111-129
In this paper we provide an upper bound to the density of a packing of circles on the sphere, with radii selected from a
given finite set. This bound is precise, e.g. for the system of incircles of Archimedean tilings (4, 4, n) with n ? 6. A generalisation to the weighted density of packing is applied to problems of solidity of a packing of circles. The
simple concept of solidity was introduced by L. Fejes Toóth [6]. In particular, it is proved that the incircles of the faces of the Archimedean tilings
(4,6,6), (4,6,8) and (4, 6, 10) form solid packings. 相似文献
3.
August Florian 《Monatshefte für Mathematik》2001,133(2):111-129
In this paper we provide an upper bound to the density of a packing of circles on the sphere, with radii selected from a
given finite set. This bound is precise, e.g. for the system of incircles of Archimedean tilings (4, 4, n) with n ? 6. A generalisation to the weighted density of packing is applied to problems of solidity of a packing of circles. The
simple concept of solidity was introduced by L. Fejes Toóth [6]. In particular, it is proved that the incircles of the faces of the Archimedean tilings
(4,6,6), (4,6,8) and (4, 6, 10) form solid packings.
(Received 21 August 2000; in revised form 21 March 2001) 相似文献
4.
This paper aims to study the local convergence of a family of Euler-Halley type methods with a parameter α for solving nonlinear operator equations under the second-order generalized Lipschitz assumption. The radius r
α
of the optimal convergence ball and the error estimation of the method corresponding to α are estimated for each α ∈ ( − ∞ , + ∞ ). For each α > 0, we get r
α
≥ r
− α
and the upper bound of the error estimation of the method with α > 0 is not larger than the one with α < 0. For each α ≤ 0, we get the precise value of r
α
, which is closely linked to the dynamical property of the method applied to a real or a complex function, and the optimal
error estimation, which decreases when α→0 − . Results show that the method corresponding to α is better than the one corresponding to − α for each α > 0 and the Chebyshev-Euler method is the best among all methods in the family with α ∈ ( − ∞ , 0] from the view of both safe choice of the initial point and error estimation. 相似文献
5.
A construction of “sparse potentials,” suggested by the authors for the lattice
\mathbbZd {\mathbb{Z}^d} , d > 2, is extended to a large class of combinatorial and metric graphs whose global dimension is a number D > 2. For the Schr?dinger operator − Δ − αV on such graphs, with a sparse potential V, we study the behavior (as α → ∞) of the number N_(−Δ − αV) of negative eigenvalues of − Δ − αV. We show that by means of sparse potentials one can realize any prescribed asymptotic behavior of N_(−Δ − αV) under very mild regularity assumptions. A similar construction works also for the lattice
\mathbbZ2 {\mathbb{Z}^2} , where D = 2. Bibliography: 13 titles. 相似文献
6.
D. Çakmak 《Ukrainian Mathematical Journal》2008,60(5):799-809
Some new oscillation criteria are given for general nonlinear second-order ordinary differential equations with damping of
the form x″+ p ( t ) x′+ q ( t ) f ( x ) = 0, where f is monotone or nonmonotone. Our results generalize and extend some earlier results of Deng.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 694–700, May, 2008. 相似文献
7.
Lithuanian Mathematical Journal - For k ≔ (k1, …, kr) ∈ ℕr and n, m ∈ ℕ, we extend the definition of classical hyperharmonic... 相似文献
8.
We call a semiring S locally closed if for all a ∈ S there is some integer k such that 1 + a + ⋯ + a
k
=1 + a + ⋯ + a
k + 1
. In any locally closed semiring we may define a star operation a ↦ a
*, where a
* is the above finite sum. We prove that when S is locally closed and commutative, then S is an iteration semiring. 相似文献
9.
We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer
k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,
this last inequality also holding if z ⩾ 2. We then use these inequalities to obtain probabilistic results and we state a conjecture. Finally, using (*), we show
that the probability that the abc conjecture does not hold is 0. 相似文献
10.
