Coefficient inequalities for a subclass of starlike functions

A function f(z) = z ? ∑^∞_{n = 2}a_nzⁿ, a_n ? 0, analytic and univalent in the unit disk, is said to be in the family $\text{T}{}^1\text{(a, b)}$, a real and b ? 0, if $\text{¦(}\text{zf′}\text{f}\text{) ? a¦ ? b}$ for all z in the unit disk. A complete characterization is found for $\text{T}{}^1\text{(a, b)}$ when a ? 1. Also, sharp coefficient bounds are determined for certain subclasses of $\text{T}{}^1\text{(a, b)}$ when a < 1; however, examples are given to show that these bounds do not remain valid for the whole family.     

Linear transformations that preserve certain positivity classes of matrices

For each of several S ? R^n,n, those linear transformations $\text{L}\text{: R}{}^{\mathrm{n,n}}\text{→ R}{}^{\mathrm{n,n}}$ which map S onto S are characterized. Each class is a familiar one which generalizes the notion of positivity to matrices. The classes include: the matrices with nonnegative principal minors, the M-matrices, the totally nonnegative matrices, the D-stable matrices, the matrices with positive diagonal Lyapunov solutions, and the H-matrices, as well as other related classes. The set of transformations is somewhat different from case to case, but the strategy of proof, while differing in detail, is similar.     

Semiclassical approximation for a nonlinear oscillator that is stochastic in the classical limit

L. V. Kirenski Institute of Physics, Siberian Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 77, No. 2, pp. 277–284, November, 1988.     

Limiting distribution of sums of nonnegative stationary random variables

Summary Let {X _n,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate mixing conditions, it is shown thatS _n=X_n,1+…+X _n,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {f _n(x)∼ defined on a stationary sequence {X _j∼, whereX _n.f=f_n(X_j). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of a general type. This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship of the National Sciences Foundation, Grant MCS 82-01119.     

The neutron zero-energy total cross section and scattering lengths for tritium

New results for the neutron total cross section for tritium extrapolate to 1.70 ± 0.03 b at zero energy. With a theoretical constraint A₁/A₀=0.92 ± 0.04, the scattering lengths A₁=3.60 ± 0.10, A₀ = 3.91 ± 0.12, and A_c=3.68 ± 0.05 fm can be inferred independently of, but consistently with, the previous experimental value for the coherent length A_c=3.82 ± 0.24 fm.     

Aneulerian digraphs and the determination of those Eulerian digraphs having an odd number of directed Eulerian paths

An antidirected path [3] in a digraph is a path with consecutive edges directed either both towards or both away from their common vertex. An aneulerian digraph is a digraph that contains a closed antidirected path passing through each edge once. It is shown that in a 4-valent Eulerian digraph $\text{D}$ every two distinct aneulerian subdigraphs are edge disjoint and the set of them cover the edges. A correspondence is given between the aneulerian subdigraphs of $\text{D}$ and the 1-difactors. The main theorem states that an Eulerian digraph which has no bivalent vertices has an odd number of directed Eulerian paths iff it is a 4-valent aneulerian digraph.     

Efficiency and production rate of a transfer line with two machines and a finite storage buffer

A markov model for a transfer line with two unreliable machines separated by a finite storage size buffer is introduced. Service time distribution for the two machines is Erlang whereas failure and repair times are assumed to be exponential random variables. The paper presents an efficient method to solve analytically the steady state probabilities of the system. This method is independent of the buffer size. We also include in the paper a study of the behavior of some systems performance measures such as the efficiency of the two machines and the production rate of the system.