Some results on two-level regular designs with multi block variables containing clear effects

2017 ◽  
Vol 60 (5) ◽  
pp. 1569-1582 ◽  
Author(s):  
Qianqian Zhao ◽  
Shengli Zhao
Keyword(s):  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuna Zhao

Blocking the inhomogeneous units of experiments into groups is an efficient way to reduce the influence of systematic sources on the estimations of treatment effects. In practice, there are two types of blocking problems. One considers only a single block variable and the other considers multi-block variables. The present paper considers the blocking problem of multi-block variables. Theoretical results and systematical construction methods of optimal blocked 2 n − m designs with N / 4 + 1 ≤ n ≤ 5 N / 16 are developed under the prevalent general minimum lower-order confounding (GMC) criterion, where N = 2 n − m .


2012 ◽  
Vol 32 (5) ◽  
pp. 419-423 ◽  
Author(s):  
Luis E. Fazzio ◽  
Nicolas Yacachury ◽  
Walter R. Galvan ◽  
Elias Peruzzo ◽  
Ricardo O. Sánchez ◽  
...  

The aim was to evaluate for 75 days the impact on production of the remaining burden of ivermectin (IVM)-resistant parasites in naturally infected feedlot calves. The herds came from tick-infested areas of cattle breeding where the systematic use of IVM to control tick increases the gastrointestinal parasites resistant to this drug. This investigation was carried out in two commercial feedlots in Buenos Aires province. In feedlot A, two groups of 35 animal each received IVM 1% and the other received ricobendazole (RBZ) 10% respectively. The same was done in feedlot B. On day 0, two groups of 35 animals were made in feedlots A and B. Fecal samples were taken on days 0, 22, 54 and 75 pos-treatment (PT), and body weight was registered, from each animal. Fecal samples were processed for individual count of eggs per gram (EPG) and pooled fecal culture was carried out for identification of the parasite genus in each sampling. Fecal egg count reduction test (FECR) was calculated on day 22 PT. The study design used was a totally randomized block, with commercial feedlot and sex as block variables. For data analysis, a mixed model of the SAS statistical program was used. The FECR average on day 22 was 28.4% in the IVM group, and 94,2 % in the RBZ group . From this date on, significant differences in EPG were kept until day 54. EPG counts were only equal near the end of the trial, on day 75 (p=0.16). In both commercial feedlots, especially in the IVM group, Cooperia spp. was the most prevalent parasite in the fecal cultures. Significant differences in weight (P<0.01) on post-treatment day 75 was found between the average weight in the RBZ and the IVM group (246 vs. 238 kg respectively), what means a difference of 8.3% in gains. The importance for production in the antiparasite failure treatment in commercial feedlots was demonstrated, and the need of pos-treatment controls to evaluate the efficacy of the antiparasitic administered is emphasized.


2010 ◽  
Vol 44 (Suppl_1) ◽  
pp. i25-i25
Author(s):  
S. Ilbeigi ◽  
F. Hagman ◽  
B. Van Gheluwe
Keyword(s):  

1997 ◽  
Vol 30 (20) ◽  
pp. 7057-7065 ◽  
Author(s):  
Michael Hörnquist
Keyword(s):  

2011 ◽  
Vol 5 (1) ◽  
pp. 161-178 ◽  
Author(s):  
Runchu Zhang ◽  
Peng Li ◽  
Jialin Wei
Keyword(s):  

2020 ◽  
Vol 26 (5) ◽  
Author(s):  
Tomoyoshi Ibukiyama

AbstractHolomorphic vector valued differential operators acting on Siegel modular forms and preserving automorphy under the restriction to diagonal blocks are important in many respects, including application to critical values of L functions. Such differential operators are associated with vectors of new special polynomials of several variables defined by certain harmonic conditions. They include the classical Gegenbauer polynomial as a prototype, and are interesting as themselves independently of Siegel modular forms. We will give formulas for all such polynomials in two different ways. One is to describe them using polynomials characterized by monomials in off-diagonal block variables. We will give an explicit and practical algorithm to give the vectors of polynomials through these. The other one is rather theoretical but seems much deeper. We construct an explicit generating series of polynomials mutually related under certain mixed Laplacians. Here substituting the variables of the polynomials to partial derivatives, we obtain the generic differential operator from which any other differential operators of this sort are obtained by certain projections. This process exhausts all the differential operators in question. This is also generic in the sense that for any number of variables and block partitions, it is given by a recursive unified expression. As an application, we prove that the Taylor coefficients of Siegel modular forms with respect to off-diagonal block variables, or of corresponding expansion of Jacobi forms, are essentially vector valued Siegel modular forms of lower degrees, which are obtained as images of the differential operators given above. We also show that the original forms are recovered by the images of our operators. This is an ultimate generalization of Eichler–Zagier’s results on Jacobi forms of degree one. Several more explicit results and practical construction are also given.


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