Refining the Diffusion Approximation for the <Emphasis Type="Italic">GI</Emphasis><Superscript><Emphasis Type="Italic">x</Emphasis></Superscript><Emphasis Type="Italic">/G/c</Emphasis> Queue

This paper deals with the GI ^x /G/c queueing system in a steady state. We refine a diffusion approximation method incorporating the constraint of traffic conservation for general queueing systems. An approximate expression for the distribution of the number of customers is obtained. Numerical results are presented to show that the refined model provides improved performance.     

Radiation patterns of electric dipole antenna in the presence of a biisotropic sphere

Analytic expressions of the dyadic Green's function of an arbitrary electric current source embedded in a general biisotropic sphere are presented at first, and the radiation characteristics of an electric dipole antenna placed on the surface of a biisotropic sphere lens are examined. The effects of the electric-and the magnetic-coefficients ( _e and _m ) of biisotropic medium on the radiation patterns of electric dipole antenna are investigated in detail.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Investigations of the interlayer coupling in high-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> cuprates

Low-field magnetizationM(H) measurements can be used to probe the nature of the screening currents and the interlayer coupling in high-T _c cuprates. Here we compare theM(H) behaviour of single crystals of Bi₂Sr₂CaCu₂O₈ and fully oxygenated and oxygen reduced YBa₂Cu₃O_7??. In YBa₂Cu₃O₇, theM(H) behaviour is consistent with anisotropic 3D superconductivity whilst in Bi₂Sr₂CaCu₂O₈, the surface screening currents are strongly affected by the presence of vortices, implying that the CuO₂ planes are coupled via a weak Josephson interaction. In oxygen-deficient YBa₂Cu₃O_6.7 (T _c =63K), theM(H) behaviour at low temperatures is similar to that found for Bi₂Sr₂CaCu₂O₈, implying that the removal of oxygen from the chains has resulted in a dimensional crossover of the superconducting state in YBa₂Cu₃O_7??. As the temperature approachesT _c , the 3D behaviour is eventually restored as thec-axis coherence length ξ _c becomes comparable with the interlayer spacingd.     

Transport studies in boron-ion implanted type II<Emphasis Type="Italic">a</Emphasis> diamond

We have investigated low-temperature electrical transport mechanisms in the surface layer of a type IIa diamond which has been heavily implanted with boron-ions at low temperatures and then annealed at high temperatures. The boron atoms occupy substitutional sites giving rise to a heavily doped wide-bandgap semiconductor. The dc-conductivity results suggest that for the maximum boron doping that has been achieved, the diamond sample is close to the insulator-metal transition. A model to account for the observed increase in activated boron centres with ion dose is presented. On the insulating side of the transition, the data are interpreted in terms of variable-range hopping laws.     

Magnetic structure of graphite ribbon

Anoble mechanism of spin polarization is proposed for finite graphite sheet with edge. For graphite ribbon with zigzag edge, there appear peculiar ‘edge states’. These localized states comprise nearly flat band at the Fermi level, which easily causes magnetic instability. Magnetic structure is suggested from Hartree-Fock analysis of the Hubbard model, where huge magnetic moments are induced at around both of edges by weak HubbardU and are coupled antiferromagnetically with each other.     

