Partial Exact Controllability of a Nonlinear System

Sin resume

High order difference schemes for the system of two space second order nonlinear hyperbolic equations with variable coefficients

AbstractIn this paper, we develop implicit difference schemes of O(k4 + k2h2 + h4), where k > 0, h > 0 are grid sizes in time and space coordinates, respectively, for solving the system of two space dimensional second order nonlinear hyperbolic partial differential equations with variable coefficients having mixed derivatives subject to appropriate initial and boundary conditions. The proposed difference method for the scalar equation is applied for the solution of wave equation in polar coordinates to obtain three level conditionally stable ADI method of O(k4 + k2h2 + h4). Some physical nonlinear problems are provided to demonstrate the accuracy of the implementation

R.K. Narayan: Straddling Metropole and Malgudi

“In her essay ‘Resistance through Sub/Mission in the Novels of R. K. Narayan,’ Hyacinth Cynthia Wyatt argues that ‘among Indian authors writing in English, R. K. Narayan was among the first to resist Western cultural dominance’…

Delayed Blanch Phenomenon in Children: Reevaluation Of 5-Year-old Children Originally Tested as Newborns

A follow-up study involving 50 children (who were 5 years old) from an original group of 100 who had been tested as newborns was carried out using the delayed blanch phenomenon. The reaction persisted in 78%. No correlation could be found between personal and family history of allergy and the presence or absence of the delayed blanch phenomenon

A dynamic and multifunctional account of middle‐range theories

This article develops a novel account of middle‐range theories for combining theoretical and empirical analysis in explanatory sociology. I first revisit Robert K. Merton’s original ideas on middle‐range theories and identify a tension between his developmental approach to middle‐range theorizing that recognizes multiple functions of theories in sociological research and his static definition of the concept of middle‐range theory that focuses only on empirical testing of theories. Drawing on Merton's ideas on theorizing and recent discussions on mechanism‐based explanations, I argue that this tension can be resolved by decomposing a middle‐range theory into three interrelated and evolving components that perform different functions in sociological research: (i) a conceptual framework about social phenomena that is a set of interrelated concepts that evolve in close connection with empirical analysis; (ii) a mechanism schema that is an abstract and incomplete description of a social mechanism; and (iii) a cluster of all mechanism‐based explanations of social phenomena that are based on the particular mechanism schema. I show how these components develop over time and how they serve different functions in sociological theorizing and research. Finally, I illustrate these ideas by discussing Merton’s theory of the Matthew effect in science and its more recent applications in sociology.This article develops a novel account of middle‐range theories for combining theoretical and empirical analysis in explanatory sociology. I first revisit Robert K. Merton’s original ideas on middle‐range theories and identify a tension between his developmental approach to middle‐range theorizing that recognizes multiple functions of theories in sociological research and his static definition of the concept of middle‐range theory that focuses only on empirical testing of theories. Drawing on Merton's ideas on theorizing and recent discussions on mechanism‐based explanations, I argue that this tension can be resolved by decomposing a middle‐range theory into three interrelated and evolving components that perform different functions in sociological research: (i) a conceptual framework about social phenomena that is a set of interrelated concepts that evolve in close connection with empirical analysis; (ii) a mechanism schema that is an abstract and incomplete description of a social mechanism; and (iii) a cluster of all mechanism‐based explanations of social phenomena that are based on the particular mechanism schema. I show how these components develop over time and how they serve different functions in sociological theorizing and research. Finally, I illustrate these ideas by discussing Merton’s theory of the Matthew effect in science and its more recent applications in sociology.Peer reviewe

Homogeneous nucleation of a non-critical phase near a continuous phase transition

Homogeneous nucleation of a new phase near a second, continuous, transition, is considered. The continuous transition is in the metastable region associated with the first-order phase transition, one of whose coexisting phases is nucleating. Mean-field calculations show that as the continuous transition is approached, the size of the nucleus varies as the response function of the order parameter of the continuous transition. This response function diverges at the continuous transition, as does the temperature derivative of the free energy barrier to nucleation. This rapid drop of the barrier as the continuous transition is approached means that the continuous transition acts to reduce the barrier to nucleation at the first-order transition. This may be useful in the crystallisation of globular proteins.Comment: 6 pages, 1 figur

Shear free solutions in General Relativity Theory

The Goldberg-Sachs theorem is an exact result on shear-free null geodesics in a vacuum spacetime. It is compared and contrasted with an exact result for pressure-free matter: shear-free flows cannot both expand and rotate. In both cases, the shear-free condition restricts the way distant matter can influence the local gravitational field. This leads to intriguing discontinuities in the relation of the General Relativity solutions to Newtonian solutions in the timelike case, and of the full theory to the linearised theory in the null case. It is a pleasure to dedicate this paper to Josh Goldberg.Comment: 17 pages, no figures. For GRG special issue in honor of Josh Goldber

Joint resummation in electroweak boson production

We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at measured boson momentum Q_T. This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero Q_T, which can be compared to resummation carried out directly in Q_T space. From the structure of the resummed expressions, we also determine the form of nonperturbative corrections to the cross section and implement these into our analysis. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.Comment: 27 pages, LaTeX, 8 figures as eps files. Some additions to earlier version, this version as published in Phys. Rev. D66 (2002) 01401

Event Shape/Energy Flow Correlations

We introduce a set of correlations between energy flow and event shapes that are sensitive to the flow of color at short distances in jet events. These correlations are formulated for a general set of event shapes, which includes jet broadening and thrust as special cases. We illustrate the method for electron-positron annihilation dijet events, and calculate the correlation at leading logarithm in the energy flow and at next-to-leading-logarithm in the event shape.Comment: 43 pages, eight eps figures; minor changes, references adde

Recoil and Threshold Corrections in Short-distance Cross Sections

We identify and resum corrections associated with the kinematic recoil of the hard scattering against soft-gluon emission in single-particle inclusive cross sections. The method avoids double counting and conserves the flow of partonic energy. It reproduces threshold resummation for high-p_T single-particle cross sections, when recoil is neglected, and Q_T-resummation at low Q_T, when higher-order threshold logarithms are suppressed. We exhibit explicit resummed cross sections, accurate to next-to-leading logarithm, for electroweak annihilation and prompt photon inclusive cross sections.Comment: minor modifications of the text, some references added. 51 pages, LaTeX, 6 figures as eps file