Mean Buffer Contents in Discrete-Time Single-Server Queues with Heterogeneous Sources

We consider discrete-time single-server queues fed by independent, heterogeneous sources with geometrically distributed idle periods. While being active, each source generates some cells depending on the state of the underlying Markov chain. We first derive a general and explicit formula for the mean buffer contents in steady state when the underlying Markov chain of each source has finite states. Next we show the applicability of the general formula to queues fed by independent sources with infinite-state underlying Markov chains and discrete phase-type active periods. We then provide explicit formulas for the mean buffer contents in queues with Markovian autoregressive sources and greedy sources. Further we study two limiting cases in general settings, one is that the lengths of active periods of each source are governed by an infinite-state absorbing Markov chain, and the other is the model obtained by the limit such that the number of sources goes to infinity under an appropriate normalizing condition. As you will see, the latter limit leads to a queue with (generalized) M/G/ȡe; input sources. We provide sufficient conditions under which the general formula is applicable to these limiting cases.AMS subject classification: 60K25, 60K37, 60J10This revised version was published online in June 2005 with corrected coverdate     

Molecular dynamics of hyperbranched polyesters in the confinement of thin films

Broadband Dielectric Spectroscopy is employed to investigate the molecular dynamics in thin films of hyperbranched polyesters (type AB₁B₂, with -OH and -OCOCH₃ as terminal groups). Three relaxation processes are detected: alpha, beta and gamma. While the latter two are not influenced by the confinement, a pronounced effect is observed on the alpha relaxation: with decreasing film thickness the slower relaxation modes of the dynamic glass transition are gradually suppressed, resulting in an increase of the average relaxation rate and in a linear decrease of the dielectric strength. This is attributed to an immobilization in confinement of the polymeric segments located at the periphery of the hyperbranched macromolecular structures.     

Chain orientation in natural rubber,Part I: The inverse yielding effect

Inhomogeneous deformations are observed in stretched natural rubber of different crosslink density; the conditions of observation, nucleation and propagation are given in the first part of the paper. In samples of low crosslink density these inhomogeneities recall necking observed in others materials and in glassy polymers when the materials are drawn above a critical draw ratio. The difference is that in natural rubbers, NR, they nucleate and propagate at constant stress during unloading. This phenomenon, called inverse yielding appears during recovery only if the samples have been drawn previously in the hardening domain. During necking propagation the stress is constant. The mechanical and crystallinity properties of samples with and without inverse yielding are studied as a function of draw ratio, crosslink density and temperature. In the second part of the paper this transition zone (neck) of thickness 2 mm is studied by WAXS at the synchrotron source. From the orientation of NR crystallites and from the orientation of the stearic acid (2%, present in this type of rubber) we conclude that the deformation in the neck follows the flow lines. From the local crystallinity of the NR crystallites one deduces the local draw ratio across this transition zone. We suggest that in all these rubbers, which present a plateau of the recovery stress strain curve, micronecking exists. This effect is discussed in the framework of the Flory theory.-1     

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.     

A search for spontaneous emission of heavy clusters in the 127I nuclide

The results of an experimental search for spontaneous cluster decay in ¹²⁷I are presented. Several possible channels have been investigated considering an exposure of 33834 kg ^. day collected by a large-mass highly radiopure NaI(Tl) set-up deep underground in the Gran Sasso National Laboratory of the INFN. New lower limits on the lifetime of ²⁴₁₀Ne, ²⁸₁₂Mg, ³⁰₁₂Mg, ³²₁₄Si, ³⁴₁₄Si, ⁴⁸₂₀Ca, ⁴⁹₂₁Sc cluster radioactivity in ¹²⁷I have been achieved.     

Fibonacci-Cayley Numbers and Repetition Patterns in Genomic DNA

Let F(k) denote the k-th Fibonacci number in the Fibonacci sequence F(0) := 0, F(1) := 1,..., F(k+1) := F(k-1)+F(k). Motivated by proposals regarding putative mechanisms that may be responsible for producing those often observed long repetitive patterns in genomic DNA, we study in this note the Fibonacci-Cayley index fc_x of positive integers x, i.e., the largest integer ent/xg80e4vv7ej7fc03/26_2003_Article_185_TeX2GIFIEq1.gif" alt=" $$ k \in \mathbb{N} $$ " align="middle" border="0"> for which positive integers a, b with x = aF(k-1)+bF(k) exist and show that ent/xg80e4vv7ej7fc03/26_2003_Article_185_TeX2GIFIEq2.gif" alt=" $$\mathrm{fc}_x -5/2 \leq ({k_r} + {k_1}) /2 \leq \mathrm{fc}_x +1$$ " align="middle" border="0"> holds for the arithmetic mean ent/xg80e4vv7ej7fc03/26_2003_Article_185_TeX2GIFIEq3.gif" alt=" $$ ({k_r} + {k_1}) /2 $$ " align="middle" border="0"> of the indices of the smallest and the largest Fibonacci numbers occurring in the Zeckendorf decomposition ent/xg80e4vv7ej7fc03/26_2003_Article_185_TeX2GIFIEq4.gif" alt=" $$ x = \sum _{i=l,\ldots,r} F(k_i) (0er="0"> AMS Subject Classification: 11B39, 11A99, 92D20.     

A note on recursive completions of the countable atomless Boolean algebras

The Baire category theorem for compact Hausdorff spaces is used to show that any recursive completion ℬ^ϕof the countable atomless Boolean algebra ℬ is ℬrecursively closed." Also, a theorem of R.D. Anderson on the simplicity of Aut(ℬ) is used to show that uncountably many automorphisms of ℬ extend to ℬ^ϕ. This revised version was published online in June 2006 with corrections to the Cover Date.     

Dispersion and alignment of carbon nanotubes in polycarbonate

Dispersion and alignment of carbon nanotubes in thermoplastic polymers such as polycarbonate have been studied. Dispersion was accomplished by mixing in a conical twin-screw extruder and alignment was carried out using a fiber-spinning apparatus. The effects of mixing time and fiber draw rates on dispersion and alignment were investigated. Uniform dispersions were produced with relatively short residence times in the extruder. Excellent alignment of carbon nanotubes in nanocomposite filaments was obtained when the fiber draw rate was greater than 70 m/min. The ability to closely control the dispersion and alignment of carbon nanotubes in polymers is expected to lead to the development of nanocomposites with desirable electronic and structural properties. Received: 7 January 2002 / Accepted: 11 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +1-508/233-5521, E-mail: Michael.Sennett@natick.army.mil     

Polymers grafted to a fluid and flexible membrane: Extreme sensitivity to the grafting density

Equilibrium phase coexistence between two chemical species implies the equality of the chemical potentials and of the osmotic pressures. We study this problem on a deformable membrane when one type of the molecules serves as anchor for polymeric chains immersed in the surrounding medium (considered as a good solvent). We derive the general conditions for phase coexistence when both the curvature of the membrane and the density field of the anchor molecule are free to adjust themselves. We show that curvature favors phase segregation. Our model predicts that membranes decorated with polymeric chains exhibit new shape bifurcations without equivalent in fixed density systems. Received: 26 November 2002 / Accepted: 2 April 2003 / Published online: 12 May 2003 RID="a" ID="a"e-mail: nicolas@drfmc.ceng.cea.fr RID="b" ID="b"e-mail: bfourcade@cea.fr