Authors:Zhao Tian, Li-Min Jia, Hong-Hui Dong, Zun-Dong Zhang, Yang-Dong Ye Abstract: Modern Physics Letters B, Volume 29, Issue 15, 10 June 2015. Traffic congestion is now nearly ubiquitous in many urban areas and frequently occurs during rush hour periods. Rush hour avoidance is an effective way to ease traffic congestion. It is significant to calculate the rush hour for alleviating traffic congestion. This paper provides a method to calculate the fuzzy peak hour of the urban traffic network considering the flow, speed and occupancy. The process of calculation is based on betweenness centrality of network theory, optimal separation method, time period weighting, probability–possibility transformations and trapezoidal approximations of fuzzy numbers. The fuzzy peak hour of the urban road traffic network (URTN) is a trapezoidal fuzzy number [m1, m2, m3, m4]. It helps us (i) to confirm a more detailed traffic condition at each moment, (ii) to distinguish the five traffic states of the traffic network in one day, (iii) to analyze the characteristic of appearance and disappearance processes of the each traffic state and (iv) to find out the time pattern of residents travel in one city. Citation: Modern Physics Letters B PubDate: 2015-06-11T09:36:23Z DOI: 10.1142/S0217984915500748

Authors:J. Z. Lou, X. Y. Fang, S. J. Wang, X. H. Dai, C. J. Jia, L. Zhang, Y. L. Jia, Y. L. Wang, L. X. Ma, B. T. Liu Abstract: Modern Physics Letters B, Volume 29, Issue 15, 10 June 2015. In order to investigate the effect of argon introduction on the structural and physical properties of Ba0.6Sr0.4TiO3 (BST) films, epitaxial BST films have been grown by pulsed laser deposition (PLD) on (001) oriented Nb-SrTiO3 (STON) substrates in the ambient gas of pure oxygen and the mixture of argon and oxygen, respectively. The atomic force microscopy (AFM) reveals that the sample deposited in the mixture of argon and oxygen has a bigger grain size than that deposited in pure oxygen. The dielectric properties of two BST films have been investigated using the Pt/BST/STON parallel plate capacitors. The tunability and the figure of merit (FOM) of the BST film deposited in the mixture gas are about 41% and 7.07 at a DC bias voltage of 8 V at room temperature, which are better than 32% and 4.51, for BST film deposited in pure oxygen. On account of the introduction of argon, the leakage current density of the BST film deposited in the mixture gas has fallen by almost five times, and the leakage current mechanism is both in accordance with ohmic conductive mechanism. Citation: Modern Physics Letters B PubDate: 2015-06-11T09:36:19Z DOI: 10.1142/S0217984915500797

Authors:A. T. Apostolov, I. N. Apostolova, S. G. Bahoosh, S. Trimper, M. T. Georgieva, J. M. Wesselinowa Abstract: Modern Physics Letters B, Ahead of Print. We propose a microscopic model in order to study the multiferroic (MF) properties of LiCuVO4 (LCVO) taking into account the competing nearest and next-nearest magnetic interactions, frustration and a linear magnetoelectric (ME) coupling. We obtain for α = ∣J2/J1∣ = 0.76. The temperature and magnetic field dependence of the polarization Pa and Pc is observed. It is shown that the dielectric constant ϵa has a kink near the magnetic phase transition TN = 2.4 K which disappears with increasing of the external magnetic field. Some differences in the MF behavior between LiCu2O2 (LCO) and LCVO are discussed. Citation: Modern Physics Letters B PubDate: Fri, 05 Jun 2015 01:22:09 GMT DOI: 10.1142/S0217984915500864

Authors:Naoya Arakawa Abstract: Modern Physics Letters B, Ahead of Print. I review many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point (QCP). These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multi-orbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multi-orbital systems. To improve this situation, I formulate the resistivity of a multi-orbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki–Thompson term. The results away from and near the antiferromagnetic QCP reproduce the temperature dependence observed in Sr2RuO4 and Sr2Ru0.075Ti0.025O4, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems. Citation: Modern Physics Letters B PubDate: Wed, 03 Jun 2015 06:53:44 GMT DOI: 10.1142/S0217984915300057

