On the global L^(1)-boundedness of Fourier integral operators with rough amplitude and phase functions

Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.

Approximations of the Scattering Phase Functions of Particles

Based on anomalous diffraction theory and the modified Rayleigh-Debye approximation, a physically realistic model in bridging form is described to approximate the scattering phase function of particles. When compared with the exact method, the bridging technique reported here provides a reasonable approximation to the Mie results over a broader range of angles and size parameters, and it demonstrates the advantage of being computationally economic. In addition, the new phase function model can be essentially extended to other shapes and conveniently used in more complicated scattering and emission problems related to the solutions of the radiative transfer equations.

Oscillatory integrals for phase functions having certain degenerate critical points

The paper is concerned with oscillatory integrals for phase functions having certain de- generate critical points. Under a finite type condition of phase functions we show the estimate of oscillatory integrals of the first kind. The decay of the oscillatory integral depends on indices of the finite type, the spatial dimension and the symbol.

IC Testing by Phase Classification Based on Behavioral Description of RTL

The growing complexity of integrated circuits (ICs) is driving the trend of IC testing towards testing based on behavioral descriptions of register-transfer level (RTL). A behavioral description contains an algorithmic specification of functionality of design. It may contain little or even no information about the design’s cycle-by-cycle behavior or structural implementation. However, it usually has an interior variable to lead the process of its functional phases. This interior variable is named phase variable. The functional behavior of a digital circuit changes according to different values of a phase variable. By analyzing some ITC99 benchmark circuits, this paper presents a way to generate tests for a circuit by tracing the value change of a phase variable in the circuit.

First-Principles Study of the High-Temperature Behaviors of the Willemite-Ⅱ and Post-Phenacite Phases of Silicon Nitride

The structural and elastic properties of the recently-discovered wⅡ- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa,respectively.The α→wⅡ phase transition can be observed at 18.6 GPa and 300 K.The β→δ phase transformation occurs at pressures of 29.6,32.1,35.9,39.6,41.8,and 44.1 GPa when the temperatures are100,200,300,400,500,and 600 K,respectively.The results show that the interactions among the N-2s,Si-3s,3p bands（lower valence band） and the Si-3p,N-2p bands（upper valence band） play an important role in the stabilities of the wⅡ and S phases.Moreover,several thermodynamic parameters（thermal expansion,free energy,bulk modulus and heat capacity） of δ-Si3N4 are also obtained.Some interesting features are found in these properties.δ-Si3N4 is predicted to be a negative thermal expansion material.The adiabatic bulk modulus decreases with applied pressure,but a majority of materials show the opposite trend.Further experimental investigations with higher precisions may be required to determine the fundamental properties of wⅡ- andδ-Si3N4.

Tunable Electronic and Magnetic Properties from Structure Phase Transition of Layered Vanadium Diselenide

The atomic geometry, structure stability, electronic and magnetic properties of VSe2 were systematically investigated based on the density functional theory（DFT）. Varying from 3D to 2D four VSe2 structures, bulk 2H-VSe2 and 1T-VSe2, monolayer H-VSe2 and T-VSe2 are all demonstrated as thermodynamically stable by lattice dynamic calculations. More interestingly, the phase transition temperature is dramatically different due to the lattice size. Finally, owing to different crystal structures, H-VSe2 is semimetallic whereas T-VSe2 is totally metallic and also they have different magnetic moments. Our main argument is that being exfoliated from bulk to monolayer, 2H-VSe2 transforms to T-VSe2, accompanied by both semimetallic-metallic transition and dramatic magnetic moment variation. Our calculations provide a novel structure phase transition and an efficient way to modulate the electronic structure and magnetic moment of layered VSe2, which suggests potential applications as high-performance functional nanomaterial.

Deduction and Validation of an Eulerian-Eulerian Model for Turbulent Dilute Two-Phase Flows by Means of the Phase Indicator Function-Disperse Elements Probability Density Function

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.

