A dimeric pervanadyl (VO2+) complex with a tridentate Schiff base ligand

A di(-oxo)-bridged dinuclear complex, [VO₂(pamh)]₂ was isolated by reacting bis(acetylacetonato)vanadium(IV) and the Schiff base, N-(anisoyl)-N-(picolinylidene)-hydrazine (Hpamh) in acetonitrile. The complex crystallizes in the space group ;1; (#2) on crystallographic inversion center. Crystal data: a = 8.2202(12) Å, b = 9.8389(19) Å, c = 10.1907(17) Å, = 68.245(15)°, = 74.47(2)°, = 66.710(19)°, V = 696.0(2) ų, and Z = 1. The physical properties of the complex and the structural parameters are consistent with the +5 oxidation state of the metal ions. The monomeric VO₂(pamh) unit is square-pyramidal. The planar mononegative ligand (pamh^–) coordinates the metal ion via the pyridine-N, the imine-N, and the amide-O atoms. One of the oxo groups completes the NNOO basal plane and also participates in the Vndash;Ondash ;V bridge formation. The other oxo group satisfies the fifth apical coordination site. The molecular structure of the dimeric complex, [VO₂(pamh)]₂ can be described as two edge-shared distorted VO₄N₂ octahedra.     

Crystal structures of 4,7-phenanthrolino-5,6:5′,6′-pyrazine tetrahydrate and 1,4,5,8,9,12-hexaazatriphenylene dihydrate

The crystal structures of 4,7-phenanthrolino-5,6:5,6-pyrazine tetrahydrate (I) and 1,4,5,8,9,12-hexaazatriphenylene dihydrate (II) have been determined from low temperature (173 K) x-ray single crystal diffraction data. I crystallizes in the triclinic system, space group P with a = 11.2687(6), b = 12.4766(6), c = 12.7068(7) Å, = 113.4740(10), = 91.605(2), = 114.587(2)°, V = 1449.33(13) ų, and Z = 4. II crystallizes in the orthorhombic system, space group Pca2₁ with a = 18.187(2), b = 9.2576(11), c = 6.9672(8) Å, V = 1173.0(2) ų, and Z = 4. In both structures the planar heterocyclic molecules stack with interplanar distances down to 3.3 Å, which is consistent with self--complexation. The crystal water molecules provide links between the columns of stacked molecules through hydrogen bonds. In each compound the N-C bond lengths fall into two distinct groups (mean values 1.330(3) vs 1.361(1) Å in I and 1.320(3) vs 1.357(5) Å in II), as do the C-C bonds of the central phenyl rings (1.411(4) vs 1.467(1) Å in I and 1.405(5) vs 1.458(4) Å in II).     

Production systems with interruptions, arbitrary topology and finite buffers

We consider a production system with finite buffers and arbitrary topology where service time is subject to interruptions in one of three ways, viz. machine breakdown, machine vacations or Npolicy. We develop a unified approximation (analytical) methodology to calculate the throughput of the system using queueing networks together with decomposition, isolation and expansion techniques. The methodology is rigorously tested covering a large experimental region. Orthogonal arrays are used to design the experiments in order to keep the number of experiments manageable. The results obtained using the approximation methodology are compared to the simulation results. The ttests carried out to investigate the differences between the two results show that they are statistically insignificant. Finally, we test the methodology by applying it to several arbitrary topology networks. The results show that the performance of the approximation methodology is consistent, robust and produces excellent results in a variety of experimental conditions.     

Simulation optimization of buffer allocations in production lines with unreliable machines

We use a recent simulationbased optimization method, sample path optimization, to find optimal buffer allocations in tandem production lines where machines are subject to random breakdowns and repairs, and the product is fluidtype. We explore some of the functional properties of throughput of such systems and exploit these properties to prove the almost sure convergence of our optimization technique, under a regularity condition on the steady state. Utilizing a generalized semiMarkov process (GSMP) representation of the system, we derive recursive expressions to compute onesided directional derivatives of throughput, from a single simulation run. Finally, we give computational results for lines with up to 50 machines. We also compare results for smaller lines with the results from a more conventional method, stochastic approximation, whenever applicable. In these numerical studies, our method performed quite well on problems that are considered difficult by current computational standards.     

Strongly Regular Graphs and Designs with Three Intersection Numbers

We investigate BIBDs with three intersection numbers,x, y, and z, such that the relation on the block set given byA B iff the cardinality of the intersectionof A and B is not equal to x is an equivalence relation. Withsuch a design, we associate a family of strongly regular graphswith the same parameters. Two constructions producing infinitefamilies of such designs are given.     

On the étale Descent Problem for Topological Cyclic Homology and Algebraic K-Theory

We investigate étale descent properties of topological Hochschild and cyclic homology. Using these properties we deduce a general injectivity result for the descent map in algebraic K-theory, and show that algebraic K-theory has étale descent for rings of integers in unramified and tamely ramified p-adic fields.     

Generalizations of Perfect, Semiperfect, and Semiregular Rings

For a ring R and a right R-module M, a submodule N of M is said to be -small in M if, whenever N + X = M with M/X singular, we have X = M. If there exists an epimorphism p: P M such that P is projective and Ker(p) is -small in P, then we say that P is a projective -cover of M. A ring R is called -perfect (resp., -semiperfect, -semiregular) if every R-module (resp., simple R-module, cyclically presented R-module) has a projective -cover. The class of all -perfect (resp., -semiperfect, -semiregular) rings contains properly the class of all right perfect (resp., semiperfect, semiregular) rings. This paper is devoted to various properties and characterizations of -perfect, -semiperfect, and -semiregular rings. We define (R) by (R)/Soc(R_R) = Jac(R/Soc(R_R)) and show, among others, the following results:

Kernel polynomials for the solution of indefinite and ill-posed problems

We introduce a new family of semiiterative schemes for the solution of ill-posed linear equations with selfadjoint and indefinite operators. These schemes avoid the normal equation system and thus benefit directly from the structure of the problem. As input our method requires an enclosing interval of the spectrum of the indefinite operator, based on some a priori knowledge. In particular, for positive operators the schemes are mathematically equivalent to the so-called -methods of Brakhage. In a way, they can therefore be seen as appropriate extensions of the -methods to the indefinite case. This extension is achieved by substituting the orthogonal polynomials employed by Brakhage in the definition of the -methods by appropriate kernel polynomials. We determine the rate of convergence of the new methods and establish their regularizing properties.     

The Dedekind-Mertens lemma and the contents of polynomials

Let be a commutative ring, let be an indeterminate, and let . There has been much recent work concerned with determining the Dedekind-Mertens number =min , especially on determining when = . In this note we introduce a universal Dedekind-Mertens number , which takes into account the fact that deg() + for any ring containing as a subring, and show that behaves more predictably than .

     

Convergence de mesures spectrales aléatoires et applications à des principes d'invariance

Nous présentons un cadre unificateur pour un certain nombre de résultats connus de convergence en loi pour des processus admettant une représentation linéaire par rapport à un bruit blanc faible pour lequel il existe un principe dinvariance faible. Nous montrons que ce principe dinvariance est équivalent à la convergence dune suite de mesures aléatoires spectrales. Ceci permet daffaiblir les hypothèses usuelles et donc dobtenir des résultats nouveaux de convergence en loi, notamment pour des processus à longue portée.