Analysis Of L2 Research Articles

On the homogeneous torsion problem for heterogeneous and orthotropic cross-sections: Theoretical and numerical aspects

For many years, torsion of arbitrary cross-sections has been a subject of numerous investigations from theoretical and numerical points of view. As it is well known, the resulting boundary value problem (BVP) governing such phenomenon happens to be a pure Neumann BVP and, therefore, its solutions are determined up to a constant. Among a large plethora of finite element method (FEM) techniques that can be used in this context, most of FEM practitioners resolve this uniqueness issue by fixing the candidate solution to a node of the domain. Although such popular and pinpointing technique is widely spread and works well for practical purposes, it does not have a continuous counterpart and therefore its justification remains a matter of debate. Hence, this self-contained work aims to address the modeling of arbitrary heterogeneous and orthotropic cross-sections as well as the theoretical and numerical aspects of their solutions. In particular, we discuss the existence of weak solutions, well-posedness, regularity of solutions, and convergence of Galerkin’s method for different variational settings (with special focus on a regularized variational approach). Moreover, we establish a connection, at a discrete level, between the convergence of solutions of well-posed variational settings and those solutions coming from the usual practice of fixing a datum at a node. Finally, we discuss some numerical aspects of all the FEM discrete formulations proposed here by performing convergence analysis in L2 and H1 norms. The section of numerical results is closed by presenting a series of study cases ranging from a square cross-section composed of two different materials to an isotropic bridge cross-section for which no analytical solution exists.

Connecting source use and argumentation in L2 integrated argumentative writing performance

Second language (L2) integrated argumentative writing is a complex process, where writers need to integrate sources to make effective arguments to demonstrate their writing proficiency. While abundant research has examined essay performance features in relation to proficiency scores, our understanding of the nature of L2 argumentation and the impact of source use on argumentation quality remains relatively limited. This short communication investigates how source use characteristics were manifested in 300 argumentative writing performances of an integrated writing test. The essays were coded and analyzed in terms of integration style, interpretation accuracy, and integration purpose along with their argumentation effectiveness, operationalized as argument structure and reasoning quality. The results showed that while source use characteristics did not show a direct relationship with score level, certain features displayed systematic differences across levels of argumentation effectiveness, which are significantly related to writing scores. The findings suggest a potential complex, indirect relationship between source use, argumentation, and writing proficiency that warrants a more thorough analysis in L2 writing research.

Expanding the Definition of Aspect in L2 Acquisition: Assessing Advanced Levels of Competence to Understand Aspectual Knowledge

In part due to the significant influence of Andersen's Lexical Aspect Hypothesis, research on the L2 acquisition of tense and aspect has focused primarily on the construct of aspect representative of the beginning and intermediate stages of acquisition. In the present article, I review the significance of two recent developments in the study of aspectual knowledge: the expansive view of recent research proposals (e.g., shifted effect of lexical aspect toward intermediate and advanced stages), and the focus on specific sub-constructs that provide a more precise target to assess ultimate attainment (e.g., iterativity versus habituality). I argue that the relevance of advanced stages of development of aspect is central to the analysis of L2 aspectual knowledge. To that effect, the objective of future studies needs to incorporate the explicit description of the connection between lexical aspect and viewpoint aspect

Fractional nonuniform multiresolution analysis in L2(ℝ)

To provide a significantly richer representation of non‐stationary signals appearing in various disciplines of science and engineering, we introduce a novel fractional nonuniform multiresolution analysis (FrNUMRA) on the spectrum Λ given by , where is an integer and r is an odd integer with such that r and N are relatively prime. The necessary and sufficient condition for the existence of nonuniform wavelets of fractional order is derived and an algorithm is also presented for the construction of fractional NUMRA starting from a fractional low‐pass filter with appropriate conditions. Besides, we provide a complete characterization for the biorthogonality of the translates of the scaling functions of two fractional nonuniform multiresolution analyses and the associated fractional biorthogonal wavelet families.

On scaling functions of non-uniform multiresolution analysis in L2(ℝ)

The main purpose of this paper is to provide a characterization of scaling functions for non-uniform multiresolution analysis (NUMRA, in short). Some necessary and sufficient conditions for scaling functions of wavelet NUMRA in the frequency domain are also obtained.

Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in L P

Perturbed Hodge-Dirac operators and their holomorphic functional calculi, as investigated in the papers by Axelsson, Keith and the second author, provided insight into the solution of the Kato square-root problem for elliptic operators in L2 spaces and allowed for an extension of these estimates to other systems with applications to non-smooth boundary value problems. In this paper, we determine conditions under which such operators satisfy conical square function estimates in a range of L p spaces, thus allowing us to apply the theory of Hardy spaces associated with an operator to prove that they have a bounded holomorphic functional calculus in those L p spaces. We also obtain functional calculus results for restrictions to certain subspaces, for a larger range of p. This provides a framework for obtaining L p results on perturbed Hodge Laplacians, generalising known Riesz transform bounds for an elliptic operator L with bounded measurable coefficients, one Sobolev exponent below the Hodge exponent, and L p bounds on the square-root of L by the gradient, two Sobolev exponents below the Hodge exponent. Our proof shows that the heart of the harmonic analysis in L2 extends to L p for all p ∈ (1,∞), while the restrictions in p come from the operator-theoretic part of the L2 proof. In the course of our work, we obtain some results of independent interest about singular integral operators on tent spaces and about the relationship between conical and vertical square functions.

Performance Analysis of L2 and L5 CNAV Broadcast Ephemeris for Orbit Calculation

Ephemeris error is a limiting factor in GPS position accuracy. The newly introduced GPS Civil Navigation (CNAV) broadcast message, an upgraded version of the legacy NAV message, is designed to provide users with more precise satellite orbit and timing parameters. A CNAV broadcast test was conducted in 2013 on the L2C and L5 bands. Since April 2014, pre-operational CNAV started to broadcast to civilian users. Baseband civil GPS signals on L1, L2, and L5 were recorded during the broadcast test and the pre-operational broadcast using wideband software radio front ends. The signals were acquired and tracked, with navigation messages decoded by the conventional Viterbi method and a computationally efficient matrix-based method. GPS ephemerides were extracted from the messages to compute satellite orbit solutions. This paper evaluates the orbit solution of both CNAV and Legacy NAV during the same time period to demonstrate the improvements in the CNAV ephemeris accuracy. Copyright © 2015 Institute of Navigation.

A Corpus-Based Contrastive Analysis of Korean College Students’ English Composition

Drawing upon the recent attention to the usefulness of contrastive interlanguae analysis of L2 writing, the current research explores the written...

An analysis of discretizations of the Helmholtz equation in [formula omitted] and in negative norms

For a model Helmholtz problem at high wavenumber k we present a wavenumber-explicit error analysis in the L2- and H−1-norms for the Galerkin FEM. For the convergence in L2, we show that the lowest order case p=1 is special in that the relative error in L2 scales at best with k whereas it does not for higher order discretizations. An alternative to the Galerkin method with better dispersion properties is the optimally blended spectral–finite element scheme of Ainsworth and Wajid (2010). For this method, we present an error analysis in L2 for the lowest order case p=1 in one dimension, showing that the L2-error is improved by a factor k compared to the lowest order Galerkin FEM.

Spin-polarized electronic structure of the core–shell ZnO/ZnO:Mn nanowires probed by X-ray absorption and emission spectroscopy

The combination of X-ray spectroscopy methods complemented with theoretical analysis unravels the coexistence of paramagnetic and antiferromagnetic phases in the Zn0.9Mn0.1O shell deposited onto array of wurtzite ZnO nanowires. The shell is crystalline with orientation toward the ZnO growth axis, as demonstrated by X-ray linear dichroism. EXAFS analysis confirmed that more than 90% of Mn atoms substituted Zn in the shell while a fraction of secondary phases was below 10%. The value of manganese spin magnetic moment was estimated from the Mn Kβ X-ray emission spectroscopy to be 4.3 μB which is close to the theoretical value for substitutional MnZn. However the analysis of L2,3 X-ray magnetic circular dichroism data showed paramagnetic behaviour with saturated spin magnetic moment value of 1.95 μB as determined directly from the spin sum rule. After quantitative analysis employing atomic multiplet simulations such difference was explained by a coexistence of paramagnetic phase and local antiferromagnetic coupling of Mn magnetic moments. Finally, spin-polarized electron density of states was probed by the spin-resolved Mn K-edge XANES spectroscopy and consequently analyzed by band structure calculations.