Phase Properties of Two-Mode Squeezing-Rotating Entangled Representation

By virtue of the squeezing-rotating entangled representation, we mainly establish the new two-mode phase operator and phase angle operat, or, which is a general form including the foregoing formalist in two-mode Fock space. In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotatlng coherent state, squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.

Unit 1 of Ling’ao Nuclear Power Plant phase II underwent hot functional test successfully

On February 25, the Unit 1 of Ling’ao Nuclear Power Plant phase II underwent a 41-day-long hot functional test successfully with its major systems satisfying the requirements for

Analysis of the optical quality by determining the modulation transfer function for anterior corneal surface in myopes

AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anterior corneal surface in myopes. METHODS: Four hundred eyes from 200 patients were examined under SIRIUS corneal topography system. Phoenis analysis software was applied to simulate the MTF curves of anterior corneal surface at vertical and horizontal meridians at the 3, 4, 5, 6, 7mm optical zones of cornea. The MTF values at spatial frequencies of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 cycles/degree (c/d) were selected. RESULTS: The MTF curve of anterior corneal surface decreased rapidly from low to intermediate frequency (0-15cpd) at various optical zones of cornea, the value decreased to 0 slowly at higher frequency (>15cpd). With the increase of the optical zones of cornea, MTF curve decreased gradually. 3) In the range of 3 mm- 6 mm optical zones of the cornea, the MTF values measured at horizontal meridian were greater than the corresponding values at horizontal meridian of each spatial frequency, the difference was statistically significant (P<0.05). At 7 mm optical zones of cornea, the MTF values measured at horizontal meridian were less than the corresponding values at vertical meridian at 10-60 spatial frequencies (cpd), and the difference was statistically significant in 25, 30, 35, 40, 45, 50 cpd(P<0.05). CONCLUSION: MTF can be used to describe the imaging quality of optical systems at anterior corneal surface objectively in detail.

Aerosol optical properties derived from simultaneous sunphotometer and aureolemeter measurements in Lhasa

In order to obtain some aerosol properties in Tibetan Plateau atmosphere, simultaneous measurements of aerosols by use of a sunphotometer and an aureolementer were performed in the summer of 1998 in Lhasa(29.65°N, 91.13°E). Optical depth, volume size distribution and phase\|function of aerosols were obtained from the measurements. Religious activities can have an effect on optical depth in Lhasa. The daily average aerosol optical depth( λ =500 nm) is less than 0.2. The diurnal variations of aerosol optical depth are relatively small during the period of summer. The maximal value of the mode radius in the volume size distribution are about 0.4, 2.0 and 4.0μm.

Multiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols

The mixture of water cloud droplets with black carbon impurities is modeled by external and internal mixing models.The internal mixing model is modeled with a two-layered sphere（water cloud droplets containing black carbon（BC） inclusions）,and the single scattering and absorption characteristics are calculated at the visible wavelength of 0.55 μm by using the Lorenz-Mie theory.The external mixing model is developed assuming that the same amount of BC particles are mixed with the water droplets externally.The multiple scattering characteristics are computed by using the Monte Carlo method.The results show that when the size of the BC aerosol is small,the reflection intensity of the internal mixing model is bigger than that of the external mixing model.However,if the size of the BC aerosol is big,the absorption of the internal mixing model will be larger than that of the external mixing model.

Temporal Spreading Effect of Oceanic Lidar System

In this paper, multipath temporal spreading distributions of laser pulses are calculated when they travel through the seawater. Individual photon is followed in Monte Carlo calculation A modified Henyey-Greenstein （HG） function is applied to represent the scattering phase function of seawater. This paper proposes a new scaling method, which uses the effective scattering thickness τd to replace the optical thickness used in the traditional scaling technique. This paper compares the temporal spreading distributions of photons on conditions of different attenuation coefficients and target depths. The experiments reveal that these mutual deviations are changing in the range from 0.5% to 5%, so long as the corresponding effective scattering thicknesses τd remains the same. Therefore, a conclusion can be obtained, that the temporal spreading distribution is only dependent on the effective diffusion thickness τd .