Authors:Mehmet Isik, Nizami Gasanly Abstract: Modern Physics Letters B, Ahead of Print. Optical properties of Ga2SeS crystals grown by Bridgman method were investigated by transmission, reflection and ellipsometry measurements. Analysis of the transmission and reflection measurements performed in the wavelength range of 400–1100 nm at room temperature indicated the presence of indirect and direct transitions with 2.28 eV and 2.38 eV band gap energies. Ellipsometry measurements were carried out in the 1.2–6.0 eV spectral region to get information about optical constants, real and imaginary parts of the pseudodielectric function. Moreover, the critical point (CP) analysis of the second derivative spectra of the pseudodielectric constant in the above band gap region was accomplished. The analysis revealed the presence of five CPs with energies of 3.87, 4.16, 4.41, 4.67 and 5.34 eV. Citation: Modern Physics Letters B PubDate: Wed, 03 Jun 2015 03:21:26 GMT DOI: 10.1142/S0217984915500888

Authors:Furkan Dincer, Muharrem Karaaslan, Emin Unal, Oguzhan Akgol, Cumali Sabah Abstract: Modern Physics Letters B, Ahead of Print. We demonstrate numerically and experimentally chiral metamaterials (MTMs) based on gammadion-bilayer cross-wires that uniaxially create giant optical activity and tunable circular dichroism as a result of the dynamic design. In addition, the suggested structure gives high negative refractive index due to the large chirality in order to obtain an efficient polarization converter. We also present a numerical analysis in order to show the additional features of the proposed chiral MTM in detail. Therefore, a MTM sensor application of the proposed chiral MTM is introduced and discussed. The presented chiral designs offer a much simpler geometry and more efficient outlines. The experimental results are in a good agreement with the numerical simulation. It can be seen from the results that, the suggested chiral MTM can be used as a polarization converter, sensor, etc. for several frequency regimes. Citation: Modern Physics Letters B PubDate: Wed, 03 Jun 2015 03:21:25 GMT DOI: 10.1142/S0217984915500876

Authors:Hui Zhang, Zhong-Yuan Jiang, Xuan He, Shuai Zhang Abstract: Modern Physics Letters B, Ahead of Print. Since the delivery capacity of each node is neither uniform nor strictly proportional to the degree in many real networked systems such as the Internet, we consider the node capacity is composed of a small uniform fraction and a large degree dependent proportion. By comparing the optimal routing strategy [B. Danila, Y. Yu, J. A. Marsh and K. E. Bassler, Phys. Rev. E74 (2006) 046106; B. Danila, Y. Yu, J. A. Marsh and K. E. Bassler, Chaos17 (2007) 026102] with the shortest path routing (SPR), the results show that the OR appears to be not efficient enough to enhance network traffic capacity. Then the efficient betweenness defined as the average betweenness for per delivery capacity is employed, and a so-called highly-efficient routing (HER) strategy is proposed. By iteratively minimizing the maximum efficient betweenness of any node in the network, the highest traffic capacity is achieved at the cost of a little average path lengthening. This work is very useful for network service providers to optimize the weight of each link incrementally to improve whole network transport ability. Citation: Modern Physics Letters B PubDate: Wed, 03 Jun 2015 03:21:19 GMT DOI: 10.1142/S0217984915500852

Authors:Alexander V. Zhukov, Roland Bouffanais, Anastasiya V. Pak, Mikhail B. Belonenko Abstract: Modern Physics Letters B, Ahead of Print. The indirect spin–spin interaction between impurities in a non-Fermi quantum liquid system is theoretically investigated in this paper. The poles of the Green's functions are shown to be responsible for the observed excitation spectra. Specifically, the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is used to gain access to the analytical expressions of the Green's functions for our particular problem. Citation: Modern Physics Letters B PubDate: Thu, 28 May 2015 10:43:28 GMT DOI: 10.1142/S0217984915500815

