EPP: can’t live with it, can’t raise without it

We argue that head movement, as an operation that builds head-adjunction structures in the syntax, has been used to model two empirically distinct classes of phenomena. One class has to do with displacement of heads (fully formed morphological words) to higher syntactic positions, and includes phenomena like verb second and verb initiality. The other class has to do with the construction of complex morphological words and is involved in various types of word formation. Based on the very different clusters of properties associated with these two classes of phenomena, we argue that they each should be accounted for by distinct grammatical operations, applying in distinct modules of the grammar, rather than by the one traditional syntactic head movement operation. We propose that the operation responsible for upward displacement of heads is genuine syntactic movement (Internal Merge) and has the properties of syntactic phrasal movement, including the ability to affect word order, the potential to give rise to interpretive effects, and the locality associated with Internal Merge. On the other hand, word formation is the result of postsyntactic amalgamation, realized as either Lowering (Embick and Noyer 2001) or its upward counterpart, Raising. This operation, we argue, has properties that are not associated with narrow syntax: it is morphologically driven, it results in word formation, it does not exhibit interpretive effects, and it has stricter locality conditions (the Head Movement Constraint). The result is a view of head movement that not only accounts for the empirical differences between the two classes of head movement phenomena, but also lays to rest numerous perennial theoretical problems that have heretofore been associated with the syntactic head adjunction view of head movement. In addition, the framework developed here yields interesting new predictions with respect to the expected typology of head movement patterns.

One major achievement in syntax has been a deep understanding of displacement in terms of Internal Merge. Therefore, displacement types initially resisting that analysis deserve scrutiny. This article investigates one. Latin verse permits tmesis – the division of “words” into nonadjacent pieces. In one subtype, radical tmesis, the cut is not obviously at a morpheme boundary. If it were not, radical tmesis would be theoretically recalcitrant. The article argues, however, that radical tmesis is actually derived by Internal Merge. The cut does occur at a morpheme boundary, despite appearances. Furthermore, the constituent orders radical tmesis produces can be derived syntactically, positing only independently motivated operations. Radical tmesis, then, is syntactic – supporting nonlexicalist frameworks, e.g., Morphology as Syntax. Even displacement types yielding apparently “irregular” outputs, then, can turn out on examination to be products of Internal Merge, a subcase of the elementary structure-building operation Merge – a theoretically welcome result, given minimalist aims.

We examine the structure of compact metal nanoparticles (NPs) forming polyhedral sections of face-centered cubic (fcc) and body-centered cubic (bcc) lattices, which are confined by facets characterized by highly dense [Formula: see text], [Formula: see text] and [Formula: see text] monolayers. Together with the constraint that the NPs exhibit the same point symmetry as the ideal cubic lattice, i.e., [Formula: see text], different types of generic NPs serve for the definition of general compact polyhedral cubic NPs. Their structural properties, such as shape, size and surface facets, can be described by only three integer-valued polyhedral NP parameters [Formula: see text], [Formula: see text] and [Formula: see text]. Corresponding analytical details are discussed with visualization of characteristic examples. While the overall NP shapes are quite similar between the different cubic lattice types, structural fine details differ. In particular, monolayer planes of adjacent NP facets can join at corners and edges which are not occupied by atoms of the ideal lattice. This gives rise to microfacets and narrow facet strips depending on the lattice type. The discussion illustrates the complexity of seemingly simple NPs in a quantitative account. The geometric relationships of the model particles can also be used to classify shapes and estimate sizes of real compact metal NPs observed by experiment.

A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in implicit form, an analytic procedure is derived to obtain the transformed dispersion relation. It is shown that the dispersion relation is generally shifted in the complex $(k,\omega)$ plane, with $k$ the wavenumber and $\omega$ the angular frequency. The value of the shift is obtained explicitly as a function of the perturbation of material constants accounting for loss. The method is shown to predict correctly the transformation of the complex band structure $k(\omega)$. Several models of the dispersion relation near a symmetry point of the Brillouin zone are analyzed. A lower bound for the group velocity, related to the local shape of the band around symmetry points, is derived for each case.