Gabor families in l2(Zd)

This paper addresses Gabor families in l2(Zd). The discrete Gabor families have interested many researchers due to their good potential for digital signal processing. Gabor analysis in l2(Zd) is more complicated than that in l2(Z) since the geometry of the lattices generated by time-frequency translation matrices can be quite complex in this case. In this paper, we characterize window functions such that they correspond to complete Gabor families (Gabor frames) in l2(Zd); obtain a necessary and sufficient condition on time-frequency translation for the existence of complete Gabor families (Gabor frames, Gabor Riesz bases) in l2(Zd); characterize duals with Gabor structure for Gabor frames; derive an explicit expression of the canonical dual for a Gabor frame; and prove its norm minimality among all Gabor duals.

A Defect‐Correction Mixed Finite Element Method for Stationary Conduction‐Convection Problems

A defect‐correction mixed finite element method (MFEM) for solving the stationary conduction‐convection problems in two‐dimension is given. In this method, we solve the nonlinear equations with an added artificial viscosity term on a grid and correct this solution on the same grid using a linearized defect‐correction technique. The stability is given and the error analysis in L2 and H1‐norm of u, T and the L2‐norm of p are derived. The theory analysis shows that our method is stable and has a good precision. Some numerical results are also given, which show that the defect‐correction MFEM is highly efficient for the stationary conduction‐convection problems.

Tight wavelet frames

holds for all f ∈ L2(R). The general scheme [1] for construction of compactly supported tight wavelet frames based on a multiresolution analysis looks as follows. Let a multiresolution analysis in L2(R) be generated by a compactly supported scaling function φ ∈ L2(R) satisfying the re nable equation φ(x) = m0(M∗x)φ(M∗x), where m0 is a trigonometric polynomial (re nable mask). For any trigonometric polynomial mν , there exists a unique set of trigonometric polynomials μνk, k = 0, . . . , m− 1, (polyphase components of mν) such that

ERP measures of auditory word repetition and translation priming in bilinguals

Motivated by the demonstration of similarly localized adaptation of the hemodynamic response in a first (L1) and second (L2) language, this study examined event-related brain potentials (ERPs) to spoken words in L1 and L2 in 15 English–French bilinguals. We examined whether the temporal pattern of N400 adaptation due to within-language repetitions (i.e., repetition priming) was similar in L1 and L2 and whether the release from adaptation elicited by a within-language word change was similar. Furthermore, using word changes across language, we examined the phonological mismatch negativity (PMN) and N400 components to determine the kind of information activated during translation priming. In contrast to within-language repetition, we expected between-language repetition (i.e., translations) to be characterized by conceptual rather than lexical/phonological word form priming. Overall, the pattern of adaptation and release from adaptation was similar in L1 and L2, with evidence of delayed semantic analysis in L2 in the form of a later N400 effect. A change in language (L1 to L2) elicited a similar pattern of PMN and N400 activity compared to a within-language change in meaning in L1, suggesting that neither word form nor conceptual information was available on-line for the forward translation. In contrast, the presence of strong PMN but minimal N400 effects for L2-to-L1 translations suggests that conceptual but not phonological information is available on-line for backwards translation. L2 proficiency influenced the extent to which conceptual representations were activated by translations. These data are discussed in light of current models of bilingual word processing and suggest modality differences in the pattern of activation of lexical and conceptual information.

Kernel density classification and boosting: an L2 analysis

Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification. A relative newcomer to the classification portfolio is “boosting”, and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research.

CONSTRUCTING MULTIPLE WAVELET PACKETS WITH FIFS

By using fractal interpolation functions (FIF), a family of multiple wavelet packets is constructed in this paper. The first part of the paper deals with the equidistant fractal interpolation on interval [0, 1]; next, the proof that scaling functions ϕ1, ϕ2,…,ϕr constructed with FIF can generate a multiresolution analysis of L2(R) is shown; finally, the direct wavelet and wavelet packet decomposition in L2(R) are given.