Authors:Xiu-Xia Wang Abstract: Modern Physics Letters B, Ahead of Print. Employing a special unitary operator and the virtue of the technique of integration within an ordered product (IWOP), we research on the quantum effects for an inductance–capacitance coupling double L–C circuit. It is found that it is convenient to research on the mesoscopic circuit with such an operator. First, eliminating the coupling term of Hamiltonian becomes easier than other methods. Second, the system's ground state can be easily generalized into a two-mode squeezed state. Thus, the quantum fluctuations of the circuit and the variances of current in each loop are calculated, the charge-current uncertainty relation is revealed. As a result, both the uncertainty relation and fluctuation of the current in each loop become larger when L0 is larger or C0 is smaller. Citation: Modern Physics Letters B PubDate: Thu, 28 May 2015 10:43:28 GMT DOI: 10.1142/S0217984915500840

Authors:Yun-Chang Xiao, Ming-Han Zhu, Zheng-Qin Liu Abstract: Modern Physics Letters B, Ahead of Print. Quantum pump set up in one-dimensional (1D) channel was proposed by the cold atom simulation. The target pumping system is driven by the double time-dependent potentials. We investigated that the system can be achieved via the study of the cold atoms simulation. And by using the Floquet scattering method and the related transport theories in the mesoscopic systems, simulations of the pumping processes were presented in detail. Citation: Modern Physics Letters B PubDate: Thu, 28 May 2015 10:43:27 GMT DOI: 10.1142/S0217984915500827

Authors:Hossein Jafarzadeh, Rajab Nasehi, Elnaz Ahmadi Sangachin, Seyyed Hossein Asadpour Abstract: Modern Physics Letters B, Ahead of Print. In this paper, we propose a model for controlling the optical bistability in four-level InGaN/GaN quantum dot nanostructure which is embedded in a unidirectional ring cavity. InGaN/GaN quantum dot nanostructure is based on our recent paper [S. H. Asadpour, Z. Golsanamlou and H. R. Soleimani, Physica E54 (2013) 45]. It is found that intensity threshold of optical bistability can be manipulated by signal intensity of applied fields. Moreover, we find that phase variation of terahertz signal field can also affect the behaviors of optical bistability and hysteresis loop. Citation: Modern Physics Letters B PubDate: Thu, 28 May 2015 10:43:24 GMT DOI: 10.1142/S0217984915500839

Authors:B. Neouioua, F. Benamira, M. A. Benbitour Abstract: Modern Physics Letters B, Ahead of Print. We discuss the quantization of two mesoscopic coupled RLC circuits with sources and a time-dependent resistances. We use unitary transformations to decouple the system and calculate the charge-current fluctuations for each loop. An adequate time-dependent form of resistances is used to simplify the quantum evolution of the system. We find that the charge-current fluctuations verify the Heisenberg principle and decrease when the time elapses. Citation: Modern Physics Letters B PubDate: Mon, 25 May 2015 09:44:51 GMT DOI: 10.1142/S0217984915500773

Authors:Hao Xu, Yuxin Song, Qian Gong, Wenwu Pan, Xiaoyan Wu, Shumin Wang Abstract: Modern Physics Letters B, Ahead of Print. Bi2Te3 has drawn great attention in recent years as both a topological insulator and the best thermoelectric material at room temperature. We report on Raman spectroscopic study on Bi2Te3 thin films with thicknesses of 20–50 nm grown on GaN by molecular beam epitaxy. All the four classical optical phonon modes are clearly revealed for the first time in ex situ Raman for epitaxial Bi2Te3. Unusual and infrared-active vibration modes are also observed and analyzed. In the resonant Raman measurements, abnormal enhancement and suppression of different modes are studied. The interface modes caused by a large density of domain boundaries formed during coalescence of crystal islands with different lattice orientations and the Fröhlich electron–phonon interaction are found to play significant roles during the Raman scattering processes. Citation: Modern Physics Letters B PubDate: Mon, 25 May 2015 09:44:51 GMT DOI: 10.1142/S021798491550075X

