Moment determinants as isomonodromic tau functions

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.Comment: 24 page

Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities

In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy) problem corresponding to Frobenius structures on Hurwitz spaces. We find a solution to this Riemann-Hilbert problem in terms of integrals of certain meromorphic differentials over a basis of an appropriate relative homology space, study the corresponding monodromy group and compute the monodromy matrices explicitly for various special cases.Comment: final versio

Memory Effects and Scaling Laws in Slowly Driven Systems

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A mathematical theory is outlined, which allows to show existence of hysteresis cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators

General Argyres-Douglas Theory

We construct a large class of Argyres-Douglas type theories by compactifying six dimensional (2,0) A_N theory on a Riemann surface with irregular singularities. We give a complete classification for the choices of Riemann surface and the singularities. The Seiberg-Witten curve and scaling dimensions of the operator spectrum are worked out. Three dimensional mirror theory and the central charges a and c are also calculated for some subsets, etc. Our results greatly enlarge the landscape of N=2 superconformal field theory and in fact also include previous theories constructed using regular singularity on the sphere.Comment: 55 pages, 20 figures, minor revision and typos correcte

The single morpheme -ed/-en of the English past/passive

All English regular verbs and about half its irregular verbs have the same form for the finite past tense and the past participle. The finite past tense is different from the participle only for a closed class of about 100 irregular verbs. These latter can be analyzed by a lexical device of wide-ranging applicability called Alternative Realization. All other Past forms of Vs, finite and non-finite, can then be derived from a single morpheme -ed which appears in two contexts: one when V is finite and one when it is selected by a semantically empty stative verb, have or be. There is also a third use of -ed to form passive participles, in both verbal and adjectival passives.The paper presents a formalized system of selection features for lexical items including but going beyond classical subcategorization. This system permits formulating a single full lexical entry for the suffix -ed that covers all its uses. The final version of this entry exemplifies how to specify Alternative Realization, uninterpretability of categories and disjunctive contexts, and independently justifies each of these notations

Lessons from the English auxiliary system

The English auxiliary system exhibits many lexical exceptions and subregularities, and considerable dialectal variation, all of which are frequently omitted from generative analyses and discussions. This paper presents a detailed, movement-free account of the English Auxiliary System within Sign-Based Construction Grammar (Sag 2010, Michaelis 2011, Boas & Sag 2012) that utilizes techniques of lexicalist and construction-based analysis. The resulting conception of linguistic knowledge involves constraints that license hierarchical structures directly (as in context-free grammar), rather than by appeal to mappings over such structures. This allows English auxiliaries to be modeled as a class of verbs whose behavior is governed by general and class-specific constraints. Central to this account is a novel use of the feature aux, which is set both constructionally and lexically, allowing for a complex interplay between various grammatical constraints that captures a wide range of exceptional patterns, most notably the vexing distribution of unstressed do, and the fact that Ellipsis can interact with other aspects of the analysis to produce the feeding and blocking relations that are needed to generate the complex facts of EAS. The present approach, superior both descriptively and theoretically to existing transformational approaches, also serves to undermine views of the biology of language and acquisition such as Berwick et al. (2011), which are centered on mappings that manipulate hierarchical phrase structures in a structure-dependent fashion

Passives and Se Constructions

In this chapter we discuss some of the main properties of constructions involving participial passives, passive se, and impersonal se in Portuguese, focusing on its two main varieties, European and Brazilian Portuguese (henceforth EP and BP, respectively).1 When the two dialects differ, we will provide the relevant judgments each dialect assigns to the data under discussion by using the abbreviations EP and BP. The chapter is organized in five sections. Section 2 deals with participial passives, distinguishing between adjectival and verbal passives and between the participial forms of passives and compound tenses. Section 3 focuses on passive se and impersonal se constructions, comparing them with verbal passives when appropriate. Section 4 concludes the paper.info:eu-repo/semantics/publishedVersio