


Paper's Title:
Wavelet Frames in Higher Dimensional Sobolev Spaces
Author(s):
Raj Kumar, Manish Chauhan, and Reena
Department of Mathematics,
Kirori Mal College, University of Delhi,
New Delhi110007,
India.
Email: rajkmc@gmail.com
Department of Mathematics,
University of Delhi,
New Delhi110007,
India
Email: manish17102021@gmail.com
Department of Mathematics,
Hans Raj College, University of Delhi,
New Delhi110007,
India
Email: reena.bhagwat29@gmail.com
Abstract:
In this paper, we present sufficient condition for the sequence of vectors to be a frame for H^{s}(R^{d}) are derived. Necessary and sufficient conditions for the sequence of vectors to be tight wavelet frames in H^{s}(R^{d}) are obtained. Further, as an application an example of tight wavelet frames for H^{s}(R^{2}) as bivariate box spline over 3direction are given.
Paper's Title:
Generalised Models for Torsional Spine Reconnection
Author(s):
Ali Khalaf Hussain AlHachami
Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
Email: alhachamia@uowasit.edu.iq
Abstract:
Threedimensional (3D) null points are available in wealth in the solar corona, and the equivalent is probably going to be valid in other astrophysical situations. Ongoing outcomes from sun oriented perceptions and from reproductions propose that reconnection at such 3D nulls may assume a significant job in the coronal dynamics. The properties of the torsional spine method of magnetic reconnection at 3D nulls are researched. Kinematic model are created, which incorporate the term ηJ that is spatially localised around the null, stretching out along the spine of the null. The null point is to research the impact of shifting the level of asymmetry of the null point magnetic field on the subsequent reconnection process where past examinations constantly considered a nonnonexclusive radially symmetric null. Specifically we analyse the rate of reconnection of magnetic flux at the spine of null point. Logical arrangements are determined for the enduring kinematic equation, and contrasted and the after effects of torsional spine reconnection models when the current is restricted in which the Maxwell conditions are illuminated. The geometry of the current layers inside which torsional spine reconnection happen is autonomous on the symmetry of the magnetic field. Torsional spine reconnection happens in a thin cylinder around the spine, with circular crosssegment when the fan eigenvalues are extraordinary. The short axis of the circle being along the solid field bearing. Just as it was discovered that the fundamental structure of the method of attractive reconnection considered is unaffected by changing the magnetic field symmetry, that is, the plasma flow is discovered rotational around the spine of null point. The spatiotemporal pinnacle current, and the pinnacle reconnection rate achieved, are found not to rely upon the level of asymmetry.
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