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Singular Term (singular + term)

Distribution by Scientific Domains

Humanities and Social Sciences	57%

Selected Abstracts

UNIFIED SEMANTICS OF SINGULAR TERMS

THE PHILOSOPHICAL QUARTERLY, Issue 228 2007
John Justice
Singular-term semantics has been intractable. Frege took the referents of singular terms to be their semantic values. On his account, vacuous terms lacked values. Russell separated the semantics of definite descriptions from the semantics of proper names, which caused truth-values to be composed in two different ways and still left vacuous names without values. Montague gave all noun phrases sets of verb-phrase extensions for values, which created type mismatches when noun phrases were objects and still left vacuous names without values. There is a single type of value for all noun phrases that dissolves the difficulties which have beset singular-term semantics. [source]

On a semilinear elliptic equation with singular term and Hardy,Sobolev critical growth

MATHEMATISCHE NACHRICHTEN, Issue 8 2007
Jianqing ChenArticle first published online: 8 MAY 200
Abstract In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with Hardy,Sobolev critical growth and singular term by using variational methods. The result obtained here, even in a particular case, relates with a partial (positive) answer to an open problem proposed in: A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations 177, 494,522 (2001). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

The Semantics of Rigid Designation

RATIO, Issue 1 2003
John Justice
Frege's thesis that each singular term has a sense that determines its reference and serves as its cognitive value has come to be widely doubted. Saul Kripke argued that since names are rigid designators, their referents are not determined by senses. David Kaplan has argued that the rigid designation of indexical terms entails that they also lack referent,determining senses. Kripke's argument about names and Kaplan's argument about indexical terms differ, but each contains a false premise. The referents of both names and indexical terms are determined by reflexive senses. It is reflexive sense that makes these terms rigid designators. [source]

What is Frege's Julius Caesar Problem?

DIALECTICA, Issue 3 2003
Dirk Greimann
This paper aims to determine what kind of problem Frege's famous "Julius Caesar problem" is. whether it is to be understood as the metaphysical problem of determining what kind of things abstract objects like numbers or value-courses are, or as the epistemological problem of providing a means of recognizing these objects as the same again, or as the logical problem of providing abstract sortal concepts with a sharp delimitation in order to fulfill the law of excluded middle, or as the semantic problem of fixing the referents of the corresponding abstract singular terms. It is argued that, for Frege, the Caesar problem is a bundle of related problems of which the semantic problem is the most basic one. [source]

Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003
Seppo Järvenpää
Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source]