This paper addresses the following question: What kind of properties must the structure-building operation Merge have such that, given a Numeration, the grammar will build the ‘right’ structure and avoid generating ill-formed configurations? The answer we will propose is that Merge should be seen as an asymmetric operation in the sense of relating two items whose sets of morpho-syntactic features are in a proper inclusion relation. In addition, we propose a partition of features into two stacks: categorial features and operator features. This distinction is independently motivated as it feeds into the definition of External Merge and Internal Merge (Chomsky’s 2001). The proper inclusion condition will be assumed to hold for both of these operations, but the set of features under consideration for the evaluation of the proper inclusion relation differs: strictly categorial features for External Merge, and the whole set of features of lexical items for Internal Merge.

This paper makes a specific proposal regarding the structure of idioms as they are listed in the lexicon, which has important ramifications. Specifically, I suggest that first Merge as well as internal Merge can target subconstituents of structures already built by Merge. This creates structures which I call Banyan trees, in which there is more than one undominated node. I suggest that this model, together with certain assumptions about phases and about the functional sequence of syntactic heads, derive important facts about the structure of idioms.

This paper reports a comprehensive phenomenological description and experimental infrared (IR) investigations of the soft-mode-driven lattice instabilities into various commensurately and incommensurately modulated phases of Cs2HgCl4 crystals. Our theoretical analysis shows that the lattice instabilities along the a and c crystallographic directions are related to low-frequency transverse optical (TO) phonon branches of Σ2 and Λ3 symmetry, respectively, which merge together in the center of the Brillouin zone at the point of B3g symmetry. As the temperature decreases both branches fall down, leading first to the direct condensation of the soft TO Σ2 mode in the symmetric Σ direction (k ∥ a*). On the other hand, coupling of the TO and transverse acoustic (TA) modes of Λ3 symmetry causes, at somewhat lower temperatures, a series of frozen modulated commensurate and incommensurate states developing along the symmetric Λ direction (k ∥ c*). Polarized far-infrared (FIR) reflectivity spectra (15–600 cm−1) of Cs2HgCl4 crystals were measured in a broad temperature region, 10–297 K. Despite a rich sequence of structurally modulated phases existing above 163 K we observed rather moderate temperature evolution of IR spectra where only a few new modes of different polarizations have been activated. However, the commensurately modulated phases occurring below 163 K made an essential impact on the spectra of all three polarizations. The process of activation of both the Raman- and the IR-active phonons in the structurally modulated phases is subjected to the phenomenological analysis.

Theoretical analysis on the effects of crystal anisotropy on wiresawing process and application to wafer slicing

A group theoretical analysis of the lattice vibrations in trigonal selenium and tellurium was performed for all symmetry lines and points in the Brillouin zone. For this analysis, the formalism of irreducible multiplier representations has been used.

Based on the principle of maximum overlap, a new simple method is suggested for constructing the symmetry orbitals of arbitrary molecules and the delocalized molecular orbitals of molecules that do not involve the rings with an odd number of atoms. All these orbitals, called “maximum overlap symmetry orbitals,” are determined by an extended maximum overlap criterion and form the bases for the irreducible representations of the molecular point symmetry group. The theoretical analysis and the numerical results show that the obtained molecular orbitals are close to those obtained from the customary LCAO method, and calculation by the proposed method requires less computing time than does the LCAO method, thus illustrating a fact that the method is not only a reasonable approximation of the LCAO method, but simpler and feasible in large molecular systems.

