THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

Calculating the electron temperature in the lightning channel by continuous spectrum

Based on the theory of plasma continuous radiation, the relationship between the emission intensity of bremsstrahlung and recombination radiation and the plasma electron temperature is obtained. During the development process of a return stroke of ground flash, the intensity of continuous radiation spectrum is separated on the basis of the spectrums with obviously different luminous intensity at two moments. The electron temperature of the lightning discharge channel is obtained through the curve fitting of the continuous spectrum intensity. It is found that electron temperature increases with the increase of wavelength and begins to reduce after the peak. The peak temperature of the two spectra is close to 25 000 K. To be compared with the result of discrete spectrum, the electron temperature is fitted by the O I line and N II line of the spectrum respectively. The comparison shows that the high temperature value is in good agreement with the temperature of the lightning core current channel obtained from the ion line information, and the low temperature at the high band closes to the calculation result of the atomic line, at a low band is lower than the calculation of the atomic line, which reflects the temperature of the luminous channel of the outer corona.

An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators

We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the absolutely continuous spectrum.

Research on modeling method of continuous spectrum water quality online detection based on random forest

It's common to use the method of continuous spectroscopy in water quality testing. But there're some problems with it. For example, the scanning results have a large number of nonlinear signals, and the covariance between variables is serious, which can lead to a decrease in the model prediction accuracy. In this paper, the standard solutions of nitrate nitrogen(NO_(3)-N) and nitrite nitrogen(NO_(2)-N) were used as the subject to be tested, and the data of the scanned waves and absorbance were obtained by use of spectral detector. The data were processed by noise reduction first and then the random forest(RF) algorithm was adopted to establish the regression relationship between concentration and absorbance. For comparison, partial least squares(PLS) and support vector machine(SVM) algorithm models were also established. For the same given data, the three reverse models can make the projection of the concentration respectively. The experimental results show that the RF algorithm predicts NO_(2)-N concentrations significantly better than the SVM algorithm and PLS algorithm. This proves that the RF algorithm has good prediction ability in spectral water quality detection because of its high model accuracy and better adaptability, which could be a reference for similar research on continuous spectral water quality online detection.

Continuous Spectrum Measure of a Class of Schrdinger Operators

We consider the discrete Schrdinger operator acting on l 2(Z) with the potential V n, the sequence consisting of k+1 symbols: {0,1,2,…,k}, and prove that it exhibits purely continuous spectrum.

Continuous Emission Spectrum Measurement for Electron Temperature Determination in Low-Temperature Collisional Plasmas

Continuous emission spectrum measurement is applied for the inconvenient diagnos- tics of low-temperature collisional plasmas. According to the physical mechanism of continuous emission, a simplified model is presented to analyze the spectrum in low temperature plasma. The validity of this model is discussed in a wide range of discharge parameters, including electron tem- perature and ionization degree. Through the simplified model, the continuous emission spectrum in a collisional argon internal inductively coupled plasma is experimentally measured to determine the electron temperature distribution for different gas pressures and radio-frequency powers. The inverse Abel transform is also applied for a better spatially resoluted results. Meanwhile, the result of the continuous emission spectrum measurement is compared to that of the electrostatic double probes, which indicates the effectiveness of this method.

Possible Spectrums of 3×3 Upper Triangular Operator Matrices

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M（D,V,F） a 3×3 upper triangular operator matrix acting on Hi ＋H2＋ H3 of theform M（D,E,F）=（A D F 0 B F 0 0 C）.For given A ∈ B（H1）, B ∈ B（H2） and C ∈ B（H3）, the sets ∪D,E,F^σp（M（D,E,F））,∪D,E,F ^σr（M（D,E,F））,∪D,E,F ^σc（M（D,E,F）） and ∪D,E,F σ（M（D,E,F）） are characterized, where D ∈ B（H2,H1）, E ∈B（H3, H1）, F ∈ B（H3,H2） and σ（·）, σp（·）, σr（·）, σc（·） denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.

Perturbation of Spectra for a Class of 2×2 Operator Matrices

In this paper, we study the perturbation of spectra for 2 ×2 operator matrices such as Mx ={A0 XB） AC and Mz = （Az CB） on the Hilbert space H K and the sets……

Contribution of vortex Rossby wave to spiral rainband formation in tropical cyclones

The contribution of the vortex Rossby wave （VRW） to framework of a barotropic non-divergent TC-like vortex model. the spiral rainband in the tropical cyclones （TCs） is studied in the The spectral function expanding method is used to analyze the disturbance evolution of a defined basic state vortex. The results show that the numerical solution of the model is a superposition of the continuous spectrum component （non-normal modes） and the discrete spectrum component （normal modes）. Only the eyewall and the rainbands in the inner core-region in a TC are related to the VRW normal modes, whereas the continuous spectrum wave components play an important role in the formation of secondary-, principal-, and distant- rainbands, especially the outer rainband, through an indirect way. The continuous spectrum can promote the development of the TC circulation for the occurrence of a mesoscale instability. The convection under a favorable moisture condition will trigger the inertial-gravitational wave to cause the formation of unstable spiral bandliked-disturbances outside of the eyewall. The complicated interaction between the basic state-vortex and the VRW disturbances will cause a positive feedback between the TC circulation and the rainband.

Modes of a Plasma-Filled Waveguide Determined by a Numerical hp Method

We present the application of the recent physics-conforming COOL method[2,4]to the eigenvalue problem of a cylindrical waveguide filled with unmagnetized plasma.Using the Fourier transform only along the waveguide and not in poloidal direction,this is a relevant test case for a numerical discretization method in two dimensions(radial and poloidal).Analytically,the frequency spectrum consists of discrete electromagnetic parts and,depending on the electron density profile of the plasma,of infinitely degenerate and/or continuous,essentially electrostatic parts.If the plasma is absent,the latter reduces to the infinitely degenerate zero eigenvalue of electrostatics.A good discretization method for the Maxwell equations must reproduce these properties.It is shown here that the COOL method meets this demand properly and to very high precision.