Viresh Patel 《Order》2008,25(2):131-152
Given a poset P = (X, ≺ ), a partition X
1, ..., X
k
of X is called an ordered partition of P if, whenever x ∈ X
i
and y ∈ X
j
with x ≺ y, then i ≤ j. In this paper, we show that for every poset P = (X, ≺ ) and every integer k ≥ 2, there exists an ordered partition of P into k parts such that the total number of comparable pairs within the parts is at most (m − 1)/k, where m ≥ 1 is the total number of edges in the comparability graph of P. We show that this bound is best possible for k = 2, but we give an improved bound, , for k ≥ 3, where c(k) is a constant depending only on k. We also show that, given a poset P = (X, ≺ ) and an integer 2 ≤ k ≤ |X|, we can find an ordered partition of P into k parts that minimises the total number of comparable pairs within parts in time polynomial in the size of P. We prove more general, weighted versions of these results.
Supported by an EPSRC doctoral training grant. 相似文献
11.
Throughout this article we assume that the df H of a random vector (X,Y) is in the max-domain of attraction of an extreme value distribution function (df) G with reverse exponential margins. Therefore, the asymptotic dependence structure of H can be represented by a Pickands dependence function D with D = 1 representing the case of asymptotic independence. One of our aims is to test the null hypothesis of tail-dependence against
the alternative of tail-independence. Thus we want to prove the validity of the model where D = 1. The test is based on the radial component X + Y. Under a certain spectral expansion it is verified that the df of X + Y, conditioned on X + Y > c, converges to F(t) = t, as c ↑0, if D ≠ 1 and, respectively, to F(t) = t
1 + ρ
, if D = 1, where ρ > 0 determines the rate at which independence is attained. Based on the limiting dfs we find a uniformly most powerful test procedure for testing tail-dependence against rates of tail-independence. In addition,
an estimator of the parameter ρ is proposed. The relationship of ρ to another dependence measure, given in the literature, is indicated.
相似文献
12.
Joseph Glaz Marco Guerriero Rohini Sen 《Methodology and Computing in Applied Probability》2010,12(4):731-747
Let X
ijk
,1 ≤ i ≤ N
1,1 ≤ j ≤ N
2, 1 ≤ k ≤ N
3 be a sequence of independent and identically distributed 0 − 1 Bernoulli trials. X
ijk
= 1 if an event has occurred at the i,j,k
th
location in a three dimensional rectangular region and X
ijk
= 0, otherwise. For 2 ≤ m
j
≤ N
j
− 1,1 ≤ j ≤ 3, a three dimensional discrete scan statistic is defined as the maximum number of events in any m
1×m
2×m
3 rectangular sub-region in the entire N
1×N
2×N
3 rectangular region. In this article, a product-type approximation and three Poisson approximations are derived for the distribution
of this three dimensional scan statistic. Numerical results are presented to evaluate the accuracy of these approximations
and their use in testing for randomness. 相似文献
13.
Ante Mimica 《Potential Analysis》2010,32(3):275-303
In this paper we prove Harnack inequality for nonnegative functions which are harmonic with respect to random walks in ℝ
d
. We give several examples when the scale invariant Harnack inequality does not hold. For any α ∈ (0,2) we also prove the Harnack inequality for nonnegative harmonic functions with respect to a symmetric Lévy process
in ℝ
d
with a Lévy density given by $c|x|^{-d-\alpha}1_{\{|x|\leq 1\}}+j(|x|)1_{\{|x|>1\}}$c|x|^{-d-\alpha}1_{\{|x|\leq 1\}}+j(|x|)1_{\{|x|>1\}}, where 0 ≤ j(r) ≤ cr
− d − α
, ∀ r > 1, for some constant c. Finally, we establish the Harnack inequality for nonnegative harmonic functions with respect to a subordinate Brownian motion
with subordinator with Laplace exponent ϕ(λ) = λ
α/2ℓ(λ), λ > 0, where ℓ is a slowly varying function at infinity and α ∈ (0,2). 相似文献
14.
