Real L2 Research Articles

RECOVERING THE SHAPE OF A QUANTUM CATERPILLAR TREE BY TWO SPECTRA

existence of co-spectral (iso-spectral) graphs is a well-known problem of the classical graph theory. However, co-spectral graphs exist in the theory of quantum graphs also. In other words, the spectrum of the Sturm-Liouville problem on a metric graph does not determine alone the shape of the graph. Сo-spectral trees also exist if the number of vertices exceeds eight. We consider two Sturm-Liouville spectral problems on an equilateral metric caterpillar tree with real L2 (0,l) potentials on the edges. In the first (Neumann) problem we impose standard conditions at all vertices: Neumann boundary conditions at the pendant vertices and continuity and Kirchhoff’s conditions at the interior vertices. The second (Dirichlet) problem differs from the first in that in the second problem we set the Dirichlet condition at the root (one of the pendant vertices of the stalk of the caterpillar tree, i.e. the central path of it). Using the asymptotics of the eigenvalues of these two spectra we find the determinant of the normalized Laplacian of the tree and the determinant of the prime submatrix of the normalized laplacian obtained by deleting the row and the column corresponding to the root. Expanding the fraction of these determinants into continued fraction we receive full information on the shape of the tree. In general case this continued fraction is branched. We prove that in the case of a caterpillar tree the continued fraction does not branch and the spectra of the Neumann and Dirichlet problems uniquely determine the shape of the tree. A concrete example is shown. The known pair of co-spectral trees with minimal number (eight) of vertices belongs to the class of caterpillar trees. Keywords: metric graph, tree, pendant vertex, interior vertex, edge, caterpillar tree, Sturm-Liouville equation, potential, eigenvalues, spectrum, Dirichlet boundary condition, Neumann boundary condition, root, continued fraction, adjacency matrix, prime submatrix, normalized Laplacian

Second Language Vocabulary Learning through Ecologically Valid Classroom Practice Can Be Indexed by Event‐Related Potentials (ERPs). A Conceptual Replication Study

AbstractPrevious research has suggested that Event‐Related Potentials (ERPs) can index form‐, meaning‐, and use‐related aspects of the second language (L2) vocabulary knowledge, through, respectively, a lexical decision task (LDT, targeting N400), a semantic relatedness task (SEMREL, targeting N400), and a grammatical judgment task (GJT, targeting P600/AN). Yet, those findings were established in the context of either laboratory‐based or longitudinal word learning studies. Therefore, this conceptual replication study investigates whether LDT, SEMREL, and GJT could reveal the aforementioned ERP components in the context of an ecologically valid short‐term intervention representative of L2 classroom practice. Twenty Dutch‐speaking participants performed reading and writing tasks in a computer‐assisted learning environment. Target words were 20 real L2 French verbs. ERPs were recorded immediately after the learning sessions. Results showed N400 for form‐ and meaning‐related knowledge and P600 for grammatical use. We conclude that ERPs can index L2 vocabulary knowledge gained through ecologically valid classroom activities.

Improving ns-3 emulation performance for fast prototyping of routing and SDN protocols: Moving data plane operations to outside of ns-3

A common problem in networking research and development is the duplicate effort of writing simulation and implementation code of routing protocols. This can be avoided by reusing simulation code in real prototyping and in production environments. In ns-3, emulation mode can be used to run simulation models of routing and Software Defined Networking (SDN) protocols on top of real L2 interfaces such as Ethernet and Wi-Fi. Although this feature is already available, the additional packet processing involved degrades the performance of the nodes and limits the amount of network traffic that can be processed.Our proposal to overcome this performance bottleneck consists in moving the data plane processing operations to outside of the ns-3 process, running such operations natively in the host Operating System (OS). Two approaches are proposed: (a) running the data plane in user space (DPU); (b) running the data plane in kernel space (DPK). Both approaches support the emulation of one or multiple nodes per emulation host machine. The experimental results show that the DPU and DPK approaches significantly improve the throughput by respectively 4.9 and 19 times when compared against traditional ns-3 emulation of a single node. For multiple nodes, the DPK approach further improves the throughput by as much as 23 times. The amount of code reuse is high – e.g., for the routing protocols used in this paper, only 1.4% and 11% of extra code is required to benefit from the performance improvements achieved respectively by the DPK and DPU approaches.

