For a sequence A = {Ak} of finite subsets of N we introduce: , , where A(m) is the number of subsets Ak ? {1, 2, …, m}.The collection of all subsets of {1, …, n} together with the operation constitutes a finite semi-group N∪ (semi-group N∩) (group ). For N∪, N∩ we prove analogues of the Erdös-Landau theorem: δ(A+B) ? δ(A)(1+(2λ)?1(1?δ(A>))), where B is a base of N of the average order λ. We prove for analogues of Schnirelmann's theorem (that δ(A) + δ(B) > 1 implies δ(A + B) = 1) and the inequalities λ ? 2h, where h is the order of the base.We introduce the concept of divisibility of subsets: a|b if b is a continuation of a. We prove an analog of the Davenport-Erdös theorem: if d(A) > 0, then there exists an infinite sequence {Akr}, where Akr | Akr+1 for r = 1, 2, …. In Section 6 we consider for analogues of Rohrbach inequality: , where g(n) = min k over the subsets {a1 < … < ak} ? {0, 1, 2, …, n}, such that every m? {0, 1, 2, …, n} can be expressed as m = ai + aj.Pour une série A = {Ak} de sous-ensembles finis de N on introduit les densités: , où A(m) est le nombre d'ensembles Ak ? {1, 2, …, m}. L'ensemble de toutes les parties de {1, 2, …, n} devient, pour les opérations , un semi-groupe fini N∪, N∩ ou un groupe N1 respectivement. Pour N∪, N∩ on démontre l'analogue du théorème de Erdös-Landau: δ(A + B) ? δ(A)(1 + (2λ)?1(1?δ(A))), où B est une base de N d'ordre moyen λ. On démontre pour l'analogue du théorème de Schnirelmann (si δ(A) + δ(B) > 1, alors δ(A + B) = 1) et les inégalités λ ? 2h, où h est l'ordre de base. On introduit le rapport de divisibilité des enembles: a|b, si b est une continuation de a. On démontre l'analogue du théorème de Davenport-Erdös: si d(A) > 0, alors il existe une sous-série infinie {Akr}, où Akr|Akr+1, pour r = 1, 2, … . Dans le Paragraphe 6 on envisage pour N∪, les analogues de l'inégalité de Rohrbach: , où g(n) = min k pour les ensembles {a1 < … < ak} ? {0, 1, 2, …, n} tels que pour tout m? {0, 1, 2, …, n} on a m = ai + aj. 相似文献
Two identical 1D autocatalytic systems with Gray–Scott kinetics—driven towards convectively unstable regimes and submitted
to independent spatiotemporal Gaussian white noises—are coupled unidirectionally, but otherwise linearly. Numerical simulation
then reveals that (even when perturbed by noise) the slave system replicates the convective patterns arising in the master
one to a very high degree of precision, as indicated by several measures of synchronization. 相似文献
Le nombre maximal de lignes de matrices seront désignées par:
1. (a) R(k, λ) si chaque ligne est une permutation de nombres 1, 2,…, k et si chaque deux lignes différentes coïncide selon λ positions;
2. (b) S0(k, λ) si le nombre de colonnes est k et si chaque deux lignes différentes coïncide selon λ positions et si, en plus, il existe une colonne avec les éléments y1, y2, y3, ou y1 = y2 ≠ y3;
3. (c) T0(k, λ) si c'est une (0, 1)-matrice et si chaque ligne contient k unités et si chaque deux lignes différentes contient les unités selon λ positions et si, en plus, il existe une colonne avec les éléments 1, 1, 0.
La fonction T0(k, λ) était introduite par Chvátal et dans les articles de Deza, Mullin, van Lint, Vanstone, on montrait que T0(k, λ) max(λ + 2, (k − λ)2 + k − λ + 1). La fonction S0(k, λ) est introduite ici et dans le Théorème 1 elle est étudiée analogiquement; dans les remarques 4, 5, 6, 7 on donne les généralisations de problèmes concernant T0(k, λ), S0(k, λ), dans la remarque 9 on généralise le problème concernant R(k, λ). La fonction R(k, λ) était introduite et étudiée par Bolton. Ci-après, on montre que R(k, λ) S0(k, λ) T0(k, λ) d'où découle en particulier: R(k, λ) λ + 2 pour λ k + 1 − (k + 2)1/2; R(k, λ) = 0(k2) pour k − λ = 0(k); R(k, λ) (k − 1)2 − (k + 2) pour k 1191. 相似文献
The hypermetric coneHn is the cone in the spaceRn(n–1)/2 of all vectorsd=(dij)1i<jn satisfying the hypermetric inequalities: –1ijnzjzjdij 0 for all integer vectorsz inZn with –1inzi=1. We explore connections of the hypermetric cone with quadratic forms and the geometry of numbers (empty spheres andL-polytopes in lattices). As an application, we show that the hypermetric coneHn is polyhedral. 相似文献
A major factor hampering the introduction of ionizing radiation as an alternative quarantine treatment to chemical fumigation for fruit and vegetables is the lack of reliable, simple and inexpensive post-treatment methods to confirm this low dose irradiation treatment. Considering this purpose, thermoluminescence (TL) measurements of the wind blown dust naturally adhered to the surface of table grapes, was surveyed. Two doses, 0.5 and 1.0 kGy, were studied, applied to the main Chilean table grape export varieties: Thompson Seedless and Flame Seedless.
TL measurements were carried out over 78 days for Thompson Seedless and 62 days for Flame Seedless varieties, both stored at 1 ± 1°C (usual handling of this fruit). TL response fading of dust samples stored at room temperature was also followed over 125 days. The TL response values obtained from the irradiated samples exceeded at least 3 times the highest ones obtained from the unirradiated counterparts. The treatment, even for the lower γ-radiation dose applied, could be properly detected well above the shipping and marketing time for this Chilean export fruit (2–8 weeks). This method also has the advantage of using relatively inexpensive equipment. 相似文献
An 1-graph is a graph whose nodes can be labeled by binary vectors in such a way that the Hamming distance between the binary addresses is, up to scale, the distance in the graph between the corresponding nodes. We show that many interesting graphs are 1-rigid, i.e., that they admit an essentially unique such binary labeling. 相似文献
By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity
upper bound is , we prove that solving this n-dimensional linear optimization problem requires at least 2n−1 iterations.
Dedicated to Professor Emil Klafszky on the occasion of his 70th birthday. 相似文献
The metric polytope metn is the polyhedron associated with all semimetrics on n nodes and defined by the triangle inequalities xij − xik − xjk ≤ 0 and xij + xik + xjk ≤ 2 for all triples i, j, k of {1,..., n}. In 1992 Monique Laurent and Svatopluk Poljak conjectured that every fractional vertex of the metric polytope is adjacent
to some integral vertex. The conjecture holds for n ≤ 8 and, in particular, for the 1,550,825,600 vertices of met8. While the overwhelming majority of the known vertices of met9 satisfy the conjecture, we exhibit a fractional vertex not adjacent to any integral vertex. 相似文献