Incommensurability in Second Language Acquisition Approaches

Researchers in the field of Second Language Acquisition （SLA） have been taking different routes. Some researchers make linguistic-cognitive issues their inquire object and pursue objectivity with quantitative research methods. Other researchers regard the social context of activity as an essential characteristic of learning and teaching. These groups of researchers make use of qualitative research methods like case study, grounded theory, narrative inquiry, and ethnography. There are many other routes that SLA researchers have taken, but the two just mentioned are perhaps the most predominant ones and the ones that are most easily contrasted. The present paper explores the disparity between the different research paths from the perspective of philosophy of science echoing the notion of incommensurability. In this paper the author argues that the differences between different SLA perspectives are not only commensurable but wholesome for the development of SLA.

Kuhnian Understanding of Incommensurability and Implications of Paradigmatic Conception of Knowledge in International Relations

In international relations theory （maybe more than in any other discipline of social sciences）, the paradigmatic construction of Thomas Kuhn and his model of incommensurability might be applied to the theoretical interpretation of phenomena; and it is one of the cornerstones of the methodological toolkit for the interpretation in this field. The paper explores the reason why Kuhn＇s understanding of incommensurability seems to be necessary for the conception of knowledge in international relations： the concept of incommensurability can be considered typical as it is meant to indicate a conflict, of one form or another, between theories. And the discipline of international relations is more than a perfect ground for considering this concept when one is having in mind the high degree of polarized debate among rivalry theoretical schools （for interpreting and describing the identical phenomena） that is present from the very beginning of the discipline. Recalling the Kuhnian conception of science in paradigmatic view with an aim for understanding--international relations theory, the paper analyzes furthermore his rejection of the traditional dichotomy between “objectivisn”and ＂subjectivism.＂

Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model

Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.

Kuhn and Taxonomies of History

This paper introduces the idea that if theories of history generate different taxonomies of history they too are incommensurable. I argue this is unavoidable for Kuhn given what he says about incommensurability and 1 investigate the consequences in relation to reflexivity, justification, and paradox for Kuhn＇s account of science. I want to do this on two levels, firstly looking at different possibilities for characterising individual paradigms. I will look at some examples from ancient and early modem astronomy as here it is clearest that paradigms can be characterised in different ways and that this has important consequences. I will argue in particular that Kuhn＇s characterisation of the paradigm for astronomy which emerges from antiquity （geocentrism） is favourable to his general account of the history of science, but that there is a very plausible and extremely damaging alternative. I argue that these differing characterisations generate differing, incommensurable taxonomies of the history of astronomy, with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice. If so, Kuhn then has problems with generating an adequate decision making protocol for choosing between the two paradigm characterisations. That is problematic in itself, but I also argue this problem is systemic and affects the evidence needed for Kuhn to justify his general account of the history of science. I also want to investigate the implications of differing taxonomies of the history of science at a more abstract level. Kuhn＇s general theory of the history of science generates a taxonomy of the history of science, as do other theories such as those of Popper and of gradualism. If so, the incommensurability involved here, again with attendant ＂local holism,＂ untranslatability of key terms and issues of theory choice, leads to issues of paradox and justification for Kuhn＇s general account of the history of science. With this broader understanding of taxonomic issues, some important Kuhn statements about scientific theories become self-referential, again generating problems of paradox and justification.

Irrationality in Scientific Development？

The paper discusses several wide-spread misunderstandings of Kuhn＇s theory of scientific development, most prominently the ascription that he conceives of scientific development as irrational. The core of this ascription is an assessment of incommensurability as implying the lack of any rational possibility of theory comparison. This is supposed to be due to Gestalt switches and a quasi-religious element of conversion in theory change. Accordingly, scientific revolutions cannot be a serious matter for philosophical analysis; they furthermore foreclose any scientific progress. It is shown that such images of Kuhn＇s theory rest on deep misunderstandings that are partly due to Kuhn＇s writing style.

Modeling of Catfish Farm Using Lexicographic Linear Goal Programming

In this paper, a fish farm was modeled using the Lexicographic linear goal programming approach due to incommensurability in objectives. The study considered the fish farming plan with two sizes of catfish from stocking to harvesting at four-month intervals. The multi-objective goals developed are required raw materials feed, water, light (resource utilization), sales revenue, profit realized, labor utilization, production costs, and pond utilization. The developed model was tested using related data collected from the farm records with the use of TORA 2007 software. The compromised solution from the results showed that the developed model is an efficient tool for decision-making process in the fish farm business organization.