Investigating pseudohomophone interference effects in young second-language learners

This study aimed to investigate phonological activation during silent word reading in French adolescents learning English as a second language (L2) at secondary school. Grade 6 and Grade 8 adolescents performed lexical decision tasks in English, where we compared processing of nonwords that were homophonic to real L2 words (i.e., pseudohomophones [PsHs]; e.g., grean) with that of orthographic control pseudowords (OCs; e.g., greun). In Experiment 1, PsHs were constructed so that they sounded like L2 words when using cross-language (L1) grapheme-to-phoneme correspondences (GPCs) only (e.g., grine), whereas PsHs were constructed with within-language (L2) GPCs (e.g., grean) in Experiment 2. Results showed a PsH interference effect as reflected by higher error rates and/or longer rejection times for PsHs compared with OCs whether using within-language or cross-language GPCs and at both grade levels. Evidence of this PsH interference effect was also observed in Experiment 3, which used PsHs that sounded like real L1 words when using L2 GPCs (e.g., droal for the French word drôle [funny in English]). We suggest that young L2 learners automatically activate both L1 and L2 GPCs during L2 silent reading in favor of strong cross-language interactions at the orthography-to-phonology interface. The results are discussed in relation to bilingual and developmental models on visual word recognition.

Phase Shifter Operation of the Azimuthally Magnetized Coaxial Ferrite Waveguide

The terms for operation of the coaxial waveguide, entirely lled with azimuthally magnetized latching ferrite, as a digital nonreciprocal phase shifter for the normal TE01 mode, are found. They are classi ed as physical, mathematical and functional ones. The physical prerequisites are drawn from the phase curves of the structure and specify the boundaries of the interval in which it produces di erential phase shift for a given numerical equivalent of the modulus of o -diagonal ferrite permeability tensor element. The mathematical condition brings the parameters of con guration together with certain roots of its characteristic equation, derived in terms of complex Kummer and Tricomi con uent hypergeometric functions and with the related to them positive real L2(c, ρ, n) numbers (c = 3, 0 < ρ < 1, n = 1). The functional criteria determine the borders of the domain of phase shifter operation of the geometry. These are functions, de ned for a xed central conductor thickness which express in normalized form the impact of the guide radius on the phase shift at the cut-o frequencies and at the envelopes, denoting the termination of the phase curves for negative ferrite magnetization from the side of higher frequencies. The same are reckoned, employing iterative methods, consisting in a repeated numerical solution of the equation mentioned, followed by a computation of the guide radius and phase constant of the wave and are plotted graphically. The in uence of the parameters of transmission line on the area referred to is analyzed.

First Language Use in Foreign Language Classroom Discourse

The present paper draws on a subset of data from a larger project collected through COLT instrument (Communicative Orientation of Language Teaching) (Spada & Fröhlich, 1995) to investigate the nature of L1 (first language) use in student/teacher's interaction while engaged in pair/group work in real L2 (second language) classroom discourse. The study reports communicative features of pair/group work activity and the features of student/teacher interactions in which L1 appeared. It explores the use of L1 in scaffolding, private speech, and humor in the classroom in light of the reported communicative features.

Automatization in second language acquisition: What does the coefficient of variation tell us?

ABSTRACTSegalowitz and Segalowitz distinguish between “speedup” (mean reaction time [RT] and mean standard deviation of responses in an RT task decrease to the same degree) and “automatization” (mean standard deviation decreases more than mean RT). The coefficient of variation, which is the standard deviation divided by the mean RT, decreases in the case of automatization while remaining unchanged in the case of speedup. We present data that are collected in two studies. The first one is a longitudinal study spanning 2 years and comprising four RT tasks, both in second language (L2) English and first language Dutch (N&gt; 200). The second study is an English L2 word training study. Students (N= 41) performed a lexical decision task before and after training. Convincing evidence for automatization was not found in either study. The main problems in testing the Segalowitz and Segalowitz hypothesis is that gains in knowledge itself and gains in processing it cannot be adequately disentangled in the RT tasks currently used, characterized by a speed–accuracy trade-off. Althoughconceptuallyskill acquisition can be distinguished from knowledge accumulation,in reality, knowledge accumulation forms part of skill acquisition because, in real L2 learning, exposure to new words goes hand in hand with exposure to words encountered previously.