Authors:R. Khordad, H. Bahramiyan Abstract: Modern Physics Letters B, Ahead of Print. In this paper, we have studied the effect of impurity on the energy levels and nonlinear optical properties of a hexagon-shaped quantum wire using finite element method (FEM). We have obtained the energy eigenvalues, their corresponding eigenfunctions and third harmonic generation (THG) with and without impurity for different sizes of inner a1 and outer a2 hexagons. It is found that all energy levels are decreased with increasing a1. There is degeneracy between energy levels without impurity. But, there is no degeneracy between the energy levels in the presence of impurity. The dipole matrix elements are increased with enhancing hexagon sizes without impurity. But, these elements have complex behaviors with impurity. The THG increases and shifts toward lower energies by enhancing a1. The influence of a2/a1 on THG is not large when a2/a1 > 2. The THG shifts toward lower energies by increasing impurity position. Citation: Modern Physics Letters B PubDate: Mon, 25 May 2015 09:44:48 GMT DOI: 10.1142/S0217984915500785

Authors:Zhenduo Geng, Yuping Wang Abstract: Modern Physics Letters B, Ahead of Print. The polarization field effects on exciton states and optical properties are studied theoretically in the wurtzite (WZ) InxGa1-xN/InyGa1-yN staggered quantum wells (QWs). Numerical results show that the polarization field effects are obvious on the Stark shifts of the exciton binding energy, the oscillator strength and the emission wavelength when the well width and Indium content y increase in the symmetric staggered QWs. However, the influences of InxGa1-xN well layer are remarkable on exciton states and optical properties when the Indium concentration y is small in the asymmetric staggered QWs. In addition, the ground state linear optical susceptibility is also investigated in the WZ staggered QWs. Citation: Modern Physics Letters B PubDate: Mon, 25 May 2015 09:44:47 GMT DOI: 10.1142/S0217984915500761

Authors:Hong Wang, Lingjuan He Abstract: Modern Physics Letters B, Ahead of Print. We proposed a new kind of 1×4 optical power splitter composed of one input photonic crystal (PC) waveguide (PCW) and two PC branches with a triangular lattice of air holes. By employing the coupling between a defect region and one input, four output PCWs, the input power can be efficiently split into four output ports. The total transmittance as high as 99.4% at the wavelength 1550 nm is achieved. By modifying two holes at junction area, the input power can be almost evenly split into four parts with a bandwidth larger than 80 nm. It provides a new method and a compact model to split input power into multiple output ports in PCW devices and may find practical applications in future photonic integrated circuits. Citation: Modern Physics Letters B PubDate: Mon, 25 May 2015 09:44:47 GMT DOI: 10.1142/S0217984915500736

Authors:Zineb Aarizou, Soumia Bahlouli, Mokhtar Elchikh Abstract: Modern Physics Letters B, Ahead of Print. Structural and magnetic properties as well as the electronic structures of [math] Heusler alloys were investigated in the framework of first principle calculation. Using the full-potential linearized augmented plane wave (FP-LAPW) in connection with the generalized gradient approximation (GGA) treatment of exchange-correlation energy, we have performed the structural optimization in the non-magnetic (NM) and three different magnetic configurations: FM, AFM-I and AFM-II. We have found that our two compounds are stable for the AFM-II state, which agree with the available experimental and theoretical results. The exchange constants [math] and [math] as well as the temperature of transition to the paramagnetic state [math] were estimated here by the use of the energy difference method and the mean field approximation. The electronic structure of our compounds in their magnetic state was also studied. The GGA [math]+ [math]U method has also been used to take into account the strong correlations among the d orbitals of [math] and [math] atoms. This has considerably improved both the electronic and magnetic results which became close to the corresponding experimental data. We have finally studied the thermodynamic properties using the quasi-harmonic Debye model as implemented in the Gibbs Program. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:27:03Z DOI: 10.1142/S0217984915500931

