In this paper, a clear expression of the null distribution function of the likelihood ratio test statistics U that is considered by Hawkins (1977) is derived when σ2 is known. The numerical tables of the distribution funtion are given.
The minimal L1 isotonic regression (ML1IR) of the mean of Laplace distribution is discussed in this paper when the variance is known and 0 is restricted by a partial order "? . The uniqueness and some properties of ML1IR are discussed and based on them an algorithm of computing ML1IR is given.
Carathéodory systems are changed into Kurzweil generalized ordinary differential equations. The existence of solutions for Carathéodory systems is discussed by using the existence theory of solution of Kurzweil generalized ordinary differential equation.
It is known [M4] that K?-orbits S and G?-orbits S' on a complex flag manifold are in one-to-one correspondence by the condition that S ∩ S' is nonempty and compact.
When the characteristic of k is 0, it is known that the invariants of d vectors, d ≥ n, are obtained from those of n vectors by polarization.
It is known thatT (A, D) tiles?n by some subset of?n.
It is known  that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ? of one variable into a function and its cosine transform in a generalized sense.
Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces.
In this paper, the following equations were studied,where P,(t) are either periodic functions or arbitrary functions of t, and some criteria for the boundedness and asymptotic behavior of solutions were obtained.