Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory

Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented. An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated. AMS Subject Classifications Primary 60K25 · 60K20     

Novel ethero atoms containing polyesters based on 2,6‐naphthalendicarboxylic acid: A comparative study with poly(butylene naphthalate)

Poly(butylene naphthalate) (PBN), poly(diethylene naphthalate) (PDEN), and poly(thiodiethylene naphthalate) (PTDEN) were synthesized and characterized in terms of chemical structure and molecular weight. The polyesters were examined by TGA, DSC, and DMTA. All the polymers showed a good thermal stability, even though depending on chemical structure. At room temperature they appeared as semicrystalline materials; the effect of the introduction along the PBN polymer chain of ether oxygen atoms or sulfur ones was a lowering in the T_g value, a decrement of T_m, and a decrease of the crystallization rate. Changing in chemical structure also affects the main α absorption associated with the glass transition which moves to lower temperature and whose energetic requirements decrease. The results were explained as due to the presence of highly flexible C? S? C or C? O? C bonds in the polymeric chain. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1694–1703, 2007     

Ethylene polymerization by novel Ziegler–Natta‐type catalysts obtained in situ by the oxidative addition of 8‐hydroxyquinoline‐based ligands to bis(1,5‐cyclooctadiene)nickel(0) and methylaluminoxane

Novel catalytic systems, prepared in situ by the oxidative addition of 8‐hydroxyquinoline ligands to bis(1,5‐cyclooctadiene)nickel(0) and activated by methylaluminoxane, were studied in ethylene polymerization. When 8‐hydroxyquinoline was employed, only oligomeric products were obtained. On the contrary, 5,7‐dinitro‐8‐hydroxyquinoline gave linear polyethylene (PE), but with a modest activity. For the catalyst based on 5‐nitro‐8‐hydroxyquinoline, the productivity was largely dependent on the content of free trimethylaluminum (TMA) present in the commercial aluminoxane. The progressive optimization of the TMA/oligomeric methylaluminoxane ratio increased the productivity, which reached 700 kg of PE/(mol of Ni × h), by an order of magnitude. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 200–206, 2006     

The influence of glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwires

The effect of the glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwire has been studied by the switching field distribution technique. The thermoactivated mechanism model is used to describe the thermally activated switching through the complex energy barrier in amorphous FeSiB microwires. Glass removal leads to the increase of the probability of the thermally activated switching pointing to the decrease of the energy barrier.     

Comparison between structural and residual error formulations of an optimum design mechanism problem

Summary The model formulation of the objective function is one of the most important steps for solving an optimization problem. Generally, the objective function of an optimal design mechanism problem can be mathematically formulated either with structural or residual errors. In this paper we have conducted some comparisons between the results obtained by the structural and residual error formulations utilized in solving the optimum design of a four-bar linkage. The optimization problem is defined as a nonlinear least-squares problem. The damped Gauss-Newton algorithm is utilized for computing the solution, which ensures a local convergence for almost all nonlinear least-squares problems.

---

Sommario La formulazione matematica della funzione obiettivo è uno degli aspetti più delicati nella soluzione di un problema di ottimizzazione. Generalmente la funzione obiettivo di un problema di progettazione ottima di un meccanismo può essere formulata sia mediante l'errore strutturale che residuo. In questo lavoro sono stati eseguiti dei confronti tra i risultati ottenuti mediante le due precedenti formulazioni, in riferimento al problema della progettazione ottima di un quadrilatero articolato. Il problema di ottimizzazione viene definito come un problema nonlineare ai minimi quadrati la cui soluzione numerica è ottenuta mediante l'algoritmo damped di Gauss-Newton.

---

---

This paper was partially discussed at theII Congegno di Meccanica Computazionale, Roma, 1987.