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1.
The size of a (v, 5, 2, 1) optical orthogonal code (OOC) is shown to be at most equal to ${\lceil{\frac{v}{12}}\rceil}$ when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to ${\lfloor{\frac{v}{12}}\rfloor}$ in all the other cases. Thus a (v, 5, 2, 1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v, 5, 2, 1)-OOCs are presented giving, in particular, a very strong indication about the existence of an optimal (p, 5, 2, 1)-OOC for every prime p ≡ 1 (mod 12). 相似文献
2.
The existence problem of a ‐cycle frame of type is now solved for any quadruple . 相似文献
3.
Marco Buratti 《Journal of Combinatorial Theory, Series A》2000,90(2):353
A Z-cyclic triplewhist tournament for 4n+1 players, or briefly a TWh(4n+1), is equivalent to a n-set {(ai, bi, ci, di) | i=1, …, n} of quadruples partitioning Z4n+1−{0} with the property that ni=1 {±(ai−ci), ±(bi−di)}=ni=1 {±(ai−bi), ±(ci−di)}=ni=1 {±(ai−di), ±(bi−ci)}=Z4n+1−{0}. The existence problem for Z-cyclic TWh(p)'s with p a prime has been solved for p1 (mod 16). I. Anderson et al. (1995, Discrete Math.138, 31–41) treated the case of p≡5 (mod 8) while Y. S. Liaw (1996, J. Combin. Des.4, 219–233) and G. McNay (1996, Utilitas Math.49, 191–201) treated the case of p≡9 (mod 16). In this paper, besides giving easier proofs of these authors' results, we solve the problem also for primes p≡1 (mod 16). The final result is the existence of a Z-cyclic TWh(v) for any v whose prime factors are all≡1 (mod 4) and distinct from 5, 13, and 17. 相似文献
4.
The notion of a symmetric Hamiltonian cycle system (HCS) of a graph Γ has been introduced and studied by J. Akiyama, M. Kobayashi, and G. Nakamura [J Combin Des 12 (2004), 39–45] for , by R. A. Brualdi and M. W. Schroeder [J Combin Des 19 (2011), 1–15] for , and then naturally extended by V. Chitra and A. Muthusamy [Discussiones Mathematicae Graph Theory, to appear] to the multigraphs and . In each case, there must be an involutory permutation ψ of the vertices fixing all the cycles of the HCS and at most one vertex. Furthermore, for , this ψ should be precisely the permutation switching all pairs of endpoints of the edges of I. An HCS is cyclic if it is invariant under some cyclic permutation of all the vertices. The existence question for a cyclic HCS of has been completely solved by Jordon and Morris [Discrete Math (2008), 2440–2449]—and we note that their cyclic construction is also symmetric for (mod 8). It is then natural to study the existence problem of an HCS of a graph or multigraph Γ as above which is both cyclic and symmetric. In this paper, we completely solve this problem: in the case of even order, the final answer is that cyclicity and symmetry can always cohabit when a cyclic solution exists. On the other hand, imposing that a cyclic HCS of odd order is also symmetric is very restrictive; we prove in fact that an HCS of with both properties exists if and only if is a prime. 相似文献
5.
Let be a 2‐factorization of the complete graph Kv admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex‐set V(Kv) can then be identified with the point‐set of AG(n, p) and each 2‐factor of is the union of p‐cycles which are obtained from a parallel class of lines of AG(n, p) in a suitable manner, the group G being a subgroup of A G L(n, p) in this case. The proof relies on the classification of 2‐(v, k, 1) designs admitting a doubly transitive automorphism group. The same conclusion holds even if G is only assumed to act doubly homogeneously. © 2006 Wiley Periodicals, Inc. J Combin Designs 相似文献
6.