The multiresolution character of collocation

An interesting theoretical connection between the statistical (non-stochastic) collocation principle and the multiresolution/wavelet framework of signal approximation is presented. The rapid developments in multiresolution analysis theory over the past few years have provided very useful (theoretical and practical) tools for approximation and spectral studies of irregularly varying signals, thus opening new possibilities for `non-stationary' gravity field modeling. It is demonstrated that the classic multiresolution formalism according to Mallat's pioneering work lies at the very core of some of the general approximation principles traditionally used in physical geodesy problems. In particular, it is shown that the use of a spatio-statistical (non-probabilistic) minimum mean-square-error criterion for optimal linear estimation of deterministic signals, in conjunction with regularly gridded data, always gives rise to a generalized multiresolution analysis in the Hilbert space L 2(R), under some mild constraints on the spatial covariance function and the power spectrum of the unknown field under consideration. Using the theory and the actual approximation algorithms associated with statistical collocation, a new constructive framework for building generalized multiresolution analyses in L 2(R) is presented, without the need for the usual dyadic restriction that exists in classic wavelet theory. The multiresolution and `non-stationary' aspects of the statistical collocation approximation procedure are also discussed, and finally some conclusions and recommendations for future work are given.

On gibb's phenomenon for sampling series in wavelet subspaces

Let {Vm be a multiresolution analysis of L2(R) such that a sampling function S for V0 exists. Then we show the sampling approximation of a function in H0,α1/2 onto Vm converges to it uniformly as m→∞. Also Gibbs phenomenon for this sampling expension is analyzed.

Convergence estimates for the wavelet-Galerkin method: superconvergence at the node points

In this paper we consider a regular 1-periodic initial value problem and Galerkin approximate solutions in subspaces νt spanned by scaled translates of a basic functionϕ. Our goal is to estimate the error whenϕ is in a class of functions which we name Open image in new window . Herer is a regularity parameter andm is related with a property (the Strang and Fix condition) which determines the best order of accuracy in theL2-norm of approximations from νh. Whenm=r, Open image in new window includes all scaling functions corresponding tor-regular multiresolution analyses ofL2(ℝ). We get the exact node values of the given initial condition as coefficients for the approximate initial data. With this procedure, the coefficients of the resulting Galerkin solution can give a very accurate approximation of the exact solution at the node points, provided thatϕ has many vanishing moments. Since this property is not satisfied in general, we work with another modified basic functionϕ* constructed from the integer translates ofϕ. GlobalL2-estimates are also obtained.

On compactly supported spline wavelets and a duality principle

Let ⋯ ⊂ V − 1 ⊂ V 0 ⊂ V 1 ⊂ ⋯ \cdots \subset {V_{ - 1}} \subset {V_0} \subset {V_1} \subset \cdots be a multiresolution analysis of L 2 {L^2} generated by the m m th order B B -spline N m ( x ) {N_m}(x) . In this paper, we exhibit a compactly supported basic wavelet ψ m ( x ) {\psi _m}(x) that generates the corresponding orthogonal complementary wavelet subspaces ⋯ , W − 1 , W 0 , W 1 , … \cdots ,{W_{ - 1}},{W_0},{W_1}, \ldots . Consequently, the two finite sequences that describe the two-scale relations of N m ( x ) {N_m}(x) and ψ m ( x ) {\psi _m}(x) in terms of N m ( 2 x − j ) , j ∈ Z {N_m}(2x - j),j \in \mathbb {Z} , yield an efficient reconstruction algorithm. To give an efficient wavelet decomposition algorithm based on these two finite sequences, we derive a duality principle, which also happens to yield the dual bases { N ~ m ( x − j ) } \{ {\tilde N_m}(x - j)\} and { ψ ~ m ( x − j ) } \{ {\tilde \psi _m}(x - j)\} , relative to { N m ( x − j ) } \{ {N_m}(x - j)\} and { ψ m ( x − j ) } \{ {\psi _m}(x - j)\} , respectively.