Multiscale mechanics of noncovalent interface in graphene oxide layered nanocomposites

Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered nanocomposites, shear-lag analysis is usually implemented to evaluate the capability of interfacial loading transfer. Here, we introduce a multiscale shear-lag model that correlates macroscale mechanical properties with the molecular mechanisms to quantify the effects of interfacial configuration in graphene oxide(GO) layered nanocomposites. By investigating the mechanical responses of commensurate and incommensurate interfaces, we identify that the commensurate interface exhibits a pronounced size effect due to the nucleation and propagation of interfacial defects, whereas the incommensurate interface displays uniform deformation. Our predictions are further validated through large-scale molecular dynamics simulations for GO layered nanocomposites. This work demonstrates how size effects and interfacial configurations can be exploited to fabricate layered nanocomposites with superior mechanical properties despite relying on weak noncovalent interfaces.

Incommensurate Antiferromagnetism in the Extended t-J Model

The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighborhopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamicalspin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spincorrelation in the t-t'-J model is the same as in the case of t-J model.

The Critical Properties of a Modulated Quantum sine—Gordon Model

A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .

Incommensurate Magnetic Order in Sm_(3)BWO_(9)with Distorted Kagome Lattice

We investigate the magnetic ground state of Sm_(3)BWO_(9)with a distorted kagome lattice.A magnetic phase transition is identified at T_(N)=0.75 K from the temperature dependence of specific heat.From 11B nuclear magnetic resonance measurements,an incommensurate magnetic order is shown by the double-horn type spectra under a c-axis magnetic field,and absence of line splitting is observed for field oriented within the ab-plane,indicating the incommensurate modulation of the internal field strictly along𝑐c-axis.From the spin dynamics,the critical slowing-down behavior is observed in the temperature dependence of 1/T_(1)with𝜇_(μ0)H⊥c-axis,which is completely absent in the case with𝜇_(μ0)H||c-axis.Based on the local symmetry of 11B sites,we analyze the hyperfine coupling tensors and propose two constraints on the possible magnetic structure.The single ion anisotropy should play an important role in determination of contrasting ground states of Sm_(3)BWO_(9) and Pr_(3)BWO_(9).

Incommensurate Antiferromagnetism in the Extended t－J Model

The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J modelin the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighborhopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamicalspin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spincorrelation in the t-t'-J model is the same as in the case of t-J model.

Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

We investigate the synchronization of a class of incommensurate fractional-order chaotic systems, and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory, the fractional order differential inequality, and the adaptive strategy. This synchronization approach is simple, universal, and theoretically rigorous. It enables the synchronization of O fractional-order chaotic systems to be achieved in a systematic way. The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.

Misfit-layered compound PbTiS_3 with incommensurate modulation:Transmission electron microscopy analysis and transport properties

The microstructural characteristic of the misfit-layered compound PbTiS3 has been studied with transmission electron microscopy. All the incommensurate modulation-induced satellite spots and main diffraction spots of basic sublattices can be indexed systematically with a superspace group method. Finally, the relationship between the electronic transport properties and the crystal structure is discussed.

INCOMMENSURATE AND COMMENSURATE PHASE TRANSITIONS IN Ti-Ni-Fe ALLOY

Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,and the second one due to the soft-mode of driving the martensitic transformation.The starting point,R_s,and finishing point,R_f,of the commensurate phase transition of the alloy have been determined.

CMC d-p π Bond in Solid State(Ⅱ) Band Structure and Metallic Properties in Incommensurate Misfit Layer Compounds(MS)_xTS_2(M=Sn, Pb and La; T=V,Nb,Ta and Cr)

In this paper, we present Continuous Multiple Center(CMC) d-p πbond in TS_2 slabs on the basis of Extended Huckle calculation for incommensurate misfit compounds (MS)_xTS_2(where M=Pb, Sn and La; T=V,Nb,Ta, Cr), and put forwards the trigonal prismatic coordination CMC d-p π conductive model. According to this model the conductivity of (MS)_xTS_2 series and the similarity between (MS)_xTS_2 and Na_xTS_2 series compounds in metallic behaviors can be explained successfully. Some relations between metallic behaviors and CMC d-p π bond (or band) are found.

Full Euclidean Algorithm by Means of a Steady Walk

Let x and y be two positive real numbers with x < y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case that y/x is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.