We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there
is a constant λ > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain—with boundary values −λ on one boundary arc and
λ on the complementary arc—the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are −a < 0 on the first arc and b > 0 on the complementary arc, then the convergence is to SLE(4; a/λ - 1, b/λ - 1), a variant of SLE(4). 相似文献
15.
We call a semiring S locally closed if for all a ∈ S there is some integer k such that 1 + a + ⋯ + a
k
=1 + a + ⋯ + a
k + 1
. In any locally closed semiring we may define a star operation a ↦ a
*, where a
* is the above finite sum. We prove that when S is locally closed and commutative, then S is an iteration semiring.
Partially supported by grant no. T30511 from the National Foundation of Hungary for Scientific Research and the Austrian–Hungarian
Bilateral Research and Development Fund, no. A-4/1999, and by the Austrian–Hungarian Action Foundation.
Partially supported by the Austrian–Hungarian Bilateral Research and Development Fund, no. A-4/1999, and by the Austrian–Hungarian
Action Foundation.
Received March 16, 2001 相似文献
16.
E. P. Golubeva 《Journal of Mathematical Sciences》2009,157(4):543-552
The solvability of the equation n = x
2 + y
2 + 6pz
2 (p is a fixed large prime) is proved under some natural congruential conditions and the assumption nm
12 > p
21. As an implication, the solvability of the equation n = x
2 + y
2 + u
3 + v
3 + z
4 + w
16 + t
4k+1 for all sufficiently large n is established. Bibliography: 13 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 5–21. 相似文献
17.
We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer
k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,
this last inequality also holding if z ⩾ 2. We then use these inequalities to obtain probabilistic results and we state a conjecture. Finally, using (*), we show
that the probability that the abc conjecture does not hold is 0.
Research supported in part by a grant from NSERC.
Re?u le 17 décembre 2001; en forme révisée le 23 mars 2002
Publié en ligne le 11 octobre 2002 相似文献
18.
BASUDEB DHARA 《Proceedings Mathematical Sciences》2012,122(1):121-128
Let R be a prime ring with its Utumi ring of quotient U, H and G be two generalized derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(H(u)u − uG(u))
n
= 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then there exist b′,c′ ∈ U such that H(x) = b′x + xc′, G(x) = c′x for all x ∈ R with ab′ = 0, unless R satisfies s
4, the standard identity in four variables. 相似文献
19.
We determine the general solution of the functional equation f(x + ky) + f(x-ky) = g(x + y) + g(x-y) + h(x) + h(y) for fixed integers with k ≠ 0; ±1 without assuming any regularity conditions for the unknown functions f, g, h, and0020[(h)\tilde] \tilde{h} . The method used for solving these functional equations is elementary but it exploits an important result due to Hosszú.
The solution of this functional equation can also be obtained in groups of certain type by using two important results due
to Székelyhidi. 相似文献
20.
Liangping Jiang 《Journal of Mathematical Sciences》2011,177(3):395-401
The classical criterion of asymptotic stability of the zero solution of equations x′ = f(t, x) is that there exists a function V (t, x), a(∥x∥) ≤ V (t, x) ≤ b(∥x∥) for some a, b ∈ K such that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) for some c ∈ K. In this paper, we prove that if V(m + 1) \mathop {V}\limits^{(m + {1})} (t, x) is bounded on some set [tk − T, tk + T] × BH(tk → +∞ as k → ∞), then the condition that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) can be weakened and replaced by that [(V)\dot] \dot{V} (t, x) ≤ 0 and − (−[(V)\dot] \dot{V} (tk, x)| + − [(V)\ddot] \ddot{V} (tk, x)| + ⋯ + − V(m) \mathop {V}\limits^{(m)} (tk, x)|) ≤ −c′(∥x∥) for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [1–10] 相似文献