is its closed normal subgroup, [Sh], [Ka]. The group Aut∗k k [n] is an infinite dimensional simple algebraic group, [Sh]. If D is a locally nilpotent k-derivation of k, then it is easily seen that exp tD ∈ Aut∗k k [n] for any t ∈ k, so D lies in Lie(Aut∗k k ). It follows from [BB1], [BB2] that n − 1 is the maximum of dimensions of algebraic tori contained in Aut∗k k , and that every algebraic t...

Partial F tests play a central role in model selections in multiple linear regression models. This paper studies the partial F tests from the view point of simultaneous confidence bands. It first shows that there is a simultaneous confidence band associated naturally with a partial F test. This confidence band provides more information than the partial F test and the partial F test can be regar...

Insect Pheromone and Traps Division, Fuji Flavor Co., Ltd., Midorigaoka 3-5-8, Hamura-shi, Tokyo 205-8503, Japan Graduate School of Life Sciences, Tohoku University, Tsutsumidori-Amamiya 1-1, Aoba-ku, Sendai 981-8555, Japan U.S. Department of Agriculture, Agricultural Research Service, Midwest Livestock Insect Research Unit, Lincoln, Nebraska 68583, U.S.A. U.S. Department of Agriculture, Agricu...

Suppose that one observes pairs (x1, Y1), (x2, Y2), . . . , (xn, Yn), where x1 ≤ x2 ≤ · · · ≤ xn are fixed numbers, and Y1, Y2, . . . , Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex function f . We present a confidence band for this regression function f using suitable multiscale signtests. While the exact ...

We consider the lacunary Dirichlet series obtained by taking the reciprocals of the s-th powers of the Fibonacci numbers. This series admits an analytic continuation to the entire complex plane. Its special values at integral arguments are then studied. If the argument is a negative integer, the value is algebraic. If the argument is a positive even integer, the value is transcendental by Neste...

Quasi-optical imaging systems require low blurring effect and large depth of focus (DOF) to get an acceptable sharpness of the image. To reduce aberration-limited blurring, the aspheric convex plano lenses with an aperture diameter of 350 mm are designed in W-band. We analyzed theoretically and experimentally the millimeter-wave band lens characteristics, such as beam spot size, spatial resolut...

Regulatory actions of calmodulin on the contractile apparatus and cytoskeleton of smooth muscle and nonmuscle tissue are mediated by a number of specific calmodulin-binding proteins that bind to F-actin in a flip-flop manner--i.e., they bind to calmodulin or F-actin depending on the presence or absence, respectively, of Ca2+. A survey for such proteins in brain, adrenal gland, and pituitary gla...