A solar radio moving type Ⅳ burst of expanding arches type involving multi-sources

A complex solar radio moving type IV burst was observed on 23 September 1998 with the broadband (1.0-2.0 GHz and 2.6-3.8 GHz) spectrometers with high temporal and spectral resolutions at National Astronomical Observatories of China (NAOC). Comparing to the high spatial resolution data of Siberian Solar Radio Telescope (SSRT), we find that this burst is a rare type of moving type IV burst which is caused by the expanding arches, and the spatial structure oscillations of the radio sources are related with the time structure pulsations of the radio emission. Furthermore, the burst is associated with the multiple quasi-periodic long-term pulsations, and this suggests the existence of multi-scale magnetic structures in a large expanding coronal arch. We think the moving type IV burst is due to the synchrotron emission of the energetic electrons trapped in the expanding arch, and the multiple quasi-periodic pulsations are due to the second harmonic plasma emission.     

Nonlinear calibration and data processing of the solar radio burst

The processes of the sudden energy release and energy transfer, and particle accelerations are the most challenge fundamental problems in solar physics as well as in astrophysics. Nowadays, there has been no direct measurement of the plasma parameters and magnetic fields at the coronal energy release site. Under the certain hypothesis of radiation mechanism and transmission process, radio measurement is almost the only method to diagnose coronal magnetic field. The broadband dynamic solar radio spectrometer that has been finished recently in China has higher time and frequency resolutions. Thus it plays an important role during the research of the 23rd solar cycle in China. Sometimes when there were very large bursts, the spectrometer will be overflowed. It needs to take some special process to discriminate the instrument and interference effects from solar burst signals. According to the characteristic of the solar radio broadband dynamic spectrometer, we developed a nonlinear calibration method to deal with the overflow of instrument, and introduced channel-modification method to deal with images. Finally the interference is eliminated with the help of the wavelet method. Here we take the analysis of the well-known solar-terrestrial event on July 14th, 2000 as the example. It shows the feasibility and validity of the method mentioned above. These methods can also be applied to other issues.     

Nonlinear calibration and data processing of the solar radio burst

The processes of the sudden energy release and energy transfer, and particle accelerations are the most challenge fundamental problems in solar physics as well as in astrophysics. Nowadays, there has been no direct measurement of the plasma parameters and magnetic fields at the coronal energy release site. Under the certain hypothesis of radiation mechanism and transmission process, radio measurement is almost the only method to diagnose coronal magnetic field. The broadband dynamic solar radio spectrometer that has been finished recently in China has higher time and frequency resolutions. Thus it plays an important role during the research of the 23rd solar cycle in China. Sometimes when there were very large bursts, the spectrometer will be overflowed. It needs to take some special process to discriminate the instrument and interference effects from solar burst signals. According to the characteristic of the solar radio broadband dynamic spectrometer, we developed a nonlinear calibration method to deal with the overflow of instrument, and introduced channel-modification method to deal with images. Finally the interference is eliminated with the help of the wavelet method. Here we take the analysis of the well-known solar-terrestrial event on July 14th, 2000 as the example. It shows the feasibility and validity of the method mentioned above. These methods can also be applied to other issues.     

Interpretation of solar microwave C type burst spectra in terms of magnetic nonhomogeneity

The solar radio spectra of the gyro-synchrotron radiation without absorption from mildly relativistic non-thermal electron have been presented using the model with the spherical symmetric nonhomogeneity. These spectra have the following features: (i) Twists and turns of the spectra, which appear at the joint between the medium and high frequencies, (ii) Flux density drop at the lower frequencies. Even if there are no absorption in the radio sources, flux density drop at the lower frequencies is still present because of magnetic nonhomogeneity. (iii) These theoretical spectra belong to C type. This provides us a new interpretation for the observed solar burst C type spectra. Project supported by the National Natural Science Foundation of China.     

A characterization of bounded symmetric domains of type IV

Let ?? be a bounded symmetric domain of type IV and dimension bigger than four. We show that a Stein manifold of the same dimension as ?? and with the same automorphism group is biholomorphic to ??.     

Theory of oscillation type viscometers IV: A thick disk

The viscous drag exerted by a fluid on an oscillating disk is determined by methods similar to those used in Part III. The present paper differs from Part III in that the boundary layer thickness is assumed here to be small compared with both the thickness and the radius of the disk. An extrapolation of the formulae derived here agree sufficiently well, however, with those derived for the thin disk (boundary layer thickness large compared with the thickness but small compared with the radius) that it is possible to make an interpolation between the present formulae and those of Part III that will permit the evaluation of the drag for arbitrary shape disks provided the boundary layer thickness is small compared with the radius.

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Zusammenfassung Der Einfluss der Zähigkeitskräfte auf eine in einer Flüssigkeit schwingende Scheibe wird nach den gleichen Methoden wie in Tiel III behandelt. Jedoch wird im Unterschied dazu vorausgesetzt, dass die Grenzschichtdicke klein ist im Verhältnis zur Dicke und zum Radius der Scheibe. Die abgeleiteten Formeln lassen sich mit gutem Ergebnis für die dünne Scheibe extrapolieren (hier ist die Grenzschichtdicke jedoch gross, verglichen mit der Scheibendicke, aber klein gegenüber dem Radius), so dass es möglich ist, zwischen diesen Formeln und denen des Teils III zu interpolieren. Damit wird die Berechnung des Reibungsmomentes für Scheiben unterschiedlichster Form ermöglicht, vorausgesetzt, dass die Grenzschichtdicke klein ist gegenüber dem Radius der Scheibe.