Resistance against being formulated as cultural other

So-called traditional theories in second langauge acquisition (SLA) have been criticized for their neglect to examine interactional, social, and political aspects in language practices. The present study will illustrate exoticization, one of the political phenomena observed in interactions between native-speaker and non-native speaker (NS/NNS). Exoticization is known as a covert power exercise where ‘self’ creates inferior ‘other’ in order to establish and maintain its superiority (Said 1978), which involves identity construction and categorization. Adopting a conversation analysis (CA) approach and utilizing NS-NNS conversations in Japanese, this study will first demonstrate how exoticization is discursively constructed through the development of interactions. Then the study will explore how the NNS participant tries to resist such practices. By so doing, this study will shed light on interactional and ideological aspects of language practices and society as a learning environment. The study will also suggest the necessity for exploring what NNSs face in real L2 societies in order to develop emic perspectives in SLA studies.

Theoretical study of the photodetachment spectroscopy of the IHBr and IDBr anions

The coupled-cluster method with a large basis set with quasi-relativistic effective core potentials on the halogens was utilized to investigate the ground electronic state X 1Σ+ of the IHBr anion. A semi-global, three-dimensional potential energy surface was obtained via spline interpolation of ab initio data. Variational rovibrational calculations were carried out with this potential energy surface, and assignment of fundamentals and low-lying overtones, as well as combination bands, is presented for IH(D)Br anions. Photodetachment spectra for IH(D)Br−+hν→[IH(D)Br]+e− were computed using three-dimensional time-independent real and complex L2 methods and a recently developed real L2 wave packet propagation technique; all methods employed a previous London–Eyring–Polanyi–Sato empirical potential for the neutral system. Well resolved fine structure is found in photodetachment spectra of IHBr−. This structure is assigned to bending excitation based on analysis of the wave functions and the neutral potential energy surface near the Franck–Condon region. This fine structure is largely eliminated in the IDBr− spectrum. The photodetachment spectrum for the first excited asymmetric stretch of IHBr− shows a new feature that is associated with sampling of the transition state region of the neutral surface. Spin-orbit corrected multi-reference configuration interaction calculations indicate that the first excited electronic state is only about 0.06 eV above the ground electronic state of the neutral IHBr system in the Franck–Condon region. The model empirical potential used in the calculations of photodetachment spectra is shown to have roughly the average behavior of these two ab initio potentials.

State-to-State Reactive Scattering via Real L2 Wave Packet Propagation for Reduced Dimensionality AB + CD Reactions

We present a computational method for the calculation of quantum state-to-state reactive probabilities for reduced dimensionality, three degree-of-freedom, AB + CD ↔ A + BCD reactions. Our approach is based on the recently developed wave packet propagation method in real L2 eigenstates [Skokov, S.; Bowman, J. M. Phys. Chem. Chem. Phys. 2000, 2, 495]. Here we show how the real L2 approach can be used for the calculation of state-to-state probabilities. The “coordinate transformation problem” is relatively easily solved in the L2-eigenstate formulation because the eigenstates used for propagation are analytical functions of the coordinates. The method is tested for the H2 + CN ↔ H + HCN reaction for zero total angular momentum, J, using a previous potential energy surface of Sun and Bowman, who reported reduced dimensionality, time-independent calculations of state-to-state reaction probabilities. New calculations for J > 0 are presented using the adiabatic rotation approximation. In this approximation the L2-eigenstates are obtained efficiently by expanding them in the basis of J = 0 eigenstates. Finally a test of J-shifting is done.

