共查询到20条相似文献,搜索用时 31 毫秒
1.
Timothy W Tillson 《Journal of Combinatorial Theory, Series B》1980,29(1):68-74
It is shown that , 2m ≥ 8, can be decomposed into Hamiltonian circuits. A direct construction utilizing difference methods is given for 2m ≡ 0 (mod 4). The case 2m ≡ 2 (mod 4) is handled inductively by means of a construction which shows that admits such a decomposition if does. 相似文献
2.
Emma Lehmer 《Journal of Number Theory》1973,5(5):385-389
An elementary proof is given of the theorem: If D = ?3q or ?27q is the discriminant of a cubic field, where q ≡ 1 (mod 4) is a prime, and if p or 4p is represented by c2 + ∥ D ∥ d2, then the fundamental unit in the field is a cubic residue of the prime p. In special cases necessary and sufficient conditions are derived. 相似文献
3.
Robert L McFarland 《Journal of Combinatorial Theory, Series A》1973,15(1):1-10
A construction is given for difference sets in certain non-cyclic groups with the parameters , , , n = q2s for every prime power q and every positive integer s. If qs is odd, the construction yields at least inequivalent difference sets in the same group. For q = 5, s = 2 a difference set is obtained with the parameters (v, k, λ, n) = (4000, 775, 150, 625), which has minus one as a multiplier. 相似文献
4.
Let Ms, be the number of solutions of the equation in the finite field GF(p). For a prime p ≡ 1(mod 3), , , and . Here d is uniquely determined by . 相似文献
5.
Let 1 < p ? 2 ? q < ∞ and X be either a Banach lattice which is p-convex and q-concave or a unitary ideal of operators on l2 which is modeled on a symmetric space which is p-convex and q-concave. If E ?X is any n-dimensional subspace, then both the distance from E to and the relative projection constant of E in X are dominated by . 相似文献
6.
Paul Terwilliger 《Discrete Mathematics》1982,41(3):295-302
We find lower bounds on eigenvalue multiplicities for highly symmetric graphs. In particular we prove:Theorem 1. If Γ is distance-regular with valency k and girth g (g?4), and λ (λ≠±?k) is an eigenvalue of Γ, then the multiplicity of λ is at least if g≡0 or 1 (mod 4), if g≡2 or 3 (mod 4) where [ ] denotes integer part. Theorem 2. If the automorphism group of a regular graph Γ with girth g (g?4) and valency k acts transitively on s-arcs for some s, , then the multiplicity of any eigenvalue λ (λ≠±?k) is at least if s is even, if s is odd. 相似文献
7.
For each odd prime q an integer NHq (NH3 = ?1, NH5 = ?1, NH7 = 97, NH11 = ?243, …) is defined as the norm from L to of the Heilbronn sum Hq = TrI(ζ)(ζ), where ζ is a primitive q2th root of unity and L ?- (ζ) the subfield of degree q. Various properties are proved relating the congruence properties of Hq and NHq modulo p (p ≠ q prime) to the Fermat quotient ; in particular, it is shown that NHq is even iff 2q ? 1 ≡ 1 (mod q2). 相似文献
8.
A directed BIBD with parameters () is a BIBD with parameters () in which each ordered pair of varieties occurs together in exactly blocks. It is shown that (mod 3) is a necessary and sufficient condition for the existence of a directed () BIBD with k = 3. 相似文献
9.
R.J. Cook 《Journal of Number Theory》1979,11(4):505-515
Let where p is a prime ≡ 3 mod 4 and k is an integer ≥ 3. Then S(k) frequently takes large values of each sign. 相似文献
10.
Milton Rosenberg 《Journal of multivariate analysis》1978,8(2):295-316
Let p, q be arbitrary parameter sets, and let be a Hilbert space. We say that x = (xi)i?q, xi ? , is a bounded operator-forming vector (?Fq) if the Gram matrix 〈x, x〉 = [(xi, xj)]i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on , the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from to . Then exists a linear operator ǎ from (the Banach space) Fq to Fp on (A) = {x:x ? Fq, is p × q bounded on } such that y = ǎx satisfies yj?σ(x) = {space spanned by the xi}, 〈y, x〉 = A〈x, x〉 and . This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes. 相似文献
11.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1980,76(2):339-368
We show that, if (F →uX) is a linear system, a convex target set and a convex functional, then, under suitable assumptions, the computation of inf ) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of , or of the infima on F of Lagrangians, involving elements of . Also, we prove similar results for a convex system (F →uX) and the convex cone Ω of all non-positive elements in X. 相似文献
12.
