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1.
In this paper the problem of finding the design efficiency is considered when a single observation is unavailable in a connected binary block design. The explicit expression of efficiency is found for the resulting design when the original design is a balanced incomplete block design or a group divisible, singular or semiregular or regular with 1>0, design. The efficiency does not depend on the position of the unavailable observation. For a regular group divisible design with 1>0, the efficiency depends on the position of the unavailable observation. The bounds, both lower and upper, on the efficiency are given in this situation. The efficiencies of designs resulting from a balanced incomplete block design and a group divisible design are in fact high when a single observation is unavailable.The work of the first author is sponsored by the Air Force Office of Scientific Research under Grant AFOSR-90-0092.On leave from Indian Statistical Institute, Calcutta, India. The work of the third author was supported by a grant from the CMDS, Indian Institute of Management, Calcutta.  相似文献   
2.
Summary In this paper we consider experimental situations in which ν treatments are to be tested inb blocks whereb i blocks containk i experimental units,i=1,...,p, k 1<k 2<...<k p . The idea of a group divisible (GD) design is extended to that of a group divisible design with unequal block sizes (GDUB design) and then a number of results concerning the E- and MV-optimality of GD designs are generalized to the case of GDUB designs.  相似文献   
3.
In this article, we mainly consider the existence problem of a group divisible design GDD ( 3 , 4 , n + s ) of type 1 n s 1 . We present two recursive constructions for this configuration using candelabra systems and construct explicitly a few small examples admitting given automorphism groups. As an application, several new infinite classes of GDD ( 3 , 4 , n + s ) s of type 1 n s 1 are produced. Meanwhile a few new infinite families on candelabra quadruple systems with group sizes being odd and stem size greater than one are also obtained.  相似文献   
4.
H. Cao  Y. Wu  H. Zhou 《组合设计杂志》2008,16(5):351-363
A modified (k, λ)‐frame of type gu is a modified (k, λ)‐GDD whose blocks can be partitioned into holey parallel classes, each of which is with respect to some group. Modified frames can be used to construct some other resolvable designs such as resolvable group divisible designs and semiframes. In this article, we shall investigate the existence of modified frames with block size 3. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 351–363, 2008  相似文献   
5.
We generalize the concept of an incomplete double group divisible design and describe some recursive constructions for such a generalized new design. As a consequence, we obtain a general recursive construction for group divisible designs, which unifies many important recursive constructions for various types of combinatorial designs. We also introduce the concept of a double frame. After providing a preliminary result on the number of partial resolution classes, we describe a general construction for double frames. This construction method can unify many known recursive constructions for frames.  相似文献   
6.
本文讨论型为2^nu^1的有对称正交侣的带洞自正交拉丁方(HSOLSSOM(2^nu^1))的谱。证明当n≤9时,HSOLSSOM(2^nu^1)存在的充分必要条件是u为偶数且n≥3u/2+1;当n≥263时,若u为偶数且n≥2(u-2),则HSOLSSOM(2^nu^1)存在。  相似文献   
7.
A pentagonal geometry PENT( k , r) is a partial linear space, where every line is incident with k points, every point is incident with r lines, and for each point x, there is a line incident with precisely those points that are not collinear with x. Here we generalize the concept by allowing the points not collinear with x to form the point set of a Steiner system S ( 2 , k , w ) whose blocks are lines of the geometry.  相似文献   
8.
H. Cao  J. Fan  D. Xu 《组合设计杂志》2015,23(10):417-435
A ‐semiframe of type is a ‐GDD of type , , in which the collection of blocks can be written as a disjoint union where is partitioned into parallel classes of and is partitioned into holey parallel classes, each holey parallel class being a partition of for some . A ‐SF is a ‐semiframe of type in which there are p parallel classes in and d holey parallel classes with respect to . In this paper, we shall show that there exists a (3, 1)‐SF for any if and only if , , , and .  相似文献   
9.
10.
We show that the necessary conditions for the existence of group divisible designs with block size four (4‐GDDs) of type are sufficient for (mod ), = 39, 51, 57, 69, 87, 93, 111, 123 and 129, and for = 13, 17, 19, 23, 25, 29, 31 and 35. More generally, we show that for (mod 6), the possible exceptions occur only when , and there are no exceptions at all if has a divisor such that (mod 4) or is a prime not greater than 43. Hence, there are no exceptions when (mod 12). Consequently, we are able to extend the known spectrum for and 5 (mod 6). Also, we complete the spectrum for 4‐GDDs of type .  相似文献   
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