Single-valued function

Abstract: structure of the latter is not represented (though this characterization is oversimplified in certain respects). Assuming so, the question of how form and meaning are related now resolves to the question of how S-structure is related to D-structure, and how these two levels are related to LF. In substantial part, this is the question of how GF-È representations are related to GF-È representations. The theory of transformational generative grammar (one variety of generative grammar) offers one answer to these questions, an answer that I think is correct in essence though insufficiently general. The answer is that D-structure, determining GF-È, is mapped onto S-structure by a certain class of rules, grammatical transformations, which perform quite independent functions in the grammar apart from expressing this relation. For example, rules of this type relate the quasi-quantifier who in (24) to the abstract variable that it binds (assuming the LF-representation (25) ), and express the fact that in (26) the subject of the predicate is here is the abstract phrase a man whom you know, along with much eise: (24) who did you think would win (25) for which ÷, ÷ a person, you thought [that ÷ would win] (26) a man is here whom you know Thus one basic assumption of transformational generative grammar is that the rules assigning GF-È, the thematically relevant grammatical functions, to elements of surface form are rules of the same kind that serve many other functions in grammar, rather than being rules of some new and distinct type. Early work in this framework attempted to develop some notion of \"grammatical transformation\" rieh enough to capture a wide r nge of properties of surface form and its relation to GF-È. The notion that was developed (e.g., in the references cited above and much related work) was rieh in descriptive power, and correspondingly weak (though not empty) in explanatory power. Since the early 1960s, and particularly in the past ten years, much effort has been devoted to showing that the class of possible transformations can be substantially reduced without loss of descriptive power through the discovery of quite general conditions that all such rules and the representations they operate on and form must meet. Given such conditions, detailed properties of the rules for particular cases need not be stipulated, so that the variety of possible rules can be reduced and explanatory power correspondingly enhanced. Among the ideas that have been explored are, e.g., the A-over-A condition, the condition of recoverability of deletion, Ross's island conditions, Emonds's analysis

Abstract: An estimation approach is described for three-dimensional reconstruction from line integral projections using incomplete and very noisy data. Generalized cylinders parameterized by stochastic dynamic models are used to represent prior knowledge about the properties of objects of interest in the probed domain. The object models, a statistical measurement model, and the maximum a posteriori probability performance criterion are combined to reformulate the reconstruction problem as a computationally challenging nonlinear estimation problem. For computational feasibility, a suboptimal hierarchical algorithm is described whose individual steps are locally optimal and are combined to satisfy a global optimality criterion. The formulation and algorithm are restricted to objects whose center axis is a single-valued function of a fixed spatial coordinate. Simulation examples demonstrate accurate reconstructions with as few as four views in a 135 degrees sector, at an average signal-to-noise ratio of 3.3. >

Abstract: The function inverfc 6 arises in certain diffusion problems when concentration is taken as an independent variable. It enters into a general method of exact solution of the concentration-dependent diffusion equation. An account is given of the properties of this function, and of its derivatives and integrals. The function