The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property
The almost everywhere convergence condition similar to the Menchoff-Rademacher condition is obtained for functional series with some weak analogue of the orthogonality property. As a corollary, results related to almost everywhere convergence of series with respect to Riesz systems, Hilbert and Bessel systems, and frames are obtained.
The article deals with the methodology and techniques of lexical typological studies. It focuses on the cross-linguistic analysis of semantic areas that are deeply involved in semantic derivation processes, i.e. they either make a wide use of words coming from other semantic domains (as is the case with pain predicates) or frequently give rise to extended meanings (as e.g. rotation verbs, sound verbs, aqua-motion verbs, adjectives of quality). Based on these data, we propose a general approach to a lexical-typological study – a frame-based approach. It is argued that semantic comparison should rely on a set of conceptual frames that underlie the domains under examination and that can be revealed through the analysis of word combinability in natural texts (corpora, spontaneous speech, etc.). The results obtained by this approach can be easily visualized as semantic maps, in which nodes are associated with frames. This technique is illustrated by several examples, which testify to its applicability not only to well-attested domains of semantic typology (like colors, body parts, cutting and breaking, etc.), but also to less observable and highly metaphorical domains. The typological analysis of these areas is appealing, as it allows not only to investigate their lexical organization, but also to compare, in a systematic way, the semantic shifts observed in different languages.
Russian FrameBank is a bank of annotated samples from the Russian National Corpus which documents the use of lexical constructions (e.g. argument constructions of verbs and nouns). FrameBank belongs to FrameNet-oriented resources, but unlike Berkeley FrameNet it focuses more on the morphosyntactic and semantic features of individual lexemes rather than the generalized frames, following the theoretical approaches of Construction Grammar (Ch. Fillmore, A. Goldberg, etc.) and of Moscow Semantic School (Ju. D. Apresjan, E. V. Paducheva, etc.).
The paper presents clustering experiments on Russian verbs based on the statistical data drawn from the Russian FrameBank (framebank.ru). While lexicology has essentially abandoned the idea of syntactic transformations as the primary basis for grouping verbs into semantic classes (Apresjan 1967, Levin 1993), the hypothesis of the same lexical and syntactic distributional profiles underlying lexical clusters is still attractive. In computational linguistics, some attempts have been made to obtain verb classes for English, German and other languages using observable morpho-syntactic and lexical properties of context (Dorr and Jones 1996; Lapata 1999; Schulte im Walde 2006; Lenci 2014, among others). Our experiments on semantic classification of Russian verbs are based on two types of tags embedded in the annotation of argument constructions: a) semantic roles and b) morpho-syntactic patterns. The domain of speech verbs is classified automatically on vectors, and the resulting clusters are contrasted against Babenko (2007)’s semantic classes and three other manual classifications. The classes within the domain of possessive verbs are constructed using rule-based solutions and evaluated against Berkeley FrameNet verb clusters. We conclude that clustering on morpho-syntactic (pure formal) patterns loses the race to more intelligent approaches which take into account semantic roles.
This book presents a systematic study of multivariate wavelet frames with matrix dilation, in particular, orthogonal and bi-orthogonal bases, which are a special case of frames. Further, it provides algorithmic methods for the construction of dual and tight wavelet frames with a desirable approximation order, namely compactly supported wavelet frames, which are commonly required by engineers. It particularly focuses on methods of constructing them. Wavelet bases and frames are actively used in numerous applications such as audio and graphic signal processing, compression and transmission of information. They are especially useful in image recovery from incomplete observed data due to the redundancy of frame systems. The construction of multivariate wavelet frames, especially bases, with desirable properties remains a challenging problem as although a general scheme of construction is well known, its practical implementation in the multidimensional setting is difficult.
Another important feature of wavelet is symmetry. Different kinds of wavelet symmetry are required in various applications, since they preserve linear phase properties and also allow symmetric boundary conditions in wavelet algorithms, which normally deliver better performance. The authors discuss how to provide H-symmetry, where H is an arbitrary symmetry group, for wavelet bases and frames. The book also studies so-called frame-like wavelet systems, which preserve many important properties of frames and can often be used in their place, as well as their approximation properties. The matrix method of computing the regularity of refinable function from the univariate case is extended to multivariate refinement equations with arbitrary dilation matrices. This makes it possible to find the exact values of the Hölder exponent of refinable functions and to make a very refine analysis of their moduli of continuity.
The article focuses upon the main frames created by leading American politicians during the latest presidential campaign to influence the nation. The work aims at the interconnection between mental and language structures in political discourse. The corpus analysis of concepts and frames in Obama and Romney texts according to conceptual metaphor theory of George Lakoff demonstrates that during 2012 presidential campaign Barack Obama successfully applied the basic conceptual metaphor of STATE AS THE NURTURANT PARENT in contrast with the basic metaphor of STATE AS THE STRICT FATHER used by the Republican leader Mitt Romney.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.