Intersections of random walks and Wiener sausages in four dimensions

Let {S ₁ (n)} _n0and {S ₂ (n)} _n0be independent simple random walks in Z ⁴ starting at the origin, and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaqGPbaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiaadggacaGGSaGaamOyaiab-LcaPiabg2da9i% ab-Tha7Hqbciab+Hha4jabgIGiolab+PfaAnaaCaaaleqabaGaaGin% aaaakiaacQdaieGacaqFtbWaaSbaaSqaaiaabMgaaeqaaOGae8hkaG% Iaa0xBaiab-LcaPiabg2da9iab+Hha4baa!5761!\[\Pi _{\rm{i}} (a,b) = \{ x \in Z^4 :S_{\rm{i}} (m) = x\]for the some % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciaa-1gacqGHiiIZtCvAUfKttLearyqr1ngBPrgaiuaacqGF% OaakcaWGHbGaaiilaiaadkgacqGFPaqkcqGF9bqFaaa!4936!\[m \in (a,b)\} \]. Let two integervalued sequences {a _n}_n0and {b _n}_n0be given, such that the limit lim_n a _nexists and lim _n b _n=+. In this paper, it is shown that the probability of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaaIXaaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiab-bdaWiab-XcaSiabg6HiLkab-LcaPiabgM% Iihlabfc6aqnaaBaaaleaacaaIYaaabeaakiab-HcaOiaadggadaWg% aaWcbaGaamOBaiaacYcaaeqaaOGaamyyamaaBaaaleaacaWGUbaabe% aakiabgUcaRiaadkgadaWgaaWcbaGaamOBaaqabaGccqWFPaqkcqGH% GjsUieaacaGFydaaaa!5904!\[\Pi _1 (0,\infty ) \cap \Pi _2 (a_{n,} a_n + b_n ) \ne \O \] is asymptotic to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaalaaabaGaaGymaaqaaiaaikdaaaGaciiBaiaac+gacaGGNbWe% xLMBb50ujbqeguuDJXwAKbacfaGae8hkaGIae8xmaeJae83kaSIaam% OyamaaBaaaleaacaWGUbaabeaakiaac+cacaWGHbWaaSbaaSqaaiaa% d6gaaeqaaOGae8xkaKIae83la8IaciiBaiaac+gacaGGNbGaamOyam% aaBaaaleaacaWGUbaabeaaaaa!5364!\[\frac{1}{2}\log (1 + b_n /a_n )/\log b_n \] if it tends to zero as n, and the probability of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaaIXaaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiab-bdaWiab-XcaSiabg6HiLkab-LcaPiabgM% Iihlabfc6aqnaaBaaaleaacaaIYaaabeaakiab-HcaOiaadggadaWg% aaWcbaGaamOBaaqabaGccaGGSaGaamyyamaaBaaaleaacaWGUbaabe% aakiabgUcaRiaadkgadaWgaaWcbaGaamOBaaqabaGccqWFPaqkcqWF% 9aqpieaacaGFydaaaa!583C!\[\Pi _1 (0,\infty ) \cap \Pi _2 (a_n ,a_n + b_n ) = \O \]is asymptotic to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% abaeqabaaabaGaam4yaiaacUfaciGGSbGaai4BaiaacEgatCvAUfKt% tLearyqr1ngBPrgaiuaacqWFOaakcaWGHbWaaSbaaSqaaiaad6gaae% qaaOGaey4kaSIaamOyamaaBaaaleaacaWGUbaabeaakiab-LcaPiab% -9caViab-XgaSjab-9gaVjab-DgaNjab-HcaOiaadggadaWgaaWcba% GaamOBaaqabaGccqGHRaWkcaaIYaGae8xkaKIae8xxa01aaWbaaSqa% beaacqWFTaqlcqWFXaqmcqWFVaWlcqWFYaGmaaaaaaa!5BAC!\[\begin{array}{l} \Pi _1 (0,\infty ) \cap \Pi _2 (a_n ,a_n + b_n ) = \O \\ c[\log (a_n + b_n )/log(a_n + 2)]^{ - 1/2} \\ \end{array}\], for some constant c, if it tends to a finite constant (1) as n. These results extend some results obtained by G. F. Lawler about the intersection properties of simple random walks in Z ⁴. By using similar arguments, we also get corresponding results for the intersections of Wiener sausages in four dimensions. In particular, a conjecture suggested by M. Aizenman, which describes nonintersection of independent Wiener sausages in R ⁴, is proven.Partly supported by AvH Foundation.     

Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

Λ-Shaped Policies to Schedule Deteriorating Jobs

We study a problem of scheduling deteriorating jobs, i.e. jobs whose processing times are an increasing function of their starting times. We consider the case of a single machine and linear job-independent deterioration. The objective is to minimize the sum of weighted completion times, with weights proportional to the basic processing times. The optimal schedule is shown to be Λ-shaped, i.e. the sequence of the basic processing times has a single local maximum. Moreover, we show that the problem is solved in O(N log N) time. In the last section we test heuristics for the case of general weights.     

Analysis of Open Discrete Time Queueing Networks: A Refined Decomposition Approach

This paper deals with approximate analysis methods for open queueing networks. External and internal flows from and to the nodes are characterized by renewal processes with discrete time distributions of their interarrival times. Stationary distributions of the waiting time, the queue size and the interdeparture times are obtained using efficient discrete time algorithms for single server (GI/G/1) and multi-server (GI/D/c) nodes with deterministic service. The network analysis is extended to semi-Markovian representations of each flow among the nodes, which include parameters of the autocorrelation function.