Let f(z) be any transcendental entire function. Let r, denote the absolute value of the zero z. of f '(z) which is nearest to the origin. Alander, Erdö's and Renyi, and Polya have investigated the relation between r, and the growth of the function /(z). Let s, denote the ... fz largest disk about the origin where / (z) is univalent. Boas, Levinson, and Polya have obtained some relations between...

This paper investigates the problem of financing infrastructure over time when the number of users also changes. The problem is confronted in many fast growing communities desiring to coordinate the timing of infrastructure and development, yet still achieve economies of scale where they exist. The temporal free rider problem is defined; whereby the group that finances the construction at a giv...

Introduction. Since the publication of Levinson's results concerning the first boundary value problem for eAu+A(x,y)ux+B(x,y)uy + C(x, y)u = D(x, y) [6], there have been a number of other papers dealing with related two-dimensional problems [l; 3; 7]. More recently a paper by O. A. Ladyjzenskaya has appeared in which an ra-dimensional extension of the original problem is discussed [4].2 It is f...

We prove a stability estimate related to the multi-dimensional Borg-Levinson theorem of determining a potential from spectral data: the Dirichlet eigenvalues λk and the normal derivatives ∂φk/∂ν of the eigenfunctions on the boundary of a bounded domain. The estimate is of Hölder type, and we allow finitely many eigenvalues and normal derivatives to be unknown. We also show that if the spectral ...

In this paper, we deal with the inverse spectral problem for the equation −(pu′)′ + qu = λρu on a finite interval (0, h). We give some uniqueness results on q and ρ from the Gelfand spectral data, when the coefficients p and ρ are piecewise Lipschitz and q is bounded. We also prove an equivalence result between the Gelfand spectral data and the Borg–Levinson spectral data. As a consequence, we ...

Musical Platonists identify musical works with abstract sound structures but this implies that they are not created but only discovered. Jerrold Levinson adapts Platonism to allow for creation by identifying musical works with indicated sound structures. In this paper I explore the similarities between Levinson’s view and Kit Fine’s theory of qua objects. Fine offers the theory of qua objects a...

In this work we are investigating the learning benefits of e-Learning principles (a) within the context of a web-based intelligent tutor and (b) in the “wild,” that is, in real classroom (or homework) usage, outside of a controlled laboratory. In the study described in this paper, we focus on the benefits of politeness, as originally formulated by Brown and Levinson and more recently studied by...

According to standard pragmatics, we should account for conversational implicatures in terms of Grice’s (1967) maxims of conversation. Neo-Griceans like Atlas & Levinson (1981) and Horn (1984) seek to reduce those maxims to the so-called Q and I-principles. In this paper I want to argue that (i) there are major problems for reducing Gricean pragmatics to these two principles, and (ii) in fact, ...

In most countries, environmental regulation focuses on local pollution, which causes damages near the emission source, while regulation on global pollutants such as greenhouse gases (GHG) has been slow. Theoretically, local and global pollutants can either be substitutes or complements in production, implying that local pollution regulation may either intensify or reduce global warming concerns...