A reduced dimensionality quantum calculation of the reaction of H2 with diamond (111) surface

We present a reduced dimensionality quantum dynamics study of the hydrogen abstraction reaction on a semirigid (111) diamond surface, Cd+H2(v,j,m)→CdH+H. A nine-dimensional potential energy surface is developed by combining a London–Eyring–Polanyi–Sato potential based on ab initio data with nonbonded and surface interactions. Four reactive degrees of freedom are treated explicitly using a recently developed wave packet approach in a real L2 basis, and the total reaction probabilities for initial states v=0–1, j=0–11, and m=0–4 are calculated over a large total energy range. The remaining five degrees of freedom are treated using energy-shift approximations, and the full cumulative reaction probability is obtained and from it the full thermal rate constant. Comparison with conventional transition state theory indicates that at 300 K tunneling accounts for 90% of the rate constant and remains significant even at high temperatures. Dynamical corrections to transition state theory become important above 1000 K. At 1200 K the tunneling and dynamical corrections nearly cancel each other and the transition state theory rate constant agrees very well with quantum rate constant. The coupling of surface and reactive modes has only a minor, less then 15%, effect on the rate constants, provided that the energetics for the relaxed surface are incorporated into the potential. The thermal rate for H abstraction from diamond, obtained from detailed balance, is in good agreement with experimental data. Under typical chemical vapor deposition conditions the thermal rate for H abstraction by diamond active sites is found to be 100 slower than the rate of competitive reaction, H addition to diamond active sites.

Wavepacket propagation for reactive scattering using real L2 eigenfunctions with damping

A wavepacket propagation method for reactive scattering using real L2 eigenstates is proposed and tested. The wavepacket propagation is carried out by explicit time evolution of a basis of real L2 eigenstates. The wavepacket is damped at each time step to avoid unphysical reflections at the grid edges and then re-expanded in terms of the real eigenstates. Most of the computational effort is associated with the calculation of eigenstates, while the propagation in the real L2 basis and analysis are relatively inexpensive. In addition, once the L2 basis is available the wavepacket propagation for any initial state can be done very efficiently. Propagation by complex L2 eigenstates is also briefly reviewed. In this approach no explicit time propagation is required since the time-to-energy wavepacket transformation is analytical for any given potential. Applications of both methods for a one-dimensional Eckart potential show excellent agreement with exact results for the energy dependence of the reaction probability. The real L2 approach is also applied to three-dimensional D+H2 for zero total angular momentum. Reaction probabilities for H2(v=0, j=0–5), summed over final DH states, as well as the cumulative reaction probability are presented over a wide energy range and compared to previous accurate results.

Calculation of resonance energies and widths using the complex absorbing potential method

The spectral properties of Hamilton operators perturbed by a complex absorbing potential (CAP) are studied. For a wide class of CAPS proper eigenvalues of the perturbed Hamilton operator converge to Siegert resonance eigenvalues of the unperturbed Hamiltonian with decreasing CAP strength. The errors in the calculation of complex resonance energies caused by the additional CAP and by finite basis set representation are examined. In order to minimize these errors a scheme of approximations is provided. The application of this method allows for the use of real L2 basis sets. The feasibility and accuracy of the proposed method is demonstrated by calculations of resonance energies of a model potential and of the 2 Pi g shape resonance of N2.

On the distribution of the characteristic values and singular values of linear integral equations

Introduction. The order of magnitude of the characteristic values ph [KI of the kernel K(x, y) of a linear integral equation has been discussed by many writers, including Fredholm [4](1), Mercer [11], Schur [12], Weyl [17, 18], Lalesco [9], Mazurkiewicz [10], Carleman [1, 2], Gheorghiu [5], and Hille and Tamarkin [8]. The order of magnitude of the singular values Xh [K], that is, E. Schmidt's characteristic values for non-symmetric kernels, was first discussed by Smithies [13]. It is natural to ask whether there is any relation between the orders of magnitude of the characteristic values and the singular values of a nonsymmetric kernel when both sets of values are infinite in number. We recall that ,u is a characteristic value of the real L2 kernel K(x, y) if there is a real non-null L2 function q (x) such that