Unique factorization of compositive hereditary graph properties

A graph property is any class of graphs that is closed under isomorphisms. A graph property P is hereditary if it is closed under taking subgraphs; it is compositive if for any graphs G1, G2 ∈ P there exists a graph G ∈ P containing both G1 and G2 as subgraphs. Let H be any given graph on vertices v1, . . . , vn, n ≥ 2. A graph property P is H-factorizable over the class of graph properties P if there exist P 1 , . . . , P n ∈ P such that P consists of all graphs whose vertex sets can be partitioned into n parts, possibly empty, satisfying: 1. for each i, the graph induced by the i-th non-empty partition part is in P i , and 2. for each i and j with i = j, there is no edge between the i-th and j-th parts if vi and vj are non-adjacent vertices in H. If a graph property P is H-factorizable over P and we know the graph properties P 1 , . . . , P n , then we write P = H [ P 1 , . . . , P n ]. In such a case, the presentation H[ P 1 , . . . , P n ] is called a factorization of P over P. This concept generalizes graph homomorphisms and (P 1 , . . . , P n )-colorings. In this paper, we investigate all H-factorizations of a graph property P over the class of all hered- itary compositive graph properties for finite graphs H. It is shown that in many cases there is exactly one such factorization.     

Stochastic scheduling of parallel queues with set-up costs

We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a set-up cost. The objective is to minimize the expected cost due to the waiting of jobs and the switching of the server. A set-up cost is required to effect an instantaneous switch from one queue to another. We partially characterize an optimal policy and provide a simple heuristic scheduling policy. The heuristic's performance is evaluated in the cases of two and three queues by comparison with a numerically obtained optimal policy. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances with four queues.     

Observedtrans influence of donor atoms in monocharged bidentate ligands: Crystal structure of the acetone solvate of 2-carboxyquinolinatocarbonyltriphenylphosphinerhodium(I)

Summary 2-Carboxyquinolinatocarbonyltriphenylphosphinerhodium(I), [Rh(Quin)(CO)(PPh₃)], was prepared by replacement of CO by PPh₃ in the corresponding dicarbonyl. The compound crystallizes in the triclinic space group Åb=17.168(6) Å,c=9.254(5) Å, =101.49(5)°, =95.74(4)°, =98.41(4)°, d_cxp=1.45g cm^–3 and Z=2. The crystal structure was dermined from 3496 observed reflections. The final R value was 0.061. This structure determination indicates that the nitrogen atom of the chelate ring has the largesttrans influence since the carbonyl grouptrans to this atom was substituted by the PPh₃ ligand. The effects of different donor atoms in bidentate ligands, as well as the ring size of the chelate ring, on the relativetrans influence of the donor atoms are discussed.     

Kinetic study of the reaction betweentrans-tetracyanodioxomolybdate(IV) and fluoride ions

Summary The kinetics of the reaction between [MoO₂(CN)₄]^4– and F^– have been studied in the pH range 8 to 11. The results indicated that the diprotonated form, [MoO(OH₂)(CN)₄]^2–, is the only reactive species and that the aqua-ligand is substituted by the F^– ion according to the following reaction. The k₁ and k_–1 values are 8.8(2) M^–1 s^–1 and 0.6(1)s^–1, respectively, at 15°C. A dissociative substitution process is proposed.     

Molecular conformation and electronic structure. II: Crystal and molecular structure ofN-(p-bromobenzylidene)-p-bromoaniline

The structure of the title compound C₁₃H₉Br₂N has been determined with MoKα₁ diffractometer data, and refined by full-matrix least squares toR = 0.061 for 888 observed reflections. The crystals are monoclinic: space groupP2₁/a,a = 24.912(13),b = 5.877(1),c = 4.046(1) Å,β = 92.42(3) °Z = 2. The uv absorption spectrum indicates a nonplanar conformation in solution. In the solid, the molecule is disordered about a crystallographic inversion center and is planar to within 0.045 Å.     

Crystal structure of tetraphenylarsonium aquatetracyanonitridorhenate(V), (AsPh4)2 [ReN(H2O)(CN)4]·5H2O

The crystal structure of (AsPh₄)₂[ReN(H₂O)(CN)₄]·5H₂O has been determined from three-dimensional X-ray diffraction data. The yellow crystals are monoclinic, space group P2₁/n with cell dimensionsa=15.482(1),b=19.950(2),c=16.999(1)? and β=101.69(6)^o,Z=4,D _expt=1.48(1)g cm⁻³ andD _calc=1.52g cm⁻³. The anisotropic refinement of 7858 observed reflections converged toR=0.055. The [ReN(H₂O)(CN)₄]²⁻ ion has a distorted octahedral geometry. Bond distances: Re≡N=1.639(8), Re−OH₂=2.496(7) and Re−C_(av)=2.11(1) ?. The rhenium atom is displaced by 0.35 ? out of the plane formed by the four carbon atoms of the cyano ligands towards the terminal nitrido ligand. TMC 2479     

Estimating variance of output from cyclic exponential queueing systems

Production systems, particularly those making use of a pull production control mechanism, are well-modeled as closed queueing networks. Average throughput is clearly one important performance measure for these systems. However, many control decisions require information concerning the variability of the output process as well as throughput. Because of this, the standard deviation of the number of outputs during a specified interval is a practical performance measure for production systems.In this paper, we consider the standard deviation of the number of outputs during a time interval from a closed queueing network consisting ofM single server exponential queues. Because computing this quantity exactly is extremely cumbersome, we introduce a simple approximation that makes use of (1) known results for the variance of the time a marked job takes to complete a round trip and (2) an approximate correction term for the covariance between successive round trips. We show through comparisons with simulation that our method is quite accurate under a variety of conditions.