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This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under contract No. AF 18 (600) 1548. Reproduction in whole or in part is permitted for any purpose of the United States Government. Part of the work was done while one of the authors (G. F. N.) was being supported by a grant from the Alfred P. Sloan Foundation.     

A strongly degenerate system involving an equation of parabolic type and an equation of elliptic type

Abstract

We show the existence of weak solutions in an elliptic region in the self-similar plane to the two-dimensional Riemann problem for the pressure-gradient system of the compressible Euler system. The two-dimensional Riemann problem we study is the interaction of two forward rarefaction waves, which are adjacent to a common vacuum that occupies a sectorial domain of 90 degrees. We assume the origin is on the boundary of the domain. In addition, the domain is open, bounded, and simply connected with a piecewise C ^2,α boundary. We resolve the difficulty that arises from the fact that the origin is on the boundary of the domain.     

A globally convergent multi-grid algorithm for moving boundary problems of two-phase Stefan type

In this paper we deal with the numerical solution of movingboundary problems of two-phase Stefan type. Based on an implicitdiscretization in time and the use of continuous, piecewiselinear finite elements in the space variables with respect tothe weak formulation of the problem, a globally convergent multi-gridalgorithm is developed. That algorithm strongly relies on thevariational characterization of the fully discretized problemas the unconstrained minimization of a subdifferentiable convexobjective functional. Numerical results indicate a significantimprovement in efficiency compared with previous multi-gridapproaches.     

A critical Kirchhoff‐type problem involving the ‐Laplacian

In this paper we provide an existence result for a nonlocal problem of Kirchhoff‐type which involves both the p‐ and the q‐Laplacian and contains a critical term. Our approach is variational: we derive the existence of one non‐trivial solution via the multidimensional mountain pass theorem.     

粘弹性方程的非协调变网格有限元方法

讨论了粘弹性方程的Crouzeix-Raviart型非协调变网格有限元方法,在不需要引入传统分析中Riesz投影的情况下得到了最优误差估计.     

Inverse modeling of a solar collector involving Fourier and non-Fourier heat conduction

This article applies the golden section search method (GSSM), simplex search method (SSM) and differential evolution (DE) for predicting the unknown Fourier number (Fo), Vernotte number (Ve) and non-dimensional solar heat flux (S¹) in a flat-plate solar collector when subjected to a given temperature requirement. The required temperature field is calculated using an analytical forward method by considering Fourier and non-Fourier heat conduction, and using this, the inverse problem is solved to predict the Fo, Ve and S¹ which are assumed to be the unknown parameters. The study reveals that the temperature field is highly sensitive to the Fo, thus even a small error in the temperature measurement can result in an unrealistic estimation of heating time of the collector. The present study is proposed to be useful in determining the time, the time lag and solar heat flux for controlled heating of an absorber plate within a stipulated time, which will be required to attain a prescribed/desired temperature distribution. Additionally, the study also shows that subjected to different time levels, the same temperature distribution is possible through different absorber plate materials. It has been observed from the present study that apart from SSM and DE, GSSM fails to estimate the unknown parameters at large value of Ve and small value of Fo, due to the associated fluctuation in the measured temperature field. The present study further discusses the computational performance of direct search method (e.g. GSSM and SSM) with that of the evolutionary method (DE) in terms of the maximum number of iteration and CPU time required to achieve the desired objective.     

A general Markov model of the HIV epidemic in populations involving both sexual contact and IV drug use

In this paper, we develop a general Markov model for the HIV epidemic involving both sexual contact and IV drug use. For this model, we derive the probability generating function of the HIV epidemic and derive equations for the means, the variances and the covariances of the numbers of susceptible people, latent people, infective people and AIDS cases. By using these equations, we generate some simulation studies to illustrate effects of some risk factors on the mean HIV behavior and on the variances and the covariances of the numbers of latent people, infective people and AIDS cases.     

Cohomology of algebras of semidihedral type. IV

The present paper continues a series of papers by the author (some of them are written in collaboration) in which the Yoneda algebra is calculated for several families of algebras of dihedral and semidihedral type (in K. Erdmann’s classification). In the present paper, the Yoneda algebra is described (in terms of quivers with relations) for algebras of semidihedral type, namely, of the families SD(2A)₁, SD(2A)₂, and SD(3A)₂. Bibliography: 13 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 319, 2004, pp. 71–116.     

Hodge structures on abelian varieties of type IV

Let A be a general member of a PEL-family of abelian varieties with endomorphisms by an imaginary quadratic number field k, and let E be an elliptic curve with complex multiplications by k. We show that the usual Hodge conjecture for products of A with powers of E implies the general Hodge conjecture for all powers of A. We deduce the general Hodge conjecture for all powers of certain 5-dimensional abelian varieties. Mathematics Subject Classification (2000): Primary 14C30, 14K20.Research supported in part by a Research and Creative Activity Award for Summer 2001 from East Carolina University.