Authors:A. Lavagno, D. Pigato, G. Gervino Abstract: Modern Physics Letters B, Ahead of Print. One of the very interesting aspects of high energy heavy-ion collisions experiments is a detailed study of the thermodynamical properties of strongly interacting nuclear matter away from the nuclear ground state. In this direction, many efforts were focused on searching for possible phase transitions in such collisions. We investigate thermodynamic instabilities in a hot and dense nuclear medium where a phase transition from nucleonic matter to resonance-dominated [math]-matter can take place. Such a phase transition can be characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the strangeness concentration) in asymmetric nuclear matter. In analogy with the liquid–gas nuclear phase transition, hadronic phases with different values of antibaryon–baryon ratios and strangeness content may coexist. Such a physical regime could be, in principle, investigated in the future high-energy compressed nuclear matter experiments which will make it possible to create compressed baryonic matter with a high net baryon density. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:27:01Z DOI: 10.1142/S021798491550092X

Authors:Zi-Wen Huang, Ji-Xuan Hou, Chun Xie, Hao Zhang Abstract: Modern Physics Letters B, Ahead of Print. We investigated a highly coarse-grained polymer model — hard-sphere (HS) model. This model is characterized by its time-saving computation and strictly guaranteed uncrossability of polymer chains. Regarding the statistical and dynamic properties of HS model, our simulating results perfectly coincide with pre-existing scaling theory. Additionally, we point out that the power exponent of scaling relationship between its relaxation time and chain length is 2.2. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:27:00Z DOI: 10.1142/S0217984915500918

Authors:Fan Yang, Guowu Yang, Yujie Hao, Qingbin Luo, Yuqi Wang Abstract: Modern Physics Letters B, Ahead of Print. This paper presents an analysis method for quantum information protocols based on model checking, with special focus on the quantum privacy comparison (QPC). The security properties of these protocols can be proved but in ways with much difficulty. Here we will discuss a probabilistic model checking tool — PRISM to verify specific properties of QPC protocol with multi-body and PRISM to verify specific properties of quantum private comparison (QPC) protocol with multi-party and d-dimensional entangled states. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:26:58Z DOI: 10.1142/S021798491550089X

Authors:E. Elkoraychy, A. Kotri, M. Mazroui, K. Sbiaai, K. Saadouni Abstract: Modern Physics Letters B, Ahead of Print. In this paper, the dynamic properties of a single adatom subject to a two-dimensional periodic potential of square symmetry are investigated. This problem is addressed through the strong-collision model, where the dynamical interaction of the adatom with the substrate is modeled by well-separated collisions that thermalize the velocity. By means of molecular dynamics simulations, we calculate the jump-length probability distribution and the diffusion coefficient as a function of x–y coupling term and of the collision frequency [math]. Our numerical results show that the x–y coupling always suppresses a large proportion of long jumps, inducing thus a decrease of the diffusion coefficient for all values of [math]. Implications of these findings are briefly discussed. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:26:56Z DOI: 10.1142/S0217984915500906

Authors:G. Subhashree, S. Sankar, R. Krithiga Abstract: Modern Physics Letters B, Ahead of Print. Self-consistent first principles calculations on type II weakly coupled superconducting [math] compounds of A15 phase are performed to understand their fundamental characteristics of the electronic, thermal and superconducting properties. The bulk modulus [math], Debye temperature [math], density of states (DOS) [math], electron–phonon coupling constant [math], superconducting transition temperature [math], and electronic specific heat coefficient [math] have been computed in terms of the electronic structure results, obtained by using the tight-binding linear muffin-tin orbital method. It is observed that all the three materials have their electronic properties dominated by d-orbital at Fermi energy. Thermal and superconducting properties calculated here are found to corroborate well with the experimental results of literature. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:26:52Z DOI: 10.1142/S0217984915500943

Authors:Le Deng, Li Bin Wang, Jie Ming Qin, Tao Zheng, Jing Ni, Xiao Peng Jia, Hong An Ma Abstract: Modern Physics Letters B, Ahead of Print. A novel chemical alloying method of high-pressure and high-temperature (HPHT) has been used for the synthesis of bulk-skutterudite [math]. Through HPHT method, the synthesis time has been shortened from a few days to 30 min. The samples of [math] skutterudites were synthesized at 1.8–3.3 GPa. We have studied the phase, the microstructure, and the temperature-dependent thermoelectric properties. The Seebeck coefficient, electrical conductivity and thermal conductivity were measured in the temperature range of 295–673 K. As we expected, the thermal conductivity of sample [math] decreased with the increase of the synthetic pressure. A maximal ZT of 0.64 was achieved for the [math] synthesized at 1.8 GPa at 673 K. These results revealed that HPHT method may be helpful for optimizing electrical conductivity and thermal conductivity in a comparatively independent way. Citation: Modern Physics Letters B PubDate: 2015-06-25T09:26:50Z DOI: 10.1142/S0217984915500955

