A classical result of Baer states that a finite group G which is the product of two normal supersoluble subgroups is supersoluble if and only if Gʹ is nilpotent. In this article, we show that if G = AB is the product of supersoluble (respectively, w-supersoluble) subgroups A and B, A is normal in G and B permutes with every maximal subgroup of each Sylow subgroup of A, then G is supersoluble (respectively, w-supersoluble), provided that Gʹ is nilpotent. We also investigate products of subgroups defined above when $ A\cap B=1 $ and obtain more general results.

ANOVA, one of the most common statistical methods applied in agronomy, offers a variety of results we can report when analyzing designed experiments. The focus, of course, is on treatment means, but what should we report to characterize precision? Should we choose treatment standard deviations (SDs) or standard errors of the mean or standard errors of the difference (SEDs)? We discuss why treatment raw SDs should not be reported as the result of ANOVA, and point out that most of the time it is SEDs that should be provided.

Residual herbicides are routinely applied to control troublesome weeds in pumpkin production. Fluridone and acetochlor, Groups 12 and 15 herbicides, respectively, provide broad-spectrum PRE weed control. Field research was conducted in Virginia and New Jersey to evaluate pumpkin tolerance and weed control to PRE herbicides. Treatments consisted of fomesafen at two rates, ethalfluralin, clomazone, halosulfuron, fluridone, S-metolachlor, acetochlor emulsifiable concentrate (EC), acetochlor microencapsulated (ME), and no herbicide. At one site, fluridone, acetochlor EC, acetochlor ME, and halosulfuron injured pumpkin 81%, 39%, 34%, and 35%, respectively, at 14 d after planting (DAP); crop injury at the second site was 40%, 8%, 19%, and 33%, respectively. Differences in injury between the two sites may have been due to the amount and timing of rainfall after herbicides were applied. Fluridone provided 91% control of ivyleaf morningglory and 100% control of common ragweed at 28 DAP. Acetochlor EC controlled redroot pigweed 100%. Pumpkin treated with S-metolachlor produced the most yield (10,764 fruits ha–1) despite broadcasting over the planted row; labeling requires a directed application to row-middles. A separate study specifically evaluated fluridone applied PRE at 42, 84, 126, 168, 252, 336, and 672 g ai ha–1. Fluridone resulted in pumpkin injury ≥95% when applied at rates of ≥168 g ai ha–1; significant yield loss was noted when the herbicide was applied at rates >42 g ai ha–1. We concluded that fluridone and acetochlor formulations are unacceptable candidates for pumpkin production.

A highly disaggregated emissions factor model is presented. The model generates changes in emissions and resource use by state and 6-digit NAICS sector. Removal of all U.S. import restrictions is examined. Results for agriculture show that composition effects explain highly varied regional patterns of emission changes. Scale effects are also important for expanding sectors. Quantitative assessments such as this may prove useful in conducting full environmental reviews of U.S. trade agreements consistent with Executive Order 13141 and the Free Trade Act of 2002.

This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem.Upper and lower bounds of the discretization error are proved forboth estimators and several computations are performed toillustrate the theoretical results.

We consider some linear regression models Y = Σα lfl(z) + X, where X is an autoregressive (AR) process. The residuals estimate the i.i.d. innovations sequence which drives the AR process. We then consider the partial sum process of the residuals and show they converge to Brownian bridges in certain cases. Some remarks are also made on similar processes when differencing is first applied to remove trends. When an AR process is differenced the residual partial sum can be asymptotically a random polynomial.