Reversion of Incommensurate Modulation in Cubic Lazurite: Example of Reversible Forced Equilibrium?

The sample of cubic lazurite, collected in the Baikal region, with incommensurately 3D modulated (ITM) structure has been studied by the method of high-temperature X-ray powder diffraction. At short time of annealing in high-temperature diffraction experiment the modulation recovery proceeds during cooling down the sample to room temperature. The identity of the period of both initial and recovered modulation demonstrates that the system has a structural memory. The acquired results are interpreted through comparison of thermal behavior of lazurite, sodalite and quartz structures. It is supposed that two kinetically different and thermally activated processes proceed under heating: 1) reversible framework expansion due to Si-O-Al angle increase, and 2) equalizing of periodic local distortions via the diffusion-controlled transfer of cage ions between adjacent subcells. The second process seems to be much slower than the first one, especially at lower temperatures. With increasing temperature, both processes are activated. However, the framework expands more rapidly than the cage clusters migrate, and the periodic distortions of the framework are aligned. Under lower temperatures, the framework shrinks and again accommodates to the configuration of cage cations (clusters), which may be changed at high temperature and sufficient time or may not at lower temperature, short time, unfavorable SO2 fugacity values. In the first case the modulation disappears entirely, while in the second case it arises again. The probable reason for ITM formation is the balance of counteracting energetic terms: the elastic strain energy of structure deformation and the energy of cluster ordering providing the state of forced equilibrium. The excess free energy due to structure distortion is compensated by the increment associated with the cluster ordering process. However, no significant variations in sulphur anion speciation for different degrees of modulation retention were observed by XPS S 2p. This may be due to the ordering of Na- and Ca-containing clusters rather than the clusters with different sulphur species. ITM reversion is considered as an example of reversible forced equilibrium with completely reproducible forcing factor.

Crystallography in Spaces E², E³, E⁴, E⁵...N⁰I Isomorphism Classes: Properties and Applications to the Study of Incommensurate Phase Structures, Molecular Symmetry Groups and Crystal Families of Space E<sup>5</sup

This paper mainly consists of the classification of all crystallographic point groups of n-dimensional space with n ≤ 6 into different isomorphism classes. An isomorphism class is defined by a type of finite mathematic group;for instance, the different types of mathematic groups have been well defined and studied by Coxeter. This classification may be used in the investigation of several domains of crystallography such as the study of the incommensurate phases, the quasi crystals … Indeed, each mathematic substitution group characterizes an isomorphism class of crystallographic point groups (spaces E2 or E3), of point groups of super crystals (spaces E4 or E5), and of molecular symmetry groups (spaces E2 or E3). This mathematic group gives interesting information about: 1) the incommensurate phase structures and their phase transitions according to the Landau’s theory in their super spaces E4, E5, E6, ···;2) the molecular symmetry group of chemisorbed molecules in space E2 (paragraph 2) or of the molecular crystal or solution in view of studying the molecule structure or its rotations or vibrationsin space E3;3) the geometric polyhedron symmetry groups as the regular rhombohedron in space E3, the rhombotope in space E4 or the rhombotope in space E5. Then, thanks to the isomorphism classes, we shall give properties of some crystal families that we have not published up to now. This formalism may be used to study crystal families in n-dimensional space with n > 6.

On fractional discrete financial system:Bifurcation,chaos,and control

The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.

Structural superlubricity at homogenous interface of pentagraphene

Two-dimensional(2D)van der Waals layered materials have been widely used as lubricant.Penta-graphene(PG),a 2D carbon allotrope exclusively composed of irregular carbon pentagons has recently been predicted to have superlubricating property.In the present study,by combining the molecular dynamics simulation and first-principles calculations,we investigated the frictional property of PG in both commensurate and incommensurate contacts.Our calculations show the ultra-low friction at the interface of relatively rotated bilayer PG with twist angles of more than 10°away from the commensurate configuration.Meanwhile,our calculations demonstrate the isotropy of the ultra-low friction at the interface of incommensurate contact,in contrast to the anisotropic of the commensurate contacting interface.Additionally,the evolution of friction force and the fluctuation of potential energy along sliding path correlate closely with the interface’s structure.The energetics and charge density explain the difference between the friction at the interfaces of the commensurate and incommensurate contacts.Not only that,we found the correlation between the intrinsic structural feature and interlayer binding energy.Importantly,our findings on the retainment of the ultra-low friction under work conditions indicates that the superlubricating state of PG has good practical adaptability.