Authors:Gang Zhang, Hong Yan Gao, Xiao Cui Tian, Li Na Zhao, Jin Wang, Wen Long Jiang, Xi Yan Zhang Abstract: Modern Physics Letters B, Ahead of Print. The effect on the properties of organic electroluminescent devices was studied using various electronic injection layers. As a result, the electron injection layer by [math] doped [math], when the mass fraction was 17% and the thickness was 1 nm, the performance of the device was significantly higher than the single [math] and [math] as electronic injection layer. The maximum power efficiency reached 0.91 lm/W, which was higher than that of [math] 0.64 lm/W and [math] 0.32 cd/A raised 1.42 times and 2.84 times, respectively. In addition, the light voltage of the doping device was 8 V, and that of the [math] and [math] device was 9 V. So the turn-on voltage was reduced. Citation: Modern Physics Letters B PubDate: 2015-06-22T09:26:30Z DOI: 10.1142/S0217984915500803

Authors:Sudip Chakravarty, Chen-Hsuan Hsu Abstract: Modern Physics Letters B, Ahead of Print. Broken symmetry states characterizing density waves of higher angular momentum in correlated electronic systems are intriguing objects. In the scheme of characterization by angular momentum, conventional charge and spin density waves correspond to zero angular momentum. Here, we explore a class of exotic density wave states that have topological properties observed in recently discovered topological insulators. These rich topological density wave states deserve closer attention in not only high temperature superconductors but in other correlated electron states, as in heavy fermions, of which an explicit example will be discussed. The state discussed has nontrivial charge [math] skyrmionic spin texture. These skyrmions can condense into a charged superfluid. Alternately, they can fractionalize into merons and anti-merons. The fractionalized particles that are confined in skyrmions in the insulating phase, can emerge at a deconfined quantum critical point, which separates the insulating and the superconducting phases. These fractional particles form a two-component spin-singlet chiral [math] wave superconducting state that breaks time reversal symmetry. Possible connections of this exotic order to the superconducting state in the heavy-fermion material [math] are suggested. The direct evidence of such a chiral superconducting state is polar Kerr effect that was observed recently. Citation: Modern Physics Letters B PubDate: 2015-06-16T09:42:01Z DOI: 10.1142/S0217984915400539

Authors:Paul Sutcliffe Abstract: Modern Physics Letters B, Ahead of Print. Skyrmions are topological solitons that describe baryons within a nonlinear theory of pions. In holographic QCD, baryons correspond to topological solitons in a bulk theory with an extra spatial dimension. Thus, the three-dimensional Skyrmion lifts to a four-dimensional holographic Skyrmion in the bulk. We begin this review with a description of the simplest example of this correspondence, where the holographic Skyrmion is exactly the self-dual Yang–Mills instanton in flat space. This places an old result of Atiyah and Manton within a holographic framework and reveals that the associated Skyrme model extends the nonlinear pion theory to include an infinite tower of vector mesons, with specific couplings for a BPS theory. We then describe the more complicated curved space version that arises from the string theory construction of Sakai and Sugimoto. The basic concepts remain the same but the technical difficulty increases as the holographic Skyrmion is a curved space version of the Yang–Mills instanton, so self-duality and integrability are lost. Finally, we turn to a low-dimensional analog of holographic Skyrmions, where aspects such as multi-baryons and finite baryon density are amenable to both numerical computation and an approximate analytic treatment. Citation: Modern Physics Letters B PubDate: 2015-06-16T09:42:01Z DOI: 10.1142/S0217984915400515