M.M Dodson 《Journal of Number Theory》1973,5(4):287-292
Let θ(k, pn) be the least s such that the congruence (mod pn) has a nontrivial solution. It is shown that if k is sufficiently large and divisible by p but not by p ? 1, then . We also obtain the average order of θ(k), the least s such that the above congruence has a nontrivial solution for every prime p and every positive integer n. 相似文献
13.
Hans J Bentz 《Journal of Number Theory》1982,15(2):252-274
Chebyshev has noticed a certain predominance of primes of the form 4n + 3 over those of the form 4n + 1. He asserted that . This was unproven until today. G. H. Hardy, J. E. Littlewood and E. Landau have shown its equivalence with an analogue to the famous Riemann hypothesis, namely, L(s, χ1mod 4) ≠ 0, . S. Knapowski and P. Turán have given some similar (unproven) relations, e.g., , which are also equivalent to the above. Using Explixit Formulas the author shows that holds without any conjecture. (In addition, the order of magnitude of divergence is calculated.) It turns out that (1) is only a special case (in several respects). At first, it may be enlarged into Then, it can be generalised to a wider class of progressions. For example, the same is true if one sums over the primes in the classes 3n + 2 and 3n + 1, with a “?” and a “+” sign, respectively. All results of this type depend on the location of the first nontrivial zero of the corresponding L-series. D. Shanks has given some arguments for the predominance of primes in residue classes of nonquadratic type. He conjectured “If m1 mod k is a quadratic residue and m2 mod k a non-residue, then there are “more” primes congruent m2 than congruent m1 mod k.” This indeed turns out to be true in the sense of (1), not only for k = 3, 4, but for some higher moduli as well. Finally, numerical calculations were made to investigate the behaviour of Δ3(X) ? π(X, 2 mod 3) ? π(X, 1 mod 3) in the interval 2 ≤ X ≤ 18, 633, 261. No zero was found in this range. In the analogue case of Δ4(X) ? π(X, 3 mod 4) ? π(X, 1 mod 4) the first sign change occurs at X = 26, 861. 相似文献
14.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
15.
J.W Layman 《Journal of Combinatorial Theory, Series A》1985,40(1):161-168
For any prime p, the sequence of Bell exponential numbers Bn is shown to have p ? 1 consecutive values congruent to zero (mod p), beginning with Bm, where (). This is an improvement over previous results on the maximal strings of zero residues of the Bell numbers. Similar results are obtained for the sequence of generalized Bell numbers An generated by . 相似文献
16.
Tor Helleseth 《Discrete Mathematics》1978,23(3):301-307
Let {aj}and {adj} be two binary maximal length linear sequences of period 2n?1. The cross-correlation function is defined as for t = 0, 1,…, 2n ? 2. We find the values and the number of occurrences of each value of Cd(t) when (mod 8). 相似文献
17.
R.J. Williams 《Advances in Applied Mathematics》1985,6(1):1-3
Let {Xt, t ≥ 0} be Brownian motion in d (d ≥ 1). Let D be a bounded domain in d with C2 boundary, ?D, and let q be a continuous (if d = 1), Hölder continuous (if d ≥ 2) function in D?. If the Feynman-Kac “gauge” Ex{exp(∝0τDq(Xt)dt)1A(XτD)}, where τD is the first exit time from D, is finite for some non-empty open set A on ?D and some x?D, then for any ), is the unique solution in of the Schrödinger boundary value problem . 相似文献
18.
Z Füredi 《Journal of Combinatorial Theory, Series A》1982,32(1):66-72
Suppose that is a finite set-system of N elements with the property |A ∩ A′| = 0, 1 or k for any two different A, A′ ?A. We show that for N > k14 where equality holds if and only if k = q + 1 (q is a prime power) and is the set of subspaces of dimension at most two of the t-dimensional finite projective space of order q. 相似文献
19.
Let G be the metacyclic group of order pq given by where p is an odd prime, q ≥ 2 a divisor of p ? 1, and where j belongs to the exponent q mod p. Let V denote the group of units of augmentation 1 in the integral group ring G of G. In this paper it is proved that the number of conjugacy classes of elements of order p in V is where ν, μ0, and H are suitably defined numbers. 相似文献
20.
Let X1, X2,… be a sequence of i.i.d. random variables and Sn their partial sums. Necessary and sufficient conditions are given for to have uniformly bounded pth moments, 0<p<q?2.Some of the results are generalized to martingle differences. 相似文献