Previous article Next article Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary ConditionsM. J. Moran and R. A. GaggioliM. J. Moran and R. A. Gaggiolihttps://doi.org/10.1137/0116018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff, Hydrodynamics: A study in logic, fact and similitude, Revised ed, Princeton Univ. Press, Princeton, N.J., 1960xi+184 pp. (1 plate) MR0122193 0095.20303 Google Scholar[2] A. J. A. Morgan, The reduction by one of the number of independent variables in some systems of partial differential equations, Quart. J. Math., Oxford Ser. (2), 3 (1952), 250–259 MR0056183 0047.33403 CrossrefGoogle Scholar[3] Aristotle D. Michal, Differential invariants and invariant partial differential equations under continuous transformation groups in normed linear spaces, Proc. Nat. Acad. Sci. U. S. A., 37 (1951), 623–627 MR0043376 0054.04904 CrossrefISIGoogle Scholar[4] M. J. Moran, Masters Thesis, A unification of dimensional and similarity analysis via group theory, Doctoral dissertation, University of Wisconsin, Madison, 1967 Google Scholar[5] R. Manohar, Some similarity solutions of partial differential equations of boundary layer, Tech. Summary Rep., 375, Mathematics Research Center, University of Wisconsin, Madison, 1963 Google Scholar[6] Arthur G. Hansen, Similarity analyses of boundary value problems in engineering, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964xiv+114 MR0178596 0137.22603 Google Scholar[7] Luther Pfahler Eisenhart, Continuous groups of transformations, Dover Publications Inc., New York, 1961ix+301 MR0124008 0096.02103 Google Scholar[8] G. F. D. Duff, Partial differential equations, Mathematical expositions no. 9, University of Toronto Press, Toronto, 1956x+248 MR0078550 0071.30903 Google Scholar[9] R. A. Gaggioli and , M. J. Moran, Group theoretic techniques for the similarity solution of systems of partial differential equations with auxiliary conditions, Tech. Summary Rep., 693, Mathematics Research Center, University of Wisconsin, Madison, 1966 Google Scholar[10] Hermann Schlichting, Boundary layer theory, Translated by J. Kestin. 4th ed. McGraw-Hill Series in Mechanical Engineering, McGraw-Hill Book Co., Inc., New York, 1960xx+647 MR0122222 0096.20105 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Group method analysis for blood‐Mn‐ZnFe 2 O 4 flow and heat transfer under ferrohydrodynamics through a stretched cylinderMathematical Methods in the Applied Sciences, Vol. 28 | 21 June 2022 Cross Ref Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary LayerMathematical Journal of Interdisciplinary Sciences, Vol. 9, No. 2 | 8 June 2021 Cross Ref Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methodsWaves in Random and Complex Media, Vol. 9 | 21 July 2020 Cross Ref Advanced Ground Truth Multimodal Imaging Using Time Reversal (TR) Based Nonlinear Elastic Wave Spectroscopy (NEWS): Medical Imaging Trends Versus Non-destructive Testing ApplicationsRecent Advances in 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The polarized infrared absorption spectrum of single crystals of Am+3(5f6) in LaCl3 has been studied from 0.79 to 16.0 μ. In almost every instance the spectrum is sharp and completely polarized, and appears in definite groupings. Transitions from the ground level, 7F0, to excited levels of the ground term, 7F1, 7F2, 7F3, 7F4, 7F5, and 7F6 have been observed. For the particular point symmetry C3h that is consistent with experiment, magnetic-dipole transitions are observed from the 7F0 level to the 7F1 level, and forced electric-dipole transitions are observed to levels J = 2, 3, 4, 5, and 6. A theoretical analysis is presented for the crystal-field split 7FJ levels. Using four parameters—A20〈r2〉=206 cm—1, A40〈r4〉=—94.1 cm—1, A60〈r6〉=—93.8 cm—1, and A66〈r6〉=1100 cm—1—excellent agreement is obtained between theory and experiment.

The strength of microwave (MW) electric field can be observed with high precision by using the standard electromagnetically induced transparency and Aulter–Towns (EIT-AT) technique, when its frequency is resonant or nearly-resonant with the Rydberg transition frequency. As the detuning of MW field increases, one of the transmission peaks (single peak) is easier to measure due to its increased amplitude. It can be found that the central symmetry point of the two transmission peaks f 1/2 is only related to the detuning of MW field Δ MW and central symmetry point f 0 of resonant MW field, satisfying the relation f 1/2 = Δ MW/2 + f 0. Thus, we demonstrate a single transmission peak method that the MW E-field can be determined by interval between the position of single peak and f 1/2. We use this method to measure continuous frequencies in a band from −200 MHz to 200 MHz of the MW field. The experimental results and theoretical analysis are presented to describe the effectiveness of this method. For 50 MHz < Δ MW < 200 MHz, this method solves the problem that the AT splitting cannot be measured by using the standard EIT-AT techniques or multiple atomic-level Rydberg atom schemes.

A theoretical analysis has been performed by means of the plane-wave expansion method to examine the dispersion properties of photons at high symmetry points of an InP based two-dimensional photonic crystal with square lattice. The Q factors are compared qualitatively. The mechanism of surface-emitting is due to the photon manipulation by periodic dielectric materials in terms of Bragg diffraction. A surface-emitting photonic crystal resonator is designed based on the phenomenon of slow light. Photonic crystal slabs with different unit cells are utilized in the simulation. The results indicate that the change of the air holes can affect the polarization property of the modes. So we can find a way to improve the polarization by reducing the symmetry of the structure.

Single-layer Ag6S2: First principles investigation of a new two-dimensional direct bandgap semiconductor