In this paper we describe the quiver representations (see Manuscripta Math. 6(1972), 71-103) which do not contain die problem of reducing a pair of matrices by similarity transformations.The concept of a quiver representation was introduced by P. Gabriel in [l]. In the terminology of [l], a quiver is a set of points which are connected by (directed) arrows. We say, as in [l], that a quiver representation over a field k is given if to each point i of the quiver there is assigned a vector space V ( ., and to each arrow going from the point i to the point / there is assigned a linear mapping a., of V i into V.. If each V. is finite-dimensional, the representation is called finite. In this paper we will consider only finite representations.Two quiver representations are called equivalent if there exist vector space isomorphisms φ Λ V i -» K ( , i = 1, ..., n, such that «^α Γ = α^φ. for all i, j.In [l], the concept of the direct sum of representations and the concept of an indecomposable representation are introduced in the natural way.Quiver representations arise naturally from the representations of algebras over fields. We remark that similar questions were also considered in [2] and [3]. It is easy to see that the problem of describing the representations of a fixed quiver can be interpreted as a matrix problem in the sense of [4], Indeed, if we fix bases in the spaces V 1? · · ·, V n , then to each operator cu.: V.-tV. there corresponds a matrix with entries from the field k. Note that the number of columns of the matrix of α.. is equal to the number of rows of the matrix of α . (and is equal to the dimension of V.);the matrices of α.. and a., have an equal number of rows, and the matrices of α .. and a, . an equal number of columns.It is not difficult to see that if two representations (V., a. ..) and (V., α..) are equivalent, then there exist nonsingular matrices φ. such that α .. = φ~ α ·.<£..We give some examples.

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In this paper a necessary and sufficient condition is given that a partially ordered set have tame type, i.e. that it admit classification of its indecomposable representations.Bibliography: 16 titles.We will say a representation of a partially ordered set ?t is given over a field k if to each i €n there is assigned a subspace V. of some linear finite-dimensionalDecomposability and equivalence of representations of partially ordered sets are defined in the natural way.Representations of partially ordered sets were introduced in [1] and [2], and used in [3] in solving the Brauer-Thrall problem for the case of a perfect field. It became apparent that representations of partially ordered sets may also be useful in other matters; for example, in studying representations of quivers ([2], [4]), quivers with relations [5], and finite groups [6] (see also [7]). As in every theory of representations, there naturally arises the problem of determining partially ordered sets of finite type, i.e. sets having a finite number of indecomposable representations. The finiteness criterion was derived in [8]:A partially ordered set is of finite type if and only if it does not contain subsets of the following forms:

We report on the generation of more than 5 dB of vacuum squeezed light at the rubidium D1 line (795 nm) using periodically poled KTiOPO 4 (PPKTP) in an optical parametric oscillator. We demonstrate squeezing at low sideband frequencies, making this source of non-classical light compatible with bandwidth-limited atom optics experiments. When PPKTP is operated as a parametric amplifier, we show a noise reduction of 4 dB stably locked within the 150 kHz-500 kHz frequency range. This matches the bandwidth of electromagnetically induced transparency (EIT) in rubidium hot vapour cells under the condition of large information delay.