THE ENDPOINT ESTIMATE FOR FOURIER INTEGRAL OPERATORS

Let T_(a,φ)be a Fourier integral operator defined by the oscillatory integral T_(a,φ)u(x)=1/(2π)^(n)∫_(R^(n))^e^(iφ(x,ξ))a(x,ξ)(u)(ξ)dξ,where a∈S_(e,δ)^(m)andφ∈Φ^(2),satisfying the strong non-degenerate condition.It is shown that if0<(e)≤1,0≤δ<1 and m≤e^(2)-n/2,thenT_(α,φ)is a bounded operator from L^(∞()R^(n))to BMO(R^(n)).

Microstructure and Properties of Cement Foams Prepared by Magnesium Oxychloride Cement

Microstructural features including pore size distribution, cell walls and phase compositions of magnesium oxychloride cement foams（MOCF） with various MgO powders and water mixture ratios were studied. Their infl uences on compressive strength, water absorption and resistance of MOCF were also discussed in detail. The experimental results indicated that moderate and slight excess MgO powders（MgO/MgCl2 molar ratios from 5.1 to 7） were beneficial to the formation of excellent microstructure of MOCF, but increasing water contents（H2O/MgO mass ratios from 0.9 to 1.29） might result in opposite conclusions. The microstructure of MOCF produced with moderate and slight excess MgO powders could enhance the compressive strength, while serious excess MgO powders addition（MgO/MgCl2 molar ratios = 9） would destroy the cell wall structures, and therefore decrease the strength of the system. Although MOCF produced with excess MgO powders could decrease the water absorption, its softening coefficient was lower than that of the material produced with moderate MgO powders. This might be due to the instability of phase 5, the volume expansion and cracking of cell walls as immersed the sample into water.

STABILITY STUDY OF AN UNSTEADY OSCILLATION FLOW

In ihis paper.an instability problem of an unsteady oscillationo flow is studied.In particultar,the phase.function of the disturbance wave.system is soived by using the charocteristic theory of partial differential equation and an expansion of Orysommerfeid eigenvalue problem.instead of using the disturbance model which is given previously The.flow considered is a combination of plane Poiseuille.flow with aflow oscillating periodically and its instability is found for a special initial value of a developing wave due to continuous oscillationg source.

Real-Time Rendering of Dynamic Clouds Using Multi-Resolution Adaptive Grids

The multi-resolution adaptive grids method is proposed to solve the problems of inefficiency in the previous grid-based methods,and it can be used in clouds simulation as well as the interactive simulation between objects and clouds.Oriented bounding box(OBB)hierarchical trees of objects are established,and the resolutions of global and local grids can be selected automatically.The motion equations of fluid dynamics are simplified.Upwind difference is applied to ensure the stability of the simulation process during the discrete process of partial differential equations.To solve the speed problem of existed phase functions,the improved phase function is applied to the illumination calculation of clouds.Experimental results show that the proposed methods can promote the simulation efficiency and meet the need for the simulation of large-scale clouds scene.Real-time rendering of clouds and the interaction between clouds and objects have been realized without preprocessing stage.

Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces

In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.

Phase behaviors of transfer functions in Vibrating systems

This paper investigates the applicabilitles of pole-zero model and wave propagation theory in estimating the phase characteristics of vibrating systems. The measured phase spectra are compared with the estlmated reverberant phase limit and wave propagation phase. The relations between transfer function phase and frequency, damping, and separation distance are described. The present results show that the pole-zero model provides a reasonable estimation of the reverberant phase limit in low frequency band below an identified transition frequency.The reverberant phase is linearly dependent on frequency in this band, but from the transition frequency and onwards the phase increases only with the square root of frequency. This behavior is characteristic for free propagating waves

High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions

The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.