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230 results on '"Maskit, Bernard"'

1. On neoclassical Schottky groups

Author

Hidalgo, Ruben A. and Maskit, Bernard

Subjects
Mathematics - Geometric Topology, 30F10, 30F40
Abstract

The goal of this paper is to describe a theoretical construction of an infinite collection of non-classical Schottky groups. We first show that there are infinitely many non-classical noded Schottky groups on the boundary of Schottky space, and we show that infinitely many of these are "sufficiently complicated". We then show that every Schottky group in an appropriately defined relative conical neighborhood of any sufficiently complicated noded Schottky group is necessarily non-classical. Finally, we construct two examples; the first is a noded Riemann surface of genus $3$ that cannot be uniformized by any neoclassical Schottky group (i.e., classical noded Schottky group); the second is an explicit example of a sufficiently complicated noded Schottky group in genus $3$., Comment: http://www.ams.org/journals/tran/2006-358-11/S0002-9947-05-03792-X/S0002-9947-05-03792-X.pdf

Published
2018
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2. Clinical and Research Perspectives on the Therapeutic Conversation: The Case of MS. M.

Author

Jaffe, Charles M., Bucci, Wilma, Maskit, Bernard, and Murphy, Sean

Subjects
SCIENTIFIC community, MEDICAL scientists, CODING theory, RESEARCH personnel, PSYCHOTHERAPY
Abstract

This paper presents a collaboration between a clinician (C.M.J.) and a research team (W.B., B.M., and S.M.) to address the question: At an operational level, what happens in the special form of conversation that is psychotherapy? How can we study, beyond a priori lenses of psychoanalytic models, what we are actually doing when we engage in this process? How can we capture from the linear flow of conversation, the simultaneous, complex, active, interwoven, dimensional emotion schemas that words can only point toward? To address the question, we first present the need for new approaches in the current climate within the clinical and research communities. Next, we address the challenges for clinicians and researchers by using multiple code theory and derived linguistic measures that offer an objective view of the processes of subjectivity. We then apply the research methods to the clinical data to illustrate the yield of the collaborative effort—a yield that captures the connection between the linear flow of words and the arousal, verbal expression, and reflection/integration of emotion schemas without the usual filters of psychoanalytic models of process and change. The project illustrates the critical value of clinicians' perspectives to guide researchers and encourages clinicians to participate in research to advance our field. For researchers, this project represents a "fourth generation" of process research that includes the criteria of video-recorded, transcribed data; the clinician's report of their experience; a theory of how emotion-laden meaning and motivations (emotion schemas) are expressed in the therapeutic conversation; and reliable, valid measures to capture and represent those processes; and that encourages researchers to access the rich contributions of clinicians' understanding. The implication for clinical practice is a new way to look beyond the lens of psychoanalytic models into what is actually unfolding in real time. [ABSTRACT FROM AUTHOR]

Published
2024
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3. Establishing a Method of Systematic and Reliable Analysis of Psychodynamic Process Notes.

Author

Rice, Timothy, Hassan, Yonis, Vickneswaramoorthy, Arthi, Dalal, Natashaa, Peral, Michael, Livshin, Anton, Maskit, Bernard, Bucci, Wilma, and Hoffman, Leon

Subjects
TREATMENT effectiveness, INTRACLASS correlation, CRONBACH'S alpha, CODING theory, INTER-observer reliability
Abstract

Introduction: Process notes contain unique information concerning core elements of a psychodynamic treatment. These elements may be both conscious and unconscious for the author. One element for study is the tendency to which a therapist writes about providing either supportive or expressive interventions. This study sought to establish a method of systematically and reliably identifying the records of therapists' interventions as supportive or expressive. Methods: Three early-career clinicians were trained in the use of a process note intervention rating scale constructed specifically for this study. Quantitative statistical analyses assessed the scale's reliability and internal consistency. Results: Interrater reliability analysis determined at a p of 0.005 a Fleiss's kappa of 0.24 and an intraclass correlation coefficient of 0.264, suggesting a low but statistically significant reliability between the raters. A Cronbach's alpha of 0.67 and a McDonald's omega of 0.53 suggested questionable internal consistency. Discussion: Early-career clinicians can reliably code the manifestations of interventions in psychodynamic process notes as supportive or expressive. Future studies may improve the reliability and internal consistency of the scale, add measures of interpretation content, and evaluate these data in relation to other core elements of process notes, such as the author's emotional engagement as manifested in language measures and clinical outcome. [ABSTRACT FROM AUTHOR]

Published
2024
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8. Experiments suggesting that the distribution of the hyperbolic length of closed geodesics sampling by word length is Gaussian

Author

Chas, Moira, Li, Keren, and Maskit, Bernard

Subjects
Mathematics - Geometric Topology, Primary 57M50, secondary 37E35
Abstract

Each free homotopy class of directed closed curves on a surface with boundary can be described by a cyclic reduced word in the generators of the fundamental group and their inverses. The word length is the number of letters of the cyclic word. If the surface has a hyperbolic metric with geodesic boundary, the geometric length of the class is the length of the unique geodesic. By computer experiments, we investigate the distribution of the geometric length among all classes with a given word length in the pair of pants surface. Our experiments strongly suggest that the distribution is normal.

Published
2013

9. On Optimal 4-Dimensional Metrics

Author

LeBrun, Claude and Maskit, Bernard

Subjects
Mathematics - Differential Geometry, Mathematics - Complex Variables, 53C25, 30F40
Abstract

We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum of five reverse-oriented complex projective planes admits such metrics., Comment: 37 pages, 5 figures

Published
2007

12. Geometric finiteness and uniqueness for Kleinian groups with circle packing limit sets

Author

Keen, Linda, Maskit, Bernard, and Series, Caroline

Subjects
Mathematics - Differential Geometry, Mathematics - Geometric Topology
Abstract

In this paper, we assume that $G$ is a finitely generated torsion free non-elementary Kleinian group with $\Omega(G)$ nonempty. We show that the maximal number of elements of $G$ that can be pinched is precisely the maximal number of rank 1 parabolic subgroups that any group isomorphic to $G$ may contain. A group with this largest number of rank 1 maximal parabolic subgroups is called {\it maximally parabolic}. We show such groups exist. We state our main theorems concisely here. Theorem I. The limit set of a maximally parabolic group is a circle packing; that is, every component of its regular set is a round disc. Theorem II. A maximally parabolic group is geometrically finite. Theorem III. A maximally parabolic pinched function group is determined up to conjugacy in $PSL(2,{\bf C})$ by its abstract isomorphism class and its parabolic elements.

Published
1991

36. Covering Spaces

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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37. B-Groups

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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38. A Trip to the Zoo

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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39. Combination Theorems

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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40. The Geometric Basic Groups

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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41. Groups of Isometries

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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42. Geometrically Finite Groups

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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43. Discontinuous Groups in the Plane

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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44. Fractional Linear Transformations

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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45. Function Groups

Author

Maskit, Bernard, Artin, M., editor, Chern, S. S., editor, Fröhlich, J. M., editor, Heinz, E., editor, Hironaka, H., editor, Hirzebruch, F., editor, Hörmander, L., editor, MacLane, S., editor, Moore, C. C., editor, Moser, J. K., editor, Nagata, M., editor, Schmidt, W., editor, Scott, D. S., editor, Sinai, Ya. G., editor, Tits, J., editor, Waldschmidt, M., editor, Watanabe, S., editor, Berger, M., editor, Eckmann, B., editor, Varadhan, S. R. S., editor, and Maskit, Bernard

Published
1988
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