33,261 research outputs found

    Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

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    The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.Comment: 12 page

    Weak turbulence theory for collisional plasmas

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    Plasma is an ionized gas in which the collective behavior dominates over the individual particle interactions. For this reason, plasma is often treated as collisionless or collision-free. However, the discrete nature of the particles can be important, and often, the description of plasmas is incomplete without properly taking the discrete particle effects into account. The weak turbulence theory is a perturbative nonlinear theory, whose essential formalism was developed in the late 1950s and 1960s and continued on through the early 1980s. However, the standard material found in the literature does not treat the discrete particle effects and the associated fluctuations emitted spontaneously by thermal particles completely. Plasma particles emit electromagnetic fluctuations in all frequencies and wave vectors, but in the standard literature, the fluctuations are approximately treated by considering only those frequency-wave number regimes corresponding to the eigenmodes (or normal modes) satisfying the dispersion relations, while ignoring contributions from noneigenmodes. The present paper shows that the noneigenmode fluctuations modify the particle kinetic equation so that the generalized equation includes the Balescu-LĂ©nard-Landau collision integral and also modify the wave kinetic equation to include not only the collisional damping term but also a term that depicts the bremsstrahlung emission of plasma normal modes

    Social Exchange and the Maintenance of Order in Status-Stratified Systems

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    This paper examines the role of social exchange in the construction of microorder within status-differentiated relations. How order is constructed and maintained in the context of social inequality is a classic sociological problem. We use a serendipitous finding from a recent experiment as a stimulus for theorizing an important feature of this larger problem of order. The finding is that, in an experiment where African-American females negotiated with white males, the white males received much larger payoffs than the African-American females. Yet, despite substantial power and profit differentiation advantaging white males, both individuals reported positive feelings (pleasure/satisfaction and interest/excitement) to the same degree, which contradicts most research on emotional responses to power. We argue that these similar emotional responses, in the context of substantial payoff inequalities, are due to parallel, joint effects of (a) status processes that create and legitimate initial profit differences and (b) exchange processes that make salient a relationship between the actors during repeated exchange. This explanation integrates notions of status value, referential structure, and legitimacy from status theories with notions of relational cohesion and shared responsibility from exchange theories. Broadly, the paper proposes some ways to productively interweave ideas from status and exchange theories to explain the emergence or maintenance of enduring social inequalities

    The Theory of Relational Cohesion: Review of a Research Program

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    In this paper we analyze and review the theory of relational cohesion and attendant program of research. Since the early 1990s, the theory has evolved to answer a number of basic questions regarding cohesion and commitment in social exchange relations. Drawing from the sociology of emotion and modem theories of social identity, the theory asserts that joint activity in the form of frequent exchange unleashes positive emotions and perceptions of relational cohesion. In turn, relational cohesion is predicted to be the primary cause of commitment behavior in a range of situations. Here we outline the theory of relational cohesion, tracing its development through the present day, and summarize the corpus of empirical evidence for the theory’s claims. We conclude by looking ahead to future projects and discussing some of the more general issues informed by our work
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