Electron Cyclotron Emission Imaging on the EAST Tokamak

An upgraded electron cyclotron emission imaging （ECEI） system consisting of new optics lenses with necessary electronics for receiving and processing signals for two dimension （2D） ECEI diagnostics was installed on EAST. Hyperboloid lens were adopted in the new system to optimize the spatial resolutions. The mixers array of sixteen elements measured the plasma electron cyclotron emission at eight frequencies simultaneously, and the profiles of the electron temperature and its fluctuation in an area of 20 cm （vertical） × 6 cm （horizontal） could then be analyzed. Evolution of sawtooth precursor and crash in EAST was observed.

On the Intersection Equation of a Hyperboloid and a Plane

In this note, the ideas employed in [1] to treat the problem of an ellipsoid intersected by a plane are applied to the analogous problem of a hyperboloid being intersected by a plane. The curves of intersection resulting in this case are not only ellipses but rather all types of conics: ellipses, hyperbolas and parabolas. In text books of mathematics usually only cases are treated, where the planes of intersection are parallel to the coordinate planes. Here the general case is illustrated with intersecting planes which are not necessarily parallel to the coordinate planes.

MATHEMATICAL MODEL AND CALCULATING METHOD OF PARAMETERS FOR TWIST DRILL HYPERBOL

Mathematical model for hyperboloid grinding of twist drill and relationships between drill design and grinding parameters are introduced.Point angles at outer corner and chisel edge corner are proposed to be used as the drill design parameters to determine the type uniquely and the relicf andgle is used as a supplement parameter.Function relations between the twist drill design and the grinding parameters are derived.Hence a theeoretical basis is estab-lised for design and grinding of the hyperboloid twist drill.

On Quadratric Rotational Curved Surface

In this paper,a deterministic theorem is proposed for quadratic rotational curved surface.The relationship between invariants for quadratic rotational curved surface is established.In addition we give each type of equitions for rotational curved surface using the invariant.

The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded

Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time solutions,provided that the initial data are compactly supported and sufficiently small in Sobolev norm.In this work,Alinhac obtained an upper bound with polynomial growth in time for the top-order energy of the solutions.A natural question then arises whether the time-growth is a true phenomenon,despite the possible conservation of basic energy.In the present paper,we establish that the top-order energy of the solutions in Alinhac theorem remains globally bounded in time.

Isometric Immersions of Higher Codimension in to the Product S~κ×H^(n+p-k)

In this paper,we obtain a sufficient and necessary condition for a simply connected Riemannian manifold（M^n,g） to be isometrically immersed,as a submanifold with codimension p 〉 1,into the product S^k×H^n＋p＋k of sphere and hyperboloid.

The pseudospectrum and spectrum(in)stability of quantum corrected Schwarzschild black hole

In this study,we investigate the pseudospectrum and spectrum(in)stability of quantum corrected Schwarzschild black hole.Methodologically,we use the hyperboloidal framework to cast the quasinormal mode(QNM)problem into an eigenvalue problem associated with a non-selfadjoint operator,and then the spectrum and pseudospectrum are depicted.Besides,the invariant subspace method is exploited to improve the computational efficiency for pseudospectrum.The investigation into the spectrum(in)stability entails two main aspects.On the one hand,we calculate the spectra of the quantum corrected black hole,then by the means of the migration ratio,the impact of the quantum correction effect on the Schwarzschild black hole has been studied.The results indicate that the so-called“migration ratio instability”will occur for small black holes with small angular momentum number l.In the eikonal limit,the migration ratios remain the same for each overtone.On the other hand,we study the spectrum(in)stability of the quantum corrected black hole by directly adding some particular perturbations into the effective potential,where perturbations are located at the event horizon and null infinity,respectively.There are two interesting observations under the same perturbation energy norm.First,perturbations at infinity are more capable of generating spectrum instability than those at the event horizon.Second,we find that the peak distribution can lead to the instability of QNM spectrum more efficiently than the average distribution.

THE ANALYSIS OF SHALLOW SHELLS BASED ON MULTIVARIABLE WAVELET FINITE ELEMENT METHOD

Based on the generalized variational principle and B-spline wavelet on the interval （BSWI）, the multivariable BSWI elements with two kinds of variables （TBSWI） for hyperboloidal shell and open cylindrical shell are constructed in this paper. Different from the traditional method, the present one treats the generalized displacement and stress as independent variables. So differentiation and integration are avoided in calculating generalized stress and thus the precision is improved. Furthermore, compared with commonly used Daubechies wavelet, BSWI has explicit expression and excellent approximation property and thus further guarantee satisfactory results. Finally, the efficiency of the constructed multivariable shell elements is validated through several numerical examples.