Marco Buratti 《Designs, Codes and Cryptography》2002,26(1-3):111-125
We prove the existence of a cyclic (4p, 4, 1)-BIBD—and hence, equivalently, that of a cyclic (4, 1)-GDD of type 4
p
—for any prime
such that (p–1)/6 has a prime factor q not greater than 19. This was known only for q=2, i.e., for
. In this case an explicit construction was given for
. Here, such an explicit construction is also realized for
.We also give a strong indication about the existence of a cyclic (4p 4, 1)-BIBD for any prime
, p>7. The existence is guaranteed for p>(2q
3–3q
2+1)2+3q
2 where q is the least prime factor of (p–1)/6.Finally, we prove, giving explicit constructions, the existence of a cyclic (4, 1)-GDD of type 6
p
for any prime p>5 and the existence of a cyclic (4, 1)-GDD of type 8
p
for any prime
. The result on GDD's with group size 6 was already known but our proof is new and very easy.All the above results may be translated in terms of optimal optical orthogonal codes of weight four with =1. 相似文献
7.
Journal of Algebraic Combinatorics - We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional “resolvability”... 相似文献
8.
Marco Buratti 《组合设计杂志》1995,3(2):161-168
For q a prime power and k odd (even), we define a (q,k,1) difference family to be radical if each base block is a coset of the kth roots of unity in the multiplicative group of GF(q) (the union of a coset of the (k ? 1)th roots of unity in the multiplicative group of GF(q) with zero). Such a family will be denoted by RDF. The main result on this subject is a theorem dated 1972 by R.M. Wilson; it is a sufficient condition for the existence of a (q,k, 1)-RDF for any k. We improve this result by replacing Wilson's condition with another sufficient but weaker condition, which is proved to be necessary at least for k ? 7. As a consequence, we get new difference families and hence new Steiner 2-designs. © 1995 John Wiley & Sons, Inc. 相似文献
9.
A new method for the evaluation of the 'total antioxidant power' of olive oils, based on a flow injection analysis system with electrochemical detection, is described. It represents a attractive alternative to the mostly used Rancimat method since it is based on the chemical structure of antioxidants and does not require the manipulation of several parameters, such as temperature and oxygen pressure, to accelerate oil oxidation. The proposed procedure is simple, rapid, allows a throughput of 90 samples h-1 and provides a good precision: an RSD of 3.5% was obtained for caffeic acid at the concentration level of 5 mg L-1 (n = 12). A comparison of the proposed was obtained for caffeic acid at the concentration level of 5 mg L-1 (n = 12). A comparison of the proposed procedure with two other methods (Rancimat method and ABTS.+ decoloration assay) was performed to investigate the applicability and limitations of the proposed method. 相似文献
10.
Buratti M Pellegrino O Valla C Rubino FM Verduci C Colombi A 《Biomedical chromatography : BMC》2006,20(9):971-978
A method suitable for the determination of unmetabolized polycyclic aromatic hydrocarbons (PAHs) excreted at trace levels (ng/L) in human urine for the monitoring of exposure of the general population to PAH contamination was developed. PAHs were determined, after enrichment by solid-phase extraction on polyurethane foam (PUF) chips, by HPLC with fluorescence detection. Different parameters affecting analyte extraction to the PUF, including urine salting-out and organic additives, and optimization of conditions for clean-up and desorption have been investigated. Optimized conditions were 40 mL acidified urine sample, added with magnesium sulfate, tetrahydrofuran and a 2 cm3 PUF chip, and extracted by shaking at 30 rpm for 1 h at ambient temperature. Desorption was performed, after a clean-up step with diluted sodium hydroxide, using a small amount of diethyl ether. The recovery of PAH congeners from spiked urines was >90% in the 2-100 ng/L range; the detection limit was 0.1-0.5 ng/L, depending on the considered PAH congener; day-to-day precision, at 50 ng/L native PAH content, was CV = 10-20%. The proposed technique provides a simple, economical and effective procedure for the determination of trace amounts of unmetabolized PAHs excreted in human urine spot samples. 相似文献