掺铒硼酸钙镧晶体的合成、生长及光谱特性

本文合成并以CaO-L i2O-B2O3为助熔剂体系生长得到了掺铒硼酸钙镧(Er3 :La2CaB10O19,Er:LCB)的晶体。X射线粉末衍射分析表明,Er:LCB和LCB具有相同的晶体结构,均属于单斜晶系,C2空间群。Er:LCB晶体的熔点大约为1048℃。测试了Er:LCB晶体的吸收光谱和荧光光谱。Er:LCB晶体在790nm和970nm附近存在的吸收,对应于A lGaAs和InGaAs激光二极管输出波长,其吸收截面分别为1.94×10-20和2.39×10-20cm2。Er:LCB在1531nm附近有发射峰最强,峰宽为16nm。其荧光寿命为0.37m s。     

Distance signless Laplacian eigenvalues of graphs

Suppose that the vertex set of a graph G is V(G)=\{v\mathrm{1},v\mathrm{2},\mathrm{...},vn\}. The transmission Tr(vi) (or D_i) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let Tr(G) be the n\times n diagonal matrix with its (i, i)-entry equal to {{\displaystyle Tr}}_G(vi). The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as L(G)=Tr(G)+D(G), where D(G) is the distance matrix of G. In this paper, we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible. We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs. Moreover, we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees, and characterize extremal graphs.     

Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket

The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M~(-1)(x + d)}_(d∈D) is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understanding the non-spectral and spectral of μM,D. As an application,we show that the L~2(μM,D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.     

Observations of extreme ultraviolet emission from plasma produced by capillary discharges

This study reports the results of a pilot experiment concerning observations of extreme ultraviolet emission from plasma produced by the capillary discharges. A few kA current was applied across the gas-filled alumina capillary (1 mm diameter and 8 mm long) to generate radiation in the EUV region (12–63 nm). Spectroscopic studies were carried out by means of a XEUV spectrometer which was upgraded for special lithography purposes. The results obtained from the EUV spectroscopic measurements provided information about the radiation processes from xenon and argon plasma and testifies that given capillary is an effective source of EUV emission. Additionally we showed a simulation which describes plasma dynamics parameters and dynamics of various ionization stages in capillary discharge. Our computer simulation confirmed the presence of ions, which spectra was registered in the experiment.     

Analysis and algorithms for a regularized cauchy problem arising from a non-linear elliptic PDE for seismic velocity estimation

In the present work we derive and study a non-linear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However, we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax–Friedrichs method. The key features of this scheme is the Lax–Friedrichs averaging and the wide stencil in space. The second approach is a spectral Chebyshev method with truncated series. We show that our schemes work because of (i) the special input corresponding to a positive finite seismic velocity, (ii) special initial conditions corresponding to the image rays, (iii) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (iv) the need to compute the solution only for a short interval of time. We test our numerical schemes on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.     

Measuring derived acoustic power of an ultrasound surgical device in the linear and nonlinear operating modes

Objective and motivationThe method for measuring derived acoustic power of an ultrasound point source in the form of a sonotrode tip has been considered in the free acoustic field, according to the IEC 61847 standard. The main objective of this work is measuring averaged pressure magnitude spatial distribution of an sonotrode tip in the free acoustic field conditions at different electrical excitation levels and calculation of the derived acoustic power at excitation frequency (f₀ ≈ 25 kHz). Finding the derived acoustic power of an ultrasonic surgical device in the strong cavitation regime of working, even in the considered laboratory conditions (anechoic pool), will enable better understanding of the biological effects on the tissue produced during operation with the considered device.Experimental methodThe pressure magnitude spatial distribution is measured using B&;K 8103 hydrophone connected with a B&;K 2626 conditioning amplifier, digital storage oscilloscope LeCroy Waverunner 474, where pressure waveforms in the field points are recorded. Using MATLAB with DSP processing toolbox, averaged power spectrum density of recorded pressure signals in different field positions is calculated. The measured pressure magnitude spatial distributions are fitted with the appropriate theoretical models.Theoretical approachesIn the linear operating mode, using the acoustic reciprocity principle, the sonotrode tip is theoretically described as radially oscillating sphere (ROS) and transversely oscillating sphere (TOS) in the vicinity of pressure release boundary. The measured pressure magnitude spatial distribution is fitted with theoretical curves, describing the pressure field of the considered theoretical models. The velocity and displacement magnitudes with derived acoustic power of equivalent theoretical sources are found, and the electroacoustic efficiency factor is calculated. When the transmitter is excited at higher electrical power levels, the displacement magnitude of sonotrode tip is increased, and nonlinear behaviour in loading medium appears, with strong cavitation activity produced hydrodynamically. The presence of harmonics, subharmonics and ultraharmonics as a consequence of stable cavitation is evident in the averaged power spectral density. The cavitation noise with continuous frequency components is present as a consequence of transient cavitation. The averaged pressure magnitude at the frequency components of interest (discrete and continous) in the field points is found by calculating average power spectral density of the recorded pressure waveform signal using the welch method. The frequency band of interest where average power spectral density is calculated is in the range from 15 Hz up to 120 kHz due to measurement system restrictions. The novelty in the approach is the application of the acoustic reciprocity principle on the nonlinear system (sonotrode tip and bubble cloud) to find neccessary acoustic power of the equivalent acoustic source to produce the measured pressure magnitude in the field points at the frequency components of interest.ResultsIn the nonlinear operating mode, the ROS model for the considered sonotrode tip is chosen due to the better agreement between measurement results and theoretical considerations. At higher excitation levels, it is shown that the averaged pressure magnitude spatial distribution of discrete frequency components, produced due to stable cavitation, can be fitted in the far field with the inverse distance law. The reduced electroacoustic efficiency factor, calculated at excitation frequency component as ratio of derived acoustic power with applied electrical power, is reduced from 40% in the linear to 3% in the strong nonlinear operating mode. The derived acoustic power at other frequency components (subharmonic, harmonic and ultraharmonic) is negligible in comparison with the derived acoustic power at excitation frequency.Discussion and conclusionsThe sonotrode tip and loading medium are shown in the strong cavitation regime as the coupled nonlinear dynamical system radiating acoustic power at frequency components appearing in the spectrum. The bubble cloud in the strong nonlinear operating mode decreases the derived acoustic power significantly at the excitation frequency.     

On the Laplacian spectral radii of trees with perfect matchings

Denote by the set of trees of order 2k with perfect matchings. GUO [Guo, Linear Algebra Appl. 368:379–385, 2003.] determined the largest value of Laplacian spectral radii μ(T) of the trees T in and gave the corresponding tree T in whose μ(T) reaches this largest value. In this paper, we determine the second to the sixth largest values of μ(T) of the trees T in and also give the corresponding trees T in whose μ(T) reach these values.     

Apo‐CopC and CopC‐Cu(II) Unfolding Characteristics in GuHCl Solution

The stability of CopC, a copper resistant protein with a Greek β‐barrel motif, in GuHCl solution was investigated by fluorescence spectra. Parameter A, characterizing position and shape of the fluorescence spectra, "phase diagram" method of fluorescence, and cupric binding capacity in GuHCl solution of different concentration showed that the denaturation transition of apo‐CopC and CopC‐Cu(II) might be fitted to a simple two‐state model. According to a two‐state model, the free energy of stabilization for apo‐CopC and CopC‐Cu(II), (17.08±0.35) and (23.81±0.45) kJ·mol^‐1 respectively, was obtained. Copper(II) increased the stability of apo‐CopC. The higher thermodynamics stability of CopC‐Cu(II) was revealed to originate in both the faster folding and the slower unfolding rates by unfolding kinetics.     

Thermal analysis,effect of dopants,spectral characterisation and growth aspects of KAP crystals

Potassium acid phthalate (KAP) which is also known as potassium hydrogen phthalate (KC₈H₅O₄), a semi-organic compound was grown from its aqueous solution only by slow evaporation method at room temperature. The effect of metallic salts HgCl₂ and PbCl₂ as dopants in the growth aspects, thermal properties and SHG efficiency of KAP were determined using UV-VIS, FTIR spectral studies, thermal (TG and DTA) analysis and NLO test. There is only one significant mass loss step on TG curve of pure and doped KAP crystal. DTA curve exhibit a higher peak temperature in case of doped KAP crystal compared to those of pure KAP crystals.     

Legendre spectral Galerkin method for second-kind Volterra integral equations

The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L ₂ norm) will decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical examples are given to illustrate the theoretical results.